Digital Indoor Transmission System in 60 GHz Band Using Adaptive Beamforming Marcin D ˛ abrowski
Digital Indoor Transmission System in 60GHz
Band Using Adaptive Beamforming
Marcin Dabrowski
ii
Streszczenie
W pracy zbadano celowosc oraz mozliwosci budowy nowych szerokopasmowych
systemów transmisji danych wewnatrz budynków w pasmie nielicencjonowanym
60GHz. W zwiazku z tym autor przeanalizował własciwosci kanału radiowego w tym
pasmie oraz własnosci liniowych szyków antenowych przy załozeniu adaptacyjnego
formowania wiazki. Praca zawiera krytyczny przeglad mozliwych do zastosowa-
nia algorytmów adaptacyjnych wraz z analiza rozwiazan konstrukcji nadajników
i odbiorników. Autor zaproponował takze szczegółowe rozwiazania techniczne doty-
czace realizacji warstwy fizycznej.
W celu przeprowadzenia eksperymentów symulacyjnych, autor opracował pakiet
oprogramowania w srodowisku M�����, które umozliwia symulacje transmisji da-
nych w rozpatrywanym systemie z terminalami ruchomymi. Praca zawiera wyniki
przeprowadzonych badan. W pełni potwierdzaja one przydatnosc algorytmu LMS
do adaptacyjnego formowania wiazki w pasmie 60GHz.
Abstract
Usefulness and possibilities of realization of new broadband indoor transmission
systems in an unlicensed band near 60GHz have been examined in this thesis. To
this end the author has analyzed radio channel characteristics in 60GHz band and
properties of uniform linear arrays of antennas using adaptive beamforming. The
thesis consists of a critical review of possible adaptive algorithms for the considered
application together with the analysis of possible structures of transmitters and
receivers. The author has suggested detailed technical solutions for the realization
of the physical layer.
In order to perform simulation experiments, the author has developed a software
package in M����� environment, which is capable of simulating data transmission
in the proposed system with mobile terminals. The thesis contains results of the
experiments carried out by the author. They fully confirm usefulness of the LMS
algorithm for adaptive beamforming in 60GHz band.
Contents
Glossary xi
1 Introduction 1
1.1 Need for High Speed Wireless Transmission Systems . . . . . . . . . . 1
1.2 Thesis Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Aim and Scope of the Work . . . . . . . . . . . . . . . . . . . 3
1.2.2 Tasks for Further Study and Implementation . . . . . . . . . . 4
2 Transmission in 60GHz Band 5
2.1 Relationship Between Frequency and Wavelength . . . . . . . . . . . 5
2.2 Antenna Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Antenna Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Directivity and Gain . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.2 EIRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Friss Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 Atmosphere Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.6 Material Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.7 Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.7.1 Multipath Channel Model . . . . . . . . . . . . . . . . . . . . 14
2.7.2 Modified Saleh-Valenzuela Model . . . . . . . . . . . . . . . . 15
2.7.3 Doppler Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7.4 Example of Channel Properties . . . . . . . . . . . . . . . . . 18
2.8 Legal Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
iii
iv CONTENTS
3 Antenna Arrays 21
3.1 Uniform Linear Array (ULA) . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Directional Ambiguity . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Example of Patterns . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.3 Element Spacing . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.4 Directivity and Gain . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Principle of Pattern Multiplication . . . . . . . . . . . . . . . . . . . 26
3.3 Rectangular Planar Array . . . . . . . . . . . . . . . . . . . . . . . . 26
4 Array Steering and Adaptive Algorithms 31
4.1 Direct Array Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Mean Square Error (MSE) . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Correlation Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Steepest Descent Method . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.5 Least Mean Square (LMS) Algorithm . . . . . . . . . . . . . . . . . . 38
4.6 Sample Covariance Matrix Inversion (SCMI) . . . . . . . . . . . . . . 40
4.7 MUSIC algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.8 ESPRIT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 System Architecture Concepts 55
5.1 Architecture Functionality and Concepts . . . . . . . . . . . . . . . . 55
5.1.1 Broadway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.1.2 IEEE P802.15 Draft Proposal . . . . . . . . . . . . . . . . . . 56
5.1.3 Integrated Mobile Broadband Mobile System (IBMS) . . . . . 58
5.1.4 Wireless Gigabit With Advanced Multimedia Support (WIG-
WAM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Selected Hardware Concepts . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.1 Remarks on the Number of Elements in Arrays . . . . . . . . 60
5.2.2 RF Front-End Technologies . . . . . . . . . . . . . . . . . . . 61
CONTENTS v
5.2.3 Phase Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.4 DOA Estimation Through Sub-band Sampling . . . . . . . . . 66
6 System Proposal and Simulation Experiments 69
6.1 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2 Phase Shifting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.3 Terminal Addressing and Packet Structure . . . . . . . . . . . . . . . 72
6.4 Connection States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.5 Adaptive Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.6 Developed Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.6.1 Simulation Environment . . . . . . . . . . . . . . . . . . . . . 77
6.6.2 Illustration Scripts . . . . . . . . . . . . . . . . . . . . . . . . 78
7 Final Conclusions 81
vi CONTENTS
List of Figures
2.1 Free space loss at 60GHz . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Broad attenuation peak near 60GHz . . . . . . . . . . . . . . . . . . 13
2.3 Saleh-Valenzuela clusters and rays illustration, [24] . . . . . . . . . . 16
2.4 Laplacian distribution, µ = 0, σ = 1. . . . . . . . . . . . . . . . . . . 17
2.5 Total received power as a function of the distance from the access
point, simulation results from [25] . . . . . . . . . . . . . . . . . . . . 18
2.6 Frequency allocations for 60GHz bands . . . . . . . . . . . . . . . . . 19
3.1 ULA containing N = 6 elements . . . . . . . . . . . . . . . . . . . . . 22
3.2 Wavefront run length differences between antennas in ULA . . . . . . 22
3.3 Example of ULA pattern with N = 2, θ0 = π/6, β = 0. . . . . . . . . 24
3.4 Example of ULA pattern with N = 4, θ0 = π/6, β = 0. . . . . . . . . 25
3.5 Example of ULA pattern with N = 8, θ0 = π/6, β = 0. . . . . . . . . 26
3.6 Example of influence of ULA element spacing on its directional char-
acteristic, d = λ/4, N = 4, θ0 = π/6, β = 0. . . . . . . . . . . . . . . 27
3.7 Example of influence of ULA element spacing on its directional char-
acteristic, d = λ/2, N = 4, θ0 = π/6, β = 0. . . . . . . . . . . . . . . 27
3.8 Example of influence of ULA element spacing on its directional char-
acteristic, d = λ, N = 4, θ0 = π/6, β = 0. A pair of grating lobes
present. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
vii
viii LIST OF FIGURES
3.9 Example of influence of ULA element spacing on its directional char-
acteristic, d = 2λ, N = 4, θ0 = π/6, β = 0. Three pairs of grating
lobes present. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.10 Rectangular planar array . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.11 Example of a rectangular planar array pattern with dx = dy = λ/2,
θ0 = 0, φ0 = 0, Nx = Ny = 8, [37] . . . . . . . . . . . . . . . . . . . . 29
4.1 Desired signal and intereference signal impinge an array . . . . . . . . 32
4.2 Model for an unknown system . . . . . . . . . . . . . . . . . . . . . . 33
4.3 Unknown system identification . . . . . . . . . . . . . . . . . . . . . . 35
4.4 An example of MSE surface . . . . . . . . . . . . . . . . . . . . . . . 36
4.5 Applying weights to antenna outputs used for receiving the desired
signal from the desired direction . . . . . . . . . . . . . . . . . . . . . 40
4.6 Matrix inversion issue, above: two examples of |R|, white color showsmaximum values, below: patterns obtained by R, a) R close to iden-
tity, b) R close to singular . . . . . . . . . . . . . . . . . . . . . . . . 42
5.1 Pilot and data subcarriers in IEEE 802.15 draft proposal for 60GHz
OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2 User groups channel allocation . . . . . . . . . . . . . . . . . . . . . . 57
5.3 WIGWAM demonstrator receiver, [64] . . . . . . . . . . . . . . . . . 59
5.4 WIGWAM demonstrator receiver parts, [64] . . . . . . . . . . . . . . 60
5.5 Virtual increase of the number of elements, [34] . . . . . . . . . . . . 60
5.6 Example of ULA with patch antennas . . . . . . . . . . . . . . . . . . 61
5.7 A GaAs MESFET transistor current and power gains as functions of
frequency, [59] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.8 Receiver design, [57] . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.9 CMOS receiver details, [57] . . . . . . . . . . . . . . . . . . . . . . . 63
5.10 CMOS receiver die photograph, [57] . . . . . . . . . . . . . . . . . . . 64
5.11 Modulator-type phase shifter . . . . . . . . . . . . . . . . . . . . . . . 64
ACKNOWLEDGEMENT ix
5.12 PIC as a phase shifter . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.13 Transmitter with MEMS phase shifters, [36] . . . . . . . . . . . . . . 65
5.14 3-bit MEMS phase shifter frequency-dependent operation, [36] . . . . 66
5.15 ULA containing eight boards with IF beamformers and patch anten-
nas, [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.16 Down-conversion and subband sampling in order to estimate DOA, [33] 68
5.17 System with sub-band sampling in order to estimate DOA, [33] . . . 68
6.1 BPSK baseband and passband signals . . . . . . . . . . . . . . . . . . 71
6.2 Average BPSK baseband signal spectrum . . . . . . . . . . . . . . . . 72
6.3 PSDU scrambler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.4 Physical layer block diagram applied in simulation of the transmitter 75
6.5 Recevier block diagram with per frame LMS part . . . . . . . . . . . 76
6.6 Simulation window screenshots from M����� . . . . . . . . . . . . . 79
6.7 beamformLms.m window part screenshot . . . . . . . . . . . . . . . . . 80
x ACKNOWLEDGEMENT
Acknowledgement
I would like to thank my supervisor Professor Krzysztof Wesołowski
for suggesting the fascinating field of adaptive beamforming.
I also appreciate his stimulation, consultation, and the literature support.
Glossary
2-D two-dimensional
3-D three-dimensional
A/D Analog/Digital
AFE Analog Front-End
AOA Angle of Arrival
AP Access Point
AWGN Additive White Gaussian Noise
BiCMOS Integration of BJT and CMOS technologies into a single device
BJT Bipolar Junction Transistor
BPF Band Pass Filter
BPSK Binary Phase Shift Keying
CEPT European Conference of Postal and Telecommunications Administrations
CMOS Complementary-symmetry Metal Oxide Semiconductor
D/A Digital/Analog
DBF Digital Beam Forming (Former)
DOA Direction of Arrival
xi
xii GLOSSARY
EIRP Effective (Equivalent) Isotropic Radiation Power
ESPRIT Estimation of Signal Parameters via Rotational Invariance Techniques
FCC Federal Communications Commission
FPGA Field Programmable Gate Array
FSL Free Space Loss
GaAs Gallium Arsenide
GMSK Gaussian Minimum Shift Keying
HEMPT High Electron Mobility Pseudomorphic Transistor
HPA High-Power Amplifiers
IBMS Integrated Broadband Mobile System
IC Integrated Circuit
IEEE Institute of Electrical and Electronics Engineers
IF Intermediate Frequency
ISM Industrial Scientific Medical
IST Information Society Technologies
ITU International Telecommunication Union
LDPC Low Density Parity Code
LMS Least Mean Square
LNA Low-Noise Amplifier
LO Local Oscillator
LOS Line of Sight
LPF Low Pass Filter
MAC Medium Access Control
MMIC Monolithic Microwave Integrated Circuit
MMW Millimeter Wave
MSE Mean Square Error
MUSIC Multiple Signal Classification
OFDM Orthogonal Frequency Division Modulation
xiii
PAN Personal Area Network
PDF Probability Density Function
PHY Physical layer
PIC Pass Invert Cancel
PLL Phase Locked Loop
PPDU Physical layer Protocol Data Unit
PSD Power Spectrum Density
PSDU Physical layer Service Data Unit
QAM Quadrature Amplitude Modulation
QMMIC Quasi-Monolithic Microwave Integrated Circuit
QoS Quality of Service
QPSK Quadrature Phase Shift Keying
RF Radio Frequency
RMS Root Mean Square
SCMI Sample Covariance Matrix Inversion
SiGe Silicon Germanium
SiGe:C Blend of Silicon Germanium and Carbon
ULA Uniform Linear Array
UWB Ultra Wideband
VCO Voltage Controlled Oscillator
WARC World Administrative Radio Conference
WIGWAM Wireless Gigabit with Advanced Multimedia
WLAN Wireless Local Area Network
WPAN Wireless Personal Area Network
xiv GLOSSARY
Chapter 1
Introduction
1.1 Need for High Speed Wireless Transmission
Systems
A success of digital wireless transmission solutions in unlicensed bands can be ob-
served in recent years. Equipment such as WiFi access points, antennas, and radio
cables are now commonly available. Radio unlicensed access to the Internet is to-
day an efficient alternative to the offer of big and inert telecommunication compa-
nies, which typically do not provide broadband access in rural areas. The practice
of recent years has shown that networks such as WiFi are reasonable for indoor
point-multipoint access as well as long distance point-point wireless bridges. How-
ever, systems defined by IEEE 802.11, Hiperlan, and WiMax standards have several
limitations among which the most significant is the effective throughput from the
end-user point of view. Even if we consider a WiFi wireless bridge operation mode
and transmission only between two terminals in indoor environment, the maximum
physical layer rate is 54 Mbit/s, which is much less than capacities of current cable
solutions, nor it can cover today needs. This is because the throughput of this level is
not sufficient for such applications as e.g. real time digital video transmission. The
present-day Personal Area Networks (PANs) were designed for short-range trans-
mission between devices like mobile phones and external microphone sets and are
1
2 CHAPTER 1. INTRODUCTION
not satisfying the growing throughput demands.
Due to above mentioned limitations of existing systems, a need for higher data
rate wireless solutions emerges. 60GHz band gives an opportunity for building a
new standard of PANs, which would allow much higher transfer rates. The new
system would be exploited in the following indoor applications:
• wireless access to 4G networks and the Internet, media supply in public areas
such as trains and busses,
• communication between mobile data terminals,
• image acquisition from digital cameras to storage devices, e.g. downloading
JPEG images from camera into laptop,
• real time video signal transmission from camera to storage device, e.g. DVD
recorder,
• raw video signal transmission from decoder to displaying device, e.g. operation
as a wireless interface between LCD screen and DVB-T STB (set-top box) or
a DVD player.
Example: Consider real time communication between a typical video camera and
a DVD recorder. Assume raw digital video signal transmitted, thus the required
throughput should be
T = (768 columns× 576 lines) /frame× (1.1)
24 bits/pixel× 25 frames/s ≈ 265Mbits/s
None of present-day indoor wireless systems working in 2.4GHz, 5.4GHz, 5.8GHz,
or other bands can satisfy (1.1).
A broad air absorption band near 60GHz gives a place for yet another unlicensed
digital transmission system. The highest specific attenuation in that band is about
17.5 dB/km. However the most significant attenuation is due to free space loss
(FSL) at 60GHz, which at the distance 100m away from the transmitter reaches
1.2. THESIS DESCRIPTION 3
100 dB. Millimeter waves are strongly attenuated by walls and other materials, thus
access points should be located in every room. In real indoor environments, strong
multipath fading is observed. Because of high attenuation, in order to build inexpen-
sive receivers using circuits with average gain and noise characteristics, directional
antennas should be used. Furthermore, as the terminals are assumed mobile, adap-
tive beamforming must be applied. These two observations are motivation for this
thesis.
1.2 Thesis Description
1.2.1 Aim and Scope of the Work
The aim of this thesis consists in examination of usefulness and possibilities of
realization of new broadband indoor transmission systems in unlicensed bands near
60GHz. The thesis describes the most important issues emerging with the advent
of 60GHz systems. The discussed fields include such topics as:
• Propagation environment at 60GHz and channel models used in indoor trans-
mission (Chapter 2),
• Properties of antenna arrays, particularly uniform linear arrays (Chapter 3);
in this work mainly 2-D models were discussed, however, a rectangular planar
array with 3-D pattern has been also briefly described,
• Mathematical basis for selected methods of adaptive beamforming (Chapter 4),
• A selection of architecture, functionality and hardware issues has been pre-
sented in Chapter 5, as the field of 60GHz mobile demonstrator systems is
now being intensively discussed and investigated by many research teams.
The experimental part of this work described in Chapter 6 consisted in proposing
and testing a system for transmission between mobile terminals. The physical layer
of such a system has been proposed and simulated by the author. A system with two
4 CHAPTER 1. INTRODUCTION
mobile terminals with uniform linear arrays (ULAs) has been developed inM�����.
An adaptive LMS algorithm per frame has been proposed and tested. Performed
simulations confirm that the implemented version of LMS leads to the optimal beam
shape within satisfactory time. Channel models used in indoor transmission have
been described in this thesis, however, they have not been used in simulations.
A collection of M����� scripts developed by the author, which is a part of this
project, is capable of simulating data transmission in the proposed, experimental
broadband transmission system with mobile terminals operating in an unlicensed
band near 60GHz.
1.2.2 Tasks for Further Study and Implementation
The developed software includes or may straightforwardly be extended in order to
include:
• different propagation environments, real channel models described in further
course may be used instead of an anechoic chamber,
• noise, e.g. the thermal noise,
• non-isotropic array elements,
• 3-D space, planar arrays,
• different adaptive algorithms, not only the LMS.
Error analysis of adaptive algorithms may be elaborated. A future cooperation
with RF circuitry and antenna design teams would be valuable. Thus, the sim-
ulations would assume real antenna patterns and data flow between stages such
baseband processors, the IF and RF blocks of the devices.
Chapter 2
Transmission in 60GHz Band
2.1 Relationship Between Frequency and Wave-
length
The speed of the electromagnetic wave in vacuum equals c ≈ 2.99792458 · 108m/ s.In further course we assume that sinusoidal wave velocity as well as group velocity
in atmosphere is c ≈ 3 · 108m/ s. A sinusoidal wave of frequency f0 = 60GHz =
6 · 1010Hz has the wavelength equal to
λ0 =c
f0≈ 3 · 108
6 · 1010 m = 0.5 · 10−2m = 5mm
Thus a band near 60GHz is referred to as millimeter wavelength (MMW) band.
The range of frequencies 40—70GHz is called the V-band.
2.2 Antenna Fields
Consider a transmitting antenna located close to the origin of a 3-D coordinate sys-
tem. Let the vector r = 1rr be the location of an observation point. Electromagnetic
field radiated by antenna in far-field region (r → ∞) can be expressed as propor-
tional to general complex amplitude vector A(k), where k is the wave propagation
5
6 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
vector defined as
k = 1kk = 1k2π
λ
where λ is the wavelength and 1k is the unit vector towards the direction of the
wave propagation. The electric and magnetic fields may expressed as
E(r) ∼ A(k)e−jkr
r
H(r) ∼ [1k ×A(k)]e−jkr
r
As far-field is considered, the location vector r and propagation vector k have the
same directions, and they are equal
1r = 1k
thus kr = kr. The complex amplitude vector is defined in such a manner, that
|A(k)|2 has the unit [W/ sr] (watts per steradian). It can be decomposed into two
components
A(k) = uA(k,u) + vA(k,v)
where
A(k,u) = A(k)u∗
A(k,v) = A(k)v∗
The u and v vectors are orthogonal unitary vectors lying on the plane tangent to
k, thus they satisfy
u = v = 1
uv∗ = vu∗ = 0
uk = vk = 0
The pairs (k,u) and (k,v) are referred to as polarization states of the considered
wave. In far-field region the field intensity in state (k,u) is defined by
Iu(k) = |A(k,u)|2
The total radiation intensity for both polarization states takes the form
I(k) = |A(k)|2= |A(k,u)|2+ |A(k,v)|2 (2.1)
2.3. ANTENNA PROPERTIES 7
2.3 Antenna Properties
2.3.1 Directivity and Gain
Consider a generator producing a signal of power Pgen and feeding the transmitter
antenna. Because of impedance mismatch between the antenna and its feeder, the
power accepted by the antenna is
Pacc = (1− |Γ|2)Pgen (2.2)
where Γ is the amplitude reflection coefficient. Due to material loss, the antenna
radiates only a part of its accepted power
Prad = ηPacc (2.3)
where η is the antenna efficiency. The directivity of a given antenna towards the
direction k is defined by
D(k) =4π
PradI(k)
where I(k) is defined by (2.1). The gain (in [38] referred to as realized gain) is
defined as
G(k) =4π
Pgen
I(k) (2.4)
Using (2.2) and (2.3), the relationship between the directivity and the gain takes
the form
G(k) = η(1− |Γ|2)D(k)
Note that G(k) ≤ D(k).
2.3.2 EIRP
Consider an ideal isotropic antenna, which has the gain equal to
Giso(k) = 1
8 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
Assume we observe the field intensity I(k) in some direction k. This field could be
produced by an isotropic antenna as well as by a real antenna with gain G(k):
I(k) =
=1︷ ︸︸ ︷Giso(k) · EIRP(k)
4π=G(k) · Pgen
4π(2.5)
where EIRP (Effective (Equivalent) Isotropic Radiated Power) is the power fed to
the hypothetical ideal isotropic antenna. Simplifying (2.5) we get
EIRP(k) = G(k) · Pgen
It may be defined also for the maximum radiation direction
EIRP = maxk
{G(k)} · Pgen
Example: According to recommendations, the power of a data transmission device
at 60GHz may be at most 100mW (EIRP). Calculate how much power we can feed
to each antenna of four element (N = 4) uniform linear array (ULA) with isotropic
elements. Neglect the material loss and the impedance mismatch. Solution: Using
formula (3.6), which will be discussed in the chapter Antenna Arrays, a ULA with
isotropic elements has the maximum gain GULA = N2 = 16. The power per element
is therefore EIRP /GULA = 100mW/16 ≈ 6.25mW.
2.4 Friss Formula
Consider communication between two terminals in free space and assume that they
are located in far-fields of each other. Let the power produced by the generator in
terminal 1 equal P1 and the power passed to the receiver in terminal 2 equal P2.
The relationship between these powers is given by
P2 = P1
(λ
4πR
)2pG1(k1)G2(−k1)
where R is the distance between terminals, k1 is the propagation vector of the
transmitting antenna, and p is the polarization efficiency defined by
p = |u1u2|2
2.5. ATMOSPHERE LOSS 9
where u1 and u2 are the polarization vectors of the transmitting and the receiving
antenna. In case of the perfect polarization match
u2 = u∗1
We take the conjugate because of opposite propagation directions of the antennas
[38]. Therefore
p = |u1u∗1|2 = 1 (2.6)
Using (2.6) we finally obtain the so-called Friss transmission formula
P2P1
=
(λ
4πR
)2G1(k1)G2(−k1) (2.7)
Free-space loss (FSL) factor is defined by:
FSL =
(4πR
λ
)2
One may notice that the lower the wavelength, the higher is the loss, which is the
reason of limiting millimeter wavelength systems to indoor applications. Figure
2.1 shows free space loss in dB (10 log10 (FSL)) as a function of distance from the
transmitter, which radiates a sinusoidal wave at f0 = 60GHz.
A proof of the Friss formula, showing particularly that the FSL factor is a func-
tion of λ is beyond the scope of this work. It may be found in [38], where the
reciprocity principle was used in the form presented in [11].
2.5 Atmosphere Loss
ITU-R Recommendation P.676-5 [52] presents methods for estimating gaseous atten-
uation in different propagation conditions determined by wave frequency, altitude,
air pressure, and other factors. The document includes formulas for estimating the
attenuation due to dry air and water vapor near 60GHz. The given formulas are
valid for altitudes from the sea level to 5 km.
10 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
0 10 20 30 40 50 60 70 80 90 100
20
40
60
80
100
Distance from the transmitter [m]
Free sp
ace loss [dB]
Figure 2.1: Free space loss at 60GHz
The specific attenuation due to dry air for f between 54GHz and 66GHz can be
estimated by
γo [dB / km] = exp
(54−N ln (γ0 (54)) (f − 57) (f − 60) (f − 63) (f − 66) /1944−−57−N ln (γ0 (57)) (f − 54) (f − 60) (f − 63) (f − 66) /486+
+60−N ln (γ0 (60)) (f − 54) (f − 57) (f − 63) (f − 66) /324−−63−N ln (γ0 (63)) (f − 54) (f − 57) (f − 60) (f − 66) /486+
+66−N ln (γ0 (66)) (f − 54) (f − 57) (f − 60) (f − 63) /1944)fN
(2.8)
2.5. ATMOSPHERE LOSS 11
where
N = 0 for f ≤ 60GHz, N = −15 for f > 60GHz
γo (54) = 2.136r1.4975p r−1.5852t exp (−2.5196(1− rt))
γo (57) = 9.984r0.9313p r2.6732t exp (0.8563(1− rt))
γo (60) = 15.42r0.8595p r3.6178t exp (1.1521(1− rt))
γo (63) = 10.63r0.9298p r2.3284t exp (0.6287(1− rt))
γo (66) = 1.935r1.6657p r−3.3714t exp (−4.1612(1− rt))
rp = p/1013
rt = 288/(273 + t)
The user given parameters are:
f [ GHz] frequency,
p [hPa] pressure,
t [ ◦C] temperature.
The water vapor specific attenuation is estimated for f < 350GHz by
γw [dB / km] = (2.9)
=
(3.13 · 10−2rpr2t + 1.76 · 10−3ρr8.5t + r2.5t
(3.84ξw1g22 exp (2.23 (1− rt))(f − 22.234)2 + 9.42ξ2w1
+
+10.48ξw2 exp (0.7 (1− rt))(f − 183.31)2 + 9.48ξ2w2
+0.078ξw3 exp (6.4385 (1− rt))(f − 321.226)2 + 6.29ξ2w3
+
+3.76ξw4 exp (1.6 (1− rt))(f − 325.153)2 + 9.22ξ2w4
+26.36ξw5 exp (1.09 (1− rt))
(f − 380)2+
+17.87ξw5 exp (1.46 (1− rt))
(f − 448)2+883.7ξw5g557 exp (0.17 (1− rt))
(f − 557)2+
+302.6ξw5g752 exp (0.41 (1− rt))
(f − 752)2
))f 2ρ · 10−4
12 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
where
ξw1 = 0.9544rpr0.69t + 0.0061ρ
ξw2 = 0.95rpr0.64t + 0.0067ρ
ξw3 = 0.9561rpr0.67t + 0.0059ρ
ξw4 = 0.9543rpr0.68t + 0.0061ρ
ξw5 = 0.955rpr0.68t + 0.006ρ
g22 = 1 + (f − 22.235)2 / (f + 22.235)2
g557 = 1 + (f − 557)2 / (f + 557)2
g752 = 1 + (f − 752)2 / (f + 752)2
rp = p/1013
rt = 288/(273 + t)
The user given parameters are:
f [ GHz] frequency,
p [hPa] pressure,
t [ ◦C] temperature,
ρ [ g/m3] water vapor density.
The total attenuation of the path is
A [dB] = (γo + γw) r0 (2.10)
where γo and γw are defined by (2.8) and (2.9), r0 [ km] is the path length.
A broad attenuation peak can be observed near 60GHz, the recommendation
says many oxygen absorption lines merge in that band. This is the reason for which
the band has been assigned to unlicensed transmission. The specific attenuations
γo and γw and the total specific attenuation γo + γw are shown in Figure 2.2 with
p = 1013 hPa, t = 20 ◦C, ρ = 7.5 g/m3. In the range 54GHz — 66GHz the formulas
(2.8) and (2.9) are to be used. The recommendation contains formulas for frequencies
below 54GHz and above 66GHz, which were used as well.
2.6. MATERIAL LOSSES 13
f[GHz]10
010
110
210
310
-4
10-3
10-2
10-1
100
101
102
f[GHz]
γo, γ
w [d
B/k
m]
50 55 60 65 700
5
10
15
20
γo+γw [dB/k
m]
γo
γw
60GHz
Figure 2.2: Broad attenuation peak near 60GHz
2.6 Material Losses
Millimeter wave attenuation strongly depends on the kind of material it impinges
on. High frequency implies high reflection and attenuation in materials such as
concrete and wood. A 15 cm thick concrete wall attenuates up to 36 dB, whereas
a glass slab attenuates from 3 to 7 dB. Thus floors and concrete walls determine
the cell boundaries. Assuming wireless access scenario, the access points should be
located in every room and corridor. Thanks to relatively small cells, echo paths are
shorter than those at lower frequencies.
2.7 Channel Models
Channel at 60GHz is strongly multipath. Millimeter waves rather reflect from walls
than travel through them. We can neglect wall penetrating waves, thus e.g. mul-
tiwall models, commonly used for 2.4GHz band are not to be applied in this case.
Atmosphere absorption given by (2.10) may be neglected in indoor channel simula-
tions.
14 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
2.7.1 Multipath Channel Model
Let a terminal transmit a signal
s(t) = u(t)ej2πfct
where u(t) is the baseband signal and fc is the carrier frequency. The signal at the
receiving terminal equals
r(t) =
L(t)−1∑
i=0
ri(t)
It is a sum of rays coming from L(t) dominant paths, which appear as a result of
reflection, diffraction, and scattering. Our channel model assumes that the com-
ponents ri(t) undergo additional local scattering in the vicinity of the receiving
terminal, thus they take the form
ri(t) =∞∑
j=0
rij(t) =∞∑
j=0
αiju(t− τ ij)ej2πfc(t−τ ij) ≈ (2.11)
≈ u(t− 〈τ i〉)ej2πfct∞∑
j=0
αije−j2πfcτ ij
where αij and τ ij are random attenuations and random delays introduced by the
j-th locally scattered ray of the i-th ray, 〈τ i〉 = E {τ ij} is the expected value of the
delays. We assume that the period of u(t) is much longer than the ray delays, thus
we approximate delays of the baseband signal by the delay expected value. Using
(2.11), the received signal may be expressed in the form
r(t) =
L(t)−1∑
i=0
ri(t) =
L(t)−1∑
i=0
u(t− 〈τ i〉)ej2πfct∞∑
j=0
αije−j2πfcτ ij = (2.12)
=
L(t)−1∑
i=0
u(t− 〈τ i〉)∞∑
j=0
αije−j2πfcτ ij
ej2πfct =
Substituting
ci(t) =∞∑
j=0
αije−j2πfcτ ij (2.13)
into (2.12) we obtain a brief form
r(t) =
L(t)−1∑
i=0
u(t− 〈τ i〉)ci(t)
ej2πfct = ur(t)ej2πfct (2.14)
2.7. CHANNEL MODELS 15
where ur(t) is the baseband signal at the receiver. Equation (2.14) leads to the
conclusion that the impulse response of the channel equals at instant t:
h(τ ) =
L(t)−1∑
i=0
ci(t)δ (τ − 〈τ i〉) (2.15)
The RMS delay spread τRMS is defined as the variance of 〈τ i〉, where the probabilisticmeasure (the weight set) are the variances σ2i = E
{|ci(t)|2
}, which represent powers
of the paths:
τRMS =
∑L(t)−1i=0 σ2i 〈τ i〉2∑L(t)−1
i=0 σ2i
Note that in (2.15) the coefficients ci(t) take values with respect to the long-term
time variable t whereas τ is used as the short-term time variable. Thus the coef-
ficients ci(t) may be considered constant in (2.15). The in-phase and quadrature
components of ci(t) can be obtained from (2.13):
cIi (t) =∞∑
j=0
αij cos(2πfcτ ij)
cQi (t) =∞∑
j=0
αij sin(2πfcτ ij)
Due to infinite sums of functions of random variables αij and τ ij, the components
cIi (t) and cQi (t) have both Gaussian distribution. Note that they have zero mean
and equal variances as well. Thus the absolute values (i.e. envelopes) |ci(t)| =∣∣∣cIi (t) + jcQi (t)∣∣∣ have Rayleigh distribution. Let us now introduce the modification
of (2.15), which may be used for uniform linear antenna arrays:
h(τ ) =
L(t)−1∑
i=0
ci(t)v(θl)δ (τ − 〈τ i〉)
where v(θl) is the array propagation vector.
2.7.2 Modified Saleh-Valenzuela Model
The model used for simulating indoor environments [20] is a multipath channel
model based on the clustering phenomenon. Rays arrive at the receiver in groups
16 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
referred to as clusters. Both entire clusters and the rays within clusters change their
amplitudes in time (figure 2.3).
Figure 2.3: Saleh-Valenzuela clusters and rays illustration, [24]
The impulse response of the channel is given by
h(t) =∞∑
i=0
∞∑
j=0
cijδ (t− Ti − τ ij)
where i is the cluster index and j counts the rays within clusters, Ti is the i-th
cluster arrival time and τ ij is the j-th ray arrival times within the i-th cluster. The
absolute values of the weights cij are Rayleigh distributed and the weight variance
is
E{c2ij}= E
{c200}e−GTi−gτ ij
where G and γ constants are referred to as the cluster and ray time decay factors.
The modification of the Saleh-Valenzuela model assumes that the channel impulse
response may be decomposed into statistically independent components of time and
angle of arrival:
h(t, θ) = h(t)h(θ)
2.7. CHANNEL MODELS 17
where the angular impulse response h(θ) is given by
h(θ) =∞∑
i=0
∞∑
j=0
cijδ (θ −Θi − ωij)
and Θi is the i-th cluster angle of arrival, which is a random variable with uniform
distribution over 〈0, 2π). The random variable ωij is the j-th ray angle relative to
the direction of the i-th cluster. It has Laplacian distribution
PDF(ωij) =1√2σe−
∣∣∣∣
√2ωij
σ
∣∣∣∣
of zero mean and standard deviation σ.It has a strong peak at ωij = 0, which means
rays within a cluster are concentrated close to the main cluster direction.
-3 -2 -1 0 1 2 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
ωij
PD
F( ω
ij)
Figure 2.4: Laplacian distribution, µ = 0, σ = 1.
2.7.3 Doppler Shift
The maximum Doppler frequency shift is given by
∆fmax = fcv
c(2.16)
18 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
where fc is the carrier frequency, v is the mobile terminal velocity and c is the speed
of the light. As indoor application is considered, we assume the terminals move due
to walking with v = 1m/ s. Substituting fc = 60GHz and v = 1m/ s into (2.16) we
have ∆fmax = 200Hz. Calculation done in [25] for OFDM with 1024 sub-carriers
show that the Doppler shift has no significant influence on performance of systems
at 60GHz. Thus the terminal motion can be neglected in the indoor scenario.
2.7.4 Example of Channel Properties
Objects in line of sight (LOS) between terminals cause that shadowmargin should be
taken into consideration, which is assumed 10 dB on average. Simulations described
in [25] show the received power rapidly changes along the path. A plot of the total
received power as a function of the distance from the access point is shown in figure
2.5. Saleh-Valenzuela model was used in the simulation. RMS delay spread τRMS
Figure 2.5: Total received power as a function of the distance from the access point,
simulation results from [25]
2.8. LEGAL ISSUES 19
fell between 18 and 20 ns in the given example. However it can reach even 100 ns if
omnidirectional antennas are used in APs and large areas are covered [61].
2.8 Legal Issues
The band 54-60GHz has been internationally adjusted by ITU for unlicensed data
transmission [51]. Transmitter power has been limited to 100mW EIRP [49]. Ac-
cording to recommendations, the band near 60GHz has been allocated for that pur-
pose in many countries. Japan has allocated quite a broad range between 59GHz
and 66GHz. FCC granted the scope 59-64GHz in the USA. In Europe the unlicensed
band is expected to be finally allocated in the range 59-62GHz. A comparison of
both licensed and unlicensed frequency allocations is shown in figure 2.6.
54 55 56 57 58 59 60 61 62 63 64 65 66
ITU ISM
54 60 61 61.5
Europe59 62
59 66
Japan
59 64
USA
GHz
Figure 2.6: Frequency allocations for 60GHz bands
According to WARC 1979 regulations for Region 2, ITU assigned 60GHz band
for radar operation. The V-band is used for mostly short-range tracking [5], however,
such coexistence will not cause interference thanks to high FSL and air attenuation.
In Poland unlicensed transmission issues are regulated by the governmental edict
[53]. So far the band 61.0−61.5GHz has been allocated as general purpose band for
ISM devices and video signal transmission. The maximum power is 100mW EIRP.
20 CHAPTER 2. TRANSMISSION IN 60GHZ BAND
60GHz band has not been assigned for unlicensed broadband data transmission.
For this purpose the only bands allocated in Poland are enumerated in Table 2.1.
Table 2.1: Unlicensed data transmission bands in Poland, excerpt from [53].
Frequency range Radiated power Remarks
2400.0− 2483.5MHz 100mW (EIRP)
5150− 5250MHz 200mW (EIRP) indoor use only
5250− 5350MHz 200mW (EIRP) indoor use only
5470− 5725MHz 1000mW (EIRP)
17.1− 17.3GHz 100mW (EIRP)
Note that band allocations differ considerably in the above-mentioned countries.
We should expect that this situation will undergo some further discussion and better
uniformity as a result. There are different bandwidths assigned, according to the
table:
Japan USA Europe ITU
6GHz
7GHz 6GHz 3GHz (only 1GHz overlapping
with Japan, USA and Europe)
Design of universal devices forces the assumption of the most restrictive options
for the bandwidth. For instance in the research project [50], 3GHz bandwidth has
been assumed for early design and simulations.
Chapter 3
Antenna Arrays
3.1 Uniform Linear Array (ULA)
Consider an array consisting of N isotropic antennas distributed along a line with
uniform element spacing d. The angle measurement convention used in this work
is shown in Figure 3.1. The angle θ denotes the incident wave direction and it
is the terminal radiation pattern variable. It is calculated relative to the terminal
diagonal. The angle β is the entire terminal rotation. Note that if we change β by
∆β, we must add −∆β to the incident wave direction θ at the same time, having
assumed the wave source a has constant position. The author decided to consider
counterclockwise angles positive, as it is often done in the elementary mathematics.
However, in literature of the field of beamforming the opposite convention is widely
adopted, e.g. in [37]. In examples of polar plots of array patterns it is assumed that
the ULA is directed as in Figure 3.1.
Signal delays or phase shifts in case of sinusoidal signals are observed between
adjacent array elements. If a signal is incoming from direction θ, the phase difference
between the elements of indices i and i+ 1 is equal to
∆ϕ = 2πd
λsin θ (3.1)
We easily obtain (3.1) using wavefront run length difference shown in Figure 3.2.
Every i-th antenna output is multiplied by a complex weight wi. Assume a plane
21
22 CHAPTER 3. ANTENNA ARRAYS
θ>0
12
34
56
d
β>0
Figure 3.1: ULA containing N = 6 elements
θ
d
i i+1
θ
. d sinθ
Figure 3.2: Wavefront run length differences between antennas in ULA
wave of the form Aej2πfct impinges on the array at angle θ. The array output takes
the form
y(t) = Aej2πfct(w∗1 + w
∗2e
j∆ϕ + w∗3ej2∆ϕ + . . .+ w∗Ne
j(N−1)∆ϕ)=
= Aej2πfct(w∗1 + w
∗2e
j2π dλsin θ + w∗3e
j2π2 dλsin θ + . . .+ w∗Ne
j2π(N−1) dλsin θ)=
= Aej2πfctF (θ)
where F (θ) is referred to as the array factor or the array pattern. Conjuctions are
taken to obtain a regular scalar product in (3.3). Let us introduce the weight vector
3.1. UNIFORM LINEAR ARRAY (ULA) 23
as
wT = [w1, w2, . . . , wN ]
and the array propagation vector as
vT =[1, ej
2πλd sin θ, ej
2πλ2d sin θ, . . . ej
2πλ(N−1)d sin θ
](3.2)
Now the array factor may be written in the form
F (θ) = wHv (3.3)
and it has the interpretation of far field radiation array pattern. We can steer the
array pattern through the weight vector v, a ULA is optimally steered towards the
angle θ0 if the weight is in the form
wT =[1, ej
2πλd sin θ0, ej
2πλ2d sin θ0, . . . ej
2πλ(N−1)d sin θ0
](3.4)
Using (3.4), the pattern peak will appear at the angle θ0:
F (θ0) =[1, e−j
2πλd sin θ0 , e−j
2πλ2d sin θ0 , . . . e−j
2πλ(N−1)d sin θ0
]
1
ej2πλd sin θ0
...
ej2πλ(N−1)d sin θ0
=
= N
3.1.1 Directional Ambiguity
Note that a ULA consisting of isotropic antennas steered towards θ0 will have addi-
tional pattern maximum at π − θ0. Indeed,
sin θ0 = sin (π − θ0)
thus using π − θ0 instead of θ0 in (3.4) will effect
F (θ0) = F (π − θ0) (3.5)
which can be observed for instance in Figures 3.3 and 3.4.
24 CHAPTER 3. ANTENNA ARRAYS
3.1.2 Example of Patterns
ULA patterns F (θ) with N ∈ {2, 4, 8}, d = λ2, θ0 = π/6, β = 0 are shown in Figures
3.3, 3.4 and 3.5. The absolute |F (θ)| values are presented as polar plots as well as
in the form
10 log(|F (θ)|2 /maxθ|F (θ)|2) = 10 log(|F (θ)|2 /N2) = 20 log(|F (θ)| /N)
in rectangular coordinates. The phases of the patterns are shown as arg {F (θ)}plots. Thin straight lines indicate values of θ0.
-100 0 100-50
-40
-30
-20
-10
0
θ [°]
|F|/m
ax(|
F|)
[dB
]
-100 0 100
-3
-2
-1
0
1
2
3
θ [°]
arg
(F)
[rad
]
Figure 3.3: Example of ULA pattern with N = 2, θ0 = π/6, β = 0.
3.1.3 Element Spacing
In most cases the element spacing d = λ2is used. If the distances between antennas
are larger, additional main lobes called the grating lobes are observed. Patterns
computed for N = 4, θ0 = π/6 and four different values of d ∈ {λ/4, λ/2, λ, 2λ} areshown in figures 3.6 - 3.9. Note the value of d is a trade-off between the angular
width of the main lobe and the number of grating lobes. The choice d = λ2is
3.1. UNIFORM LINEAR ARRAY (ULA) 25
-100 0 100-50
-40
-30
-20
-10
0
θ [°]
|F|/m
ax(|
F|)
[dB
]
-100 0 100
-3
-2
-1
0
1
2
3
θ [°]
arg
(F)
[rad
]
Figure 3.4: Example of ULA pattern with N = 4, θ0 = π/6, β = 0.
optimal in the meaning it gives the narrowest main lobes if the smallest number of
main lobes including grating lobes (equal 2) is assumed.
3.1.4 Directivity and Gain
The array factor F (θ) describes how the complex amplitude of the radiated wave
changes around the array. If each element in a ULA has directivity D(k) = D(θ)
and gain G(k) = G(θ) then the array gain is
DULA(θ) = |F (θ)|2D(θ)
GULA(θ) = |F (θ)|2G(θ)
If ULA consists of isotropic elements, the maximum array gain equals
GULA = GULA(θ0) = |F (θ0)|2 = N2 (3.6)
26 CHAPTER 3. ANTENNA ARRAYS
-100 0 100-50
-40
-30
-20
-10
0
θ [°]
|F|/m
ax(|
F|)
[dB
]
-100 0 100
-3
-2
-1
0
1
2
3
θ [°]
arg
(F)
[ra
d]
Figure 3.5: Example of ULA pattern with N = 8, θ0 = π/6, β = 0.
3.2 Principle of Pattern Multiplication
So far examples of arrays with isotropic elements have been presented. However,
more accurate results can be obtained with the assumption that the elements are
non-isotropic and have patterns f(θ). Then the total array pattern results from the
principle of pattern multiplication:
K(θ) = f(θ)F (θ) (3.7)
This principle is also useful for planar array calculations, where we can use the 3-D
version:
K(θ, φ) = f(θ, φ)F (θ, φ) (3.8)
3.3 Rectangular Planar Array
A rectangular planar array consists of Nx×Ny isotropic elements distributed over a
rectangular grid with element spacing dx and dy (Figure 3.10). In order to find the
array pattern we consider the rectangular array as a linear array of linear arrays.
3.3. RECTANGULAR PLANAR ARRAY 27
-100 0 100-50
-40
-30
-20
-10
0
θ [°]
|F|/m
ax(|
F|)
[dB
]
Figure 3.6: Example of influence of ULA element spacing on its directional charac-
teristic, d = λ/4, N = 4, θ0 = π/6, β = 0.
-100 0 100-50
-40
-30
-20
-10
0
θ [°]
|F|/m
ax(|
F|)
[dB
]
Figure 3.7: Example of influence of ULA element spacing on its directional charac-
teristic, d = λ/2, N = 4, θ0 = π/6, β = 0.
We assume that the arrays parallel to x-axis are ULAs with isotropic elements.
According to (3.3), the array factors of them will take the form
Fx(θ) = wHx vx
where
vx =[1, ej
2πλdx sin θ, ej
2πλ2dx sin θ, . . . ej