Mobile Radio Propagation: Small-Scale Fading and Multipath

Fading

Last lecture



Large scale propagation properties of wireless s

ystems - slowly varying properties that depend

primarily on the distance between Tx and Rx.

 Free space path loss

 Power decay with respect to a reference point

 The two-ray model

 General characterization of systems using the path l oss exponent.

 Diffraction

I. Fading

 _{Fading: rapid fluctuations of received signal strength o}

ver short time intervals and/or travel distances

 Caused by interference from multiple copies of Tx sign al arriving @ Rx at slightly different times

 _{Three most important effects:}

1. Rapid changes in signal strengths over small travel dista nces or short time periods.

2. Changes in the frequency of signals.



_Fading

_{signals occur due to reflections from gr}

ound & surrounding buildings (clutter) as well

as scattered signals from trees, people, towers, e

tc.

 often an LOS path is not available so the first multi path signal arrival is probably the desired signal (th e one which traveled the shortest distance)



_{Even stationary}

_{Tx/Rx wireless links can experi}

ence fading due to the motion of objects (cars, p

eople, trees, etc.) in surrounding environment of

f of which come the reflections



_{Multipath signals have randomly distributed am}

plitudes, phases, & direction of arrival

 _{vector summation of (A} ∠ _{θ) @ Rx of multipath lea}

 received signal strength can vary by Small-scale fading

over distances of a few meter (about 7 cm at 1 GHz)!

 _{This is a variation between, say, 1 mW and 10}-6 _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 b}

e moving and can change the fading characteristics.

 And if we have another antenna, say only 7 to 10 cm se parated from the other antenna, that signal could be goo d.

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

1) Multipath Propagation

 # and strength of multipath signals

 time delay of signal arrival

 large path length differences → large differences in del ay between signals

 urban area w/ many buildings distributed over large spatial scale

 large # of strong multipath signals with only a few havi ng a large time delay

 suburb with nearby office park or shopping mall

2) Speed of Mobile

 relative motion between base station & mobile caus es random frequency modulation due to Doppler shi ft (f_d)

 _{Different multipath components may have different}

frequency shifts.

3) Speed of Surrounding Objects

 also influence Doppler shifts on multipath signals

 _{dominates small-scale fading if speed of objects >}

mobile speed

4) Tx signal bandwidth (

B

_s

)

 _{The mobile radio channel (MRC) is modeled as filt}

er w/ specific bandwidth (BW)

 _{The relationship between the signal BW & the MR}

C BW will affect fading rates and distortion, and so will determine:

a) if small-scale fading is significant

Doppler Shift

 _{motion causes frequency modulation due to Doppler sh}

ift (f_d)

 v : velocity (m/s)

 λ : wavelength (m)

 θ : angle between mobile direction

and arrival direction of RF energy



_{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 t he car and is received somewhere else.



_{Example 5.1, page 180}

 Carrier frequency = 1850 MHz

 _{Vehicle moving 60 mph}

 Compute frequency deviation in the following situa tions.

(a) Moving directly toward the transmitter



_{Note: What matters with Doppler shift is not th}

e absolute frequency, but the shift in frequency

relative to the bandwidth of a channel.

 _{For example: A shift of 166 Hz may be significant f}

or a channel with a 1 kHz bandwidth.

III. MRC Impulse Response Model



_{Model the MRC as a linear filter with a time va}

rying

characteristics



_{Vector summation of random amplitudes & pha}

ses of multipath signals results in a "filter"



_{Time variation due to mobile motion → time de}

lay of multipath signals varies with location of

Rx

 _{Can be thought as a "location varying" filter.}

 As mobile moves with time, the location changes w ith time; hence, time-varying characteristics.



_{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}



_{How is the impulse response of an MRC determ}

ined?

 “channel sounding” → like radar

 _{transmit short time duration pulse (not exactly an i}

 short duration Tx pulse ≈ unit impulse

 define excess delay bin as

 amplitude and delay time of multipath returns change as mobile m oves

 Fig. 5.4, pg. 184 → MRC is time variant

1

i i



_{model multipath returns as a sum of unit impuls}

es

 a_i ∠ θ _i = amplitude & phase of each multipath sign al

 _{N = # of multipath components}

 a_i is relatively constant over an local area

 _{The useful frequency span of the model :}

 The received power delay profile in a local area:

 Assume the channel impulse response is time invariant, or

2

( ) _b( ; )

P

_

_ k h t

_

Relationship between Bandwidth and Received Power



_{The average small-scale received power}

 The average small scale received power is simply th e sum of the average powers received in each multi path component

 _{Average power for a CW signal is equivalent to the ave}

rage received power for a wideband signal in a small-s cale region.

 _{The received local ensemble average power of wideba}

nd and narrowband signals are equivalent.

 _{Tx signal BW > Channel BW Rx power varies ver}

y small

 _{Tx signal BW < Channel BW large signal fluctuat}

ions (fading) occur

 _{The duration of baseband signal > excess delay of channel}  _{due to the phase shifts of the many unsolved multipath comp}

 The Fourier Transform of h_b ( t,τ) gives the spectral cha racteristics of the channel → frequency response

 MRC filter passband → “Channel BW” or Coherence BW = B_c

 range of frequencies over which signals will be transmitted w ithout significant changes in signal strength

 channel acts as a filter depending on frequency

IV. Multipath Channel Parameters



_{Derived from multipath power delay profiles (E}

q. 5-18)



P

(τ

_k

)

:

relative

power amplitudes of multipath s

ignals (absolute measurements are not needed)

 Relative to the first detectable signal arriving at the Rx at τ₀



_{Time Dispersion Parameters}

 “excess delay” : all values computed relative to the time of first signal arrival τ_o

 _{mean excess delay →}

39

 maximum excess delay ( τ_X): the largest time where the mul tipath power levels are still within X dB of the maximum po wer level

 worst case delay value



τ and σ

_τ

provide a measure of propagation delay

of interfering signals

 Then give an indication of how time smearing migh t occur for the signal.

 A small σ_τ is desired.

 _{The noise threshold is used to differentiate between}

 Coherence BW (B_c) and Delay Spread ( )

 The Fourier Transform of multipath delay shows frequen cy (spectral) characteristics of the MRC

 B_c : statistical measure of frequency range where MRC r esponse is flat

 MRC response is flat = passes all frequencies with ≈ equal gain & linear phase

 amplitudes of different frequency components are cor related

 if two sinusoids have frequency separation greater th





amplitude correlation → multipath signals have

close to the same amplitude → if they are then o

ut-of-phase they have significant destructive int

erference 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 fro

m the channel.



_{so the coherence bandwidth is “the range}



estimates

 _{0.9 correlation → Bc ≈ 1 / 50 (signals are 90% correlat}

ed with each other)

 0.5 correlation → Bc ≈ 1 / 5 Which has a larger band width and why?



specific channels require detailed analysis for a parti

cular transmitted signal – these are just rough estimat

es









_{A channel that is not a flat fading channel is call}

ed

frequency selective fading

because different

frequencies within a signal are attenuated differ

ently by the MRC.

 _{these parameters do NOT characterize the time-varying}

nature of the MRC due to the mobility of the mobile and /or surrounding objects

 that is to say, B_c and characterize the statics, (how multipat h signals are formed from scattering/reflections and travel diffe rent distances)

 B_c and σ_τ do not characterize the mobility of the Tx or Rx. 



Doppler Spread (

B

_D

) & Coherence Time (

T

_c

)

 B_D : measure of spectral broadening of the Tx signal caused by motion → i.e., Doppler shift

 B_D = max Doppler shift = f_max = v_max / λ

 _{In what direction does movement occur to create this w} orst case?



T

_c

: statistical measure of the time interval over

which MRC impulse response remains invarian

t → amplitude & phase of multipath signals ≈ c

onstant

 Coherence Time (T_c) = passes all received signals with virtually the same characteristics because the c hannel has not changed



Two signals arriving with a time separation grea

ter than

T

_c

are affected differently by the channe

l, since the channel has changed within the time

interval



For digital communications coherence time and

Doppler spread are related by

V. Types of Small-Scale Fading



Fading can be caused by two

independent

MRC pr

opagation mechanisms:

1) time dispersion → multipath delay (B_c , )

2) frequency dispersion → Doppler spread (B_D , T_c)

 _{Important digital Tx signal parameters → symbol per}

iod & signal BW





_{A pulse can be more than two levels, however, s}

o each period would be called a "symbol perio

d".

 _{We send 0 (say +1 Volt) or 1 (say -1 Volt) → one bit}

per “symbol”

1)

Fading due to Multipath Delay

A

）

Flat Fading →

B

_s << B_c or T_s >>



 signal fits easily within the bandwidth of the channel

 channel BW >> signal BW



spectral properties of Tx signal are preserved

 _{signal is called a narrowband channel, since the bandwidt}

h of the signal is narrow with respect to the channel band width

 _{signal is not distorted}



What does

T

_s

>> mean??

 _{all multipath signals arrive at mobile Rx during 1 symbol}

period

∴

Little intersymbol interference occurs (no multipath com





_{flat fading is generally considered}

_desirable

 _{Even though fading in amplitude occurs, the signal}

is not distorted

 Forward link → can increase mobile Rx gain (auto matic gain control)

 _{Reverse link → can increase mobile Tx power (pow}

er control)

 _{Can use diversity techniques (described in a later le}

B)

Frequency Selective Fading →

B

_s

>

B

_c

or

T

_s

<



 B_s > B_c → certain frequency components of the signal a re attenuated much more than others

10 s

T _{ }





Ts

<

σ

_τ

→ delayed versions of Tx signal arrive

during

different

symbol periods

 _{e.g. receiving an LOS → “1” & multipath “0” (fro}

m prior symbol!)

 This results in intersymbol interference (ISI)

 _Undesirable



But for high bandwidth applications, channels with

likely be frequency selective

 a new modulation approach has been developed to com bat this.

 Called OFDM



One aspect of OFDM is that it separates a wideban

d signal into many smaller narrowband signals

 OFDM is used in the new 802.11g 54 Mbps standar d for WLAN’s in the 2.4 GHz band.

 _{Previously it was thought 54 Mbps could only be o}

btained at 5.8 GHz using CDMA, but 5.8 GHz sign als attenuate much more quickly.

 _{Signals are split using signal → FFT, break into pie}

2) Fading due to Doppler Spread

 Caused by motion of Tx and Rx and reflection sour ces.

A) Fast Fading → B_s < B_D or T_s > T_c

 B_s < B_D

 _{Doppler shifts significantly alter spectral BW of TX sig} nal

 signal “spreading”

B)

Slow Fading

→

T

_s

<<

T

_c

or

B

_s

>>

B

_D

 _{MRC constant over many symbol periods}  slow amplitude fluctuations

 for v = 60 mph @ f_c = 2 GHz → B_D = 178 Hz

∴ B_s ≈ 2 kHz >> B_D

 B_s almost always >> B_D for most applications

VI. Fading Signal Distributions

 _{Rayleigh probability distribution function →}

 Used for flat fading signals.

 Formed from the sum of two Gaussian noise signals.

 σ : RMS value of Rx signal before detection (demodulation)

 common model for Rx signal variation

 urban areas → heavy clutter → no LOS path

73

 r_mean : The mean value of Rayleigh distribution

 σ_r2 _{: The variance of Rayleigh distribution; ac power of signal}

envelope

 σ : RMS value of Rx signal before detection (demodulation)



_{Ricean Probability Distribution Function}

 one dominant signal component along with weaker multipath signals

 _{dominant signal → LOS path}

 suburban or rural areas with light clutter