SYSC 4607 – Lecture 13 Outline
Review of Previous Lecture
 Outage Probability and Average Ps


Doppler Effects on Differential Modulations

ISI Effects for Frequency-Selective Fading

Modulations for Major Wireless Standards
Review of Previous Lecture

Error Probability Analysis – AWGN Channel

Ps   M Q  M  s


Performance of Digital Modulations on FlatFading Channels (Outage Probability and
Average Probability of Error)
Linear Modulations in Fading

For fading channels, SNR γs, and thus probability of
error Ps are random.

Performance metrics:
- Outage Probability Pout=p(Ps > Ptarget)=p(γs < γtarget)

- Average Ps :
Ps   Ps ( ) p ( ) d
0
- Combined outage and average Ps
Outage Probability
Ps
Outage
Ts
Ps(target)
t or d

Probability that Ps is above target

Equivalently, probability that s is below
target

Used when Tc>>Ts
Average Ps
Ts
Ps   Ps ( s ) p( s )d s
Ps
Ps
t or d




Expected value of random variable Ps
Used when Tc~Ts
Error probability much higher than in AWGN alone
Alternate Q function approach greatly simplifies
calculations
Average BER in AWGN and
Rayleigh Fading Channels
BER=10-3: SNR=8dB for AWGN
SNR=24dB for Rayleigh
Combined Outage and Average Ps
 s : random SNR for fixed path loss and shadowing, but
random fast fading.
Probability of Error = Ps(γs)
 s : random SNR for fixed path loss and random
shadowing, but averaged over fast fading, i.e.,  s  E( s )
Average Probability of Error = Ps ( s )
s
: average SNR for a fixed path loss; averaging
over fast fading and shadowing, i.e.,  s  E ( s )  E[ E ( s )]
Combined outage and average Ps
Ps(s)
Ps(s)
Outage
Pstarget
Ps(s)



Used in combined shadowing and flat-fading
Ps varies slowly, locally determined by flat fading
Declare outage when Ps above target value
Doppler Effects

High Doppler causes channel phase to
decorrelate between symbols

Leads to an irreducible error floor for
differential modulation schemes such as DPSK,
i.e., increasing power does not reduce error

Error floor depends on BDTs (equivalently,
Ts/Tc)
DPSK – Rician Fading

K b 
1  1  K   b (1   c ) 


Pb  
exp


2
1 K   b
1

K


b 



ρc is channel correlation coefficient after a bit time Tb,
and K is the ratio of LOS power to multipath power
Letting  b   : Pb, floor
(1   c )e  K

2

1  1   b (1   c ) 


P

 b
2
1  b

For K  0 (Rayleigh): 
1   c  c 0 1
P


 b, floor
2
2
Irreducible BER due to Doppler
f DTb  Tb / Tc

For fixed fD,
decreasing Tb
(increasing the bit rate)
decreases the error floor
DPSK in fast Rician fading ( Pb vs. b )
ISI Effects (Frequency-Selective Fading)


Delay spread exceeding a symbol time causes
ISI (self interference).
2
0
Ts
3
4
5
Tm
ISI leads to irreducible error floor


1
Increasing signal power increases ISI power
For ISI-free transmission: Ts>>Tm (Rs<<Bc)
ISI Effects (Frequency-Selective Fading)

Irreducible error rate is difficult to analyze. It depends
on the specific channel model and choice of
modulation. Closed form solution is often not possible.
Simulation-based studies available.

An approximation:
Pr
ˆ s 
, Ps   Ps (ˆ s ) p(ˆ s )dˆ s
N0 B  I
Pr and I are the power of LOS and ISI, respectively.
Irreducible BER due to ISI

Simulation results
(Ave. Irreducible BER
vs. d = σTm / Ts )
σTm
Rs
2.5μs
40 Kbaud
25μs
4 Kbaud
50ns
2Mbaud
Modulations for Major Standards

Second Generation:
- GSM: GMSK
- IS136: π/4DQPSK
- IS-95: BPSK/QPSK
- PDC: π/4DQPSK

Third Generation:
- CDMA2000: QPSK (DL), BPSK (UL) Phase I
MPSK (DL), QPSK (UL) Phase II
- W-CDMA: QPSK (DL), BPSK (UL)
Modulations for Major Standards

Wireless LAN
- 802.11: BPSK, QPSK
- 802.11a: BPSK, QPSK, MQAM
- 802.11b: BPSK, QPSK
- 802.11g: BPSK, QPSK, MQAM

Short Range Wireless Network
- ZigBee (802.15.4): BPSK, OQPSK
- Bluetooth(802.15.1): GFSK
- UWB (802.15.3): BPSK, QPSK (proposal)
Main Points

Fading greatly increases average Ps
- Alternate Q function approach simplifies Ps calculation, especially
its average value in fading
- Moment Generating Function approach can be used effectively for
average error probability calculations in fading



Doppler spread only impacts differential modulation,
causing an irreducible error floor at low data rates
Delay spread causes ISI and irreducible error floor or
imposes limits on transmission rates
Need to combat flat and frequency-selective fading
- Focus of the rest of the course