1. 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

2. 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)

3. Large-Scale Path Loss (Scatter Plot)

4. 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

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

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

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

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

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

10. 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

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

12. 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

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

14. 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).

15. 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!)

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

17. 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.

18. 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.

19. 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.

20. 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?

21. 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?

22. 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/.

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

24. 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.

25. 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.

26. 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.

27. 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

28. 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!

29. 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.

30. 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)

31. 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-

32. 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

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