Introduction to Wireless Networking - UMKCsce2.umkc.edu/csee/beardc/WirelessNets_SP2008/WirelessNets_Lect_… · Lecture 11, Page 2 of 20 II. Fading (From Rappaport’s Chapter 5

Lecture 11, Page 1 of 20

Introduction to Wireless Networking ECE 401WN Spring 2008

Lecture 11: The Uniqueness of Wireless Communications – Part II

Last lecture: Large scale propagation properties of wireless systems - slowly varying properties that depend primarily on the distance between transmitter and receiver.

♦ Free space path loss, power decay with respect to a reference point ♦ The two-ray model ♦ General characterization of systems using the path loss exponent. ♦ Diffraction ♦ Scattering

This lecture: Rapidly changing signal characteristics primarily caused by movement and multipath.

I. Fading in the Mobile Environment (Section 5.4)

♦ Multipath Propagation

Multiple versions of the transmitted signal will arrive at a receiver.


II. Fading (From Rappaport’s Chapter 5 – Mobile Radio Propagation: Small-Scale Fading and Multipath)

♦ Fading: rapid fluctuations of received signal strength over short time intervals and/or travel distances

♦ Caused by interference from multiple copies of a transmitted signal arriving @

the receiver at ________________ times

♦ Three most important effects: 1. Rapid changes in signal strengths over small travel distances or short time

periods. 2. Changes in the frequency of signals. 3. Multiple signals arriving a different times (echoes). When added together

at the antenna, signals are spread out in time. This can cause a smearing of the signal and interference between bits that are received.

♦ _________ signals occur due to reflections from ground & surrounding buildings (clutter) as well as scattered signals from trees, people, towers, etc.

⇒ often an LOS path is not available but the first multipath signal arrival is probably the desired signal (the one which traveled the shortest distance)

⇒ allows service even when the receiver is severely obstructed by surrounding clutter

♦ Even ______ Transmitter/Receiver wireless links can experience fading due to the motion of objects (cars, people, trees, etc.) in surrounding environment off of which come the reflections

♦ Multipath signals have randomly distributed amplitudes, phases, & direction

of arrival ⇒ Vector summation of (A ∠ θ ) @ receiver of multipath leads to

constructive/destructive interference as the mobile receiver moves in space with respect to time


⇒ Received signal strength can vary by _________ over

distances of ______ (about 7 cm at 1 GHz)! • This is a variation between, say, 1 mW and 0.0001 mW. • If a user stops at a deeply faded point, the signal quality can be

quite bad. • However, even if a user stops, others around may still be moving

and can change the fading characteristics. • And if we have another antenna, say only 7 to 10 cm separated

from the other antenna, that signal could be good.

− This is called making use of _______ which we will study later in this lecture.

⇒ λ / 4 → 5−10 cm or 3−5 msec (for v = 40 miles per hour) ⇒ Fading occurs around received signal strength predicted from large-

scale path loss models (Figure 4.1, page 106)

III. Physical Factors Influencing Fading in Mobile Radio Channel (MRC)

1) Multipath Propagation ⇒ Depends on # and strength of multipath signals ⇒ Time delay of signal arrival

• Large path length differences → large differences in delay between signals


⇒ Urban area w/ many buildings distributed over large spatial scale • Large # of strong multipath signals with only a few having a large

time delay ⇒ Suburb with nearby office park or shopping mall

• Moderate # of strong multipath signals with small to moderate delay times

⇒ Rural → few multipath signals (maybe only LOS + ground reflection)

2) Speed of Mobile

⇒ Relative motion between base station & mobile causes random frequency modulation due to Doppler shift (fd)

⇒ Different multipath components may have different frequency shifts.

3) Speed of Surrounding Objects

⇒ Also influences Doppler shifts on multipath signals ⇒ Dominates small-scale fading if speed of objects > mobile speed

• Otherwise ignored

4) Transmitted signal bandwidth (Bs)

⇒ The mobile radio channel (MRC) is modeled as a filter w/ specific bandwidth (BW)

⇒ The relationship between the signal BW & the MRC BW will affect fading rates and distortion, and so will determine:

a) If the signal is distorted b) If small-scale fading is significant c) If time distortion of signal leads to inter-symbol interference (ISI)

(show ISI)

⇒ An MRC can cause distortion/ISI or small-scale fading, or both. • But typically one or the other.


♦ Doppler Shift

⇒ Motion causes frequency modulation due to Doppler shift (fd)

fd = (v/λ) cosθ v : velocity (m/s) λ : wavelength (m) θ : angle between mobile direction and arrival direction of RF energy + shift → mobile moving toward X − shift → mobile moving away from X

⇒ Two Doppler shifts to consider above 1. The Doppler shift of the signal when it is received at the car. 2. The Doppler shift of the signal when it bounces off the car and is

received somewhere else. ⇒ Multipath signals will have different fd’s for constant v because of

random arrival directions of the signals.

Example 5.1, page 180 Carrier frequency = 1850 MHz Vehicle moving 60 mph Compute frequency deviation in the following situations. (a) Moving directly toward the transmitter

Lambda = c/fc =3e8/1850e6=0.162 m (60 mph) => 26.82 m/s Fd = v/lambda*cos(theta) = 26.8224/0.162162*cos(0) = 165.6 Hz f=1850.0001656 MHz

X

vθ

BaseStatio


(b) Moving perpendicular to the transmitter

cos(pi/2) = 0, no Doppler shift, 0 Hz f=1850MHz

⇒ Note: What matters with Doppler shift is not the absolute frequency,

but the shift in frequency relative to the bandwidth of a channel. • For example: A shift of 166 Hz may be significant for a channel

with a 1 kHz bandwidth. • In general, lower bit rate (low bandwidth) channels are affected

by Doppler shift. ⇒ Note: Doppler shift affects how fast signals change with time. How

fast the fading occurs.

IV. MRC Impulse Response Model

♦ To include fading considerations, we can model the MRC as a _____

with ____________ characteristics.

♦ Vector summation of random amplitudes & phases of multipath signals results in a "filter"

⇒ That is to say, the MRC takes an original signal and in the process of sending the signal produces a modified signal at the receiver.

♦ Time variation due to mobile motion → time delay of multipath signals varies

with location of receiver ⇒ Can be thought as a "location varying" filter. ⇒ As mobile moves with time, the location changes with time; hence,

time-varying characteristics.

♦ The MRC has a fundamental bandwidth limitation → can model as a band pass filter


♦ Linear filter theory y(t) = x(t) ⊗ h(t) or Y(f) = X(f) ⋅ H(f)

⇒ How is an unknown h(t) determined? • Let x(t) = δ(t) → use a delta or impulse input • y(t) = h(t) → impulse response function • Impulse response for standard filter theory is the same regardless

of when it is measured → time invariant

♦ How is the impulse response of an MRC determined?

⇒ “Channel sounding” → like radar ⇒ Transmit a short time-duration pulse (not exactly an impulse, but with

wide BW nonetheless) and record multipath echoes @ receiver

⇒ Short duration transmitted pulse ≈ unit impulse

⇒ Define ___________ time as τ = t - τo where t > τo delays beyond the arrival of the first multipath component.

⇒ Amplitude and delay time of the multipath components change as mobile moves.

x(t) y(t)h(t)

input outputimpulse response

time

Tx Pulse

t = 0

Multipath Echoes → MRC hb ( t,τ )

first arrival@ t = τo


⇒ Fig. 5.4, pg. 184 → MRC is time variant • Different responses at times t0, t1, t2, and t3.

⇒ A power delay profile is found by taking the average over measurements at several places within a local area.

⇒ Then model multipath returns as a sum of unit impulses

hb ( t,τ ) = ∑−

=

1

0

N

iai ( t,τ ) exp { jθ i ( t,τ )} δ (τ - τ i ( t ))

→ ai ∠ θ i = amplitude & phase of each multipath signal → N = # of multipath components → ai is relatively constant over an area → But θ i will change significantly because of different path lengths

(direct distance plus reflected distance) at different locations.

⇒ The Fourier Transform of hb ( t,τ ) gives the spectral characteristics of the channel → frequency response

f

Hb( f ) passband


⇒ MRC filter passband → “Channel BW” or Coherence BW = Bc

• Range of frequencies over which signals will be transmitted without significant changes in signal strength

• The channel acts as a filter that depends on frequency • Signals with narrow frequency bands are not distorted by the

channel

⇒ The Rappaport textbook gives more mathematical details in Sections 5.2 and 5.3 that we will not consider.

V. Multipath Channel Parameters

♦ Derived from multipath power delay profiles ⇒ P ( τ k ) : relative power amplitudes of multipath signals (absolute

measurements are not needed) at different time delays ⇒ Use ensemble average of many profiles in a small localized area →

typically 2−6 m spacing of measurements→ to obtain average small-scale response

♦ Time Dispersion Parameters

⇒ “Excess delay” : all values computed relative to the time of first signal

arrival τo

⇒ Mean excess delay → ∑

∑=

kk

kk

k

P

P

)(

)(

τ

τττ , weighted average based on

power values

⇒ RMS delay spread → 22 )()( ττστ −= Avg where Avg(τ 2) is

∑

∑=

kk

kk

k

P

PAvg

)(

)()(

2

2τ

τττ

⇒ Avg(τ 2) is found using the same computation as above as used for τ

except that τ k → τ k2

• A simple way to explain RMS delay spread is “the range of time within which most of the delayed signals arrive”


• Table 5.1, page 200.

→ Outdoor channel ~ on the order of microseconds → Indoor channel ~ on the order of nanoseconds

⇒ Maximum excess delay (τX): the largest time where the multipath power

levels are still within X dB of the maximum power level • Worst case delay value • Depends very much on the choice of the noise threshold

⇒ Fig. 5.10, pg. 200


⇒ τ and στ provide a measure of propagation delay of interfering signals • Then give an indication of how time smearing might occur for the

signal. • A small στ is desired. • Example: If a bit time is 10 microseconds (100 kbps), what

might the signal look like if received for τX = 7 microseconds and τX = 1 microsecond? Assume only one multipath component is received. Draw the diagrams.

First received signal (at time τ0) τX = 7 microseconds τX = 1 microsecond


⇒ This “smearing” has the more official term – __________ ___________________

♦ Coherence BW (Bc) and Delay Spread (στ)

⇒ The Fourier Transform of multipath delay shows frequency (spectral) characteristics of the MRC (see page 8 of these notes)

⇒ Bc : statistical measure of frequency range where MRC response is flat

• ________ = passes all frequencies with ≈ equal gain & linear phase, close to an ideal filter in this range of frequencies

• So amplitudes of different frequency components are correlated • If two sinusoids have frequency separation greater than Bc, they

are affected quite differently by the channel • Amplitude correlation → multipath signals have close to the same

amplitude → if they are then out-of-phase they have significant destructive interference with each other (deep fades)

• So a flat fading channel is both “good” and “bad” − Good: The MRC is like a bandpass filter and passes signals

without major attenuation from the channel (low distortion). − Bad: Deep fading can occur (high fading) if there are long

enough time delays between multipath components to make the signals 180 degrees out of phase.

• So the coherence bandwidth is “the range of frequencies over which two frequency components have a strong potential for amplitude correlation.” (quote from textbook)

• Estimates 0.9 correlation → Bc ≈ 1 / 50 στ (signals are 90% correlated

with each other) 0.5 correlation → Bc ≈ 1 / 5 στ (signals are 50% correlated

with each other)


• Which has a larger bandwidth and why?

0.5 correlation: a wider range of frequencies can contain more signals that are less correlated.

• Specific channels require detailed analysis for a particular transmitted signal – these are just rough estimates

⇒ A channel that is not a flat fading channel is called

_________________ because different frequencies within a signal are attenuated differently by the MRC.

• Note: The definition of flat or frequency selective fading is defined with respect to the bandwidth of the signal that is being transmitted. For example, narrowband signals (low bandwidth) are unlikely to find any environment to be frequency selective.

⇒ Bc and στ are related quantities that characterize time-varying nature of

the MRC for multipath interference from frequency & time domain perspectives

• If the coherence bandwidth is large, how does it affect the ISI illustrated above?

Large coherence BW – low delay spread – little ISI or distortion

• These parameters do NOT characterize the time-varying nature of

the MRC due to the _____________ of the mobile and/or surrounding objects

• That is to say, Bc and στ characterize the __________, (how multipath signals are formed from scattering/reflections and travel different distances)


• Bc and στ do not characterize the mobility of the transmitter or receiver, or how fast fading might change.

♦ Doppler Spread (BD) & Coherence Time (Tc)

⇒ BD : measure of spectral broadening of the transmitted signal caused by

motion → i.e., Doppler shift • BD = max Doppler shift = fmax = vmax / λ • In what direction does movement occur to create this worst case?

Toward the transmitter • If transmitted signal bandwidth (Bs) is large such that Bs >> BD

then effects of Doppler spread are NOT important − So Doppler spread is only important for low bps (data rate)

applications (e.g. paging, OFDM)

⇒ Tc : coherence time is the statistical measure of the time interval over which MRC impulse response remains invariant → amplitude & phase of multipath signals ≈ constant

• __________ = passes all received signals with virtually the same characteristics because the channel has not changed

• The time duration is long over which two received signals have a strong potential for amplitude correlation

• Two signals arriving with a time separation greater than Tc are affected differently by the channel, since the channel has changed within the time interval

• For digital communications coherence time and Doppler spread can be related by

Tc ≈ 0.423 / BD

• If a channel is not a slow fading channel, it is called ____ _________.


♦ Types of Small-Scale Fading Fading can be caused by two independent MRC propagation mechanisms:

1) Time dispersion → multipath delay (Bc , στ) 2) Frequency dispersion → Doppler spread (BD , Tc)

♦ Important parameters for digital signals → symbol period & signal BW

⇒ In this example, one "symbol" = one "bit".

♦ Fig. 5.11, pg. 206 → illustrates types of small-scale fading ⇒ Flat fading or frequency selective fading ⇒ Fast fading or slow fading.

Symbol Period = Ts

Signal BW = Bs ≈ 1 / Ts

00 0 0 01 1 1


1) Fading due to Multipath Delay A) Flat Fading → Bs << Bc or Ts >> στ

⇒ Signal fits easily within the bandwidth of the channel ⇒ Channel BW >> signal BW

⇒ Note: It is probably better to think of “flat” fading from the frequency domain perspective → the “flat” corresponds to the channel characteristic where the amplitude response looks flat.

⇒ This is the most commonly occurring type of fading ⇒ Spectral properties of the transmitted signal are preserved

• The signal is called a narrowband signal, since the bandwidth of the signal is narrow with respect to the channel bandwidth

• The signal is not distorted ⇒ What does Ts >> στ mean?? → all multipath signals arrive at the mobile

receiver during 1 symbol period ∴ Little intersymbol interference occurs (no multipath components arrive late to interfere with the next symbol)

⇒ Flat fading is generally considered desirable • Even though deep fades in amplitude occur, the signal is not

distorted → distortion is harder to overcome that fading. • Can use diversity techniques to overcome this fading (described

in a later lecture)

f

Bc

Bs

fc


B) Frequency Selective Fading → Bs > Bc or Ts < στ

⇒ Bs > Bc → certain frequency components of the signal are attenuated much more than others

⇒ Ts < στ → delayed versions of transmitted signal arrive during different symbol periods

• E.g. receiving an LOS → “1” & multipath “0” (from prior symbol)

• This results in intersymbol interference (ISI) • Undesirable

⇒ It is very difficult to predict mobile receiver performance with

frequency selective channels ⇒ But for high bandwidth applications, channels will likely be frequency

selective • A new modulation approach has been developed to combat this.

• Called __________________ ____________________ __________________

• One aspect of OFDM is that it separates a wideband signal into many smaller narrowband signals − (For those familiar with Digital Signal Processing) Signals are

split using FFT → take FFT, break into pieces in the frequency domain, use Inverse FFT to create individual signals from each piece, then transmit.

f

Bc

Bs

fc


− Then OFDM adaptively adjusts the power of each narrowband signal to fit the characteristics of the channel at that frequency.

− This results in much improvement over other wideband transmission approaches (like CDMA), since it essentially makes the channel a flat fading channel.

− CDMA is spread over a wide bandwidth and usually undergoes frequency selective fading.

− OFDM is used in the 802.11g 54 Mbps standard for WLAN’s in the 2.4 GHz band, and for WiMax.

− Previously it was thought 54 Mbps could only be obtained at 5.8 GHz using CDMA, but 5.8 GHz signals attenuate much more.

2) Fading due to Doppler Spread

⇒ Caused by motion of transmitter and receiver and reflection sources.

A) Fast Fading → Bs < BD or Ts > Tc

⇒ Bs < BD • Doppler shifts significantly alter spectral BW of transmitted

signal • Signal “spreading”

⇒ Ts > Tc

• MRC changes within 1 symbol period • Rapid amplitude fluctuations

⇒ Uncommon in most digital communication systems, but possibly a

problem with OFDM, since OFDM uses low bandwidth individual signals.

B) Slow Fading → Ts << Tc or Bs >> BD

⇒ MRC constant over many symbol periods ⇒ Hence, the term “slow” → so think about Doppler spread from a time

domain perspective. ⇒ Slow amplitude fluctuations


⇒ For v = 60 mph @ fc = 2 GHz → BD = 178 Hz ∴ Bs ≈ 2 kHz >> BD → Bs almost always >> BD for most applications

Example: Given a typical suburban environment for a mobile traveling on a highway, how would the channel be characterized when trying to transmit a data signal at 10,000 symbols per second at 800 MHz? NOTE: Typically use a factor of 10 to designate “>>”. Typical suburban: sigma_tau <= 310 ns v=100 km/hr = 100*(1000 m/km)/(3600 sec/hour) = 27.8 m/s fd,max = v/lambda = v*fc/c = (27.8)(800e6)/3e8 = 74.1 Hz = BD rs = 10,000 symbols/sec, bandwidth ~ 10 kHz = Bs Ts = 1/rs = 100 microseconds Flat or frequency selective?

0.9 correlation → Bc ≈ 1 / 50 στ = 645 kHz Bc vs. BS 645e3 >> 10e3 FLAT FADING

Tc ≈ 0.423 / BD = 5.7e-3 (5.7 milliseconds) Tc vs. Ts 5.7e-3 >> 100 e-6 SLOW FADING How high of a symbol rate could be supported (assume use of a 90% coherence BW)? Bc ≈ 645 kHz Bc = 10 Bs Bs = 645/10 = 64.5 kHz 64.5 kbps


VI. Fading Signal Distributions

♦ Rayleigh probability distribution function → p(r) = (r/σ 2) exp ( − r 2 / 2σ 2) 0 ≤ r ≤ ∞

⇒ Used for flat fading signals. ⇒ Formed from finding the amplitude of the sum of two Gaussian noise

signals. ⇒ σ : RMS value of received signal before detection (before

demodulation) ⇒ This is a common model for receiver signal variation

• Urban areas → heavy clutter → no LOS path ⇒ Defines the probability that signal exceeds predefined threshold level R

• Prob (r ≥ R) = p(r) dr = exp (− R2 / 2σ 2)

⇒ Figure 5.15, page 211.

0 0.5 1 1.5 2 2.5 3 3.5 4

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

r/σ

Ray

leig

h pr

obab

ility

Peak at r/σ = 1, Peak value = 0.6065/σ

♦ Ricean Probability Distribution Function ⇒ One dominant signal component along with weaker multipath signals ⇒ Dominant signal → LOS path

• Suburban or rural areas with light clutter ⇒ Becomes a Rayleigh distribution as the dominant component weakens ⇒ See pg. 213 for equations

The remainder of Rappaport’s Chapter 5 gives many models for correlating measured data to a model of an MRC. Nothing else in Chapter 5 will be covered here, however.

Introduction to Wireless Networking - UMKCsce2.umkc.edu/csee/beardc/WirelessNets_SP2008/WirelessNets_Lect_… · Lecture 11, Page 2 of 20 II. Fading (From Rappaport’s Chapter 5

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