Radio Propagation Review Large scale effects Path loss Shadow fading Small-scale effects Rayleigh fading Doppler shift; Doppler spectrum Coherence time: time over which channel is stationary Coherence bandwidth: bandwidth over which channel is constant Delay spread: duration of multipath Intersymbol interference: interference among nearby transmitted symbols

Attenuation Power Law In dB: Pr = P0 (dB) – 10 n log (d) distance d reference distance d0=1 Reference power at reference distance d0 Path loss exponent P0 slope (n=2) = -20 dB per decade In dB: Pr = P0 (dB) – 10 n log (d) Pr (dB) slope = -40 (n=4) log (d)

Large-Scale Path Loss (Scatter Plot)

Shadow Fading Random variations in path loss as mobile moves around buildings, trees, etc. Modeled as an additional random variable: “normal” (Gaussian) probability distribution Pr = P0 – 10 n log d + X “log-normal” random variable standard deviation -  received power in dB For cellular:  is about 8 dB

Urban Multipath No direct Line of Sight between mobile and base Radio wave scatters off of buildings, cars, etc. Severe multipath

Small-Scale Fading Fade rate depends on Mobile speed Speed of surrounding objects Frequency

Combined Fading and Attenuation Received power Pr (dB) distance attenuation Time (mobile is moving away from base)

Combined Fading and Attenuation Received power Pr (dB) distance attenuation shadowing Time (mobile is moving away from base)

Combined Fading and Attenuation Received power Pr (dB) distance attenuation shadowing Rayleigh fading Time (mobile is moving away from base)

Time Variations: Doppler Shift velocity v distance d = v t Propagation delay = distance d / speed of light c = vt/c transmitted signal s(t) received signal r(t) propagation delay Received signal r(t) = sin 2f (t- vt/c) = sin 2(f – fv/c) t received frequency Doppler shift fd = -fv/c

Doppler (Frequency) Shift in phase out of phase Frequency= 1/50 Frequency= 1/45

Scattering: Doppler Spectrum distance d = v t transmitted signal s(t) Doppler Spectrum (shows relative strengths of Doppler shifts) Doppler shift fd power power 2fd frequency frequency of s(t) frequency frequency of s(t) + Doppler shift fd

Rayleigh Fading deep fade phase shift Received waveform Amplitude (dB)

Channel Coherence Time Coherence Time: Amplitude and phase are nearly constant. Rate of time variations depends on Doppler shift: (velocity X carrier frequency)/(speed of light) Coherence Time varies as 1/(Doppler shift).

Channel Characterizations: Time vs. Frequency Frequency-domain description Time-domain description Multipath channel Amplitude attenuation, Delay (phase shift) input s(t) is a sinusoid “narrowband” signal The impulse response is analogous to echoes heard when clapping your hands in an auditorium. r(t) s(t) Multipath channel time t time t multipath components input s(t) is an impulse (very short pulse) “wideband” signal (Note: an impulse has zero duration and infinite bandwidth!)

Pulse Width vs. Bandwidth Power signal pulse bandwidth = 1/T Narrowband frequency time T signal pulse Power bandwidth = 1/T Wideband time frequency T

Urban Multipath Delay spread s(t) Delay spread r(t) time t time t r(t) different location for receiver time t Spacing and attenuation of multipath components depend on location and environment.

Delay Spread and Intersymbol Interference s(t) r(t) Multipath channel time t time t Time between pulses is >> delay spread, therefore the received pulses do not interfere. r(t) s(t) Multipath channel time t Time between pulses is < delay spread, which causes intersymbol interference. The rate at which symbols can be transmitted without intersymbol interference is 1 / delay spread.

Coherence Bandwidth channel gain frequency f1 f2 coherence bandwidth Bc channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. frequency f1 f2 The channel gain is approximately constant within a coherence bandwidth Bc. Frequencies f1 and f2 fade independently if | f1 – f2 | >> Bc. If the signal bandwidth < coherence bandwidth Bc, then the channel is called flat fading, and the transmitted signal is regarded as narrowband. If the signal bandwidth > Bc, then the channel is called frequency-selective and the signal is regarded as wideband.

Coherence Bandwidth and Diversity signal power (wideband) coherence bandwidth Bc channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. frequency f1 f2 Frequency-selective fading: different parts of the signal (in frequency) are affected differently by fading. Wideband signals exploit frequency diversity. Spreading power across many coherence bands reduces the chances of severe fading. Wideband signals are distorted by the channel fading (distortion causes Intersymbol interference). What are advantages and disadvantages of frequency-selective fading?

Narrowband Signal signal power channel (narrowband) gain frequency f1 coherence bandwidth Bc channel gain Frequencies far outside the coherence bandwidth are affected differently by multipath. frequency f1 f2 Flat fading: the narrowband signal fades uniformly, hence does not benefit from frequency diversity. For the cellular band, Bc is around 100 to 300 kHz. How does this compare with the bandwidth of cellular systems?

Coherence Bandwidth and Delay Spread frequency channel gain coherence bandwidth Bc delay spread  channel gain delay spread  coherence bandwidth Bc frequency Coherence bandwidth is inversely proportional to delay spread: Bc ≈ 1/.

Pulse Width vs. Bandwidth Power signal pulse bandwidth = 1/T Narrowband frequency time T signal pulse Power bandwidth = 1/T Wideband T time frequency

Bandwidth and Multipath Resolution reflection (path 2) direct path (path 1) multipath components are resolvable received signal pulses  (delay spread) received signal pulses T >   T <  T Wide bandwidth  high resolution Receiver can clearly distinguish two paths. Narrow bandwidth  low resolution Receiver cannot distinguish the two paths.

Bandwidth and Multipath Resolution reflection (path 2) direct path (path 1) multipath components are resolvable signal pulse The receiver can easily distinguish the two paths provided that they are separated by much more than the pulse width T. Since the signal bandwidth B ≈ 1/T, this implies B >> 1/, or B >> Bc . . What are the advantages of having a wideband signal with resolvable multipath?  Wide bandwidth  high resolution Receiver can clearly distinguish two paths.

Multipath Resolution and Diversity reflection (path 2) direct path (path 1) multipath components are resolvable signal pulse Each path may undergo independent fading (i.e., due to Doppler). If one path is faded, the receiver may be able to detect the other path. In the frequency domain, this corresponds to independent fading in different coherence bands.  Wide bandwidth  high resolution Receiver can clearly distinguish two paths.

Bandwidth and Geolocation reflection delay  = 2 x distance/c delay  s(t) s(t) r(t) r(t) time t Narrow bandwidth pulse time t High bandwidth pulse

Bandwidth and Geolocation reflection delay  = 2 x distance/c s(t) The resolution of the delay measurement is roughly the width of the pulse. Low bandwidth  wide pulse  low resolution High bandwidth  narrow pulse  high resolution r(t) time t Ex: If the delay measurement changes by 1 microsec, the distance error is c x 10-6 = 300 meters!

Fast vs. Slow Fading transmitted bits time time received amplitude Fast fading: channel changes every few symbols. Coherence time is less than roughly 100 symbols. Slow fading: Coherence time lasts more than a few 100 symbols.

Fade Rate (Ex) fc = 900 MHz, v = 60 miles/hour  Doppler shift ≈ 80 Hz. Coherence time is roughly 1/80, or 10 msec Data rate (voice): 10 kbps or 0.1 msec/bit  100 bits within a coherence time (fast fading) GSM data rate: 270 kbps  about 3000 bits within a coherence time (slow fading)

Types of Small-Scale Fading Based on multipath time delay spread Flat Fading 1. BW of signal < Coherence BW 2. Delay spread < Symbol period Frequency Selective Fading 1. BW of signal > Coherence BW 2. Delay spread > Symbol period Based on Doppler spread Fast Fading 1. High Doppler spread 2. Coherence time spans a few symbols. 3. Channel variations faster than base- band signal variations Slow Fading 1. Low Doppler spread 2. Coherence time spans many symbols. 3. Channel variations slower than base-

Types of Small-Scale Signal Fading as a Function of Symbol Period and Signal Bandwidth Relative to delay spread T Flat Slow Fading Flat Fast Fading delay spread Frequency-Selective Slow Fading Frequency-Selective Fast Fading T  (coherence time) Symbol Period relative to coherence time. Signal BW relative to channel BW B Frequency Selective Fast Fading Frequency Selective Slow Fading coherence BW Bc Flat Fast Fading Flat Slow Fading B Bd = fd (Doppler shift) Signal bandwidth relative to Doppler shift

Fading Experienced by Wireless Systems Standard Flat/Freq.-Sel. Fast/Slow AMPS Flat Fast IS-136 Flat Fast GSM F-S Slow IS-95 (CDMA) F-S Fast 3G F-S Slow to Fast (depends on rate) 802.11 F-S Slow Bluetooth F-S Slow