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Characterization of Ultra Wideband Communication
Channels
by
Ali Hussein Muqaibel
Time Domain and RF Measurement Laboratory The Mobile and Portable Radio Research Group
Dissertation Submitted to the Faculty of
The Bradley Department of Electrical and Computer Engineering Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY in
Electrical Engineering
Co-Chairmen
Dr. Sedki M. Riad Dr. Brian D. Woerner Dr. Ahmad Safaai-Jazi
Committee Members Dr. Ioannis M. Besieris Dr. William Tranter
styrofoam slab. The characterization method is based on measuring an insertion transfer
function, defined as the ratio of two signals measured in the presence and in the absence
of the material under test. The insertion transfer function is related to the dielectric
constant of the material through a complex transcendental equation that can be solved
using numerical two-dimensional root searching techniques. The insertion transfer
function can be obtained either through frequency-domain measurements using a vector
network analyzer, or by performing time-domain measurements using a pulse generator
and a sampling oscilloscope and then Fourier transforming the measured signals into the
frequency domain. In this research, both frequency-domain and time-domain
measurement techniques are used to validate the results and ensure the accuracy of
measurements by capitalizing on the advantages of each technique. The material
characterization data can be used in studying channel modeling problems.
The work on ultra wideband characterization of building materials resulted in an
additional interesting contribution. As mentioned above, the dielectric constant is
determined by solving a complex transcendental equation, a process which is often time
consuming due to slow convergence and the existence of spurious solutions. A new
formulation for evaluating the complex dielectric constant of low-loss materials, which
involves solving real equation and thus requiring only one-dimensional root searching
techniques, was found. The results derived from the exact complex equation and the new
formulation are in excellent agreement. This formulation reduces the computation time
significantly and is highly accurate for the characterization of low-loss materials.
After studying ultra-wideband propagation properties of typical building
materials, an indoor UWB measurement campaign is undertaken. The measurements are
performed using Gaussian-like pulses with a duration less than 100 ps. Two sets of
3
Chapter 1. Introduction
measurements are performed, one set with directional TEM horn antennas and another
with omni-directional biconical antennas. A total of about 400 signal profiles are
collected. The TEM horn and biconical antennas may be considered as representative
examples for stationary line-of-sight and mobile applications, respectively. The
measurements are carried out in two buildings on Virginia Tech Campus; namely,
Whittemore Hall and Durham Hall. Typical indoor scenarios, including line-of-sight
(LOS), non-line-of-sight (NLOS) in room-to-room, within-the-room, and in hallways are
considered.
Results for indoor propagation measurements are presented for local power delay
profiles (local-PDP) and small-scale averaged power delay profiles (SSA-PDP). Site-
specific trends and general observations are discussed. Some statistical analyses of the
measured data are presented and compared with the previously published UWB and
narrowband results. The results for pathloss exponent and time dispersion parameters are
presented. The analyses results indicate the immunity of UWB signals to multipath
fading which occurs in narrowband signals. Furthermore, the measurement results clearly
show that UWB signals, unlike narrowband signals, do not suffer from small scale
fading, unless the receiver is too close to walls.
A further step is taken by employing a deconvolution technique to extract more
information about the channel, particularly the number of multipath components.
Characterization of UWB channels can be performed by sounding the channel with
pulses, and thereby obtain the impulse response. Multipath components have different
waveforms depending on the type of transmitter and receiver antennas used and the
angles of transmission and reception. A modified deconvolution technique is introduced
to extract the UWB channel response. The application of deconvolution techniques
results in resolving multipath components with waveforms different from those of the
sounding pulse. Resolving more components can improve the design of the rake receiver.
Accurate characterization of the impulse response of a UWB communication system
facilitates performance evaluation studies.
4
Chapter 1. Introduction
The final part of this research work is devoted to illustrating an example of
utilizing measurement results to improve the receiver design. So far, receivers designed
for multiple access ultra-wideband communication systems, known as impulse radio, are
based on conventional single-user matched-filter detectors. Here, we elaborate on the
nature of multiple access interference and illustrate the application of multi-user detection
to improve the performance of impulse radio systems. Measured dispersion parameters
and their effects on the multiple access parameters are discussed.
1.2 Literature Survey of UWB Channel Measurements
Many researchers have studied the propagation of narrowband electromagnetic
waves through walls and floors at 900 MHz, 1.8 GHz, 2.4 GHz, 5.85 GHz, 60 GHz, and
other dedicated narrowband frequency ranges [Zha94], [Dur98], [And02a]. In many
narrowband measurements, only the magnitude of insertion transfer function (i.e., loss)
has been the quantity of interest. However, in UWB communication systems, as in
ground penetrating radars, in addition to the signal magnitude, the phase information
(delay) is an equally important factor that needs to be taken into account in studying the
propagation effects [Dan96]. Therefore, narrowband measurements, although helpful in
providing some general understanding, are not adequate for UWB propagation analyses
and channel modeling.
Some results on ultra wideband characterization of building materials have been
reported during the past decade. Hashemi has presented an excellent review and
comparison of published results for different indoor penetration losses in the UWB
frequency range [Has93a]. However, these results are often inconsistent, making the
assessment of indoor UWB propagation effects unreliable. For example, in [Has93a]
significantly different measured values of 7 dB, 8.5-10 dB, 13 dB and 27 dB for the
insertion loss of concrete blocks are cited. Moreover, in some cases, the relationship
between the expected loss and the operating frequency has not been satisfactorily
addressed. Though it is a common observation that the loss increases with frequency,
some published data indicate a decrease in loss when frequency increases. In a ground
floor experiment, de Toledo and Turkmani [Tol92] report measured average penetration
5
Chapter 1. Introduction
losses of 14.2 dB, 13.4 dB, and 12.8 dB at 900 MHz, 1800 MHz, and 2300 MHz,
respectively. Another example is the data reported by Zhang and Hwang [Zha01] who
performed measurements in the frequency range of 900 MHz to 18 GHz. According to
their investigation, the indoor penetration loss increases with frequency for reinforced
concrete wall but this trend is not generally realized for plasterboard.
At the statistical level, there has been some research on narrowband indoor
channel characterization. Of special value is a series of publications by Saleh and
Valenzuela [Sal87], Hashemi [Has93a], [Has93b], Anderson et al. [And02a], Durgin and
Rappaport [Dur00], and Rappaport [Rap92], [Rap89], [Rap96]. The primary objective of
these researchers has been to develop models that describe the system performance
adequately. A successful characterization requires extensive and accurate measurements.
The accuracy of the model depends mainly on the accuracy of the measurements.
Due to the rapidly growing interest in UWB communications, researchers are
nowadays devoting considerable efforts and resources to develop robust channel models
that allow for reliable and accurate ultra-wideband performance simulation. At present,
the amount of available measurement data is very limited and more are needed to support
a comprehensive channel modeling study. The issue becomes more complicated due to
the fact that UWB pulse measurements are antenna dependent. The spectrum and the
shape of the pulse also affect the measurements.
The analysis of indoor communication systems based on simulation of the entire
transmission link using statistical methods is most useful in assessing the system
performance [Has93a]. This approach, however, requires extensive propagation
measurements. Some research work on both deterministic [Ugu02] and statistical
modeling [Zhu02], [Cas01] has been reported. More recently, Cassioli et al. [Cas02] have
presented simulation results for UWB indoor communications, while Chalillou et al.,
[Cha02] have discussed the main structure of a general simulator for UWB
communication systems. However, there still remain many unresolved issues and hence
the need for more UWB propagation measurements. Different measurement conditions,
insufficient measurement data, and the effect of different excitation pulses are among the
6
Chapter 1. Introduction
priority issues that demand additional measurements in order to formulate comprehensive
and robust models before designing simulators.
The most notable UWB time-domain measurement campaign is that by the Ultra
Lab group conducted at the University of South California (USC), in collaboration with
the Time Domain Corporation [Sch97]. Their measurements were performed using a
sampling oscilloscope, a pulse generator and wideband antennas. The results of these
measurements were used to develop further models [Cra02], [Cas01], but no information
on the pulse shape and the characteristics of the antennas used in their measurements are
provided. Only in a separate study they mention that a diamond dipole antenna has been
used [Sch01]. A disadvantage of this antenna is that it covers a small frequency band.
Also, they used a wireless device in their triggering system. Multiple reflections from the
surroundings may cause mis-triggering in such a wireless triggering system. One further
step was taken with the aim of characterizing a more realistic UWB communication
rather than simple periodic pulses [wit99], [Dic99]. In this scenario, the pulses were
modulated and time dithered to emulate real communication environments. However, at
this stage of the UWB technology evolution, more fundamental investigations are
required in order to achieve a better understanding of the channel characteristics.
Acquiring the transfer function or the impulse response of the channel will help
communication engineers to study the effects of time dithering or any other techniques
through simulation.
Another approach for UWB channel characterization is to perform propagation
measurements in the frequency domain and convert the results to the time domain by
means of inverse Fourier transform. The advantage of this approach is that the sensitivity
of the equipment used, particularly the vector network analyzer, is much higher than that
of the time-domain measurement equipment such as sampling oscilloscope. The chief
disadvantage of frequency-domain measurements is that long high-quality RF cables are
required for connecting the network analyzer to both transmitting and receiving antennas
[Gha02]. Furthermore, double shielding of these cables is often required in order to avoid
coupling of radiated signals from the air through the cable to the receiver. These cables
represent a major limitation for long distance measurements. On the other hand, in direct
7
Chapter 1. Introduction
time-domain measurements, it is only required to use a cable for carrying the triggering
signal from the source at the transmitting side to the sampling oscilloscope at the
receiving end. The bandwidth of the triggering signal is usually much less than the
bandwidth of the pulse. Thus, long cables with moderate attenuation and dispersion levels
are adequate for triggering purposes, making time-domain measurements of UWB signals
at larger distances between the source and the observation point much easier.
A number of researchers have studied UWB channel propagation using
frequency-domain measurements, including Ghassemmzadeh et al. [Gha02], Prettie et
al. [Pre02], Keignart and Daniele [Kei02], Kunisch and Pamp [Kun02], Street et al
[Str01], and Hovinen et al. [Hov02]. Only Ghassemmzadeh et al. [Gha02] used
substantially long cables; up to 45 m, while most others who have described their
measurement setups have used cables of up to nearly 10 m. They have also used different
bandwidths in their measurements. Ghassemmzadeh et al. [Gha02] have performed their
measurements in the Unlicensed National Information Infrastructure (UNII) band. The
bandwidth in their measurements was either 1 GHz or a maximum of 2.5 GHz centered at
a frequency of 5 GHz. Prettie et al. [Pre02] and Hovinen et al. [Hov02] have used a
frequency range of 2 GHz to 8 GHz. Keignart and Daniele [Kei02] have used a smaller
frequency range from 2 GHz to 6 GHz, while Kunisch and Pamp [Kun02] conducted
UWB channel measurements in the range of 1 GHz to 11 GHz. The time-domain
resolution and the time delay that can be obtained from frequency-domain measurements
depend on the minimum and the maximum frequencies in a given bandwidth and the
number of frequency points at which measurements are taken.
Ghassemmzadeh et al. [Gha02] have presented extensive frequency-domain
measurements in 23 residential homes. No multipath component was observed in their
measurements beyond 70 ns of excess delay with a 30 dB threshold. These measurements
were used by Turin et al. [Tur02] to develop an autoregressive model for an indoor UWB
Channel. The generated model allows for simple simulations. However, the parameters of
the model are location dependent. Kunisch and Pamp [Kun02] observed that the channel
gain tends to decrease with frequency. But, details of their measurement system are not
revealed, yet the authors report that all results account for frequency dependent antenna
8
Chapter 1. Introduction
characteristics. Cramer [Cra99] demonstrated that multipath components result in an
extended channel impulse response. The study suggested a window of 300 ns to account
for all multipath components which contain an appreciable amount of power. Diversity is
also considered in this work to extract the structure of the channel from the received array
of data. Beamformer response at different projection angles has also been studied. Prettie
et al. [Pre02] have presented spatial correlation of their UWB measurements. Another
direction for evaluating UWB channels is based on narrowband models. However, such
models are formulated for specific frequency bands and are suitable for interference
studies, but cannot be directly used for UWB channel characterization [Kis01], [Dep].
To illustrate the deficiency of models based on these measurements, Cramer et al.
[Cra99] suggested modeling the UWB channel as a summation of the Hermite
polynomials. Their justification was based on the heuristic approach that the signal
driving the antenna is often modeled as Gaussian and some of the propagation and
reflection effects tend to have the characteristics of the signal derivatives. Later studies
revealed that derivative behavior is a result of the specific antenna transfer function
[Muq02]. Recently, Lee [Lee00] presented a deterministic multipath analysis using a
two-ray model and characterized the time of arrival using Saleh-Valenzuela model
[Sal87]. Another statistical model was also reported by Foerster [Foe01]. The presented
results by both Lee and Foerster are based on simplified assumptions and call for further
experimental support.
1.3 Dissertation Organization
In Chapter 2, a theoretical background for understanding UWB communications
is presented. In particular, important attributes of narrowband and UWB communication
systems are compared, including historical evolutions, bandwidth requirements and
definitions, shapes and spectra of information signals, coding schemes and modulation
techniques, interference, security issues, hardware aspects, and applications. Emphasis is
placed on UWB systems, assuming that the reader is familiar with narrowband systems.
Details on narrowband system can be found in [Hay83],[Pro89], and [Skl88]. Time-
Domain and Frequency-domain techniques and measurement setups are discussed and
9
Chapter 1. Introduction
compared in Chapter 3. Understanding the details of measurement system is very
important for properly interpreting the experimental results. Sources and antennas are
characterized and their effects are examined. Chapter 4 devoted to studying the
propagation of UWB signals through walls and common materials encountered in indoor
communication environments. Ten typical building materials are characterized. Results
for an indoor UWB measurement campaign are presented in Chapter 5. Measurement
results for two typical office buildings are analyzed. Pathloss and time dispersion
parameters are studied using directive and omnidirectional antennas. More advanced
analysis based on extracting the channel impulse response using deconvolution
techniques is discussed in Chapter 6. Multi-template subtractive deconvolution is used to
estimate the number of significant multipath components and the percentage of power
associated with them. Motivated by the experimental view a proposal for utilizing multi-
user detection techniques for UWB communication systems is presented in Chapter 7.
Finally, summary and conclusions are provided in Chapter 8. Appendix A is dedicated to
theoretical analyses and derivations, while Appendix B is devoted to additional details
and miscellaneous items.
10
“An intriguing alternative which may eventually become practical, and even legal, for short-range communication between static terminals is ultra-wideband impulse radio.”
“In fact, the principle of impulse radio is firmly grounded in information theory: maximum power efficiency is achieved by pulse-position modulation in an infinite bandwidth channel”
“although the whole band occupied by the transmission, say, from DC to a few gigahertz is “owned” by other systems, much of it is unused at any given time. Thus, reasonable receiver sensitivity can indeed be achieved with very low transmitted power”
Sergio Verdú [Ver00]
Chapter 2
Ultra Wideband vs. Narrowband
Communication Schemes
2.1 Background and Historical Evolution
Ultra wideband (UWB) systems use precisely timed, extremely short coded pulses
transmitted over a wide range of frequencies. Although UWB technology had some old
roots, ultra wideband communication is a relatively new technology. The technology is
radical departure from current wireless communication methods.
Ultra wideband technology originated from work in time-domain
electromagnetics begun in 1962 [Fon]. The concept started with the objective of
characterizing linear time invariant systems by measuring the output as a result of an
impulse excitation, instead of using the more conventional means of swept frequency
response. However, that was not possible until the developments in the techniques for
subnanoseconds (baseband) pulse generation, which are needed to approximate the
impulse excitation and to make the measurements feasible.
11
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
It became obvious that short pulse radar and communication systems can be
developed in the same way. In 1978 efforts turned toward the communication using
UWB signals. An experiment was successfully presented where intelligible voice signals
could be communicated over hundreds of feet without the need for synchronization. Six
years later, greater ranges were possible. Harmuth has published two books about the
transmission of information using orthogoanal functions and the applicability of using
nonsinusoidal waves for radar and radio communication [Har].
The term “ultra wideband” was not used until around 1989. By that time, the
theory of UWB has experienced thirty years of developments. Further historical
information about UWB technology can be found in [Bar01].
In this chapter UWB communication is compared with narrowband
communications. The comparison includes: definition and frequency band allocation,
communication signal (shape and spectrum), coding and modulation, interference,
security, hardware, and applications.
2.2 Definition and Band Allocation
In principle UWB technology is the use of short pulses instead of continuous
waves to transmit information. The pulse directly generates a very wide instantaneous
bandwidth signal according to the time-scaling properties of the Fourier transform
relationship between time, t, and frequency, f.
Before presenting a formal definition for ultra wideband signals and systems, it
should be noted that different terms are used in the literature which essentially refer to the
same thing such as impulse radio, orthogonal functions, Walsh waves, nonsinusoidal,
sequency theory, carrier-free, video-pulse transmission, large relative bandwidth, time-
domain techniques, baseband, large-relative bandwidth and ultra wideband [Har], [Bar].
Researches from Russia and China have been actively developing and testing
UWB impulse generators [Kis92]. The Soviets developed the “superwideband” signal
definition. All RF signals with a low frequency bound, fl, and high frequency bound, fh,
12
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
have a corresponding index of breadth of band, bµ , or relative bandwidth [Har81],
[Ast97],
)(5.0 lh
lhb ff
ff+
−=µ (2.1)
Researchers from Russia and China term an impulse-like signals
“superwideband” or UWB when 0.1≥bµ . Although, spread spectrum communications
can be designed with 0.1≥bµ , they are not called UWB because they do not possess the
transient behavior.
There is no general definition of UWB in the IEEE dictionary. However US
Defense Advanced Research Project Agency (DARPA) defined UWB for EM waves
with instantaneous bandwidth greater than 25% of center frequency [Pan99].
It is important to note that some technical terms can have different meaning based
on the subject where they are used. Narrowband (NB), wideband (WB) or broadband
(BB) and ultra wideband (UWB) can have different definitions based on the application,
i.e. communication, radar, electromagnetic interference (EMI) / electromagnetic
cancellation (EMC), etc. In mobile communication it is common to refer to the system’s
bandwidth as being narrow or wide relative to the coherence bandwidth. However, the
terminology used here is the one used by RF engineers based on the ratio of the
bandwidth relative to the carrier frequency [Cas02].
Table 2.1 presents both general and percentage bandwidth definitions. Percentage
bandwidth (%BW) – which is directly related to the breadth factor – is the bandwidth of
interest divided by the center frequency,
13
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
14
%100
2
% ×
+
−=
lh
lh
ffff
BW . (2.2)
2.3 Communication Signal (Shape and Spectrum)
Table 2.1. Definitions of NB, WB & UWB signals
Definitions NB WB UWB
% BW
EM waves with
instantaneous bandwidth
less than 1% of center
frequency (%BW <1%)
EM waves with instantaneous
bandwidth greater than 1%
and less than 25% of center
frequency (1% < %BW<25%)
EM waves with
instantaneous bandwidth
greater than 25% of center
frequency (%BW>25%)
General
Any radio or
communication signals
which is not wideband. 5
kHz for telephones and
AM radio, 25 kHz for FM
radio (military)
Any radio or other
communication signal which
is wider than narrow band.
High bit rate telephone data
circuits, (25 kHz for 9600
BPS) and TV channels (6-10
MHz) are generally considered
wideband signals
None in the IEEE dictionary
or other sources. However
US Defense Advanced
Research Projects (DARPA)
panel on UWB technology
published same as
percentage bandwidth.
Note: table is reproduced from [Pan99]
Narrowband communication is usually achieved by modulating a sinusoidal
carrier with the information to be transmitted. The resultant signal possesses the
sinusoidal nature and occupies a narrow band in the frequency domain. On the other
hand, for UWB applications, any waveform that satisfies the definition of UWB signal
can be used. The choice of a specific waveform is driven by system design and
application requirements. There has been many attempts to choose a signal waveform
suitable for UWB applications and yet has minimal interference with proximity systems
[Ham01a],[Ham01b].
The basic theoretical model for impulse radio uses a class of waveforms known as
“Gaussian waveforms”. They are called Gaussian waveforms because they are very
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
similar to the Gaussian function. In the time domain a Gaussian waveform, vg(t), is given
by
2
)()( τ
t
g etv−
= . (2.3)
where t is the time and τ is a parameter which represents the temporal width of the pulse.
Another waveform can be created by filtering or differentiating the Gaussian pulse to get
the Gaussian Monocycle∗. For the Gaussian monocycle, τ is the time between minimum
and maximum amplitudes and it defines the time decay constant that determines the
monocycle’s duration. The Gaussian monocycle has a single zero crossing and it is given
by
2
)()( τ
τ
t
m ettv−
= . (2.4)
By increasing the order of differentiation, the number of zero-crossings increases,
the bandwidth decreases and the center frequency increases. Utilizing the following
Fourier transform identity
22
22)(
)()( ττ ττ
ft
ejffVettv −−−=⇔= , (2.5)
and assuming A to be the peak amplitude of the monocycle, and fc to be the center
frequency, then, the Gaussian monocycle in the time domain is given by
2)(22),,( ctf
ccm eAtfeAftv ππ −= , (2.6)
and in the frequency domain it is given by
2
21
2222),,(
−
−= cff
ccm e
fejfAAftV π
π. (2.7)
∗ Some authors refer to the first derivative as doublet and some refer to it as Gaussian monocycle and they refer to the second derivative as doublet. To avoid confusion, we will refer to the first derivative as Gaussian monocycle and to the second derivative as doublet consistently.
15
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
16
a) Gaussian, Gaussian monocycle, and doublet waveforms
b) Normalized spectrum for Gaussian, Gaussian monocycle, and doublet
waveforms
Figure 2.1. Gaussian, Gaussian monocycle, and doublet waveforms and their
corresponding normalized frequency spectrum
0 2 4 6 8 10 12
10 -8
10 -6
10 -4
10 -2
10 0
Frequency (GHz)
Nor
mal
ized
Mag
nitu
de
GaussianGaussian Monocycle Doublet
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1
-0.8 -0.6 -0.4 -0.2
0
0.2 0.4 0.6 0.8
1
Time (ns)
Nor
mal
ized
Am
plitu
de
GaussianGaussian Monocycle Doublet
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
Gaussian excitation pulse provides excellent radiation properties [Bor99]. Other
possible waveforms include pulse like triangular, trapezium and other shaped pulses.
Figure 2.1 illustrates the basic Gaussian, and its first and second derivatives, which are
the Gaussian monocycle and the doublet waveforms. The corresponding normalized
frequency spectrum is shown in the same figure. Practical implementation of such
Gaussian monocycle remains an important issue.
To get more insight on the signal shape and spectrum, one has to address the
multiple access system. The following subsection is dedicated to the discussion of the
signal waveform and spectrum as applied to multiple access UWB system (impulse
Radio).
2.3.1 Multiple Access Impulse Radio System
Multiple access techniques for narrowband systems include: time, frequency, and
code division techniques. The multiple access UWB system model proposed by Scholtz
[Sch93] is based on time hopping codes. The typical hopping format will be given first,
followed by detailed explanation of the terms and the way they affect the signal
waveform and the spectrum.
In a typical hopping format for impulse radio with pulse position modulation, the
time access is divided into frames, Tf, and every frame is subdivided into time slots, Tc.
Every transmitter send a pulse per frame at different time slots from frame to another.
The signal transmitted by the kth user is given by [Sch97]
∗, (2.8) ( ) ( ) ( )∑∞
−∞=
−−−=j
kNjc
kjf
ktr
kktr s
dTcjTtwts )(/
)()()( δ
where wtr(t) is the transmitted pulse. Superscript k indicates transmitter related quantity.
Tf is the period of the frame or average pulse repetition time. Each user is assigned a time
hopping sequence shift pattern c . This hopping sequence provides an additional shift )(kj
∗ Note that j is not used to indicate imaginary terms. The variable j is used as a counting variable for the summation. It is consistently used in the literature.
17
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
of . The transmission rate, Rs, determines Ns which is the number of monocycle to
be modulated by a given binary symbol. Pulse position modulation is used with δ added
delay if the modulated bit is one. The term dn refers to the nth binary symbol.
ck
j Tc )(
The assumed channel model is that Nu users are active during transmission. The
received waveform is generally different from the transmitted one. Signal undergoes
constant amplitude attenuations and waveform deformation because of the antennas and
the propagation channel. Because of the antenna, the received signal is related to the
derivative of the transmitted signal. For example, for TEM horn antennas in boresight
configuration, if a Gaussian pulse is transmitted then a Gaussian monocycle is received.
On the other hand, if a monocycle is transmitted, the expected received waveform will
have a doublet shape. This is because the response of the radiating system will act as a
differentiator.
When the number of users is Nu, the received signal is [Sch97]:
(2.9) ( ) ( )∑=
+−=uN
kk
kreck tntsAtr
1
)( )(τ
where Ak is the attenuation of the propagation path of the signal, , received
from the kth transmitter. The time delay between the kth transmitter and the receiver is
represented by
( )k τ−)(krec ts
kτ and the Gaussian noise at the receiver input is represented by n(t).
The signal emitted by the kth transmitter consists of a large number of pulses
shifted to different times. Figure 2.2 illustrates an example for four users impulse radio.
Four time frames are presented with each frame divided into four time slots. Each user is
coded with different color. It is important to note that (2.9) and this discussion assumes
no multipath components.
The jth monocycle nominally starts at time
( ) ( )kjc
kjf dTcjT ++ . (2.10)
18
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
kk ==11
kk ==22
kk ==33
kk ==44
Tf Nu =4 Tc
J=0 J=1 J=2 J=3
Figure 2.2. Illustration of four users time hoping multiple access format (impulse radio)
To explain the previous terms in (2.10) and their effects on the spectrum, each time shift
will be examined separately assuming Gaussian monocycle as the pulse. The quantity
represents the monocycle waveform that nominally begins at time zero on the kth
transmitter’s clock. In regard to the first term in (2.10), the quantity represents
the monocycle in the j frame.
)( )(ktw
)( fjTtw −
Figure 2.3 illustrates the transmitted monocycle
and the shifted version of it,
)( )(ktw
)( fjTtw − .
A single bit of information is generally spread over multiple monocycles to form
a train of pulses. The quantity represents a uniform pulse train. The frame
time, Tf, may be 100 to 1000 times the monocycle width, resulting in a signal with very
low duty cycle. Both time-domain and frequency-domain plots for a uniform monocycle
pulse train are presented in
∑∞
−∞=
−j
fjTtw )(
Figure 2.4.
The second term in (2.10) is now considered. Multiple access signals composed of
uniformly spaced pulses are vulnerable to occasional catastrophic collisions. To eliminate
19
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
20
0 0.5 1 1.5 2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (ns)
Nor
mal
ized
Am
plitu
de
a) Gaussian monocycle )(tw
0 1 2 3 4 5 6 7 8 9 10 -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (ns)
Nor
mal
ized
Am
plitu
de Frame Time
b) Shifted Gaussian monocycle )( fjTtw −
Figure 2.3. The basic Gaussian monocycle and its frame-shifted version
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
21
0 2 4 6 8 10 12 14 16 18 20 -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (ns)
Nor
mal
ized
Am
plitu
de
a) Uniform train of Gaussian monocycles ∑∞
−∞=
−j
fjTtw )(
0 2 4 6 8 10 12
10 -8
10 -6
10 -4
10 -2
10 0
Frequency (GHz)
Nor
mal
ized
Mag
nitu
de
Gaussian Monocycle Monocycle Pulse Train
b) Normalized spectrum for the uniform train of Gaussian monocycles
Figure 2.4. Uniform train of Gaussian monocycles in time and frequency domains
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
catastrophic collisions, each link (k) uses a distinct pulse shift pattern . The hopping
sequence is periodic with period Np, which means that
( )kjc
jiNj ccp=+ , i is an integer. (2.11)
Each element of the time-hopping sequence is an integer satisfying the following bound
(2.12) hk
j Nc <≤ )(0
Hence the additional time shifts caused by the time-hopping sequence are discrete values
between 0 and . It is assumed that chTN
fch TTN ≤ (2.13)
Since the pseudorandom time-hopping sequence has period Np , then the waveform is
periodic with period
Tp=NpTf (2.14)
It can be shown that the time-hopping sequence effectively reduces the power
spectral density (PSD) of the uniformly spaced pulse train from a line spectral density
(1/Tf apart) down to a spectral density with finer lines 1/Tp. The time domain and the
normalized frequency spectrum representations for the non-uniform pulse trains are
presented in Figure 2.5.
The last term in the time index is for the pulse position modulation (PPM). PPM
is expected to distribute the RF energy across the band by smoothing the spectrum of the
signal [Sch93]. This should make the signal less detectable. The spectral smoothing effect
of PPM is relatively small. This is because the PPM only moves the pulse a very small
fraction of the pulse width. For example, a bit representing an information bit “1” will be
delayed by 0.156 ns compared with a bit representing “0” for a total pulse width of 1.5
ns. More details about PPM are presented in Section 2.4.2.
22
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
23
0 2 4 6 8 10 12 14 16 18 20 -1
-0.8
-0.6
-0.4
-0.2
0 0.2 0.4 0.6 0.8
1
Time (ns)
Nor
mal
ized
Am
plitu
de
a) Non-uniform train of Gaussian monocycles ∑∞
−∞=
−−j
ck
jf TcjTtw )( )(
0 2 4 6 8 10 12
10 -8
10 -6
10 -4
10 -2
10 0
Frequency (GHz)
Nor
mal
ized
Mag
nitu
dfe
Gaussian Monocycle Monocycle Pulse Train
b) Normalized spectrum for the non-uniform train of Gaussian monocycles
Figure 2.5. Non-uniform train of Gaussian monocycles in time and frequency domains
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
To give the reader a practical view of the signal characteristics, an example of a
typical signal used by Time Domain Corporation have the following characteristics:
Bandwidth of 2 GHz (>1 GHz). fc typically in the range 650 MHz – 5GHz. Tightly controlled pulse-to-pulse interval. Pulse width 0.2 –1.5 ns. Pulse-to-Pulse interval 100-1000 ns.
2.4 Coding and Modulation
Coding and modulation were discussed briefly in the previous section. In this
section more details about these topics are presented.
2.4.1 Coding
All source and channel coding applicable for narrowband systems are also
applicable for UWB systems. The advantage for UWB communication is the fact that
UWB signals seems to be easier to deal with because the signal is readily presented in a
digital form. UWB technology can be considered as the modulation layer of the
communication system. Thus, the remaining coding principles for the higher-level
communication layers, which are used in narrowband communications, are also valid for
UWB communication
Pulse position coding or “dithering” [Ful91] is a basic building block of the
proposed multiple access UWB system. Pseudo-random noise coding (PN Code) is used
for channelization. The code is used to apply a relatively large time offset at every frame.
Each user has a different code. Only the receiver with the same code can decode the
transmission. In the frequency domain the PN code makes the signal like noise. The code
is essential to suppress multiple access interference [Mar00]. PN codes must be
orthogonal to one another. They must effectively smooth the energy distribution and
allow fast signal locking [Ful00].
In addition to channelization and energy spectrum smoothing, the PN code makes
the UWB signal highly resistant to jamming as explained in Section 2.5.1. It is worth
24
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
mentioning that time dithering is also essential in radar applications for decorrelating the
ambiguous returns because of the high repetition rate [Ful91].
As was previously mentioned all coding concepts that are applicable for
narrowband can be extended for UWB systems. [For00] presented a practical low rate
convolutional error-correcting code for UWB communication. As expected, the coded
scheme outperforms the uncoded one. In other words, at a given bit error rate the coded
system increases the number of users by a factor which is logarithmic in the number of
pulses used by the time hopping spread spectrum system. [For00]
2.4.2 Modulation
Narrowband modulation includes amplitude modulation (AM), frequency
modulation (FM), phase modulation (PM) and many other variations [Skl88]. UWB
impulse radio can be modulated in analog form or digital form. [Win97a] presented a
comparison between analog and digital impulse radio for wireless multiple-access
communications.
UWB signals are usually time domain modulated using pulse position
modulation. This modulation allows for the use of an optimal receiving matched filter
technique [Pul00]. Pulse position modulation is accomplished by varying the pulse
position about a nominal position. For example in a 10 Mpps (Mega pulse per second)
system, pulses would be transmitted nominally every 100 ns. If the information bit is “0”,
the pulse would be transmitted 100 ps early. For a digital bit of “1”, the pulse would be
transmitted 100 ps late.
As it was mentioned before, PPM is expected to distribute the RF energy across
the band by smoothing the spectrum of the signal [Sch93]. However, the spectral
smoothing is small because the pulse position modulation only moves the pulse a very
small fraction of the pulse width.
[Ram98a], [Ram98b], and [Ram99] discussed higher order time domain M-ary
pulse position modulation. It was shown that by increasing M to a value more than 2, it is
25
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
possible to reduce the bit error rate, BER, or to increase the number of users at the same
bit error rate. [Sus00] presented a novel chaotic secure modulation. It is different than the
PN code because the sequence need not be periodic. In a chaotic transmitter, a message
signal undergoes two levels of pulse modulation. First, a frequency modulation is used to
modulate the message into subcarrier to be used as the clock pulses of a chaotic circuit.
The modulated clock pulses drive the coaotic circuit to generate the positions of the
carrier impulses. The objective is to guarantee that the time interval between the pulses is
chaotic. Thus the spectrum is smoother. Demodulation is done in two stages. First, the
timing between the pulses is recovered. Second, with the knowledge of the transmitter the
locations of the inner clock pulses are used to demodulate the message signal. No special
synchronization at any level is needed in this chaotic modulation. The level of security
depends on the hardware parameters of the chaotic circuit and the inner clock pulse train.
A single bit of information is generally spread over multiple monocycles. Thus, to
demodulate the received signal, the receiver sums the proper number of pulses to recover
the transmitted information. The receiver is based on decorrelating the received impulse
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.5
-1
-0.5
0
0.5
1
1.5
Time (ns)
Ampl
itude
received signal bit=0received signal bit=1template signal v(t)
Figure 2.6. Typical received signal for bit=0, bit=1 and the typical
waveform used by the receiver correlator
26
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
with a template signal as the one shown in Figure 2.6 assuming that the received signal
has the doublet shape. The template signal is the difference between the pulse that
represent an information bit=1 and the pulse used for an information bit=0.
2.5 Interference
Interference on UWB systems can result from other UWB users - multiple access-
, multipath, other narrowband systems, etc. Similarly, interference to narrowband system
could be multiple access, co-channel, multipath, leakage from other narrowband systems,
or UWB interferences. First, the interference from other radiators to UWB systems is
reviewed. Second, the interference on other narrowband systems as a result of UWB
system will be discussed.
2.5.1 Interference from Other Radiators to UWB Systems
UWB receiver has to deal with many narrowband radiators. The external
interference to the UWB receiver strongly depends on the antenna. Measurements of the
received power across the spectrum using UWB antenna give an illustrative image of the
interfering signals. A significant amount of lower frequency interference power (TV, FM,
and land mobile radiators) can get through the antenna’s frequency side lobs below the
main pass band of the UWB antenna system.
A specific UWB antenna tested by [Sch00] resulted in an interference power of
about -33.5 dBm when the entire system spectrum was utilized. The level of the
interfering power was reduced greatly by using a bandpass filter at the front end of the
receiver. With 97% bandwidth usage (780 MHz, 2.05 GHz) the interference power level
reduced to -40 dBm. A further reduction to 86% bandwidth usage (960 MHz, 1.93 GHz)
removed the strong interference at the edges (900 MHz). The captured signal approached
the noise floor of the spectrum analyzer which is nearly -60dBm.
The previous analysis suggests the possibility of incorporating a notch filter to
remove the strongest interferer. It is important to note that since the noise is highly
dominated by specific interferers, the level of the interferer power would be sensitive to
27
Chapter 2. Ultra Wideband vs. Narrowband Communication Schemes
the location of the measurements. This is because the interferer signal may suffer from
multipath enhancement or fading [Sch00].
UWB Multipath interference is not a problem due to the high time resolution.
Signals reflected from different objects can be easily resolved from the line of site signal.
Practical multiuser interference rejection performance is not guaranteed. The processing
gain is used as a theoretical measure to the system ability to reject interference.
Processing Gain and Interference Resistance
The inherent pseudo-random code that is usually associated with UWB
communication system makes the system highly resistant to interference. All other
signals act as jammers to the UWB communication system. UWB signals are designed to
share the same band as other existing systems.
The processing gain reflects the ability of the system to resist interference. It is
defined as the ratio of the RF bandwidth of the signal to the information bandwidth of the
signal. A UWB system that transmits 8 kHz of information using 2GHz of bandwidth has
a processing gain of 250,000 or 54 dB. For example, a 2 GHz with 10 Mpps transmitting
8 kbps would have a processing gain of 54 dB, because 0.5 ns pulse width with a 100 ns
UWB technology is also promising in other fields such as automobile collision
avoidance, computational fluid dynamics [Ful00]. Bennett and Ross have reviewed
different applications of UWB technology [Ful00]. More sophisticated applications are
expected due to the recent developments in application specific integrated circuits
[Dic99].
Based on the previous discussion, there is a strong relation between the term time
domain and the term UWB. On the other hand, narrowband communication lends itself to
frequency domain techniques. In the next chapter time domain and frequency domain
techniques are compared as alternatives to characterize the UWB communication
channel.
36
“When you can measure what you are speaking about,
and express it in numbers, you know something about it.”
Lord Kelvin
Chapter 3
Time Domain and Frequency Domain
Channel Measurement Techniques and
Setups
3.1 Introduction
UWB characterization can be achieved by performing measurements in the time
domain or in the frequency domain. The goal of studying different alternatives for
measurements is to come up with measurements that are reliable, repeatable, not overly
complicated, cost effective and reflects the real characterizing parameters.
Channel characterization may refer to extracting the structure of the channel from
the measured data. Data can be measured in different ways using variations of setups.
The objective of this chapter is to compare frequency-domain vs. time-domain techniques
to characterize the UWB communication channel. In this regard the following issues are
addressed: measurables, measurement approaches and setups, and calibration schemes.
The pros and cons of each technique are highlighted. Moreover, in this chapter the
measurement setups including the antennas are characterized to serve as base for
37
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
interpreting the results to follow in the next chapters. Characterizing the pulse generators,
the antennas and the receiver is an integrated part of the UWB channel characterization
efforts, as their effect cannot be completely deconvolved from the presented results.
3.2 Channel Impulse Response and Measurable Parameters
In time domain, a system -being it a communication channel or not - is described
by its impulse response. The transfer function is the corresponding frequency domain
alternative for describing the system. Though, one can transfer from one domain to
another, some parameters are easily measured in the domain in which they are defined. It
is not always convenient to present the channel by its impulse response or transfer
function because of the large data storage and processing requirements. Parameters based
on the received time domain waveform or spectrum distribution are used instead.
In the following section, measurable parameters are reviewed. At the fundamental
level, pulse parameters including pulse risetime and bandwidth should be accurately
measured. A measure that gained special importance for the UWB channel is the material
penetration/reflection capability. This is because the proposal of UWB promised an
excellent through-the-wall communication capability. Multipath response of the channel
is an important measure that helps characterizing the performance of communication
systems. The multipath response is well represented using the multipath power delay
profile.
3.2.1 Pulse-Shape and Frequency Distribution
Occupied bandwidth represents a main feature of communication systems. When
characterizing UWB signals, it is important to be able to accurately measure signal
spectrum or the corresponding pulse shape and transient durations. As the pulse width
decreases, the risetime becomes a significant fraction of the total signal pulse duration.
For this reason, the bandwidth for transient pulses is related to pulse risetime instead of
pulse width [Kis92]. UWB communication results in no generic pulse shape, all are
damped transient. The effect of transient RF signals, as opposed to steady state signals on
material and circuits is a complex subject [Bar01].
38
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
An important measure is pulse risetime or alternatively the occupied bandwidth.
Manufacturers of transient, single-shot collection equipment recommend that the analog
input (3dB) bandwidth should support at least three samples along a signal’s rising edge
to reduce error in risetime measurements.
3.2.2 Material Penetration/Reflection Capability
Materials encountered in indoor wireless communication channels need to be
characterized. The reflection of the ceiling, floors, inner walls and external walls are
different due to the difference in the effective permittivity. Effective Permittivity for the
floor, ceiling, external walls, and inner walls are reported to be 6.2, 6.2, 4.2, and 5.0
respectively [Kon99][Rap96]. Permittivity is frequency dependent. Due to the ultra
wideband proposal, the effective permittivity needs to be re-evaluated for indoor
construction materials.
The insertion transfer function is first measured across the spectrum of interest,
then different parameters can be extracted from it. Parameters of interest include the
complex effective permittivity or alternatively the dielectric constant and the loss tangent.
Propagation through different materials can also be characterized in the form of
attenuation constant and phase constant.
3.2.3 Multipath Profile Parameters
When the channel is exited with a pulse, the received waveform is a summation of
modified pulses with different attenuation factors and different time delays. The received
waveform is referred to as multipath profile and the individual pulses are referred to as
multipath components because they arrive to the receiver through different paths.
The pulse travels from the transmitter to the receiver through different paths
having real positive gain, , and propagation delays, ka kτ , where k is the path index.
Assuming no-dispersion within individual pulses, the channel impulse response is real
and can be represented as a superposition of these paths as in [Win97b]
39
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
∑ −=k
kk tath )()( τδ , (3.1)
where (.)δ is the Dirac delta function. An example of a discrete-time impulse response of
a multipath indoor channel is depicted in Figure 3.1. The excess delay is a measure of
time delay relative to the first arriving component
Excess Delay τ ∆
Maximum Excess Delay
N ∆τ
τ
) ( τ r P
Figure 3.1. Example of discrete-time impulse response model for a multipath indoor channel
The signal at the input of the receiving antenna is the time convolution of the
radiated pulse, , and the channel impulse response, h(t), as follows )(tp
)()( kk
k tpatr τ−= ∑ . (3.2)
The signal to noise ratio can be improved by different techniques. For example,
the signal can be matched-filtered. The filtered signal is given by
)()( kk
kf tatr τγ −= ∑ , (3.3)
where )(tγ is the convolution of p(t) with p(-t). Assuming that there is no overlap of
pulses, i.e., >− lk ττ resolution, e.g. 2 nanoseconds when lk ≠ , the filtered power
profile after passing through a square envelope detector is
40
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
∑ −== 222)()()( kkff tatrtP τγ . (3.4)
The unfiltered power delay profile can be expressed as
∑ −=k
kk tpatP )()( 22 τ (3.5)
Based on (3.5) some different time dispersion parameters can be defined.
Time Dispersion Parameters
All time dispersion parameters are measured relative to the time of arrival of the
first component. The profile energy is normalized and all signals below a specific
threshold X dB relative to the maximum are forced to zero. Presenting the time dispersion
parameters for a specific threshold eliminates the noise that varies from measurement
setup to another.
The maximum excess delay (X dB), maxτ , of a power delay profile is defined as
the time required for the energy to fall X dB relative to the maximum [Rap96]. The mean
excess delay is the first moment of the power delay profile [Rap96]
∑
∑∑
∑==
kk
kkk
kk
kkk
P
P
a
a
)(
)(
2
2
τ
ττττ , (3.6)
and the RMS delay spread is the square root of the second central moment of the power
delay profile [Rap96]
22 )(ττστ −= , (3.7)
where
∑
∑∑
∑==
kk
kkk
kk
kkk
P
P
a
a
)(
)( 2
2
22
2
τ
ττττ . (3.8)
41
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
The ratio of the mean excess delay to the RMS delay spread can be used as a measure of
the time dispersion for UWB signals.
In the frequency domain, similar quantities are defined and widely used in
narrowband communications. For example, the coherence bandwidth, BC, is a statistical
measure of the range of frequencies over which the channel is considered flat. Within this
band different frequency components have strong amplitude correlation. If the coherence
bandwidth is defined as the bandwidth over which the frequency correlation function is
above 0.9, then the coherence bandwidth is approximately [Rap96]
τσ50
1≈CB . 90% (3.9)
For 0.5 frequency correlation, the coherence bandwidth is approximately
τσ5
1≈CB . 50% (3.10)
Pathloss and Power Attenuation
Another useful parameter is the total multipath power gain. It describes the energy
characteristics of the multipath profile P(t) and it is given by
∑=k
kaP 2 . (3.11)
The spatial average of the power gain, P as a function of the distance d from the
transmitter is generally a decreasing function of the distance d. The logarithmic value of
this attenuation is
−=
)()(log10)(
010 dP
dPdPL (3.12)
where is a reference distance. The last quantity can be compared to the free space
propagation loss for different values of pathloss exponent, n, like 2 and 3,
0d
. (3.13) )(log10)( 10n
n ddPL −−=
42
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
Although all these measurable parameters were developed for narrowband
systems, many researchers are extending their use to UWB characterization problems.
However, new parameters may be more efficient in characterizing the UWB multipath
propagation channels.
3.3 Measurement Setups
Wideband measurements are performed using setups assembled and tested in the
Time Domain Laboratory at Virginia Tech. The objective of the following sections is to
characterize the measurement setup to be used for wideband material characterization and
indoor UWB measurements. Measurements are performed using both frequency-domain
and time-domain techniques. The measurements presented in this section help de-
embedding the effect of the sources and sampling scopes. The effect of the antennas and
the phase shifters associated with them is also studied to allow for a partial de-
embedding. Details about the equipment are given to ensure repeatability of
measurements and corresponding results.
3.3.1 Time Domain Measurement Setup
One of the essential properties of time domain measurement techniques is the
ability to distinguish discontinuities and time separations between them. A schematic
illustration of the components of a time domain measurement system is shown in Figure
3.2a. The pulse generator triggers a sampling oscilloscope as the pulse enters the system
under test. The figure displays the measurement locations of both time domain reflection
(TDR) and transmission (TDT) measurements. In the case of the Gaussian-like pulse
input, which has frequency spectra that extend to dc, the time-domain resolution depends
on the risetime of the pulse, which is inversely related to the pulse’s bandwidth.
An experimental setup was established to evaluate the performance of impulse
radio. The setup is shown in Figure 3.2b. It consists of a pulse generator that furnishes
pulses to the transmitting antenna. The antenna is preceded by a balun which converts the
unbalanced coaxial terminals to two terminals feeding the signal to the balanced antenna
terminals. The baluns and the antennas, on both the transmitting and receiving sides, have
43
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
sufficient bandwidth such that the spectral characteristics of the pulse signal are not
degraded. Radiated pulses propagate through the channel and are captured by the
receiving antenna. Received pulses are acquired by means of a sampling oscilloscope and
a data acquisition unit. The received signal suffers attenuation and dispersion whose
degree depends on the characteristics of the channel as well as the radiation patterns of
both transmit and receive antennas. Matched load calibration is used to cancel the
oscilloscope offset.
Synchronization is achieved through an external circuit. The sampling
oscilloscope requires a pre-trigger. The oscilloscope has to receive the pre-trigger 80 ns
before the trigger signal to the transmitter. This is achieved by using a step generator
driver that can supply the required trigger and pre-trigger. The trigger setup on the
sampling oscilloscope is set to the negative slope with about 350 mV. It is seen that
lower or higher trigger levels resulted in higher jitter for the used setup.
As the distance between the receiver and the transmitter increases, the need for a
wideband amplifier becomes more pronounceable. Different sets of antennas or different
sizes in conjunction with different various sources for generating pulses can also be used.
The setup can be manipulated to handle multiple antennas for diverse communication.
Table 3.1 below exhibits a more detailed list of the apparatus used for the ultra wideband
experiments.
44
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
45
RF PULSE GENERATOR
SAMPLING OSCILLOSCOPE
BRIDGING T NETWORK
Transmission Reflection
Channel or DUT
(a)
(b)
Figure 3.2. Time domain measurement setup,
a) General TDR and TDT measurement setup, b) Illustration of the time domain measurement setup.
Radiated Measurements
Conducted Measurements
2*10 dB amplifier, up to 15 GHz
trigger input
trigger
pre-trigger
Running LabView® 6.0i
Channel
Balun and wideband horn receiving antenna/ biconical antenna
Balun and wideband horn transmitting antenna/ biconical antenna
Data Acquisition Unit
Step Generator Pulse Generator PSPL-4100/4050A
Digitizing Oscilloscope
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
Table 3.1. Component specifications used for the time domain measurement setup
Equipment Description Pulse Generator Picosecond Pulse Generator 4050A / 4100 Digital Sampling Oscilloscope Tektronix 11801 or HP 54120A with HP
54124A Four Channel Test Set. Trigger Box (Controlled Delay)
TDL home made
Thin Semi-Ridged Cables To connect the signal BNC Cable Pre-trigger and trigger connection, low noise
coaxes 50Ω and connectors. 20dB Attenuator DC-26.5 GHz HP 33340C, for conducted measurements Data Acquisition Unit Collect Data, Laptop or Desktop with GBIP card BNC to male SMA Connect the pre-trigger cable to the scope Antennas (Horn) #1 A pair of horn antennas with baluns Horn array Antenna #2 A pair of horn antennas array with wider
bandwidth and 180 phase shifter at the input Biconical Antennas#3 A pair of wideband omnidirectional biconical
antennas Balun or 180 phase shifter Required to change to/from co-axial
configuration, The PSPL Model 5320A BALUN is used with antenna#1, [PSPL-5320A] and the Krytar 4010124, 1-12.4 GHz is used with antenna#2
Ultra wideband Amplifier 10dB inverting, 15GHz, , two amplifiers may be cascaded I\5828 Ultra-Broadband Amplifier, [PSPL-5828]
3.3.2 Frequency Domain Measurement Setup
The frequency domain measurement system is displayed in Figure 3.3a. The
general block diagram for both the frequency domain reflection (FDR) and frequency
domain transmission (FDT) are shown on the same figure. It is important to note the
presence of the vector analyzer, which is needed for recovering the amplitude and phase
of the system response. Vector analyzers employ calibration standards to reduce the
reflection and transmission errors at the expense of an increased number of measurements
resulting in increased measurement time. System bandwidth determines the limits to
pulse and spectral line widths as well as line separation in the frequency spectra, which
determines the time duration.
46
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
47
(a)
(b)
Figure 3.3. Frequency domain measurement setup;
(a) General FDR and FDT measurement setup, (b) Illustration of the frequency domain measurement setup
Directional Coupler
DirectionalCoupler
Reference Reflection
DirectionalCoupler
Directional Coupler
Reference
Reflection
SYNTHESIZEDSWEEPER
Channel orDUT
VECTOR ANALYZER
Data Acquisition unit
Port 1
X(ω)
Port 2
Y(ω)
Balun and wideband transmitting antenna
)()()()(21 ω
ωωωXYHS =∝
S-parameters test set
Vector Network Analyzer withSwept Frequency Oscillator
Balun and wideband receiving antenna
Channel
)(ωH
[ ])()( ωHIFFTth =
Inverse FFT Processing
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
Figure 3.3b is a more detailed and illustrative view of the frequency-domain
characterization. A network analyzer is used for performing swept frequency
measurements. Port 1 is connected to the transmitter and the receiver is connected
through port 2. The network analyzer sweeps the frequency within the measured band of
interest. For UWB characterization, one has to trade off the frequency resolution with the
required number of measurements, which is directly proportional to the time it takes to
perform the experiment as well as data storage requirements. Decision has to be made on
the measured bandwidth, number of points and the sweep time. The inverse Fourier
transform is used to obtain the impulse response of the UWB channel. Neither pulse
generator nor sampling oscilloscope is needed for the frequency domain measurements.
The additional equipment for the frequency domain measurements is the HP 8510
network analyzer.
3.4 Source Characterization and Conducted Measurements
In time domain, a full understanding of the characteristics of UWB propagation
requires two different types of measurements. First, individual pulses are captured
directly in time domain at the output of the pulse generator device. This procedure is
most commonly referred to as “conducted” measurements [Kis01]. Secondly, received
pulse is captured using a specific transmitter and receiver antennas. The following
section presents the results for such measurements.
Two pulse generators are used. The first pulse generator is the Picosecond Pulse
Labs® 4050A which has time jitter of ±2.5 ps. A 10 V, 45 ps pulse rise time is generated
in a remote fast pulser head module. A high quality 50 Ω cable is used to connect the
step generator to the pulse head. The pulse head allows us to connect the fast 45 ps pulse
directly to the input before the antenna. This approach eliminates the rise time slowing
effects of interconnecting coaxial cables. The generated pulse is a clean pulse with a
manufacturer nominal value of 0.3% for the precursor and 2% overshoot [PSPL-4050A].
To add variability dimension another source is also used. The second pulse generator to
be used is the Picosecond Pulse Labs® 4100 with ±2.5 ps time jitter. The generated
48
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
pulse has 5 V amplitude and an 85 ps rise time. More details about the second source can
be found in [PSPL-4100].
The output of the pulse generator is directly captured using a sampling
oscilloscope. A 20 dB attenuator is used to protect the input of the sampling
oscilloscope. The setup used for the conducted source measurements is further clarified
in Figure 3.4.
Pulse Generator
Delay Generator (Trigger Box)
Digitizing Oscilloscope
Data Acquisition unit
pretrigger
trigger
trigger input
trigger input
Pulse Head (and/or) Atten.
Figure 3.4. The setup used for the conducted source measurements
The measured pulse for the 4050A generator is shown in Figure 3.5. The shape of
the pulse is far from being Gaussian due to the smooth falling edge. It is apparent that
the pulse is smooth and ringing effect is not pronounced. The precursor and the
overshot are within the manufacturer specifications as can be seen from the zoomed view
in Figure 3.5b. The spectral occupancy is shown in the normalized frequency plot in
Figure 3.5c. It is worth to mention that due to the periodic nature of the pulse, the
frequency representation is discrete. However, the plot is represented with continuous
line. Such continuous representation is used for the sake of clarity. Only positive
frequency values are plotted due the symmetry of the frequency response.
For the 4100 source, the output pulse waveform and the normalized spectrum are
both shown in Figure 3.6. The main pulse duration is shorter compared with the 4050A
pulse, but damped ringing effects are much larger.
49
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4 6 8
10
Time ns
Ampl
itude
in V
Picosecond 4050A
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.2
-0.1
0
0.1
0.2
Time ns
Ampl
itude
in V
Picosecond 4050A, Zoomed
-20
0
dB
FFT
)
)
)
(c)(c
(b)(b
(a(a
50
Figure 3.5. The resulting waveforms for the Picosecond 4050A generator, (a) The generated waveform, (b) Zoomed version of the generated waveform, (c) Spectrum of the generated waveform.
0 5 10 15-60
-40
Frequency GHz
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
)
)
)
itude
i
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0 2 4 6 8
10
Time ns
Ampl
itude
in V
Picosecond 4100
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-0.2
0
0.2
0.4
Time ns
Ampl
n V
Picosecond 4100, Zoomed
-20
0
dB
FFT
(c(c)
(b(b)
(a(a)
51
Figure 3.6. The resulting waveforms for the Picosecond 4100 generator, (a) The generated waveform, (b) Zoomed version of the generated waveform, (c) Spectrum of the generated waveform.
0 5 10 15-60
-40
Frequency GHz
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
For both measurements mentioned above, two disparate quantities can be
computed. The first of which is the total peak power; ‘instantaneous’ power embedded
in the kth sample point on the transmitted or received waveform. The kth element in the
waveform should be the maximum absolute value in the array in order to calculate the
direct peak power as follows:
0
2 )max(Z
aP k
peak = (3.14)
where ak represents the instantaneous measured value point in the waveform sequence
and Z0 is the input impedance of the measurement equipment which is 50 in the
present case. The total average power is another quantity which can be computed using
the acquired time domain information as follows:
Ω
ta
PRRP k
kavg ∆
= Σ 50
2
, (3.15)
where Pavg is the average power, PRR is the pulse repletion rate, and ∆t is the sample
interval. The PRR is 1/177.3E-6 where 177.3E-6 is the pulse repetition interval as
determined by the trigger signal. For signal generated by the 4050A, the total peak
power is 33.46 dBm while the total average power is –22.30dBm. For signal generated
by the 4100, the total peak power is 29.58 dBm and the average power is -34.98 dBm.
The –10 and –20 dB bandwidth can be extracted from the frequency domain power
spectrum. These specific spectral characteristics are summarized below in Table 3.2.
Table 3.2 Total peak power, average power, and emission bandwidth for the used sources Device Peak Power
(dBm)
Average
Power (dBm)
-10 dB
Bandwidth
(GHz)
-20 dB
Bandwidth
(GHz)
-40 dB
Bandwidth
(GHz)
PSPL 4050A 33.46 –22.30 0.781 2.148 9.961
PSPL 4100 29.58 -34.98 7.813 9.765 12.891
52
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
53
The effect of the coax connecting cables is illustrated in Figure 3.7. Due to the
mismatch at the connection points there are some reflections in time domain plots. High
quality cables are used to minimize those reflections.
0 2 4 6 8 10 12 14 16 18 20 - 0.1
- 0.08
- 0.06
- 0.04
- 0.02
0
0.02
0.04
0.06
0.08
0.1
Time (ns)
Ampl
itude
(V)
Picosecond 4050A, Zoomed
Figure 3.7. Effect of connection coaxial cables, indicated by the circle
3.5 Antenna Characterization and Radiated Measurements
Our case consists of three pairs of antennas. Two of them are based on TEM horn
structure and the third pair has biconical design. The second TEM horn pair is wider in
bandwidth than the first TEM horn pair. Using different antennas enables variability
study and sheds more light on the importance of antennas to the UWB system.
For impulsive free-space measurements a TEM horn is suggested by [Law78].
TEM horns are quite broadband in receiving mode, both in magnitude and phase. The
suggested antenna was reproduced and tested in the Time Domain and RF Measurements
Laboratory at Virginia Tech. Structures and configurations for the antennas in
experimentation are described in Appendix B1.
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
Radiated measurements are used to characterize the antennas. The two antennas
are placed facing each other at a separation distance that ensures far field approximation.
If the time domain signals are acquired with the same receiver settings, and over a short
frame for good instrument stability, the received signal can be used as a reference. Under
same measurements settings, there would be no need to specify the transfer function of
the receiving system [Aur96]. The setup for the radiated measurements is similar with
those introduced in Figures 3.2 and 3.3.
The approximate separation requirement in order to achieve far-field or
Fraunhofer region characterization is given by the Fraunhofer distance which is as
follows [Rap96]:
λ
22Dd f = (3.16)
where λ is the wavelength and D is the largest physical linear dimension of the antenna.
To reside in the far field region two other conditions on df must be met, which can be
written as
(3.17) Dd f >>
λ>>fd (3.18)
For the two antenna pairs under consideration, D is 0.213 m and 0.279 m,
respectively. The required far field distances versus frequency are shown for the two
TEM antenna pairs in Figure 3.8. In view of the plot, to cover the frequency range of
interest up to 15 GHz, the far distances are approximately 4.5 m and 8 m, respectively for
the two antennas.
54
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
55
0 5 10 15 0
1
2
3
4
5
6
7
8
Frequency GHz
Far d
ista
nce
(m)
Antenna#1 Antenna#2
Figure 3.8. The distances required for far-field approximation vs. frequency
The antennas were placed facing each other as shown earlier in Figure 3.2. The
distance was fixed to 2.5 m and 7 m based on the antenna pair due to far-field
requirements. The measurements should be done in a reference channel that has minimal
multipath effect, such as anechoic chamber. However, a large enough chamber was not
at the time available for use. Therefore, the measurements were taken in an environment
with minimum reflectors. The main reflection is due to the ceiling and the floor. The first
antenna pair was characterized in the Time Domain Lab at Virginia Tech, with a total
height of 2.42 m. The antennas were kept at 1.03 m from the floor. A laser pointer was
used to direct the antennas. This setup results in a main reflection from the floor with a
time delay 2.46 ns relative to the line of sight path. Time gating can be applied safely if
the main received pulse width is less than 2.46 ns. For the second antenna pair the
experiment was carried out on the 3rd floor of Whittemore building on the open area
where there is no ceiling. The antenna elevation was increased to 1.42 m to increase the
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
delay of the reflection from the floor. The time gating capability for this setup then
becomes 1.81 ns.
The radiated measurements for the first antenna pair were carried out using time
domain and frequency domain techniques. The time domain radiated measurements were
performed using two sources. The received waveforms together with the gated
waveforms are shown in Figure 3.9 for source1 and source2. Time gating is less accurate
using source#2, because the ringing effect cannot be isolated from the multipath
reflection. The time-gated waveforms are then converted to frequency domain data using
FFT and divided by the corresponding frequency transform of the input signal to obtain
the transfer function. A set of 1024 points was acquired in a 5 ns window, which resulted
in a 5 ps sampling time. The acquired data are based on 128 averaged measurements.
Furthermore, the frequency domain measurements using the same antenna setup
were considered using network analyzer, as demonstrated in Figure 3.3. The S21
parameter was measured in the range of 45 MHz-15 GHz, where 801 points were
acquired in order to complete the experiment.
The magnitude of the transfer function for antenna#1 is presented in Figure 3.10
acquired by both the time and frequency domain measurements. The frequency plot is
based on 16+1 points moving average. The acquired frequency domain data within the
aforementioned range is first transformed to time domain to allow for time gating and
then transformed back to frequency domain. A Kaiser window with β=20 is used to
smoothly gate the required duration. However, time gating is not perfect because the
incomplete frequency information introduces error in the time domain representation.
The difference between time and frequency domain responses could be a result of un-
gated multipath components.
56
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Time (ns)
Ampl
itude
(V)
Received
Time gated
0 0.5 1 1.5 2 2.5 3 3.5 4-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
Time (ns)
Am
plitu
de (V
)
ReceivedTime-gated
(b)
(a)
Figure 3.9. Received and time-gated waveforms for antenna #1 at a distance of 2.5 m
(a) with the 4050A generator.
(b) with the 4100 generator.
57
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
0 5 10 15 -65
-60
-55
-50
-45
-40
-35
Frequency (GHz)
Tran
sfer
Fun
ctio
n Am
plitu
de (d
B)
4050A4100HP 8510 Network Analayzer
(a)
0 5 10 15 -3
-2
-1
0
1
2
3
Frequency (GHz)
Phas
e fo
r Ant
enna
#1 (r
adia
ns)
4050A 4100
(b)
Figure 3.10. Frequency domain transfer function for antenna #1 using the time domain measurements (a) Magnitude and (b) phase
58
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
The difference between the two time-domain measurements could be due to the
different spectral occupancy or errors in time gating as source2 has the ringing effect
which lasts longer than the time gating capability of the setup. The linearity of the phase
for the same antenna pair is shown in Figure 3.10. The relevant phase information could
not be extracted from the network analyzer measurements because of uncontrolled
multipath reflections. The frequency domain result pertaining to the antenna #1 shown in
Figure 3.10 confirms that the response is reasonably flat (± 3 dB) up to 7 GHz. [Law78]
showed that the far-field time-domain response of the transmitting antenna is a constant
times the derivative of the time domain response of the receiving antenna. In other
words, in the transmit mode, the low frequency roll off with decreasing frequency is
nearly 6 dB/octave steeper than in the receive mode.
The large distance required for far field performance limits the time gating
capability. Furthermore, frequency domain measurements are much harder to be
performed as inconveniently long wideband cables are needed to connect to the network
analyzer. Thus, antenna#2 is characterized only by source 4050A. The received and time
gated waveforms are shown in Figure 3.11. The magnitude and phase of the transfer
function for antenna#2 compared with antenna#1 are shown in Figure 3.12. Antenna#2
covers more bandwidth up to 12 GHz with some variation on the pass band. The phase is
linear in this band as can be seen from Figure 3.12. Linear phase components could be
added to the plots to account for the exact delay.
The biconical antenna has a wideband that covers 0.1-18 GHz. It has the
advantage of being omnidirectional. Time gating with biconical antenna is more difficult
because the antenna is omnidirectional and it is not optimized for impulsive radiation.
59
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Time (ns)
Ampl
itude
(V)
received time gated
Figure 3.11: Received and time-gated waveforms demonstrated for the antenna #2 with the 4050A generator at a distance of 7 m.
60
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
0 5 10 15 -65
-60
-55
-50
-45
-40
-35
Frequency (GHz)
Mag
nitu
de (d
B)
Antenna#1 Antenna#2
(a)
0 5 10 15 -3
-2
-1
0
1
2
3
Frequency (GHz)
Phas
e i(r
adia
ns)
Antenna#1 Antenna#2
(b)
Figure 3.12. Frequency domain transfer functions of the two antennas using their time domain measurements with 4050A generator at a distance of 7 m
(a) Magnitude, and (b) phase.
61
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
0 1 2 3 4 5 6 7 8 9 10
0
0.0
0.0
0.0
0.0
0.1
Time (ns)
Ampl
itude
(V)
Figure 3.13. Received signal for biconical antenna (antenna#3) with the 4100
generator at a distance of 1 m.
62
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
3.5.1 Relation between Multipath Angle and Pulse Shape
It should be noted that previously presented radiated measurements are for
boresight direction. However, in practical cases, the antenna pattern plays an important
role for both the receiver and the transmitter. To illustrate this, the effect of the angle of
arrival using the antenna#1 with source#1 (PSPL-4050A) is considered in this subsection.
Vertical Rotation Measurements
The first scenario is to investigate the effect of vertical rotation of an antenna (E-
plane scan). In this case, the transmitting antenna is kept fixed at a height of 1.03 m
above the ground, whereas the receiving antenna at the same height is rotated along the
elevation angle, θ. Measurements are performed at different angles; namely ±150, ±300,
±450, ±600.
The schematic diagram embedded in Figure 3.14 demonstrates the first two
multipath components that are expected to be captured in time domain. Spherical lines
covering the receiver represent the rotation in the vertical direction as well as the antenna
far-distance electric field lines. Negative angles refer to rotation towards floor, and on the
other hand, positive angles in the reverse direction. When the receiver antenna is tilted
more towards floor – i.e. negative angles, – the line-of-sight pulse and the reflection off
the floor tend to move toward each other and vice versa. Another interesting feature is the
broadening of the original pulse when compared directly to the boresight reception.
Horizontal Rotation Measurements
The second scenario is to investigate the effect of horizontal rotation of an
antenna (H-plane scan). Similarly, the transmitting antenna is kept fixed at a height of
1.03 m above the ground, whereas the receiving antenna at the same height is rotated
along the spherical angle, φ, – i.e. in the horizontal plane. Measurements in time
63
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
0 1 2 3 4 5-0.02
0
0.02
0.04
0.06
0.08
Time ns
Am
plitu
de in
V
015-30-45-60-
0 1 2 3 4 5-0.02
0
0.02
0.04
0.06
0.08
Time ns
Am
plitu
de in
V
015+30+45+60+
ceiling
floor
Rx Tx
receiving antenna
60o
-60o
-45o
-30o
-15o
0o
15o
30o
45o
(a)
(b)
(c)
Figure 3.14. Received waveforms at different receiver elevation angles (E-scan), using antenna#1 and source#1 (a) experimental view, (b) negative elevation angles comparison, (c) positive elevation angles
64
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
i i
60o
-45o
-30o
-15o
0o
15o
30o
45o
Side Wall
Side Wall
Rx Tx
(a)
-60o
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.02
0
0.02
0.04
0.06
0.08
Time ns
Am
plitu
de in
V
015-30-45-60-
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.02
0
0.02
0.04
0.06
0.08
Time ns
Am
plitu
de in
V
015+30+45+60+
(b)
(c)
Figure 3.15. Received waveforms at different azimuth receiver angles (H-scan), using antenna#1 and source#1 (a) experimental view, (b) negative elevation angles comparison, (c) positive elevation angles
65
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
domain are repeated for various angles; namely ±150, ±300, ±450, ±600.
The schematic diagram embedded in Figure 3.15 demonstrates placement of the
antennas in the laboratory room. Spherical lines covering the receiver represent both the
rotation in the horizontal plane and antenna far-field lines. Negative angles refer to left
rotation, positive angles to right. In view of Figure 3.15 either rotation reveals identical
results when compared to each other. That is because the left and the right rotations are
symmetrical about the boresight direction. Another important feature is the swift
broadening of the original pulse when compared directly to the boresight reception.
A more comprehensive characterization can be done in an anechoic chambers.
Usually, antenna characterization is done in the frequency domain for only specific
frequencies. For accurate time domain applications, such task requires a huge number of
frequency measurements. The setup and the radiation pattern at 5GHz are displayed in
Appendix B1.
More discussions about the effect of the pulse shape on estimating the channel
impulse response and receiver design are presented in Chapter 6.
3.6 Calibration Schemes
Imperfections of the system components used in the measurement process can
result in errors. As an example, the calibration of the measurement system may require
some type of interfacing with the system under test. The identical interfacing used to
allow for the calibration standards is also used to connect the system under test to the
measurement system. Some effects of this interfacing can be included as part of the
system components as an imperfection. Other imperfections could force a proposed
characterization technique not to converge, or become unstable.
Another systematic measurement error, which is always common in measurements, is
the noise content of the measured waveforms. Noise can result from imperfections in the
calibration or from the effects of not calibrating all error components within the system.
Noise can also be introduced from external sources near the measurement system or the
66
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
system under test. Repeating the experiment and taking the average can reduce the
effects of the noise. [Yoh01]
For the frequency domain measurements the system can be calibrated using short,
open and matched load standard kits at both ports. A standard is a physical device having,
precisely defined characteristics, that is used as a reference for a unit of measurements
[Su92]. Through calibration can be done by connecting port 1 to port 2 directly. The
network analyzer adjusts the measurements based on the calibration.
For time-domain calibration, early calibration technique for networks involved the
use of a short circuit standard to produce a reference waveform. Two transmission lines
can be used as time-domain isolators (to isolate secondary reflections due to impedance
mismatch between the scope and the device under test (DUT). It is important to note that
the commercially available standards for frequency calibration might not be applicable
for time domain measurements due to the large bandwidth requirements. However, a
coaxial precision line can simulate a known impedance over a relatively wideband of
frequencies due to the ability to gate time domain waveforms. [Su92].
The channel can be measured with no input to account for any persisting signals
due to the setup or other sources. If the received signal does not average to zero while the
input is zero, it means that this measured signal has to be subtracted from the channel
measurements when the input is applied. Another process that might add to the
calibration is the deconvolution process where the input or conducted measurements is
deconvolved from the radiated measurements. Such procedure should result in an ultra
high-resolution channel characterization [Vau99] [Mov98]. In principle, this should make
the channel characterization independent of the input signal assuming the signal spectrum
cover the entire frequencies of interest. Ultra wideband application requires more
accurate and wideband measurement techniques.
3.7 Pros and Cons
Advantages and disadvantages of both the time domain and the frequency domain
will be discussed in this section. Rather than providing the reader with a list of pros and
67
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
cons, they are discussed to engage the reader in a thoughtful study of both techniques.
Making a decision on the technique to be used does not avoid the engineering tradeoffs.
Next paragraphs emphasize the time domain pros and cons followed by an emphasis on
the frequency domain.
One advantage of time-domain measurements is that they require only a single
measurement where the frequency domain techniques require frequency sweeping, which
involves a measurement at each discrete frequency. Sounding a channel with time
domain pulse requires relatively a simple implementation. Another advantage of the time-
domain technique is that the resulting waveform immediately gives a physical insight into
the characterization problem, whereas calculations (i.e. pulse development, convolution,
inverse Fourier transforms) need to be performed to the frequency domain equivalent
measurement before information is visually realizable by the user. Time-domain methods
are capable of operating directly on the time domain data, as the name suggests. The
advantage of performing the measurements in the time domain is a reduction of error
caused by the Fourier and inverse Fourier transform operators used to transform the data
to and from the frequency domain, respectively.
One problem associated with time-domain technique is that the method is more
susceptible to noise compared with frequency-domain techniques due to the wide variety
of noise reducing algorithms in the frequency domain. Moreover, typical measurements
that provide low noise results are designed for continuous signals rather than transient
signals [Bar01]. Also, time-domain measurement is limited by the pulse generating
equipment with respect to the pulse characteristics that may be used.
Synchronization requirements remain an issue for time domain measurements.
Any time jitter that exists on the system will deteriorate the quality of measurements.
Especially when the distance between the transmitter and the receiver increases, the
trigger signal will suffer more attenuation and dispersion. On the other hand, the vector
network analyzer (VNA) must be physically connected to the transmitter and receiver.
This limits the application of VNA measurements to channel length where the cable is
practical and does not cause dramatic attenuation at the frequency band of interest.
68
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
As mentioned earlier, frequency domain technique has the advantage of an
improvement in signal noise and jitter due to the ease of application of noise reduction
algorithms and the use of calibration techniques. Another advantage is that the limitation
on waveforms is reduced; waveforms can be created and applied through frequency
domain convolution before the Fourier transformation operation is applied.
Frequency domain technique is a good candidate for interference characterization.
Network and spectrum analyzers are industrial standard pieces of equipment. On the
other hand, digital sampling oscilloscopes are not common and more difficult to deal
with. Moreover, narrowband linear amplifiers are easier to build “cheaper” when
compared to the low noise ultra-wide amplifier required for time domain measurements.
The time required for data acquisition limit the application of the measurement
technique to slow varying channels. When the network analyzer is used, the sweeping
time represents a limiting factor since the impulse response can be calculated at the end
of the sweep. In time domain, real time measurements can be performed using real time
oscilloscopes. However, when digital sampling oscilloscopes are used, sampling and
averaging will limit the application to relatively slower channels.
It should be noted that power spectrum or power density spectrum does not easily
apply to single transient events unless careful attention is given to the sampling rate.
State-of-the art spectrum analyzers do not sample fast enough to capture the peak power
of the individual UWB. Even fast (>20 GHz) scopes will not sample the peak from
different emitters in the case of multiple access or multiuser UWB systems. Only real-
time oscilloscopes are capable of capturing UWB aperiodic transient noise. [Bor01]
With a constant energy, J, greater field strengths and powers can be obtained by
shortening the duration of the pulse. This is why the use of power spectral density as a
measure for the UWB emission should be questioned. [Bor01]
On one hand, the frequency domain method allows for convenient noise reduction
algorithms to be used. Filtering algorithms may be application specific and can be easily
implemented using frequency domain techniques. On the other hand, the application of
69
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
filters in the frequency domain as well as the Fourier transform errors could result in a
non-causal response and instability. Time domain processing thus preserves the causal
and stable nature of the signal.
An argument that has to be clarified that practical time domain and frequency
domain techniques are not equivalent. Transformation from one domain to the other is
not a reversible process in the digital domain. Leakage errors are a redistribution of
energy due to data windowing, which result from the Fourier or inverse Fourier
transforms. Leakage error occurs when the values on each side of the time or frequency
domain window are not continuous before performing the transformation operation.
These discontinuities are normally caused by windowing of obtained data or by the time
duration limitation or bandwidth limitation of the measurement equipment.
To clarify the difference between the two techniques, we will consider the
resolution, spectral occupancy, and dynamic range of both techniques.
3.7.1 Time and Frequency Resolutions
When conducting measurements in the discrete domain one is limited by
complexity and hardware to a maximum of N points. The relationship between limited
transition duration, τ, and frequency bandwidth, BW, is an inverse relation. The number
of points in the time domain transition duration, Nτ, and the number of points in the
frequency domain bandwidth, NBW, are given as
t
N∆
=τ
τ , (3.19)
f
BWNBW ∆= , (3.20)
where ∆t is the time spacing, or time resolution, and ∆f is the frequency spacing, or
frequency resolution. Multiplying Nτ and NBW results in the following relation
70
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
ft
BWNN BW ∆∆⋅
=τ
τ (3.21)
For passive networks, which are not under-damped, the bandwidth for transient
pulses is related to pulse risetime [Kis92] as
BW
35.0≅τ . (3.22)
Applying the same methodology to the number of points, N, results in the
following [Yoh01]
NNN BW 35.0≅τ (3.23)
Substituting (3.22) and (3.23) into (3.21), the number of points is related to the
time and frequency domain resolution as follows
N
ft 1=∆∆ (3.24)
In (3.22), the time duration is shown to be related to the reciprocal of the
bandwidth. It is obvious that higher speed transition duration results in a wideband signal
in the frequency domain. So faster pulses are needed to extend the bandwidth of the
measurements.
In the case of time and frequency domain resolution, the ideal situation is to have
the time spacing, ∆t, equal to zero which result in an infinite time duration, T = ∞, and an
infinite number of samples, N = ∞. This unrealistic situation is even more noticeable
noting that the measurement equipment would have to have an infinite bandwidth. The
equation that relates the time and frequency domain resolution to the number of samples
is shown in (3.24) where ∆t is the time spacing, or time resolution, and ∆f is the
frequency spacing, or frequency resolution. The time resolution depends on the risetime,
which is inversely related to the bandwidth of the pulse excitation function. A faster
excitation risetime gives higher time resolution while compromising the frequency
71
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
domain resolution as a result of the corresponding increase in bandwidth. The number of
samples, N, is limited by the measurement equipment, so through investigating (3.24),
there is an obvious trade off between frequency domain resolution and time domain
resolution. Higher frequency domain resolution will result in lower time domain
resolution and vise versa. The application determines the weight of the resolution of each
domain and how they need to be modified to obtain desired results.
Some methods to increase time and frequency domain resolution, which are
usually limited by the measurement equipment, will be investigated. The obvious
method of increasing the resolution is by increasing the number of points, which will
result in higher resolutions in both domains. An increase in the time domain resolution
can be obtained by increasing the sampling frequency. As in relationship (3.24), when
increasing the time domain resolution by increasing the sampling frequency, the
frequency domain resolution will be compromised,
sf
t 1=∆ . (3.25)
Another method for increasing resolution is through interpolation. Interpolation
can be accomplished through zero padding before the Fourier or inverse Fourier
transforms. This process manually increases the number of points which increases
resolution. One has to tradeoff the resolution when conducting the experiment. [Yoh01]
3.7.2 Dynamic Range and Spectral Occupancy
Dynamic range is defined as the ratio between the maximum to the minimum
input level which the system provides with reasonable signal quality. The input pulse of
the system compromises the dynamic range in the time domain. The power applied by
the input pulse is non-uniform or spread throughout the frequency range, which restricts
the amount of power applied over the frequency spectra of the input pulse. At
frequencies where the power of the input pulse is compromised, the system noise could
cause measurement difficulties. The level of power supplied by the input pulse generator
is also limited by the tolerances of the sampling head; therefore, introducing a high-
72
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
powered pulse to increase the dynamic range of the time domain measurement system is
limited. Since the frequency measurements are taken using discrete methods one
frequency at a time, the amount of power applied for each frequency point is fairly
uniform with respect to the system noise. Since uniform power can be applied at all
frequencies, the dynamic range of the frequency domain measurement system is much
greater than that of the time domain counterpart. [Yoh01]
One disadvantage of time domain characterization is that partial channel sounding
is achieved. Full channel sounding requires the use of an input signal that has high
spectral occupation. Spectral occupation efficiency is a measure of how similar the
spectrum of the pulse and the channel are [Vau99]. It could be written as,
ωωω
ωωωη
dgg
dggsoe
))()((
)()(222
21
21
+=
∫∫ (3.26)
where )(1 ωg is the channel spectral support region and )(2 ωg is the pulse power
spectrum. An obvious solution might be to decrease the rise time which results in more
details and more accurate to model. Unfortunately, this results in a more difficult
characterization [Fid90].
3.8 Conclusive Remarks
In this chapter, the measurement techniques of ultra-wideband characterization
are discussed. Two different kinds of measurements are carried out, namely: source
conducted and radiated measurements. The first type can be used to learn more about
sources in experimentation. We also included structures of three sets of UWB antennas
in hand along with their main operational characteristics. Additionally, radiated
measurements were carried out as to figure out more closely the effects of these antennas.
Based on the previous discussion and the availability of equipment, the proposed
measurement systems for material characterization and through-the-wall propagation are
based on both time-domain and frequency-domain setups. Indoor measurements are
73
Chapter 3. Time Domain and Frequency Domain Channel Measurement Techniques and Setups
based on time-domain measurements because of the current distance limitation on the
wideband frequency measurements.
74
Chapter 4. Through-the-wall Propagation and Material Characterization
75
the electrical parameters (conductivity and permittivity) also vary with frequency. This area has not received much attention to date, and publications that are available are form the field of microwave heating, so tend to deal with foodstuffs and human tissue rather than building materials ..
[Div91]
Chapter 4
Through-the-Wall Propagation and Material Characterization*
4.1 Introduction
The introduction of UWB communication promises an excellent indoor alternative due to
the expected through-the-wall propagation capabilities. The main reason is low signal attenuation
at low frequencies. However, to avoid interference with existing systems the bandwidth of
operation should be shifted to frequencies above 3 GHz. In this chapter, quantitative results
versus frequency are given for the delay and loss associated with the propagation through typical
walls encountered in indoor environments. Results of this research provide valuable insights into
the transient behavior of a pulse as it propagates through typical construction materials and
structures. Some research work has been performed at the statistical level with the aim of
characterizing the UWB communication channel. The results of these studies cannot be validated
or explained due to the lack of understanding of basic characteristics of pulse propagation in
typical UWB communication environments. A study of propagation through different materials
and scatterers would facilitate the development of a basic theory for pulse shaping, receiver
design, and channel modeling. Though there has been some research on pulse propagation in the
radar field and related electromagnetic aspects, this study has a unique communication flavor.
* [Muq03a],[Muq03b],[Muq03c],[Muq03d]
Chapter 4. Through-the-wall Propagation and Material Characterization
76
Generally speaking, material characterization is performed using different techniques,
including capacitor, resonator, and coaxial cavities methods, and radiated measurements as well
[Bak98], [Muq02b], [Muq02c]. This work concentrates on ultra wideband signal propagation
through different materials and structures and measures their characteristics as they are
encountered in the actual UWB communication applications. Radiated measurements allow for
non-destructive and broad-band applications [Zha01]. The importance of the measurements in
hand stems from the fact that the data available above 1 GHz are not adequate for UWB material
characterization. Some data at specific frequencies are available through studies of wireless
communication inside buildings. Many researchers have examined propagation through walls
and floors, but these data are often limited to specific frequency ranges and are also limited to
only few materials, thus not adequate for the proposed ultra wideband applications. Moreover,
with the inconsistency in published results, understanding and characterization of UWB
propagation through walls and in building environments become more compelling.
In this chapter, the effects of structures as well as materials on UWB propagation are
investigated. Some typical obstacles and materials encountered in the indoor wireless
propagation channel are studied. These include wooden doors, concrete blocks, reinforced
concrete pillars, glass, brick walls, dry walls, and wallboards. In addition to the time-domain
transient response, for some materials the following information is also presented: insertion
transfer function (impulse response), relative permittivity, loss tangent, attenuation coefficient,
and time delay. Measured data are provided for a frequency range of 1 to 15 GHz. Both
frequency-domain and time-domain measurement techniques are used to validate the results and
also capitalize on the advantages of each technique.
In section 2 the electromagnetic theory of wave propagation through a material slab is
reviewed. Then, the measurement procedure and the techniques used to relate the acquired data
to the electrical parameters of materials are discussed in sections 3 and 4. Comparison of results
obtained from various techniques for a sample material is presented in section 5. Section 6 is
devoted to a comprehensive discussion of the signal processing required to extract the
parameters. Detailed descriptions and dimensions for sample materials to be tested are given in
Section 7. Main results and observations are presented in Section 8. Additional measurement
issues such as distance between the antennas and the sample, repeatability, and variability are
Chapter 4. Through-the-wall Propagation and Material Characterization
77
also addressed in this section. Finally, section 10 includes some remarks on pulse shaping, UWB
receiver design, and modeling hints. Appendices provide details of some mathematical analyses
and additional results.
4.2 Propagation of Electromagnetic Waves in Dielectric Materials
In this section, propagation of electromagnetic waves through a lossy dielectric material
is reviewed and important parameters are defined. Assuming steady-state time-harmonic
electromagnetic fields, a TEM (transverse electromagnetic) plane wave propagating in the +z
direction can be represented using the phasor expression ztj eeEzE γωω −= 0),( , where fπω 2= is the
radian frequency (f is the frequency in Hz) and γ is the complex propagation constant given as
( ) ( ) ( )j jγ ω α ω β ω ω µε≡ + = . ( 4.1)
where α is the attenuation constant in Np/m, β denotes the phase constant in rad/m, andε and
µ are, respectively, permittivity and permeability of the material. For non-magnetic
materials 00 µµµµ ≅= r can be safely assumed.
The dielectric polarization loss may be accounted for by a complex permittivity
( ) ( ) ( )jε ω ε ω ε ω′ ′′≡ − , where 0εεε r=′ is the real permittivity with rε being the relative
permittivity constant (≥1). The imaginary part of the complex permittivity, ε ′′ , represents the
dielectric loss. The dielectric loss is also represented by a parameter referred to as loss tangent
and is defined as ( ) tan ( ) / ( )p ω δ ε ω ε ω′′ ′= ≡ . It should be noted form (4.1) that the attenuation
constant and the phase constant are both functions of the complex permittivity.
The conductivity loss can be modeled by an additional imaginary term in the complex
permittivity, ( )( ) j σε ω ε ε ω′ ′′= − + , where σ (ω) is the macroscopic conductivity of the
material of interest. The conductivity loss cannot be easily separated from the dielectric loss but
the two losses may be combined and represented by an effective loss tangent [Poz98],
( )epσε ε σωωε ε ωε
′′ + ′′= = +
′ ′ ′. ( 4.2)
Chapter 4. Through-the-wall Propagation and Material Characterization
78
A complex effective relative permittivity can now be defined as
[ ]( ) ( ) 1 ( )re r ejpε ω ε ω ω= − . ( 4.3)
To characterize any subsurface material, two parameters should be measured:
• the dielectric constant, ( )rε ω
• the effective loss tangent ( )ep ω , or a directly related parameter.
The complex propagation constant is then given by
( ) (1 )re r ej j jpc cω ωγ ω ε ε= = − , ( 4.4)
where 800 103/1 ×≅= εµc m/s is the speed of light in vacuum. For a TEM plane-wave
propagating inside the material, the attenuation coefficient and the phase constant can be
separated in the exponent
( ) ( ) ( )0 0( , ) z j z zE z E e E e eγ ω β ω α ωω − − −= = . ( 4.5)
The attenuation constant is given by
12
2( ) 1 12
rep
cεωα ω = + −
Np/m, ( 4.6)
while the phase constant becomes
12
2( ) 1 12
rep
cεωβ ω = + +
rad/m. ( 4.7)
A more widely used unit for the attenuation constant α is dB/m. The conversion to dB/m
Chapter 4. Through-the-wall Propagation and Material Characterization
86
djdd eEeEeEdHdH 03
1
22232 )()( βγγ
ηη −++−−+ =−⇒= . ( 4.26)
We need to find T=0
30
i
dj
EeE β−+
which is equivalent to S21 in the scattering parameters terminology.
Manipulating the boundary conditions, we obtain
(4.23)+(4.24) ! )1()1(22
12
2
120 η
ηηη −++= −+ EEEi , ( 4.27)
(4.25)+(4.26) ! )1(21
232
0
ηηβγ += −+−+ djd eEeE , ( 4.28)
(4.25) - (4.26) ! )1(21
232
0
ηηβγ −= −++− djd eEeE . ( 4.29)
Substituting for +2E from (4.28) and for −
2E from (4.29) into (4.27) yields,
)1)(1(21)1)(1(
212
2
1
1
2)(3
2
1
1
2)(30
00
ηη
ηη
ηη
ηη βγβγ −−+++= −−+−++ djdj
i eEeEE . ( 4.30)
The transmission coefficient is now readily obtained as
−−+
++
==−
−+
1
2
2
1
1
2
2
10
3
22
40
ηη
ηη
ηη
ηη γγ
β
ddi
dj
eeEeET ( 4.31)
Based on the definition of the insertion transfer function given in (4.12), we can write
)(0
0ωβ
β jHTee
TEEEE dj
dji
fst
it === − . ( 4.32)
Thus,
)2()2(
4)(
1
2
2
1
1
2
2
1
0
ηη
ηη
ηη
ηηω
γγ
β
−−+++=
− dd
dj
ee
ejH . ( 4.33)
4.4.2.1 Exact Solution
When the complex insertion transfer function H(jω) is determined by measurements as
described in Section 4.3, equation (4.33) can be solved for the complex dielectric constant
Chapter 4. Through-the-wall Propagation and Material Characterization
87
rrr jεεε ′′−′= . In terms of the scattering parameter 21S , (4.33) with the help of (4.13) can be
easily cast into the following form [Alq96],
02)cosh(2)sinh(1
21
=−+
+
SxPxP
xx , ( 4.34)
where rx ε= and djP 0β= . An alternative derivation of (4.34) based on bounce diagram is
presented in Appendix A2. This equation can be solved numerically using two-dimensional
search algorithms. The convergence of this algorithm is not always guaranteed taking into
account possible multiple solutions and noise in the measurements. In the next section, using
reasonable assumptions, (4.33) is reduced to a one-dimensional problem involving real equations
only.
4.4.2.2 Approximate Solution *
When the material occupying region II is low loss, rε ′′ / 1rε ′ << and the following
approximations can be used,
)211(
)211()(
0
0000
r
rr
r
rrrr
jj
jjjjj
εεεβ
εεεεµωεεεµωβαγ
′′′
−′=
′′′
−≅′′−′=+=
and
rrrr j ε
ηεεµ
εεεµη
′=
′≅
′′−′= 1
0
0
02 )(
.
Then, r
r
rr ε
εε
εηη
ηη
′+′
=′
+′≅+11
1
2
2
1 and (4.33) reduces to
)12()12(
4)()()(
0
r
rdj
r
rdj
dj
ee
ejH
εε
εεω
βαβα
β
′+′−+
′+′+
=+−+
. ( 4.35)
Rewriting the insertion transfer function in terms of magnitude and phase, we obtain
* This formulation is submitted for publication, refer to [Muq03a], [Muq03b] by Ali Muqaibel and A. Safaai-Jazi.
Chapter 4. Through-the-wall Propagation and Material Characterization
88
21
22
2
2
2 14)2cos(21212
16)(
′+′−+
′+′−+
′+′+
=−
r
r
r
rd
r
rd dee
jH
εεβ
εε
εε
ωαα
( 4.36)
and
φβω −=∠ djH 0)( ( 4.37)
where
⋅
′+′−+
′+′+
′+′
−−
′+′
+
=−
−
− )tan(1212
12
12
tan 1 d
ee
ee
r
rd
r
rd
r
rd
r
rd
β
εε
εε
εε
εε
φαα
αα
. ( 4.38)
Equation (4.38) can be written in a more compact form as
⋅
+−= −
−− )tan(
11tan 2
21 d
QeQe
d
d
βφ α
α
( 4.39)
where
2
2
2
11
)1()1(
1212
12
12
+′−′
−=+′−′
−=+′+′−′−′
=
′+′+
′+′−
=r
r
r
r
rr
rr
r
r
r
r
Qεε
εε
εεεε
εεε
ε
. ( 4.40)
For most applications of interest Q has a small value. For example, for the relative
permittivities of 2.0, 4.0, and 8.0, Q is about 0.02, 0.1, and 0.3, respectively. Later we will use
this fact to further simplify the solution. For the time being no assumption is made about Q.
Letting Xe d =− α2 , then
( ) ( ) ( )244
2
1)2cos(211116)(
−′−−′++′
′=
rrr
r
dXX
jHεβεε
εω , ( 4.41)
or
Chapter 4. Through-the-wall Propagation and Material Characterization
89
( ) ( ) ( ) 01)(
81)2cos(214
2242 =+′+
′+−′−−′ r
rrr X
jHdX ε
ωεεβε ,
which is a quadratic equation in terms of X. Solving this equation or X, we have
( ) ( ) ( )
( )44
2
22
22
2
1
1)(
81)2cos()(
81)2cos(
−′
−′−
′+−′±
′+−′
== −
r
rr
rr
r
djH
djH
d
eXε
εω
εεβω
εεβα
( 4.42)
Only the solution with negative sign in (4.42) is valid (the proof is given in Appendix A3.
Substituting for X from (4.42) in the phase expression (4.39), we obtain the following equation,
which is only in terms of rε ′ .
[ ] 0)tan(11)(tan 0 =+−+∠− d
QXQXjHd βωβ ( 4.43)
Solving this equation numerically, rε ′ is readily determined. Then, X and subsequentlyα are
found from (4.42). Finally, rε ′′ is calculated using
ωεα
ε rr
c ′=′′
2. ( 4.44)
Special Case
If it can be further assumed that 12 <<− de α , then (4.39) becomes
dd ββφ =≈ − ))(tan(tan 1 ,
and
rddddjH εββββω ′−=−=∠ 000)( , where rεββ ′≈ 0 and 2
0
2
0
0 )(1)(
∠−=
∠−=′djH
djHd
r βω
βωβε . ( 4.45)
Once rε ′ is determined, α and then rε ′′ can be found from 2)( ωjH using the following
relationships,
Chapter 4. Through-the-wall Propagation and Material Characterization
90
′+′
−+
′+′
+
≈22
2
2
14)2cos(2
12
16)(
r
r
r
rd de
jH
εεβ
εε
ωα
( 4.46)
′+′
′−′+
=
r
r
r
rdjH
dε
ε
εεβ
ωα
4
2
2
)1(
)1()cos(2)(
16
ln21
. ( 4.47)
This simplified analysis reduces to the single pass case as in [Aur96], where the wall is assumed
to be thick and single transmitted pulse can be time gated. This is because the assumption
12 <<− de α has the implication that the multiple-pass components of the received signal are very
small, as for αd>>1 these components are attenuated significantly more than the single-pass
signal.
4.5 Comparison of Various Techniques
In Section 4.4.1 two sets of expressions for the calculation of dielectric constant and loss
tangent, based on single-pass insertion transfer function ( )spH f , were presented. These are
equations (4.14) and (4.15) for single-pass involving phase derivative, and equations (4.16) and
(4.15) for single-pass involving the phase itself. Similarly, in Section 4.4.2 two sets of
expressions for the calculation of dielectric constant and loss tangent or attenuation coefficient,
based on multiple-pass insertion transfer function ( )H jω , were presented. These are equations
(4.34) or (4.35) for exact solutions (material need not be assumed low loss), and equations
(4.42), (4.43), and (4.44) for approximate solutions applicable to low loss materials. Here, the
results obtained from these solutions are calculated and compared in order to better appreciate
the accuracy as well as the applicability of each method. Measurements are carried out for a
sample wooden door representing the slab. The results for the dielectric constant obtained from
the four sets of solutions mentioned above are shown in Figure 4.3. It is noted that the results
Chapter 4. Through-the-wall Propagation and Material Characterization
91
from other three solutions are in excellent agreement. This agreement is due to the fact that for
this specific sample (wooden door), multiple reflections inside the door are very small compared
to the first single-pass. It is further noted that the results obtained from the exact and
approximate solutions (multiple-pass) are nearly identical, indicating that the door material is
low loss. The fact that the search for a complex solution problem can be reduced to a one-
dimensional problem is illustrated in Figure 4.4. This figure illustrates that the complex search
problem is separable, as any cut on a constant rε ′′ plane results in the same minimum. For better
visualization, a vertical cut at rε ′′ =0.14 is also shown.
Both the exact complex and approximate real equations have spurious solutions that can
be avoided by starting with an initial guess obtained from the single-pass solution at a high
frequency and by using a constrained search. At high frequencies the wavelength is smaller and
the assumption of thick slab become more reasonable. The solution obtained at a high frequency
point is then used as an initial guess for the next frequency point, because variations of the
dielectric constant versus frequency are slow over a narrow frequency range.
Whenever single-pass time gating is possible, the single-pass analysis technique can be
used. Using time-domain measurements, this technique is applicable if one of the following two
requirements is met: (i) the pulse has a width shorter than the transit time through the slab, (ii)
the material has a sufficiently high loss so that the second and higher-order reflections are
attenuated much more than the first single-pass signal. If single-pass time gating is not possible,
the multiple-pass analysis technique should be used. First the approximate solution is attempted,
but the result has to be validated by comparing with the exact solution to see if the low loss
requirement is met. Whenever possible, the results from both time-domain and frequency-
domain measurements should be obtained and compared to ensure the validity of measurements
and also avoid any spurious results.
Chapter 4. Through-the-wall Propagation and Material Characterization
2 3 4 5 6 7 8 9 101.9
1.95
2
2.05
2.1
2.15
2.2
2.25
2.3
Frequency GHz
Die
lect
ric C
onst
ant
Exact, Two Dimensional SearchNew Formulation, One Dimensional SearchSingle-Pass
Figure 4.3. Comparison between the different measurement and analysis techniques
Figure 4.4. Two-dimensional search example, illustrating the possibione-dimensional search
rε ′′rε ′
Mag
nitu
de
02468100
1
2
3
4
5
6
'
Mag
nitu
de
rε ′′ =0.14
92
lity of reducing it to a
rε ′
Chapter 4. Through-the-wall Propagation and Material Characterization
93
In order to assess the accuracy of the approximate method presented above, we take a
data point from the measured insertion transfer function, H(jω), for the sample wooden door at a
frequency of 5.00 GHz and artificially increase the loss by decreasing the magnitude of H(jω).
This is achieved by multiplying H(jω) by a constant a as given in the first row of Table 4.1. A
zero-loss case is also included in the table by choosing a such that a|H(jω)|=1. As noted, the
errors are less than 1% for loss tangents about 0.2, a representative upper-limit loss factor for
most dielectric materials of practical interest. Only for very high loss cases (tan δ>0.9) the errors
become significant, about 15% for this example. As expected, for the zero-loss case
(corresponding to a=1.23 in this example) the approximate solution for the dielectric constant
becomes exact. Although this error analysis is for a specific example, it provides a realistic
measure of the accuracy of the approximate method presented here.
Table 4.1. Errors in dielectric constant and loss tangent obtained form the approximate formulation. (The data point used in this analysis is H(jω)= -0.3317 - j0.7418).
Figure 4.6. Illustration of the frequency domain measurements, (a) Measured magnitude, (b) Measured phase, (c) Filter and filtered un-gated insertion transfer function, and (d) Impulse response and weighted gating window
Mag
nitu
de (d
B)
Chapter 4. Through-the-wall Propagation and Material Characterization
Figure 4.7. Illustration of the Time domain measurements, (a) Measured through and free space signals (b) Illustration of the correlation function to estimate the time delay.
Chapter 4. Through-the-wall Propagation and Material Characterization
98
4.6.2 Time Delay and Initial Guess for Permittivity
The through and free-space time-domain measured signals or the corresponding
impulse responses obtained from frequency-domain measurements are correlated using a sliding
correlator to obtain the first guess on the delay and effective dielectric constant. The shape of the
correlator output is illustrated in Figure 4.7b. An estimate of the average dielectric constant could
also be obtained through peak-to-peak impulse time delay, τ∆ . An average value of the
dielectric constant that does not reflect the frequency dependence is given by
2
1
∆+≅′cdrτε , ( 4.48)
where d is the thickness of the slab and c is the speed of light in free-space.
4.6.3 Time Gating
Time gating is required to remove multi-pass components in received signals, as they are
not accounted for in the calculation and extraction of material parameters. Multiple reflections
should be gated out too if single-pass technique is used. In multiple-pass technique, perfect time
gating cannot be achieved because, strictly speaking, infinite acquisition time is required to
capture infinite number of multiple reflections. However, because higher-order multiple
reflections die out quickly for materials of interest in this research, satisfactory time gating is still
achievable.
Time gating capabilities are enhanced with shorter pulse durations and longer distances
between the test material and reflectors and scatterers. If single-pass is desired, pulse duration
should be shorter than the twice the travel time through the slab to avoid pulse overlapping.
To avoid abrupt changes on the signal level, the gating-window should have smooth
transition from zero to the flat level. This window is based on the modified Kaiser window with
a flat region in the middle. However, the results for material parameters should be essentially
independent of the used window. Various parameters of the window are changed to make sure
Chapter 4. Through-the-wall Propagation and Material Characterization
99
that the results are not sensitive to the details of the window. A Kaiser window of length M has a
time domain sequence h(n) given by [Pro96],
2 2
0 0
0 0
1 12 2
12
M MI n
MI
α
α
− − − −
−
, 10 −≤≤ Mn , ( 4.49)
where I0 is the modified Bessel function of order zero and 0α is a design smoothing factor set
equal to 25. The window size was chosen to be 2 ns for source#1, 0.5 ns for source#2, and 3ns
for the Fourier-transformed data measured with the network analyzer. These values were chosen
to allow for nearly optimum time gating. The windows have two symmetrical transition regions
and a flat region defined by the intervals (0.2,1.6,0.2), (0.1,0.3,0.1), and (1,1,1) ns, parameters
within parentheses refer to (risetime, width of flat region, fall time), respectively as illustrated
in Figure 4.8.
Figure 4.8. Three different time domain gating windows
If the through and free-space signals both return to the zero level in the window, the
gating can be implemented easily. If the signal does not become exactly zero in the window, the
window opening for the received signal is delayed by an amount equal to 0τ . After time gating
0 0.5 1 1.5 2 2.5 3-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
time ns
Am
plitu
de
Source 1 WindowSource 2 WindowWindow for NA
Chapter 4. Through-the-wall Propagation and Material Characterization
100
the signals with proper zero padding, the fast Fourier transform (FFT) and (4.12) are used to
calculate the insertion transfer function.
4.6.4 Propagation and Material Parameters
Form the complex insertion transfer function, the dielectric constant and loss tangent of
the material under test can be extracted. Table 4.2 summarizes the analysis techniques and the
corresponding equations required to extract the material parameters. The choice of the analysis
technique is based on how satisfactorily time gating can be implemented. In many cases,
multiple reflections inside the slab decay rapidly so that single-pass or multiple-pass techniques
essentially yield the same results.
Six different measurements are performed for the characterization of each material. These
include four time-domain measurements, with two different pairs of antennas and two pulse
generators, and two frequency-domain measurements using two pairs of antennas. The results for
six different time-gated measurements for a sample door are given in Figure 4.9.
Table 4.2 Summary of analysis techniques and required equations
Figure 4.9. Time domain representation of the six different measurements for the sample door
Chapter 4. Through-the-wall Propagation and Material Characterization
102
(a) 0 5 10 15
-6
-5
-4
-3
-2
-1
0
Frequency (GHz)
Inse
rtion
Los
s (d
B)
FitS1A1S2A1S1A2S2A2NA,A1NA,A2
(b) 0 5 10 15
0
20
40
60
80
100
120
140
Frequency (GHz)
Atte
nuat
ion
Con
stan
t (dB
/m)
FitS1A1S2A1S1A2S2A2NA,A1NA,A2
(c) 0 5 10 15
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
Frequency (GHz)
Die
lect
ric C
onst
ant
FitS1A1S2A1S1A2S2A2NA,A1NA,A2
(d) 0 5 10 15
0
0.05
0.1
Frequency (GHz)
Loss
Tan
gent
FitS1A1S2A1S1A2S2A2NA,A1NA,A2
Figure 4.10. Comparison for the sample door parameters extracted using different measurement techniques, (a) time-gated insertion transfer function , magnitude, (b) attenuation constant, (c) dielectric constant, and (d) loss tangent.
Chapter 4. Through-the-wall Propagation and Material Characterization
103
4.7 Description of Samples and Wall Materials
Ten different wall materials commonly encountered in building environments are
selected for UWB characterization. These include drywall, glass, wallboard, styrofoam, cloth
Note: The first number in the dimensions column is the thickness of the sample; i.e. the propagation path length through the material.
The requirement that free-space and through measurements should be performed with
the same antenna spacings, makes in-situ measurements very difficult. After the in-situ through
measurements are performed, the free-space measurements should be made at a different
location but with the same distance between the transmiting and receiving antennas as in the
through measurement setup. Since it is impossible to have exactly the same distances between
the antennas for measurement setups at two different locations, errors will inevitably result in the
Chapter 4. Through-the-wall Propagation and Material Characterization
104
calculation of insertion transfer function. For example, at 10 GHz the wavelength is about 3cm,
then1mm change in the spacing between the two antennas results in 12 degrees phase error. This
is an extremely tight tolerance requirement that cannot be met easily. To overcome this problem,
a moving platform was constructed, and bricks and blocks were used to build walls on it. This
allows us to move the wall between the two antennas and make repeated measurements while the
setup is kept at a fixed location. Figure B2-1 illustrates the brick and block samples, moving
walls built with bricks, blocks, and styrofoam. Styrofoam slabs are used to secure the walls on
the platform. One styrofoam slab was also measured to estimate its loss and dielectric constant
and hence its impact on the measurement of other materials. It has very low loss and a dielectric
constant close to unity, thus it can be assumed to be effectively air.
A reinforced concrete pillar in the 3rd floor of Whittemore Hall, the building that houses
the Electrical Engineering Department of Virginia Tech, was also measured. Another reinforced
pillar in the Time Domain Lab (TDL) located in the 4th floor of Whittemore Hall was also
measured.
The cloth office partitions that were tested have round edges at the upper ends with
wooden caps for holding the cloth material tight. Each partition has two metal stands and as well
as support pieces inside. Figure B2-2 shows the different materials and walls used in
measurements.
4.8 Measurement Results
The dielectric constant and the loss at 5 GHz as representative values of parameters for
the selected materials are listed in Table 4.3. The frequency of 5-GHz is in a region of bandwidth
where the measurements are believed to be most accurate, because the results obtained from
different techniques agree very well and the amount of power transmitted in this region is
significantly far above the noise floor. It is emphasized that for most materials measuring the loss
is more difficult than measuring the real part of effective permittivity [Gey90]. A straight line is
used to model the insertion loss versus frequency [Gib99]. The fitted insertion transfer functions
for different materials are shown in Figure 4.11 and the corresponding parameters for the linear
fit are also given in Table 4.3. The insertion transfer function for the door is re-plotted in part (b)
of Figure 4.11 for ease of comparison. Cloth partition shows higher loss due to support elements
Chapter 4. Through-the-wall Propagation and Material Characterization
105
inside the partitions. Similarly, the dielectric constants are presented in Figure 4.12. The results
for the brick wall and the concrete block wall are over smaller bandwidths because of higher
losses of these materials that reduce their useful bandwidths. The dielectric constant versus
frequency can be modeled as a straight line with very small negative slop. However, the
dielectric constant for the brick has a small positive slope that is believed to be due to the non-
homogeneity of the sample. Attenuation constants for the door, wood, and structure wood sample
are given in Figure 4.13. It was possible to extract the attenuation constant for these materials
due to their moderate loss and homogenous structure.
To gain more insight into the effects of various walls on the propagation of UWB pulses,
the free-space and through gated signals for all the measured materials are presented in
Figures 4.14 through 4.19. For the case of blocks and bricks, the un-gated signals are presented
due to the difficulty of gating.
The dielectric constant of the glass sample could not be measured using the time delay
between peaks of the received pulses and the single-pass technique. This is because of the small
thickness of the glass that does not allow multiple reflections to be avoided, thus the multiple-
pass analysis should be used.
The reinforced concrete wall resulted in a very small amount of received power. No
further processing could be done, but an average dielectric constant was obtained by measuring
the time delay between the incident and received pulses. For better viewing, a longer time
window is shown in Figure 4.19. This figure illustrates multiple reflections inside the reinforced
concrete pillar. It is important to note that this window includes multipath components that might
not have traveled through the pillar. A repeated W shape is observed in the receiver signal. For
reinforced concrete, concrete block, and brick walls, a 10 dB gain and 15 GHz bandwidth
amplifier was used at the receiver side to increase the measured signal level.
Chapter 4. Through-the-wall Propagation and Material Characterization
106
0 5 10 15-10
-8
-6
-4
-2
0
Frequency (GHz)
Inse
rtion
loss
(dB)
door foam structure glass partition
0 5 10 15-15
-10
-5
0
Frequency (GHz)
Inse
rtion
loss
(dB
)
door board bricks blockswood
Figure 4.11. Insertion transfer function plotted versus frequency for different materials
Chapter 4. Through-the-wall Propagation and Material Characterization
107
0 5 10 15
1
2
3
4
5
6
7
Frequency (GHz)
Die
lect
ric C
onst
ant
doorfoamstructure woodglasspartition
0 5 10 15
1
2
3
4
5
6
7
Frequency (GHz)
Die
lect
ric C
onst
ant
doorboardbricksblockswood
Figure 4.12. Dielectric constant plotted versus frequency for different materials
Chapter 4. Through-the-wall Propagation and Material Characterization
108
0 5 10 150
50
100
150
200
250
300
Frequency (GHz)
Atte
nuat
ion
Con
stan
t (dB
/m)
d oorstructu re woodwood
Figure 4.13. Attenuation constant plotted versus frequency for different materials
Chapter 4. Through-the-wall Propagation and Material Characterization
109
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.06
-0.04
-0.02
0
0.02
0.04
0.06
time (ns)Am
plitu
de (V
)
Free-Space ReferenceThrough
0 1 2 3 4 5 6 7 8 9 10-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
Figure 4.14. Blocks wall and wallboard free-space and through measurements; plots (a) and (b) are ungated time-domain waveforms for blocks as the material using sources #1 and #2, respectively. Plots (c) and (d) are time-gated waveforms for the board using sources #1 and #2, respectively.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
Board
0 1 2 3 4 5 6 7 8 9 10-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
(a) (c)
(d) (b)
Blocks wall
Chapter 4. Through-the-wall Propagation and Material Characterization
110
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.02
0
0.02
0.04
0.06
0.08
0.1
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.06
-0.04
-0.02
0
0.02
0.04
0.06
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.06
-0.04
-0.02
0
0.02
0.04
0.06
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
Figure 4.15. Cloth office partition and structure wood free-space and through measurements; plots (a) and (b) are time-gated waveforms for cloth partition as the material using sources #1 and #2, respectively. Plots (c) and (d) are time-gated waveforms for the structure wood using sources #1 and #2, respectively.
(a) (c)
(d) (b)
Cloth Partition Structure Wood
Chapter 4. Through-the-wall Propagation and Material Characterization
111
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.06
-0.04
-0.02
0
0.02
0.04
0.06
time (ns)Am
plitu
de (V
)
Free-Space ReferenceThrough
Figure 4.16. Door and wood free-space and through measurements; plots (a) and (b) are time-gated waveforms for sample door as the material using sources #1 and #2, respectively. Plots (c) and (d) are time-gated waveforms for the wood using sources #1 and #2, respectively.
(a) (c)
(d) (b)
Door Wood
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
time ns
Am
plitu
de V
Free-Space ReferenceThrough
Chapter 4. Through-the-wall Propagation and Material Characterization
112
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.06
-0.04
-0.02
0
0.02
0.04
0.06
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.06
-0.04
-0.02
0
0.02
0.04
0.06
time (ns)Am
plitu
de (V
)
Free-Space ReferenceThrough
Figure 4.17. Glass and styrofoam free-space and through measurements; plots (a) and (b) are time-gated waveforms for glass as the material using sources #1 and #2, respectively. Plots (c) and (d) are time-gated waveforms for Styrofoam using sources #1 and #2, respectively.
(a) (c)
(d) (b)
Glass Styrofoam
Chapter 4. Through-the-wall Propagation and Material Characterization
113
0 1 2 3 4 5 6 7 8 9 10-0.04
-0.02
0
0.02
0.04
0.06
0.08
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
time (ns)
Ampl
itude
(V)
Free-Space ReferenceThrough
0 2 4 6 8 10 12 14-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
time (ns)
Ampl
itude
(V)
Reference10*Through
0 2 4 6 8 10 12 14-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
time (ns)
Ampl
itude
(V)
Reference10*Through
Figure 4.18. Bricks wall and reinforced concrete pillars free-space and through measurements; plots (a) and (b) are ungated time-domain waveforms for bricks as the material using sources #1 and #2, respectively. Plots (c) and (d) are ungated waveforms for reinforced concrete pillars (Whittemore and TDL) using sources #1 and #2, respectively.
(a) (c)
(d) (b)
Bricks wall Reinforced Concrete Pillars (c) Whittemore and (d)TDL)
Chapter 4. Through-the-wall Propagation and Material Characterization
114
0 5 10 15-0.4
-0.2
0
0.2
0.4
time (ns)
Am
plitu
de (V
) Reference
0 5 10 15-0.04
-0.02
0
0.02
0.04
time (ns)
Ampl
itude
(V) Through
0 10 20 30 40 50 60 70 80 90 100-0.04
-0.02
0
0.02
0.04
time (ns)
Ampl
itude
(V) Through, Long Profile
Figure 4.19. TDL reinforced concrete pillar free-space and through measurements; plot (a) is the reference measurement. Plot (b) indicates the measurement through the reinforced concrete pillar (TDL). Plot (c) demonstrates a longer profile for the through measurement.
(a)
(b)
(c)
Chapter 4. Through-the-wall Propagation and Material Characterization
115
4.9 Related Issues
In the following section, some points related to validity of the measurements are
discussed. These include distance between the samples and antennas, slab thickness and multi-
layer study, repeatability, and variability.
4.9.1 Distance from the Sample
The distance between a sample and the antenna should be long enough to ensure that the
sample is in the far field of the antenna. On the other hand, as the sample is moved away from
the antenna, edge and scattering effects cannot be gated out. Hence, a trade-off has to be made
without degrading the results. Moreover, as the distance increases the signal level decreases and
hence the frequency range over which reliable characterization can be made becomes smaller.
Most of our measurements were performed with a total distance of 1-3 meters. However, the
effect of the distance would not be pronounced if the free-space and through measurements
are carried out with exactly the same setup. An experiment was done by varying the distance
between the antennas and the sample in steps of 0.25m. No significant change was observed
other than the signal level.
4.9.2 Wall Thickness and Multi-layer Study
The thickness of the layer under study is critical to the measurement outcomes. If the
thickness is very small error becomes more pronounced. For example, to estimate the dielectric
constant of a slab of glass with 2 mm thickness, we should be able to measure the delay as result
of passing through this thin layer. If the thickness is larger, there will be a larger delay to
measure and hence less relative error in the thickness of the layer. On the other hand, very thick
slabs may cause high losses, resulting in weak signal levels that cannot be accurately measured.
For the case of glass sample, slabs consisting of one, two, and three layers were tested to confirm
the obtained parameters. The layers were carefully aligned to reduce the air gap. For the case of
the board, two layers were tested to confirm the results.
4.9.3 Repeatability Analysis
Repeatability analysis describes the process of evaluating the precision of measurements
taken at different instances of time. Measurements that have high precision are said to be
Chapter 4. Through-the-wall Propagation and Material Characterization
116
repeatable [Yoh01]. One important factor is to allow the equipments to warm up for a stable
performance. There is a small drift in the pulse with respect to the time axis when the equipment
warms up. Figures 4.20, and 4.21 illustrate the repeatability of the frequency and time-domain
measurements, respectively. Three different measurements of the wallboard sample are shown.
The wallboard was chosen as they have smaller thickness and low loss compared with other
materials. Examining the plots of insertion transfer functions and dielectric constants and noting
that the differences in the measurement results are minor lead to the conclusion that the
measurements are repeatable. The differences noticed in the plots must include tolerances of the
measurement setup.
4.9.4 Variability Analysis
Variability analysis describes the process of evaluating the precision of measurements of
different samples of the same material. Different measurements of different samples that have
high precision are said to have low variability. In the case of wall measurements, two different
samples of two different wallboards were measured (using the same calibration). The results of
these measurements are given in Figures 4.20 and 4.21. It should be noted that the results for
both repeatability and variability analyses are shown on the same plots. Examining these plots
and noting the differences in the measurement results are minor lead to the conclusion that the
two wallboards have a low variability, yet the differences indicate that there is some degree of
variability in the walls. In indoor environments, wallboards built from different materials and by
different manufacturers are used. But, this should not be a concern as the primary objective of
the material/wall characterization effort is to obtain estimates of the loss and the associated delay
for different construction materials and gain insights into how UWB propagation is affected by
these materials.
Chapter 4. Through-the-wall Propagation and Material Characterization
Figure 4.21. Repeatability and variability of time domain measurements
Chapter 4. Through-the-wall Propagation and Material Characterization
119
4.10 Remarks on Pulse Shaping, UWB Receiver Design, and Modeling Hints
The following section is dedicated to putting the results of measurements into perspective
with regard to receiver design, pulse shaping, and channel modeling.
4.10.1 Receiver Design and Pulse Shaping
The idea of using correlators at the receiver might not work very well in a non-line-of-
site configuration. The pulse seems to undergo shape deformation as it propagates through
structures with small dimension due to inter-pulse interferences. Multiple reflections within the
material and multipath components have a significant impact on the maximum data rate and/or
multiple access capabilities of UWB systems. The claim that UWB has high multipath resolution
works very well in a free-space line-of-site configuration but seems to be less certain in
structures with fine details relative to the pulse duration.
Two seemingly contradicting requirements have to be traded off. One would like to have
the pulse with very short duration and at the same time to have enough low frequency
components. As the pulse gets shorter, its spectral contents are shifted to higher frequencies
which suffer more attenuation as the pulse propagates. When deciding on the spectrum to be
used, it is important to note that as the signal is shift to higher frequencies, the original reasons
for proposing UWB including spectrum reuse and propagation through-the-wall become
irrelevant. Reception based on pulse shape might not be the best approach for indoor
environments. Other means of capturing the signal energy might prove to be more practical.
The originally proposed modulation scheme, in which a bit is demodulated as a zero or
one based on the time delay, is also vulnerable to errors [Sch93]. Walls and barriers can
complicate the demodulation process as they introduce more delays. This might not be a major
problem as the tight synchronization requirement is an integrated part of UWB systems.
Chapter 4. Through-the-wall Propagation and Material Characterization
120
4.10.2 Modeling and Large-Scale Path-losses
The physical models used to predict pulse propagation in dielectric materials are based on
two techniques; namely, electromagnetic wave theory and geometrical optics. The latter method
is only applicable when the wavelength of the applied electromagnetic signal is considerably
shorter than the dimension of object or medium being excited [Dan96].
One way of modeling large-scale path losses is to assume logarithmic attenuation with
various types of structures between the transmitter and receiver antennas [Has93a]. It has also
been stated that adding the individual attenuations results in the total dB loss [Has93a].
Furthermore, it is important to note that when assuming no dispersion takes place, a narrow band
approximation is implied. This assumption is not as good for UWB because the dielectric
constant decreases slowly with frequency.
Many results for the propagation through walls have been published. A good summary is
given in [Has93a]. However, these results were often obtained at specific frequencies and
measurements were not performed with sufficient care to remove the effects of scattering from
edges. The measurements carried out in our lab have been crosschecked by using both time-
domain and frequency-domain techniques
4.11 UWB Partition Dependent Propagation Modeling
Many of the narrowband channel characterization efforts are performed at specific
frequencies. For UWB characterization, one has to define the pulse shape or its spectrum
occupancy. Results generated for a specific pulse might not be generalized to other UWB
signals.
In this section, the results for the loss of the tested materials are used to develop partition-
dependent propagation models. The partition based penetration loss is defined as the path-loss
difference between two locations on the opposite sides of a wall [And02a]. The penetration loss
is equal to the insertion loss presented earlier. The free space path-loss exponent is assumed to be
n=2. The total loss along a path is the sum of free-space path loss and loss associated with
partitions present along the propagation path.
Chapter 4. Through-the-wall Propagation and Material Characterization
121
In the narrowband context, the path loss with respect to1 m free space at a point located a
distance d from the reference point is described by the following equation
........)(log20)( 10 ba XbXaddPL ×+×+= , ( 4.50)
where a, b, etc., are the numbers of each partition type and Xa, Xb, etc., are their respective
attenuation values measured in dB [Dur98]. To extend this concept to UWB communication
channels, we introduce the frequency dependent version of equation (4.50),
)........()()(log20),( 10 fXbfXadfdPL ba ×+×+= , ( 4.51)
where Xa(f), Xb(f) are the frequency dependent insertion losses of partitions. Equation (4.51)
gives the path loss at single frequency points. In order to find the pulse shape and the total power
loss we need to find the time domain equivalent of (4.51) by means of inverse Fourier transform
over the frequency range of the radiated signal. In doing so, we start with the radiated pulse
prad(t). In most wideband antennas such as TEM horns, this signal is proportional to the
derivative of the input signal to the antenna. Then, we determine the spectrum of the received
signal at the location of the receive antenna using the following relation ship,
d
fPfPfXbfXa
radrec
ba
⋅
=×+×
20).......)()((
10
)()( ( 4.52)
It is important to note that the attenuation is applied to the radiated signal rather than the input to
the antenna. The transmit antenna alters the spectrum of the input signal as illustrated in Figure
4.22. Starting with a Gaussian pulse, the time-domain received signal )(tprec is obtained by
inverse Fourier transforming )( fPrec . With the received pulse determined, one is able to assess
pulse distortion and the total power loss. It has been assumed that the dielectric constant of the
partitions remain constant over the spectrum of the radiated signal.
Example:
In this example we illustrate how to utilize the material characterization results and apply
them to a partition problem. The objective is to find the power loss through a propagation path
Chapter 4. Through-the-wall Propagation and Material Characterization
122
and to estimate the pulse shape and the frequency distribution of the received signal. Consider a
line-of-site path with two partitions between two TEM horn antennas as shown in Figure 4.23a .
The first partition is a sheet of glass and the second is a wooden door with the same thickness as
those that have been characterized. The input signal to the antenna and that radiated from it are
displayed in this figure. These signals are obtained through measurements.
To estimate the signal passed through the glass partition, Fourier transform is used to
determine the spectrum of the radiated signal and the frequency dependent loss is applied to this
spectrum. Inverse Fourier transform is then used to obtain the time-domain signal passed the
glass sheet. The same procedure is repeated to estimate the signal passed through the wooden
door partition. Examining The loss in the signal power is evident in Figure 4.23b. It is also noted
that higher frequencies are smoothed out. The change in frequency distributions is more evident
in Figure 4.23c. At lower frequencies, the spectra of the radiated signal, signal after the glass and
signal after the wooden door are very close, whereas at higher frequencies the differences are
more pronounced. This analysis is helpful in link-budget analysis and understanding of potential
interference effects from indoor to outdoor environments.
Figure 4.22 Gaussian (TEM horn input signal) and Gaussian monocycle (TEM horn radiated signal) waveforms and their corresponding normalized spectra.
0 2 4 6 8 10 12
10-8
10-6
10-4
10-2
100
Frequency (GHz)
Nor
mal
ized
Mag
nitu
de
Gaussian and Gaussian Monocycle in Frequency Domain
GaussianGaussian Monocycle
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (ns)
Nor
mal
ized
Am
plitu
de
Gaussian and Gaussian Monocycle Waveforms
GaussianGaussian Monocycle
(a) Gaussian and Gaussian monocycle waveforms (b) Normalized spectra for Gaussian and Gaussian monocycle waveforms
Chapter 4. Through-the-wall Propagation and Material Characterization
123
Figure 4.23 Illustrative example for UWB partition dependent modeling
(a) Illustration of the partitions setup, (b) Radiated signal, signal after the glass partition, and the signal after the wooden door, (c) Frequency distribution of the signal at different points.
Er E
0 0.5 1 1.5 2 2.5 3-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
time (ns)
Am
plitu
de (V
)
0 0.5 1 1.5 2 2.5 3-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
time (ns)
Am
plitu
de (V
)
0 0.5 1 1.5 2 2.5 3-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
time (ns)
Am
plitu
de (V
)
0 0.5 1 1.5 2 2.5 3-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
time (ns)
Am
plitu
de (V
)
Glass Wooden Door
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
time (ns)
Am
plitu
de (V
)
Radiated SignalAfter Glass PartitionAfter Wooden Door
0 2 4 6 8 10 12-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (GHz)
Nor
mal
ized
Mag
nitu
de d
B
Radiated SignalAfter Glass PartitionAfter Wooden Door
(a)
(b) (c)
Chapter 4. Through-the-wall Propagation and Material Characterization
124
4.12 Concluding Remarks
Electromagnetic characterization of materials and walls commonly encountered in indoor
environments was undertaken with the aim of assessing their impacts on UWB propagation.
Measurements were carried out in both time domain and frequency domain. Also, whenever
possible, both single-pass and multiple-pass analysis techniques were used. A new formulation
for the characterization of low-loss materials has been presented which requires solving real
equations only and converges more rapidly, thus requires much less computation time than that
based on solving the complex equation relating the insertion transfer function to the dielectric
constant of the material under test. The new formulation can be used to accurately characterize
many materials of practical applications which are low loss. Results from different techniques
agree well, thus ensuring the reliability and accuracy of the measurements. Ten different
materials were tested and results were presented in terms of insertion loss and dielectric constant.
The presented results should serve as a basis for further studies in developing appropriate models
for UWB channels. The results are also useful in UWB link budget analysis.
Chapter5. Time Domain Indoor Channel Measurements
“… Any realistic channel model…should derive its parameters from actual field measurements rather than basing them on simplified theory”
H. Hashemi [Has93a]
Chapter 5
Indoor UWB Channel Measurements*
5.1 Introduction
The objectives of this report are to present time-domain measurements and
characterization of ultra-wideband (UWB) propagation in indoor environments and to
detail the experimental procedures and measurement setup used to collect data. First,
experimental procedures and locations where the measurements were carried out are
described. Then, post-processing of the acquired data is explained. Finally, the results
pertaining to the signal quality, small-scale effects, large-scale pathloss exponents, and
time dispersion parameters are discussed. Some site-specific trends and observations are
described and channel performances for two types of directive and omni-directional
antennas are compared.
* [Muq03e][Muq03f]
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Chapter5. Time Domain Indoor Channel Measurements
5.2 Description of Measurement Procedure and Locations
In this section the details about the measurements procedure are presented.
Locations where the measurements were conducted are also described to allow for
understanding some of the site-specific trends.
5.2.1 Measurement Procedure and Setup
Time domain measurements were performed using a sampling oscilloscope as a
receiver and a Gaussian-like pulse generator as transmitter. Two low noise wideband
amplifiers were used at the receiver side. Each amplifier has a again of 10 dB and a 3dB-
bandwidth of 15 GHz. The width of the excitation pulse is less than 100 ps. Offset
calibration is carried out with a matched load before performing any measurements. The
original data were over-sampled in the time domain with 10 ps/sample which results in a
noise tail in the frequency domain. An acquisition time window of 100 ns was selected by
making sure all observable multipath components are accounted for. This time window is
consistent with the maximum excess delay of 70 ns reported by other investigators
[Hov02]. The sampling oscilloscope allows a maximum of 5K points at a time. The 5K
points correspond to 50 ns time window. Two measured 50 ns time windows were
cascaded to yield a 100 ns acquisition time. The process was semi-automated using
LabView ® software. A total of about 400 profiles were collected. The spatial width of
the used pulse in our measurements is much smaller than the one used in previously
published measurements. The spatial width is small enough to make the line-of-site path
always resolvable from any other multipath component. Information about the excitation
pulse allows for deconvolution and hence generalization of results for use in other
communication applications in the covered frequency range [Vau99].
In indoor environments, the time varying part of the impulse response is typically
due to human movements. By conducting measurements during low activity periods and
by keeping both the transmitter and the receiver stationary, the channel can be treated as
126
Chapter5. Time Domain Indoor Channel Measurements
being quasi-stationary. This allows us to average 32 measurements, thus effectively
canceling out the noise.
Two different sets of measurements were performed based on TEM horn antennas
(antenna#1) and biconical antennas. Details about the antennas are presented in Chapter
3. Both transmitter and receiver antennas were placed on plastic moving carts at an
elevation of about 1.25 m above the floor. Styrofoam slabs were used to adjust the
elevation without introducing reflectors around the antenna. The TEM horn antennas
were aligned for maximum boresight reception. The advantage of using TEM horn
antennas is that they are ultra wideband radiators designed and optimized for time-
domain impulse response measurements. TEM horn antennas emulate sectored antenna
proposed for gaga-Hertz frequency indoor application. The TEM horn antenna has very
narrow beamwidth and thus is highly directional. With TEM horns fewer multipath
components are received, and almost none from behind the receiver. TEM horns have
been used for channel characterization in the past. For example, [Dav91] and [And02a]
used a TEM horn as the transmitting antenna and a TEM horn or an omnidirectional
antenna as the receiving antenna for channel characterization in the 60 GHz band. The
extent of multipath effects due to directional antennas on measurements is highlighted in
[Dur00]. On the other hand, biconical antennas are omni-directional and are more likely
to be used in mobile applications. The biconical antennas used in this investigation are
not designed as impulse antennas but they are impedance matched over a very wide
bandwidth.
Two levels of measurements are performed to characterize the small-scale and the
large-scale fading parameters of the channel. A 77 × grid with 15 cm spacing between
adjacent points was designed and used in the measurements. Since no small-scale fading
due to phase cancellation was observed, only a 3 3× measurement grid with 45 cm
spacing between adjacent points was used, except for measurements in the 4th floor
corridor in Whittemore Hall where one measurement was performed with the TEM horn
antennas and four measurements were made using the biconical antennas per each large-
scale location. The measurement grid is illustrated in Figure 5.1. The triggering signal
127
Chapter5. Time Domain Indoor Channel Measurements
was carried by a coaxial cable to the sampling oscilloscope. As the distance between
transmitter and receiver increased the loss and dispersion in the triggering cable increased
too, resulting in a higher jitter. An effort was made to use higher quality cables and
minimum possible length for the triggering cable. A personal computer was used to store
and post process the data.
(1,1) (1,4) (1,7)
(4,1) (4,4) (4,7)
(7,1) (7,4) (7,7)
Figure 5.1. Measurement grid
90cm
90 cm
5.2.2 Description of Measurement Locations
The measurements were carried out in two buildings on Virginia Tech Campus,
namely; Whittemore Hall and Durham Hall. The former building comprised mainly of
offices and classrooms. Most walls are made of drywalls with metallic studs. Some walls
at certain locations including stairwells are made of cinderblock and poured concrete. In
Durham Hall, interior walls are largely made of drywalls and cinderblocks. The floor is
covered with ceramic tiles in hallways and with carpet inside the rooms. An advantage of
performing UWB experiments in these buildings is that they have been characterized for
some narrowband measurements and site-specific ray tracing studies [Sei94], [Haw91],
[Rap92], [And02a], [And02b]. This allows one to compare the narrowband and the UWB
channel characterization results.
128
Chapter5. Time Domain Indoor Channel Measurements
In Whittemore Hall, the measurements were performed in three different floors;
along the hallways on the second floor, in a narrow corridor on the fourth floor and in a
conference room on the sixth floor. Appendix B3 shows the blue prints and photographs
of measurement locations. In Durham Hall, all measurements were carried on the fourth
floor. Five different transmitter locations were considered. For every location,
measurements at different receiver locations were performed, as indicated on the
blueprints in Figure B3.3a. To visualize the measurements environment, photographs of
the measurement locations are presented in Figures B3.3b and B3.3c.
Different scenarios are considered. Line-of-site (LOS) and non-line-of-site
(NLOS) topographies are of paramount interest. Room-to-room, within the room and
hallways are all typical indoor environments. Shadowing effects can also be assessed in
some scenarios. Table 5.1 summarizes the locations and scenarios measured.
5.3 Signal Processing and Data Analysis
A major challenge in UWB channel measurements is that the measurement
bandwidth is open to any signal. When taking measurements close to utility rooms or
laboratories that are radiating electromagnetic signals, there is an apparent increase in the
noise floor. To reduce the interference from undesirable sources, the acquired profile is
filtered in the time domain to remove some signals that are not part of the transmitted
pulse. The 3 dB bandwidth of the bandpass filter used for interference rejection occupies
a frequency range from 0.1 GHz to 12 GHz. The corner frequencies of the filter were
chosen by observing the spectrum of the radiated pulse and making sure that there is no
significant energy outside the pass band. The filtering process has three advantages. First,
the noise energy is reduced by eliminating out of band noise resulting from over
sampling. Second, any dc offset that has not been taken into account by the calibration is
removed. Finally, the lower frequency signals radiated from the pulse generator’s internal
electronics are eliminated. It was noted that the pulse generator gives off low frequency
components in the 30 MHz range that can be picked up by the biconical antenna. This is
illustrated in Figure 5.2 where a typical profile measured with the biconical antennas and
its filtered version are compared.
129
Chapter5. Time Domain Indoor Channel Measurements
Table 5.1. Measurement locations and scenarios
# Location Description
# profiles (TEM
)
# profiles (B
iconical) d
W2.A Hallways in 2nd floor LOS, Hallways 9 9 9.3
W2.B Hallways in 2nd floor LOS, Hallways 9 9 17.6
W2.C Hallways in 2nd floor NLOS, Hallways 0 0 -
W2.D Hallways in 2nd floor NLOS, Hallways 0 0 -
W2.E Hallways in 2nd floor LOS, Hallways 9 9 15.4
W2.F Hallways in 2nd floor LOS, Hallways 9 9 30.9
W2.G Hallways in 2nd floor LOS, Hallways 9 9 49.1
W2.H Hallways in 2nd floor NLOS, Hallways 0 0 -
W2.I Hallways in 2nd floor NLOS, Hallways 0 0 -
W4 Corridor in the 4th floor LOS, Small corridor 12 25 Varying
W6.A Conference Room in 6th floor LOS, Within a room 9 9 5.1
W6.B Conference Room in 6th floor LOS, Within a room 9 9 6.2
Precursor and noise before the arrival of the first component are forced to zero in
order to ensure the causality of results in the processing stage. For energy calculation and
large-scale pathloss analysis, a noise threshold is introduced below which all data are
assumed to be zero. The threshold was set at 6 dB above the noise floor determined as the
maximum level of the profile tail in the last 5 ns of the 100 ns time window.
5.4 Results and Analysis
The results for measurements with the TEM horn and biconical antennas are
presented separately. At locations W2.C, W2.D, W2.H, W2.I and D4.B no signal could
be clearly detected by the receiver. At the first four locations there was no line-of-sight
between the transmitter and the receiver, because the obstructed path is either through
concrete walls or through multiple drywalls with metallic studs. The insertion loss is a
function of frequency. Thick reinforced concrete walls are impenetrable at high
frequencies [Dav91]. At the location D4.B, the line-of-sight is obstructed with office
cubical metallic partitions. The use of the omnidirectional antenna did not improve the
measurements at those locations. The reason is that the pulse spectrum contains
substantial high frequency contents. At higher frequencies, the line-of-sight component is
the most significant part, since diffracted components and through-the-wall propagation
are much weaker. Moreover, indoor path loss generally increases with frequency. Small-
scale effects, large-scale path loss and time dispersion parameters are discussed
separately in the following subsections.
5.4.1 Small-Scale Fading and signal Quality
In narrowband communication systems, small-scale fading describes the
fluctuation due to constructive and destructive interference of the multipath components
at the receiver when sub-wavelength changes are made in the receiver position
[Rap96][Dur00]. Such definition can be extended to UWB communication as the
constructive and destructive interference of the multipath components at the receiver due
to a change in its position in the order of sub-spatial-width of the transmitted pulse.
132
Chapter5. Time Domain Indoor Channel Measurements
Sample results are presented for measured delay profiles, referred to as local
power delay profiles (local-PDP). The remaining results are presented for small-scale
averaged power delay profile (SSA-PDP). In the SSA-PDP the nine measurements are
properly delayed and averaged. Figure 5.3 illustrates how SSA-PDP are different from
the local-PDP. The first three plots, Figure 5.3a to 5.3c, are local-PDPs and the last one,
Figure 5.3d, is the average of all 9 local measurements. When delay-and-average is used,
the line of site components tend to prevail and the other components spread out on the
time axis such that they do not add coherently because of the high resolution of the
transmitted pulse. Small-scale processing shows the capability for using a delay-and-sum
beamformer to process a received array of signals from different antennas located in a
very small area [Cra98]. It is important to note that small-scale and large-scale
terminologies are used as relative measures of distances between the receiver locations
compared with the wavelength. These terminologies do not fit well to our analysis
because any movement tends to be large compared to the effective wavelength.
In narrowband measurements, the spacing between the local measurements is
related to the wavelength, λ . It is reported in [Dur98] that one can cancel out small-scale
effects by averaging power along 20λ linear or circular paths independent of the signal
bandwidth. An established fact is that local fading results from the destructive
interference of multipath components [Rap89]. However, for UWB signals there is no
single frequency or single wavelength, thus no destructive interference can occur over the
entire bandwidth of the pulse. Our observations of received signals at different points in
a grid confirm the absence of small-scale fading. To quantify this effect, let us consider
the signal quality as defined in [Win98b]
01010 log10log10 EEQ −= (5.1)
where E is the received signal energy given by
(5.2) dttrET
∫=0
2 )(
133
Chapter5. Time Domain Indoor Channel Measurements
134
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
2
4
6x 10-3
time (ns)
v2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
2
4
6x 10-3
time (ns)
v2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
2
4
6x 10-3
time (ns)
v2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
2
4
6x 10-3
time (ns)
v2
(a)
(b)
(c)
(d)
Figure 5.3. Comparison between small-scale averaged power delay profiles (SSA-PDP) and local power delay profiles. Measurements were performed at location W2 (TEM horn antennas, Whittemore, 2nd floor)
(a) measured power delay profile (PDP) at location (1,1) (b) measured power delay profile (PDP) at location (1,4) (c) measured power delay profile (PDP) at location (1,7) (d) small-scale averaged power delay profiles (SSA-PDP) for the nine
measurements on the grid.
Chapter5. Time Domain Indoor Channel Measurements
where is the measured multipath profile and T is the observation time. E0 is the
energy measured at a reference location, which is usually chosen to be at a 1 m distance
from the transmitter. The cumulative distribution functions (CDF)s for the signal quality
for all measured grids are shown in Figure 5.4. There is almost no fading as a result of
interference. All local PDPs are within 3 dB of the average level unless some profiles are
obstructed with some objects in the channel or they belong to points close to walls. If
transmitter and/or receiver locations are close to walls, the received profile is affected
significantly [Rap89]. Robustness of UWB communication systems, insofar as multipath
is concerned, is manifested by small variations in signal quality at various grid locations
[Sch97].
)(tr
5.4.2 Pathloss and Large-Scale Analysis
The energy in the received profile, statistically speaking, decreases with the
distance between the receiver and the transmitter. The pathloss exponent, n, is a measure
of decay in signal power with distance, d, according to 1 . A reference measurement
is performed at a distance of 1 m form the transmitter. Subsequent energy measurements
are performed with respect to the reference measurements. Using the log-normal
shadowing assumption, the path loss exponent, n, is related to the received energy at
distance d and the reference measurement by
/ nd
σXddndPLdPL +
+=
0100 log10)()( (5.3)
where is the reference distance,0d )( 0dPL is the average measured energy at the
reference distance and is a zero-mean Gaussian distributed random variable in (dB)
with standard deviation equals
σX
σ [Rap96]. The path loss exponent is obtained by fitting
a line on the logarithmic scatter plot of energy versus distance. The standard deviation for
the Gaussian random variable is obtained by calculating the deviation from the obtained
fit. The reference measurement is very important as it defines the intercept with the
vertical axis and hence affects the fitted slope. Many reference measurements can be
averaged together to reduce the effect of the measurement environment.
135
Chapter5. Time Domain Indoor Channel Measurements
-35 -30 -25 -20 -15 -1010
20
30
40
50
60
70
80
90
100
Signal Quality (dB)
Per
cent
age
less
than
Abs
ciss
a
TEM Horn Antennas
-35 -30 -25 -20 -15 -1010
20
30
40
50
60
70
80
90
100
Signal Quality (dB)
Per
cent
age
less
than
Abs
ciss
a
Biconical Anteenas
(a)
W2W6D1D2D3D4D5
W2W6D1D2D3D4D5
(b)Figure 5.4. The cumulative distribution of the signal quality based on 9 spatial sample
points;
(a) with TEM horn antennas (b) with biconical omnidirectional antennas
136
Chapter5. Time Domain Indoor Channel Measurements
In narrowband characterization, the local PDPs, small-scale averaged PDPs (SSA-PDP)
are usually used to eliminate any small-scale effect. The same technique is implemented
by Cassioli et al. [Cas01] to generate local and global parameters.
In the present analysis, the UWB pulse delay time is used to find the distance
between the receiver and the transmitter. First, the distance between the transmitter and
the receiver is measured at a reference position. Then, other distances separating the
receiver from the transmitter are calculated using the pulse delay time. This allows us to
take measurements at locations with small separation distances and reduces the error
associated with distance measurements. Measured points are distributed across the entire
scattering plots rather than being clustered. This distribution reduces the error associated
with reference measurements. The scatter plots for global data are presented in Figure
5.5.
Scatter plots for LOS and NLOS scenarios are shown separately in Figure 5.6.
The extracted parameters for each scenario are listed in Table 5.2. The minimum path
loss exponent is 1.27 for the case of the narrow corridor which has nearly the behavior of
a lossy waveguide structure. The maximum pathloss exponent is 3.29 in the obstructed
scenario D1. The global line-of-sight parameters are n=1.61 and σ =1.58 dB for the
TEM horns and n=1.58 andσ =1.91 dB the biconical antennas. The NLOS scenarios
have pathloss exponents greater than 2 and also have larger σ values compared with LOS
scenarios.
In general, there is a close agreement between the results obtained with directive
antennas and the results obtained with omni-directional antennas. This similarity of
results obtained with the two types of antennas de-emphasizes the contribution of the
back reflection components. A notable difference is lower σ value when directive
antennas are used, especially in NLOS scenarios as directive antenna can be easily
shadowed by any object in the channel while omni-directional antennas can still receive
some components.
137
Chapter5. Time Domain Indoor Channel Measurements
15
20
25
30
35 TEM Horn Antennas
1m
free
spa
ce p
ath
loss
(dB)
W2W4
Fig
(a)
10 0 101
10 2 0
5
10
Transmitter-receiver separation distance (m)
Path
loss
with
resp
ect t
o W6D1D2D3D4D5Fit, n=1.8274n=2
20
25
30
35 Biconical Antennas
free
spa
ce p
ath
loss
(dB )
W2W4
u
(b)
10 0 101
10 2 0
5
10
15
Transmitter-receiver separation distance (m)
Path
loss
with
resp
ect t
o 1m W6
D1D2D3D4D5Fit, n=1.7482n=2
re 5.5. Scatter plot for the relative pathloss versus frequency for all locations
(a) using TEM horn antennas, (b) using biconical antennas.
138
Chapter5. Time Domain Indoor Channel Measurements
100 101 1020
5
10
15
20
25
30
35LOS using the TEM Horn Antennas
Transmitter-receiver Separation Distance (m)
Pat
hlos
s w
ith re
spec
t to
1m fr
ee s
pace
pat
h lo
ss (d
B) LOS
Fit, n=1.6077n=2
100 101 1020
5
10
15
20
25
30
35
40NLOS using the TEM Horn Antennas
Transmitter-receiver Separation Distance (m)
Pat
hlos
s w
ith re
spec
t to
1m fr
ee s
pace
pat
h lo
ss (d
B)
NLOSFit, n=2.6039n=2
100 101 1020
5
10
15
20
25
30
35
40NLOS using the Biconical Antennas
Transmitter-receiver separation sistance (m)
Pat
hlos
s w
ith re
spec
t to
1m fr
ee s
pace
pat
h lo
ss (d
B)
NLOSFit, n=2.4118n=2
100 101 1020
5
10
15
20
25
30
35LOS using the Biconical Antennas
Transmitter-receiver Separation Distance (m)
Pat
hlos
s w
ith re
spec
t to
1m fr
ee s
pace
pat
h lo
ss (d
B)
LOSFit, n=1.5826n=2
(b) (a)
(d) (c)
Figure 5.6. Scatter plots for the pathloss versus distance, for LOS and NLOS scenarios:
(a) LOS using TEM horn antenna, (b) NLOS using TEM horn antenna, (c) LOS using biconical antenna, (d) NLOS using biconical antenna.
139
Chapter5. Time Domain Indoor Channel Measurements
Table 5.2. Large-scale pathloss parameters for both TEM horn and biconical antennas
The reported pathloss exponents for narrowband systems are 1.6-1.8 for in-
building line-of-sight environments and 4-6 for obstructed in-building environments
[Rap96]. As noted from Table 2, The pathloss exponents for UWB are comparable with
pathloss exponents for narrowband LOS scenarios but are smaller for NLOS scenarios.
The results for pathloss exponent and the standard deviation introduced by Ghassem-
zadeh et al. [Gha02] are also comparable to the results obtained from our measurements.
[Gha02] performed UWB frequency domain measurements around 5 GHz, which is close
to the center frequency in the spectrum of the pulse used in our experiments. Their
parameters are n=1.7, σ =1.6 dB for LOS scenarios and n=3.5,σ =2.7 dB for NLOS
scenarios.
5.4.3 Time Dispersion Results
The time dispersion parameters shed some light on the temporal distribution of
power relative to the first arriving components. Delay spreads restrict transmitted data
rates and could limit the capacity of the system when multi-user systems are considered.
140
Chapter5. Time Domain Indoor Channel Measurements
The time dispersion of UWB pulses can be presented as the ratio of the average arrival
time to the spread of the arrival time. Time dispersion parameters formulation can be
found in Chapter 3.
The ratio of the mean excess delay to the RMS delay spread can be used as a
measure of the time dispersion for UWB signals. If τστ = , then the multipath delay
profile decays exponentially. The same situation corresponds to two multipath
components with equal power where the second path is 2τ away from the first
component. High concentration of power at small excess delay values is reflected by
τστ / <1. When the energy arrive at the mid point of the power delay profile and not at
the earliest part then τστ / >1 [Rap89].
The cumulative distribution function (CDF) for the RMS delay spread is plotted
in Figure 5.7. All multipath components within 20 dB of the maximum are included.
Obstructed and non-line-of-sight scenarios resulted in higher time dispersion. The
variations between different scenarios and buildings are less for the omnidirectional
antennas when compared with the directive TEM horns. When the biconical antennas are
used the values are higher because receive bicone can receive more multipath
components. The results for SSA-PDPs are presented in Table 5.3 for the TEM horn and
in Table 5.4 for the biconical antenna. It should be noted that the instantaneous delay
spreads cannot be averaged to give the delay spread. Instead, for the SSA-PDPs, the
power delay profiles are averaged and then the delay spread is calculated. Individual
power delay profiles are averaged, weighted by their own power [Vau99].
Time Dispersion Parameters Correlation with channel Parameters
Now, the correlation between the channel time dispersion parameters is examined.
The relation between the mean excess delay and the RMS delay spread is illustrated in
Figure 5.8. The ratio τστ / is mostly in the range of 0.25-1. The small values for this
ratio imply high concentration of power at small excess delay. Obstructed measurements
141
Chapter5. Time Domain Indoor Channel Measurements
0 5 10 15 20 250
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMS Delay Spread (ns)
Pro
babl
ilty
RM
S D
elay
Spr
ead<
Abs
ciss
a
TEM Horn
D1D2D3D4D5
0 5 10 15 20 250
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMS Delay Spread (ns)
Pro
babl
ilty
RM
S D
elay
Spr
ead<
Abs
ciss
a
Biconical Antennas
W2W4W6
0 5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMS Delay Spread (ns)
Pro
babl
ilty
RM
S D
elay
Spr
ead<
Abs
ciss
a
Biconical Antennas
D1D2D3D4D5
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RMS Delay Spread (ns)
Pro
babl
ilty
RM
S D
elay
Spr
ead<
Abs
ciss
aTEM Horn
W2W4W6
(b)(a)
(c) (d)
Figure 5.7. Cumulative distribution functions (CDF)s for the RMS delay spread (20 dB), for Whittemore and Durham Halls:
(a) Whittemore Hall using TEM horn antenna, (b) Whittemore Hall using TEM horn antenna, (c) Durham Hall using biconical antenna, (d) Durham Hall using biconical antenna.
142
Chapter5. Time Domain Indoor Channel Measurements
Table 5.3. Parameters for small-scale averaged PDP (SSA-PDP) TEM horn antennas
Threshold 10 dB 20 dB Location d τ σ maxτ % τ σ maxτ %
min 3.54 0.000 0.030 0.00 16.91 1.139 2.356 14.93 50.84
max 49.34 18.622 13.698 64.52 75.38 28.781 22.086 92.35 99.88
mean 15.43 2.770 2.377 12.00 44.13 6.682 7.134 41.93 77.02
median 9.44 0.579 0.768 2.81 44.13 3.172 4.377 26.42 78.75 All time variables are in ns
144
Chapter5. Time Domain Indoor Channel Measurements
0 5 10 15 20 250
5
10
15
20
25
RMS Delay Spread (ns)
Mea
n E
xces
s D
elay
(ns)
TEM Horn
W2W4W6D1D2D3D4D5slope=1
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
RMS Delay Spread (ns)
Mea
n E
xces
s D
elay
(ns)
TEM Horn
W2W4W6D1D2D3D4D5slope=1
0 5 10 15 20 25 300
5
10
15
20
25
30
RMS Delay Spread (ns)
Mea
n E
xces
s D
elay
(ns)
Biconical Antenna
W2W4W6D1D2D3D4D5slope=1
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
5
6
7
8
9
10
RMS Delay Spread (ns)
Mea
n E
xces
s D
elay
(ns)
Biconical Antenna
W2W4W6D1D2D3D4D5slope=1
(b) (a)
(c) (d)
Figure 5.8. Scatter plot for the mean excess delay versus the RMS delay spread, for the TEM horn and the biconical antennas,
(a) TEM horn antenna, all scenarios, (b) TEM horn antenna, zoomed view, (c) Biconical antenna, all scenarios, (d) Biconical antenna, zoomed view.
145
Chapter5. Time Domain Indoor Channel Measurements
tend to have τστ / =1 which means that the power decays exponentially with time. For
the LOS scenarios the mean excess delay is close to zero, indicating that only the LOS
component is within the specified level of power. The number of dominant multipath
components is limited to two in LOS scenarios. This is consistent with the measurement
carried out at the same location in Durham Hall by [And02b].
Scatter analysis of our UWB measured data indicates that there is no relationship
between delay spread and transmitter-receiver (T-R) separation. This is in agreement with
that reported in [Rap89] and [Sal87] for narrowband systems. On the other hand, when
considering the relation between the received energy and the delay spread, lower energy
signals might seem to have large excess delay. However, this is because the locations
where the received energy is low are usually obstructed and signals arrive at the receiver
through many multipath components. In general received power is not correlated with the
excess delay parameters. In [Rap89] and [Sal87] scatter plots of RMS delay spread versus
pathloss indicate no correlation. The scatter plots relating the RMS delay spread to each
of the T-R separation and the received energy are presented in Figure 5.9.
Comparison with UWB and Narrowband Published Results
In the 5-30 m range, indoor channels are expected to have an RMS delay spread
of 19-47 ns [Fos01] and mean values in the range of 20-30ns [Has93b]. Keignart and
Daniele [Kie02] presented their measurements for a maximum range of 10 m in an indoor
UWB channel. They found that their measured RMS delay spread varies between14 to 18
ns which is a lower than that reported by Hashemi [Has93b]. They also found that the
mean excess delay increases when transmitter/receiver antenna separation increases. The
mean excess delay in their experiment was 4-9 ns for LOS and 17-23 ns for NLOS
scenarios.
146
Chapter5. Time Domain Indoor Channel Measurements
0 5 10 15 20 250
5
10
15
20
25
30
35
40
45
50
RMS Delay Spread (ns)
Dis
tanc
e (m
)
TEM Horn
W2W4W6D1D2D3D4D5
0 5 10 15 20 25 300
5
10
15
20
25
30
35
40
45
50
RMS Delay Spread (ns)
Dis
tanc
e (m
)
Biconical Antenna
W2W4W6D1D2D3D4D5
0 5 10 15 20 25 30-35
-30
-25
-20
-15
-10
-5
0
RMS Delay Spread (ns)
Pat
hlos
s w
ith re
spec
t to
1m fr
ee s
pace
pat
h lo
ss (d
B)
Biconical Antenna
W2W4W6D1D2D3D4D5
0 5 10 15 20 25-35
-30
-25
-20
-15
-10
-5
0
RMS Delay Spread (ns)
Pat
hlos
s w
ith re
spec
t to
1m fr
ee s
pace
pat
h lo
ss (d
B)
TEM Horn
W2W4W6D1D2D3D4D5
(a) (b)
(c) (d)
Figure 5.9. Scatter plots to examine the correlation between RMS delay spread and distance/pathloss.
(a) TEM horn antenna, distance versus the RMS delay spread, (b) TEM horn antenna, pathloss versus the RMS delay spread, (c) Biconical antenna, distance versus the RMS delay spread, (d) Biconical antenna, pathloss versus the RMS delay spread.
147
Chapter5. Time Domain Indoor Channel Measurements
When comparing the results for the published narrowband and UWB propagation
experiments, one has to consider the difference between the used pulse-shape and the
associated frequency spectrum. Time dispersion parameters are functions of the noise
floor, thus without considering the noise power level, time dispersion parameters lose
their significance. For the presented results, we used 10 dB and 20 dB from the maximum
instantaneous signal power. Unless stated otherwise, down to 20 dB below the maximum
instantaneous power is considered.
5.5 Summary and Conclusions
Time-domain measurements were presented for indoor channel characterization.
The performed measurements have high resolution thus suitable for developing accurate
UWB communication channel models. The high-resolution pulses used in these
measurements are good candidates for small cells scenarios, such as single-cell-per-room
where few obstructions exist. Directive TEM horn antennas were compared with the
omnidirectional biconical antennas. Site-specific trends and general observations were
also discussed. Some statistical analyses of the measured data were presented and
compared with the previously published UWB and narrowband results. These
measurements and their corresponding statistical analysis clarified the immunity of UWB
signal to multipath fading compared with the narrowband signals. The calculated pathloss
exponent was as low as 1.27 for a narrow corridor. For LOS and NLOS scenarios the
global pathloss exponents were found to be nearly 1.6 and 2.7, respectively. The
calculated time dispersion parameters for the measured results indicate high
concentration of power at low excess time delays.
Combining the results of penetration loss presented in a previous chapter with the
results of pathloss and time dispersion parameters presented in this report should
facilitate the development better UWB communication channel models. Results might
also prove to be useful for narrowband characterization.
In the next chapter, deconvolution is applied to extract more information about the
UWB channel from the performed measurements.
148
Chapter 6. UWB Channel Model-Deconvolution
“Frequently, knowledge from electrophysics will be employed to formulate a model which
is consistent with physical fact (not mathematical fancy)”
Norris S. Nahman [Nah78]
Chapter 6
UWB Channel Model-Deconvolution*
6.1 Introduction
Before UWB impulse radio can be implemented for indoor applications, the UWB indoor
channel must be accurately characterized and modeled. The importance of accurate channel
characterization cannot be underestimated. The early measurement attempts reported in the
literature extend the narrowband measurement scenarios to the UWB case. Both the approach
and the results need to be verified. For narrowband characterization, usually no deconvolution is
needed and the excitation signal is assumed to be close to an ideal Dirac-delta impulse which
means that the received signal can approximate the impulse response. For narrowband channels,
deconvolution was only used when super-resolutions were required [Vau99], [Mor98].
Deconvolution is most needed for the characterization of wideband devices and channels due to
the limited bandwidths of available test signals as compared to the bandwidths of devices and
channels themselves [Par83]. Since the channel under study is wideband, deconvolution
techniques are needed to estimate the UWB channel impulse response. Moreover, with
deconvolution the estimated channel impulse response is independent of the excitation signal,
which allows for the simulation of different waveforms for wave-shaping studies.
* [Muq02d]
149
Chapter 6. UWB Channel Model-Deconvolution
In the previous chapter some non-model characterization were presented, namely: signal
quality, pathloss exponent, and time dispersion parameters. In this Chapter, a modified model is
proposed for the UWB channel. It is based on the fact that UWB antennas result in different
impulse response depending on the angle of transmission and angle of arrival. Model-
deconvolution is then used to estimate the number of significant multipath components. The
results are compared with the usual technique where the delay axis is discretized into bins of τ∆
seconds. The selection of the bin size should be equivalent to the measurement resolution
[Has93a] [Has93b]. A multipath component with magnitude ia is said to exist at ττ ∆= ii , if
the integrated power within the ith delay bin interval of the received signal exceeds the
minimum detectable signal threshold. The dominant paths are the paths with the largest
amplitudes [Win97c]. If the number of dominant paths components is small, e.g. 5, ray tracing
can be used as modeling technique. However, one has to employ statistical analysis as the
number of dominant paths increases and ray tracing becomes more complicated and site-specific
[Win97c].
2ia
In section 2 the deconvolution problem is formalized. The incentive for the proposed
multi-template model deconvolution is given through experimental means. Improvements and
results of applying the multi-template deconvolution algorithm on estimating the number of
multipath components and the energy associated with them are presented in section 3
6.2 Deconvolution
Channels can be characterized by their transfer function in the frequency domain or by
their impulse response in the time domain. The measurements under investigation are conducted
in the time domain. Deconvolution of the time-domain waveforms can be used to determine the
impulse response of a linear time-invariant system. The indoor channel is assumed to be time-
invariant if the transmitter and the receiver are static and no motions take place in the channel. If
h(t) is the impulse response of such a channel whose input is x(t), then the output y(t) is given by
the convolution integral,
∫+∞
∞−
−⋅=∗= τττ dthxthtxty )()()()()( , (6.1)
150
Chapter 6. UWB Channel Model-Deconvolution
where * denotes the convolution operation. In the frequency domain, convolution transforms into
multiplication as follows,
)()()( ωωω jHjXjY ⋅= , (6.2)
where Y(jω), X(jω) and H(jω) are the frequency-domain representations of y(t), x(t), and h(t),
respectively.
The process of obtaining h(t) knowing both x(t) and y(t) is called deconvolution. Ideally,
deconvolution can also be performed in the frequency domain using the Fourier transform. Thus,
from (6.2)
)(/)()( ωωω jXjYjH = . (6.3)
Due to measurement and signal processing limitations, simple division will result in noise-like
error around the zeros of X(jω). Filtering should be used to improve the estimation of the
impulse response [Ria86].
An example of a typical channel profile, y(t), using source#2 and the TEM horn antenna
(Antenna#1) is shown in Figure 6.1. Let x(t) be the received line-of-sight reference gated-pulse
using source#2 and antenna#1 presented in Chapter 3. The received profile, as shown in Figure
6.1, is not a simple summation of delayed pulses. It is evident from the received profile that
multipath components have different waveforms compared with the reference pulse. Though, the
transfer function and the impulse response give full channel description, only few parameters can
be used by the receiver for channel estimation. Model deconvolution is usually used to
characterize the channel with few parameters [Nah81].
6.2.1 Model Deconvolution
Recall that the impulse response of the propagation channel is often modeled as a
summation of effective scatterers,
∑ −=k
kk tath )()( τδ (6.4)
151
Chapter 6. UWB Channel Model-Deconvolution
where ak is the magnitudes of the kth scatterers. The model in (6.4) is widely used and can
adequately represent the channel for many narrowband communication purposes. This model
does not perfectly fit the UWB channel because the delta function at the receiver implies an
infinite channel bandwidth, which is not possible or acceptable approximation. To make the
model more accurate, the reference pulse used is the convolution of the sounding pulse with the
impulse response of the transmitter antenna, receiver antenna, and the sampling oscilloscope.
This reference pulse is measured in a well-behaved channel where the multipath reflections can
be gated out, as shown in Figure 6.2. The transmitter and the receiver antennas are facing each
other with a distance that guarantees far field reception for the antenna under use. Both the
transmitted and received pulses are presented in Chapter 3.
Though this technique is widely used, the assumption that the received pulses through
different paths have the same waveform is not justified. This assumption requires that both the
transmitter and the receiver antennas have isotropic radiation patterns at all frequencies. It was
noted in [Cra02] that if the antenna is electrically large compared to the wavelength of the center
frequency of the received signal, the waveforms radiated in different directions from the
transmitter antenna look considerably different in the far field region. In Chapter 3, it was also
demonstrated that the signal received at different angles, have considerably different waveforms.
Another illustrative experiment is performed with the two antennas directed towards a reflecting
surface (floor). The setup for this experiment and the received waveforms are displayed in Figure
6.3. For the setup shown in the figure, the waveform associated with the direct path is totally
different from the reference waveform.
5 1 0 1 5 2 0 2 5-0 . 0 8
-0 . 0 6
-0 . 0 4
-0 . 0 2
0
0 . 0 2
0 . 0 4
0 . 0 6
0 . 0 8
T im e (n s )
Am
plitu
de (V
)
Figure 6.1. Typical received LOS multipath profile (Whittemore 2nd floor Hallway)
152
Chapter 6. UWB Channel Model-Deconvolution
153
Tx Horn Rx Horn Ideal Channel
Sampling O’Scope
Pulse Gen.
x(t)
h(t) Tx Horn Rx Horn
Sampling O’Scope
Pulse Gen.
y(t)
Figure 6.2. Illustration of the measurements of an ideal channel and a multipath indoor channel
RRX x
ceiling
floor
Tx
3 4 5 6 7 8-0 .03
-0 .02
-0 .01
0
0 .01
0 .02
0 .03
0 .04
0 .05
Tim e ns
Am
plitu
de in
V
Figure 6.3. (a) Setup and (b) received waveform with both transmitter and receiver antennas pointing to the reflection surface.
Chapter 6. UWB Channel Model-Deconvolution
On the other hand, the reflection from the floor, which has the same angle of arrival and
transmission relative to the antennas, has the same shape as the reference waveform. The
reference waveform is reproduced as an inset of the plot for comparison.
6.2.2 Multi-Template Model-Deconvolution
Based on the previous experiments, it is evident that the assumption that multipath
components have shapes similar to that of the reference line-of-sight template is far from being
valid. The same conclusion can be extended to other practical antennas. With this perception, the
model can be modified to allow for more than one received pulse waveform. The proposed
model is antenna specific and is given by
∑ −=k
kj
k thath )(~)( τ (6.5)
where is the impulse response of a system, whose output is the jth template jh~ jp~ , when excited
by the line-of-sight pulse 1~p . When the received signal is the line-of-sight, corresponds to jh~
)(~1h = tδ . Assuming k different templates, the subtractive deconvolution algorithm is modified
from that described in [Vau99] as follows:
1. Initialize the dirty map with the received waveform r(t), d(t)=r(t) and the clean map
with c(t)=0;
2. Form the correlation coefficient functions (normalization is
understood and means correlation) for j=1,2,…k;
)()(~)( tdtp jj Θ=Γ τ
Θ
3. Find the peaks (max , j=1,2,…k ), and their positions, jiΓ iτ , in the ; )(τjΓ
4. If all Γ < threshold, go to step 8; ji
5. Clean the dirty map by inserting zeros in place of the detected multipath component;
6. Update the clean map by using . )()()( ijj
i thtctc τ−Γ+=
7. Go to step 2;
8. The impulse response is then . )()(ˆ tcth =
154
Chapter 6. UWB Channel Model-Deconvolution
Note that in step (5) updating the dirty map is done by inserting zeros in place of the
detected component rather than updating it by replacing d(t) with )(~)( ijj
i tptd τ−Γ− as in
[Vau99]. This inherently assumes that multipath components do not overlap. This assumption is
justified by the dispersive nature of the channel. If the dirty map is updated as in [Vau99],
invalid multipath components will be produced as a result around the previously detected
components. As a result of zeroing the window of the detected component, not all the energy
can be captured. In the next section, the modified model deconvolution is applied to indoor
channel measurements presented in Chapter 5.
6.3 Results and Analysis
The energy in the multipath profiles from the measurement campaign presented in
Chapter 5 is now captured using a correlator with a fixed template and compared with that
obtained using the proposed multi-template correlator. For optimal selection of the receiver
templates a full antenna characterization should be performed. Unfortunately, antennas were
usually characterized in the frequency domain and for small frequency bands. The TEM horns
used in the presented measurements were characterized in Chapter 3. Research on developing
UWB antenna characterization is under development. In this section, we present a simple
experiment for characterizing the received pulse to illustrate the idea. Figure 6.4 illustrates the
experiment. The separation between the two antennas is 3 m and the distance, d, shown in Figure
6.4 is increased in steps of 20 cm which result in changing the elevation angle (E-scan). The
antennas are then rotated for H-scan where the azimuth angle changes with d. For our purpose of
experimenting the model-deconvolution, the reference templates are based on antenna
measurements at different elevation angles because the directivity of the antenna cause the more
reflections to result from the floor and the ceilings. Figure 6.5 presents the improvement in the
captured energy versus the number of captured multipath components. Different traces are
shown for different number of templates. For the case of single template, the reference template
was measured at d=0. For the case of two templates, the reference templates were measured at
d=0 and d=120 cm. For the case of four templates, the two templates and their inversion are
considered because reflection from different objects at different angles causes the received pulse
to change sign. The choices of templates were not fully optimized but rather were based on the
155
Chapter 6. UWB Channel Model-Deconvolution
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-0.1
-0.05
0
0.05
0.1
time (ns)
volta
ge (v
)
d=0d=20d=40d=60d=80d=100d=120
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
-0.1
-0.05
0
0.05
0.1
0.15H scan
time (ns)
volta
ge (v
)
d=0d=20d=40d=60d=80d=100d=120
(b)
(a)
d
d increases
d increases
0.15E scan
(c)
Tx-Rx separation 3m
Figure 6.4. Different received waveforms at locations when scanning on the E-plane and the H-
plane (a) received waveforms with E-scan (b) received waveform with H-scan, and
(c) experimental setup (antennas are rotated 90 degrees for the H-scan)
156
Chapter 6. UWB Channel Model-Deconvolution
0 2 4 6 8 10 12 14 16 18 20
20
30
40
50
60
70
80
90
Number of Single-Path Correlators
% E
nerg
y C
aptu
reLOS, TEM Horn
1 Template2 Templates4 Templates
0 2 4 6 8 10 12 14 16 18 20
20
30
40
50
60
70
80
90
Number of Bins
% E
nerg
y C
aptu
re
LOS, TEM Horn
100 ps200 ps300 ps
0 2 4 6 8 10 12 14 16 18 20
20
30
40
50
60
70
80
90
Number of Single-Path Correlators
% E
nerg
y C
aptu
re
NLOS, TEM Horn
1 Template2 Templates4 Templates
0 2 4 6 8 10 12 14 16 18 20
20
30
40
50
60
70
80
90
Number of Bins
% E
nerg
y C
aptu
reNLOS, TEM Horn
100 ps200 ps300 ps
(d) (c)
(b) (a)
Figure 6.5. Improvement in captured energy
(a) versus number of multipath bins for different bin sizes (LOS), (b) versus number of single-path correlator for different number of templates. (LOS), (c) versus number of multipath bins for different bin sizes (NLOS), (d) versus number of single-path correlator for different number of templates
(NLOS).
157
Chapter 6. UWB Channel Model-Deconvolution
shape of the reference waveform to allow capturing more energy. All templates are normalized
to have the same energy.
As depicted in Figure 6.5, using two templates resulted in more than 10% increase in the
captured energy for the LOS scenarios as opposed to 5% for the NLOS scenarios. As the
number of templates is increased to four, the energy capture improved by more that 10% again in
the LOS case. In the NLOS scenario less gain is achieved by increasing the number of templates
as the pulse shape undergoes significant change and the energy is distributed through many
components. With 20 single-path correlators, the performance saturated with four templates at
about 72% of the received energy. The limit in the maximum captured energy is a direct result of
the assumption that multipath components are not allowed to overlap.
Using the traditional technique of discretizing the delay access into bins and evaluating
the energy in every bin, similar conclusions can be drawn. Three different bin sizes are
presented because the duration of the pulse is different based on the path. Figure 6.5c and 6.5d
illustrate the percentage energy capture for bin size of 100 ps, 200 ps, and 300 ps. By comparing
the results when using the correlator receiver and the traditional technique, one can asses the
performance of the correlator receivers compared to the total energy capture. It is also important
to note that the plots in Figure 6.5 have sharp peaks at the first five bins or correlators which
suggest that rake receiver need not have a complexity more than 5. Ray tracing is usually a good
candidate for channel modeling when the number of dominant multipath components is small as
in the presented results
6.4 Summary and Conclusions
In this chapter, a modified model was presented based on experimental results which
illustrates that UWB multipath components may have dramatically different waveforms at
different angles relative to the transmitter and receiver antennas. A multi-template UWB
propagation model was proposed to account for the received components at different angles.
Subtractive deconvolution was modified and used to extract the model parameters from
measured channel profiles. The resultant impulse response is antenna-specific. It was shown that
the captured energy increases by more than 10% when using two reference waveforms. For rake
receiver design only 5 correlators would be necessary to capture the energy without high
158
Chapter 6. UWB Channel Model-Deconvolution
complexity. NLOS pulses undergo dramatic changes and adding more reference template does
not increase the captured energy significantly. Ray tracing is a good technique for modeling
LOS scenarios as the dominant paths are less than 5. Further extension of this work can include
optimizing the choices of reference templates based on extensive antenna measurements.
159
Chapter 7. UWB Multi-User Detection
“Multi-access noise has considerable structure, and certainly much less randomness
than white Gaussian background noise. By exploiting that structure, multi-user detection can
increase spectral efficiency, receiver sensitivity, and the number of users the system can
This appendix is dedicated for presenting the derivation of the short-pulse propagation
measurements. The analysis presented here follows closely the analysis given by [Aur96]. A
short duration electromagnetic pulse, Ei(t) is applied to a homogenous, isotropic material layer of
thickness d. The transmitted signal, Et2(t) is measured at the other side of the material. To
simplify the problem we assume normal incidence to the material surface and we assume that the
duration of the pulse is less than the transient time through the material. Multiple reflections
inside the layer as a result of the finite-sized layer can be eliminated. Same technique can be used
to eliminate antenna ringing and extraneous paths. In summary, this is a single-pass time-
duration-limited transient measurement procedure which assumes 1-D model of plane-wave
propagation through a planer layer.
To get more insight into the problem, the lattice or bounce diagram is shown in Figure
A2-1. Note that this is not steady state harmonic analysis which include the internal ringing. Two
signals are measured:
• the transmitted ‘through’ pulse, Et2(t), with the layer in place; and • a free-space reference pulse, ,which is the received wave without the layer. )(2 tE fs
t
The two measurements should be done with exactly the same distance and antenna setup.
The free space measurement is used as a reference to account for all the effects, which are not
due to the material under test, for example, the antennas and the receiver.
The partial reflection coefficient at the first boundary is defined as the ratio of the first
reflection, Er(t), to the incident pulse, Ei(t):
)()()( 1
fEtEf
i
r≡Γ (A1-1)
Like the TEM transmission line theory, the partial reflection coefficient in terms of the
wave impedance in the layer and the free-space wave impedance is given by:
The derivation of the complex dielectric constant equation based on a multi-pass analysis
is presented in this appendix. Assuming a uniform plane-wave normally incident on an infinite
material slab, the partial reflection coefficient at the first boundary, denoted as ρ , is given by
12
12
ηηηη
ρ+−
= (A 2-1)
where η1 and η2 are the intrinsic impedances of air (essentially free space) and the material of the
slab under test, respectively. The transmission coefficient at the first boundary is obtained from
the relationship 1τ =1+ ρ . At the second boundary, when propagation is in the direction of the
material toward air, the partial reflection coefficient is equal to − ρ , while the partial
transmission coefficient is 2τ =1− ρ . Thus, the first partial transmitted wave through the slab is
T 1τ 2τ Ei =T(1- 2ρ )Ei, where Ei is the incident field and
T (A 2-2) de γ−=
accounts for propagation through the slab thickness, with γ being the complex propagation constant of the slab. Using the bounce diagram shown in Figure A2-1, the overall transmission coefficient through the slab, which is the same as the scattering parameter , is obtained from 21S
( )( ) ( )22
244222
21 1111
TTTTTS
ρρρρρ
−−
=⋅⋅⋅+++−= (A 2-3)
In case of the free-space measurements 0=fsρ , and S21 is given by
dja
fs aeTS β==21 (A 2-4)
Relating the two measurements, one can write the insertion transfer function as
( ) ( )( )22
2
21
21
11
TTT
SSjH
afs ρ
ρω−−
== (A 2-5)
By substituting (A2-1) and (A2-2) into (A2-5) one can write
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