1. EEE 441 Wireless And Mobile Communications
Lecture 11
EEE 441 Wireless And Mobile Communications

2. Mobile Multipath Channel Parameters
Time Dispersion Parameters
Mean Access Delay
RMS Delay Spread
Coherence Bandwidth
Doppler Spread and Coherence Time

3. Time Dispersion Parameters
Measured from Power Delay Profiles
Plots of relative received power as a function of excess delay
Found by averaging intantaneous power delay measurements over a local area
Outdoor local area usually no greater than 6 metres
Indoor local area usually no greater than 2 metres
Samples taken at l/4 metres approximately

4. Outdoor Power Delay Profile

5. Indoor Power Delay Profile

6. Noise Threshold
The values of time dispersion parameters also depend on the noise threshold
Noise level = the level of power below which signal is considered noise
If noise threshold is set too low, then the noise will be processed as valid multipath component
Thus causing the parameters to be higher

7. Time Dispersion Parameters: Eqns
Determined from a power delay profile
Mean excess delay( ):
Rms delay spread (st):

8. Example 1 Pr(\tau) in dB -10 -20 \tau in microseconds 1 2 5
-10
-20
\tau in microseconds 1 2 5
E[\tau] = [(0.01)(0)+(0.1)(1)+(0.1)(2)+(1)(5)]/[ ]
= 4.38 microseconds;
E[\tau^2] = [(0.01)(0^2)+(0.1)(1^2)+(0.1)(2^2)+(1)(5^2)]/[ ]
= microseconds;
RMS delay spread = sqrt[ E[\tau^2] – {E[\tau]}^2 ] = 1.37 microseconds.

9. Coherence Bandwidth
Bc = Range of frequencies over which the channel can be considered flat
i.e. channel passes all spectral components with equal gain and linear phase
Is a function of the RMS delay spread
Two sinusoids with frequency separation > Bc are affected differently by the channel f1
Receiver f2
Multipath Channel
Frequency Separation: |f1-f2|

10. Coherence Bandwidth (cont’d)
Frequency correlation between two sinusoids: 0 <= C[f1, f2] <= 1
If we define Coherence Bandwidth (BC) as the range of frequencies over which the frequency correlation is above 0.9, then:
s is rms delay spread.
If we define Coherence Bandwidth as the range of frequencies over which the frequency correlation is above 0.5, then:
s is rms delay spread.

11. Example 1 (cont’d) For a multipath channel, s is given as 1.37ms
Then 50% coherence bandwidth will be:
1/5s = 146 kHz
This means that, the range of transmission frequency (channel bandwidth) should not exceed 146kHz
Then all frequencies in the band will experience the same channel characteristics
This coherence bandwidth enough for AMPS channel (30kHz channels), but not GSM channel (200kHz channels)

12. Doppler Spread and Coherence Time
Time Dispersion Parameters and Coherence Bandwidth
describe the time-dispersive nature of the channel with a stationary receiver
Doppler Spread and Coherence Time
describe the time varying-nature of the channel with relative motion between the Tx and Rx,
or by motion of objects in the channel
Coherence Time is time-domain dual of Doppler Spread

13. Doppler Spread
Measure of spectral broadening caused by relative motion
We know how to compute Doppler shift: fd
Doppler Spread, BD = fm is defined as the
maximum possible Doppler shift
If the Signal Bandwidth >> BD = fm,
then effect of Doppler Spread negligible at receiver

14. Doppler Spread and Coherence Time: Equations
Doppler shift : fd = (v/).cos,
where wavelength  = c / fc
Doppler Spread, BD = fm = Max possible Doppler shift = v/
Coherence Time,

15. Doppler Spread and Coherence Time: Equations (cont’d)
Coherence time is also defined as:
Coherence time definition implies that two signals arriving with a time separation greater than TC are affected differently by the channel

16. Minimum Symbol Rate needed to counter Doppler Spread
Coherence Time is the time duration over which the channel impulse response is essentially invariant
If symbol period of baseband signal Ts > coherence time TC , then the signal will distort, since channel will change during the transmission TS TC f2 f1
Dt=t2 - t1 t1 t2

17. Doppler Spread and Coherence Time: Summary
Doppler Spread definition implies that if the signal bandwidth is much greater than BD = fm, then effect of Doppler frequency shift is negligible at the receiver
Coherence time definition implies that two signals arriving with a time separation less than TC are affected similarly by the channel

18. Types of Fading

19. Types of Small-scale Fading

20. Flat Fading Occurs when Signal BW, BS << coherence BW, BC
Implies that channel has constant gain and linear phase response over BW which is > signal BW
Usually manifested by amplitude falling with distance according to the Rayleigh distribution
Counteract problem by increasing Tx power

21. Flat Fading: Figures t << TS Occurs when:
h(t,t)
s(t)
r(t)
t << TS TS t
TS+t
S(f)
R(f)
H(f) fC fC fC
Occurs when:
BS << BC
and
TS >> st
BC: Coherence bandwidth BS: Signal bandwidth
TS: Symbol period st: Delay Spread

22. Frequency Selective Fading
Occurs when Signal BW, BS > Coherence BW, BC
Then symbol period < channel multipath delay spread
Leads to
symbols facing Time Dispersion
channel facing Intersymbol Interference (ISI)

23. Frequency Selective Fading: Figures
h(t,t)
s(t)
r(t)
t >> TS TS t TS
TS+t
Causes distortion of the received baseband signal
Causes Inter-Symbol Interference (ISI)
Occurs when:
BS > BC
and
TS << st
As a rule of thumb:
TS < 10st

24. Fast Fading Due to Doppler Spread
Occurs when rate of change of signal < rate of change of channel characteristics
Happen when symbol period TS > coherence time TC
Only occurs for very low data rates (i.e. large TS)
Occurs when:
BS < BD
and
TS > TC
BS: Bandwidth of the signal BD: Doppler Spread
TS: Symbol Period TC: Coherence Bandwidth

25. Slow Fading Due to Doppler Spread
Occurs when rate of change of signal >> rate of change of channel characteristics
Happen when symbol period TS << coherence time TC
Velocity of mobile determines BD, hence determines if fading is Fast or Slow
Occurs when:
BS >> BD
and
TS << TC
BS: Bandwidth of the signal BD: Doppler Spread
TS: Symbol Period TC: Coherence Bandwidth

26. Different Types of FadingTS
Flat,
Fast
Flat,
Slow
Symbol Period of
Transmitting Signal st
Frequency Selective,
Slow
Frequency Selective,
Fast TS TC
Transmitted Symbol Period
w.r.t SYMBOL PERIOD

27. Different Types of Fading (cont’d)BS
Frequency Selective,
Fast
Frequency Selective,
Slow
Transmitted Baseband
Signal Bandwidth BC
Flat,
Fast
Flat,
Slow BS BD
Transmitted Baseband Signal Bandwidth
w.r.t BASEBAND SIGNAL BANDWIDTH

28. Notices Read Rappaport, Ch. 5.4-5.5
Special Attn: Rappaport, Examples