Mobile Radio Propagation: Small-Scale Fading and Multipath

Fading

  

Mobile Radio Propagation: Small-Scale

Fading and Multipath

  1

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

  

  Scattering

   This lecture: Rapidly changing signal characteri stics primarily caused by movement and multip ath.

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.

  3. Multiple signals arriving a different times. When added together at the antenna, signals are spread out in time. T his can cause a smearing of the signal and interference b etween bits that are received.

   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)

  

  allows service even when Rx is severely obstructed by surrounding clutter

   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 ∠ ds to constructive/destructive interference as mobile

  Rx moves in space with respect to time

  

  received signal strength can vary by Small-scale fading over distances of a few meter (about 7 cm at 1 GHz)!

• _-6

   This is a variation between, say, 1 mW and 10 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.

   This is called making use of ________ which we wil l study in Chapter 7.

   fading occurs around received signal strength predicted fro m large-scale path loss models

  

  # 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

   moderate # of strong multipath signals with small to m oderate delay times

  

  rural → few multipath signals (LOS + ground reflec tion)

  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

   otherwise ignored

  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

  b) if time distortion of signal leads to inter-symbol interfer ence (ISI) 

  An MRC can cause distortion/ISI or small-scale fad ing, or both.

   But typically one or the other.

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

  

+ shift → mobile moving toward S

   − shift → mobile moving away from S

   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.

  

 Multipath signals will have different f ’s for co

d nstant v because of random arrival directions!!

   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 (b) Moving perpendicular to 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.

  

  In general, low bit rate (low bandwidth) channels ar e affected by Doppler shift.

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" 

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

   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.

   The MRC has a fundamental bandwidth limitati on → 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 determ ined? 

  “channel sounding” → like radar

  

  transmit short time duration pulse (not exactly an i mpulse, but with wide BW) and record multipath ec hoes @ Rx

   short duration Tx pulse ≈ unit impulse

   define excess delay bin as    _i

_

_{1 i}

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

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

   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 

  But θ _i will change significantly because of different pa th lengths (direct distance plus reflected distance) at dif ferent locations.

  

  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 WSS ²

  ( ) ( ; ) _b P k h t

     2 /

   

  

Relationship between Bandwidth and Received Power



  A pulsed, transmitted RF signal of the form

   For wideband signal

   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

  

  The Rx power of a wideband signal such as p(t) doe s not fluctuate significantly when a receiver is move d about a local area.

   CW signal (narrowband signal ) is transmitted in to the same channel

  

  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 onents

  The Fourier Transform of h ( t,τ) gives the spectral cha

   _b

  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

   signals with narrow frequency bands are not distorted by the channel

IV. Multipath Channel Parameters

   Derived from multipath power delay profiles (E q. 5-18)

  P (τ ) : relative power amplitudes of multipath s  k ignals (absolute measurements are not needed) 

  Relative to the first detectable signal arriving at the Rx at τ  use ensemble average of many profiles in a smal l localized area →typically 2 − 6 m spacing of measurements→ to obtain average small-scale r esponse

   Time Dispersion Parameters 

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

  

  mean excess delay →

  

  RMS delay spread → ₂ where Avg( τ ) is the same computation as above as used for except that

   A simple way to explain this is “the range of time withi n which most of the delayed signals arrive”

  

 maximum excess delay ( τ ): the largest time where the mul

_X tipath power levels are still within X dB of the maximum po wer level  worst case delay value

   depends very much on the choice of the noise threshold

   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 received multipath components and thermal noise

  

  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 an B _c , they are affected quite differently by the chann el ^

  

   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.

   Bad: Deep fading can occur.

   so the coherence bandwidth is “the range of frequencies over which two frequency

components have a strong potential for a

mplitude correlation.” (quote from textbo ok)

   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.

  

  Note: The definition of flat or frequency selective f ading is defined with respect to the bandwidth of th e signal that is being transmitted.

  

 B and σ are related quantities that characterize

c τ time-varying nature of the MRC for multipath i nterference from frequency & time domain pers pectives

  

  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 and characterize the statics, (how multipat  _c

   _ h signals are formed from scattering/reflections and travel diffe rent distances) B and σ do not characterize the mobility of the Tx or Rx.

   _{c τ}

   Doppler Spread (B ) & Coherence Time (T )

  D c

   B : measure of spectral broadening of the Tx signal _D

  caused by motion → i.e., Doppler shift

   B = max Doppler shift = f = v / λ _{D max max}

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

   if Tx signal bandwidth (B ) is large such that B >> B t _{s s D} hen effects of Doppler spread are NOT important so D oppler spread is only important for low bps (data rate) applications (e.g. paging)

   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

  

  time duration over which two received signals have a strong potential for amplitude correlation

   Two signals arriving with a time separation grea ter than T are affected differently by the channe c l, since the channel has changed within the time interval

   For digital communications coherence time and Doppler spread are related by

  9 0.423 T _c   ₂ 16 f f

   _{m m}

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 , T ) _{D 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”

  

  Or we could send 10 (+3 Volts) or 00 (+1 Volt) or 0 1 (-1 Volt) or 11 (-3 Volts) → two bits per “symbol”

  illustrates types of small-scale fading

   A Flat Fading → B << B or T >>  ） _{c s} s

  T

  10 _s   _

   T

  10  signal fits easily within the bandwidth of the channel

    s

    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 ponents arrive late to interfere with the next symbol)

   

   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 cture) 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 → delayed versions of Tx signal arrive τ during different symbol periods 

  e.g. receiving an LOS → “1” & multipath “0” (fro m prior symbol!)

  

  This results in intersymbol interference (ISI)

  

  Undesirable

   it is very difficult to predict mobile Rx perform ance with frequency selective channels

   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 

  Then adaptively adjusts the power of each narrowband s ignal to fit the characteristics of the channel at that frequ ency.

   Results in much improvement over other wideband tran smission approaches (like CDMA).

  

  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 ces in the frequency domain, use inverse FFT to cre ate individual signals from each piece, then transmit .

  

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

  A) Fast Fading → B < B or T > T _{s D s c} 

  B < B _{s D} 

  Doppler shifts significantly alter spectral BW of TX sig nal  signal “spreading”

   Ts > Tc 

  MRC changes within 1 symbol period  rapid amplitude fluctuations

  

  uncommon in most digital communication systems

  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

  

• NOTE: Typically use a factor of 10 to design ate “>>” **

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

   probability that signal does not exceeds predefined threshold l evel R ^{2 2 2}

  ( ) exp

  2 r r P r r

            

   

   r : The mean value of Rayleigh distribution _{mean }  r E r [ ] rp r dr ( ) 1.2533

      _mean  

  

  2

  2

 σ : The variance of Rayleigh distribution; ac power of signal

_{r  2} envelope _{2 2 2 2}  

  E r [ ] E r [ ] r p r dr ( )  _r    

  

  2 ₂  ₂   2 0.4292

        

  2   

  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

  

  becomes a Rayleigh distribution as the dominant co mponent weakens