ECE 476/ECE 501C/CS 513 - Wireless Communication Systems Winter 2003 Lecture 6: Fading Last lecture: Large scale propagation properties of wireless systems - 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 loss exponent. Diffraction Scattering This lecture: Rapidly changing signal characteristics primarily caused by movement and multipath. Chapter 5 Mobile Radio Propagation: Small-Scale Fading and Multipath I. Fading Fading: rapid fluctuations of received signal strength over short time intervals and/or travel distances Caused by interference from multiple copies of Tx signal arriving @ Rx at slightly different times Three most important effects: 1. Rapid changes in signal strengths over small travel distances or short time periods. 2. Random 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. This can cause a smearing of the signal and interference between bits that are received. Lecture 6, Page 1 of 13
Multipath 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 so the first multipath signal arrival is probably the desired signal (the one which traveled the shortest distance) allows service even when Rx is severely obstructed by surrounding clutter Multipath signals have randomly distributed amplitudes, phases, & direction of arrival vector summation of (A θ ) @ Rx of multipath leads to constructive/destructive interference as mobile Rx moves in space with respect to time received signal strength can vary by 30-40 db over distances of λ / 4! (between say, 1 mw and 0.0001 mw) λ / 4 5 10 cm or 3 5 msec (for v = 40 miles per hour) fading occurs around received signal strength predicted from largescale path loss models (Figure 4.1, page 106) Even fixed Tx/Rx wireless links can experience fading due to motion of objects (cars, people, trees, etc.) in surrounding environment off of which come the reflections 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 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 (LOS + ground reflection) Lecture 6, Page 2 of 13
2) Speed of Mobile relative motion between base station & mobile causes random frequency modulation due to Doppler shift (f d ) X Base Station f d = (v/λ) cosθ θ v 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 f d s for constant 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 situations. (a) Moving directly toward the transmitter (b) Moving perpendicular to the transmitter Lecture 6, Page 3 of 13
3) Speed of Surrounding Objects also include Doppler shifts on multipath signals dominates small-scale fading if speed of objects > mobile speed otherwise ignored 4) Tx signal bandwidth (B s ) MRC modeled as filter w/ specific bandwidth (BW) relationship between signal BW & MRC BW will determine: a) if small-scale fading is significant b) if time distortion of signal leads to inter-symbol interference (ISI) III. MRC Impulse Response Model Model MRC as linear filter with **time-varying** 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 Rx 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 model as a band pass filter Linear filter theory x(t) input h(t) impulse response y(t) output y(t) = x(t) h(t) or Y(f) = X(f) H(f) Lecture 6, Page 4 of 13
How is unknown h(t) determined? let x(t) = δ(t) delta or impulse input then 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 short time duration pulse (not exactly and impulse, but wide BW) and record multipath echoes @ Rx Tx Pulse Multipath Echoes MRC h b ( t,τ ) t = 0 first arrival @ t = τ o time short duration Tx pulse unit impulse define excess delay time as τ = t - τ o where t > τ o amplitude and delay time of multipath returns change as mobile moves Fig. 5.4, pg. 184 MRC is time variant model multipath returns as sum of unit impulses N h b ( t,τ ) = 1 i= 0 a i ( t,τ ) exp { jθ i ( t,τ )} δ (τ - τ i ( t )) a i θ i = amplitude & phase of multipath signals (δ ) N = # of multipath components Fourier transform of h b ( t,τ ) gives spectral characteristics of channel freq. response H b ( f ) passband f Lecture 6, Page 5 of 13
MRC filter passband Channel BW or Coherence BW = B c range of frequencies over which signals will be transmitted without significant changes in signal strength channel acts as a filter depending on frequency signals with narrow frequency bands are not distorted by the channel The textbook gives lots of mathematical details that will not consider, except the following material. IV. Multipath Channel Parameters Derived from multipath power delay profiles P ( τ k ) : relative power amplitudes of multipath signals use ensemble average of many profiles in small localized area typically 2 6 m obtain average small-scale response Time Dispersion Parameters excess delay : all values computed relative to time of first signal arrival τ o mean excess delay τ = P( τ k ) τk k P( τ k ) k 2 2 RMS delay spread σ τ = Avg ( τ ) ( τ ) where Avg(τ 2 ) same as above for τ except τ k τ k 2 A simpler way to explain this is the range of time within which most of the delayed signal arrive typical values: Shown in Table 5.1, page 200. outdoor channel ~ 2 5 µsec indoor channel ~ 20 100 nsec maximum excess delay (X db): largest time where multipath power levels are still within X db of the maximum power level worst case delay value Lecture 6, Page 6 of 13
Fig. 5.10, pg. 200 τ and σ τ provide a measure of propagation delay of interfering signals Desire small σ τ Example: If a bit time is 10 microseconds (100 kbps), what signal do you expect to receive for σ τ = 5 microseconds and σ τ = 1 microsecond? Draw the diagrams. Transmitted signal σ τ = 5 microseconds σ τ = 1 microsecond Coherence BW (B c ) and Delay Spread (σ τ ) Fourier transform of multipath delay shows frequency (spectral) characteristics of MRC (see page 5 of these notes) Lecture 6, Page 7 of 13
B c : statistical measure of frequency range where MRC response is flat flat fading = passes all frequencies with equal gain & linear phase amplitudes of different frequency components are correlated if two sinusoids have frequency separation greater than B c, they are affected quite differently by the channel estimates 0.5 correlation B c 1 / 5 σ τ 0.9 correlation B c 1 / 50 σ τ (worst case/conservative) amplitude correlation multipath signals have close to the same amplitude if they are then out-of-phase they have significant destructive interference between each other specific channels require detailed analysis for a particular transmitted signal B c and σ τ are related quantities that characterize time-varying nature of MRC from multipath interference for frequency & time domain perspectives they do NOT characterize time-varying nature of MRC due to motion of the mobile and/or surrounding objects that is to say, B c and σ τ characterize the environment, not the mobility of Tx or Rx Doppler Spread (B D ) & Coherence Time (T c ) B D : measure of spectral broadening of 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 worst case? if Tx signal bandwidth (B s ) is large such that B s >> B D then effects of Doppler spread are NOT important so Doppler spread is only important for low bps (data rate) applications (e.g. paging) Lecture 6, Page 8 of 13
T c : statistical measure of time interval over which MRC impulse response remains invariant amplitude & phase of multipath signals constant slow fading = passes all received signals with virtually the same characteristics because the channel has not changed time duration over which two received signals have a strong potential for amplitude correlation two signals arriving with a time separation greater than T c are affected differently by the channel, since the channel has changed within the time interval for digital communications coherence time and Doppler spread are related by T c 0.423 / B D V. Types of Small-Scale Fading Fading can be caused by two independent MRC propagation mechanisms: 1) time dispersion multipath delay (B c, σ τ ) 2) frequency dispersion Doppler spread (B D, T c ) Important digital Tx signal parameters symbol period & signal BW 0 1 0 0 1 0 1 0 Symbol Period = T s Signal BW = B s 1 / T s In this example, one "symbol" = one "bit". A pulse can be more than two levels, however, so each period would be called a "symbol period". 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 01 (-1 Volt) or 11 (-3 Volts) two bits per symbol Fig. 5.11, pg. 206 types of small-scale fading Flat fading or frequency selective fading Fast fading or slow fading. Lecture 6, Page 9 of 13
1) Fading due to Multipath Delay A) Flat Fading B s << B c or T s >> σ τ signal fits easily within the bandwidth of the channel channel BW >> signal BW B c B s f f c common type of fading spectral properties of Tx signal are preserved signal is called a narrowband signal signal is not distorted What does T s >> σ τ mean?? all multipath signals arrive at mobile Rx during 1 symbol period No intersymbol interference occurs (no multipath components arrive late to interfere with the next symbol) interference does cause signal amplitude to vary from symbol to symbol The channel gain varies with time causing deep fades fades ~ 20 30 db Rayleigh fading generally considered desirable even though fading in amplitude occurs, the signal is not distorted forward link can increase mobile Rx gain (automatic gain control) reverse link can increase mobile Tx power (power control) can use diversity techniques (described in a later lecture) Lecture 6, Page 10 of 13
B) Frequency Selective Fading B s > B c or T s < σ τ B s > B c certain frequency components of signal attenuated B c f c f B s T s < σ τ delayed versions of Tx signal arrive during different symbol periods e.g. receiving an LOS 1 & multipath 0 (from prior symbol!) undesirable very difficult to predict mobile Rx performance Summary: Why is flat fading most desirable? 2) Fading due to Doppler Spread Caused by motion of Tx and Rx and reflection sources. A) Fast Fading T s > T c or B s < B D T s > T c MRC changes within 1 symbol period rapid amplitude fluctuations Lecture 6, Page 11 of 13
B s < B D Doppler shifts significantly alter spectral BW of TX signal signal spreading only occurs for low data rate applications (i.e., those with large T s ) uncommon in most digital communication systems 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 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? Lecture 6, Page 12 of 13
How high of a symbol rate could be supported? VI. Fading Signal Distributions Rayleigh probability distribution function p(r) = (r/σ 2 ) exp ( r 2 / 2σ 2 ) 0 r 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 exceeds predefined threshold level R Prob (r R) = p(r) dr = exp ( R 2 / 2σ 2 ) Figure 5.15, page 211. Ricean Probability Distribution Function one dominant signal component along with weaker multipath signals dominant signal LOS path suburban or rural areas with light clutter see pg. 213 for equations Nothing else in Chapter 5 will be covered. Next lecture: Modulation techniques particularly suited for mobile radio. Lecture 6, Page 13 of 13