1. EE 6332, Spring, 2017 Wireless Telecommunication
                                                           
Zhu Han
Department of Electrical and Computer Engineering
Class 17
Mar. 27th, 2017

2. Outline BER Performance AWGN Channel Fading Channel Chapter 6.1 AWGN
ECE 6331, Spring 2009 2

3. Baseline: Stationary Channel
BPSK modulation
y: the received signal
x: the transmitted signal with amplitude a
w: white noise with power N0

4. Bit Error Probability d(i) gTx(t) gRx(t) Noise na(t) We assume:
binary transmission with
transmission system fulfills 1st Nyquist criterion
noise , independent of data source
Probability density function (pdf) of
Mean and variance

5. Conditional pdfs
The transmission system induces two conditional pdfs depending on if if

6. Example of samples of matched filter output for some bandpass modulation schemes

7. Figure 5.8 Illustrating the partitioning of the observation space into decision regions for the case when N  2 and M  4; it is assumed that the M transmitted symbols are equally likely.

8. Probability of wrong decisions
Placing a threshold
Probability of wrong decision
When we define and as equal a-priori probabilities of and
we will get the bit error probability s

9. Conditions for illustrative solution
With 
and 
equivalently
with 
substituting
for

10. Special Case: Gaussian distributed noise
Motivation:
many independent interferers
central limit theorem
Gaussian distribution é ù 2 1 ê 2 - ú  = - ò P 1 e 2 s 2 d ê N b ú 2 2 p s ë ê N ú û
no closed solution
Definition of Error Function and Error Function Complement

11. Error function and its complement
function y = Q(x)
y = 0.5*erfc(x/sqrt(2)); -3 -2 -1 1 2 3
-1.5
-0.5
0.5
1.5
2.5
erf(x)
erfc(x)
erf(x), erfc(x) x

12. Bit error rate with error function complement
Expressions with and
antipodal:
unipolar
Q function

13. Bit error rate for unipolar and antipodal transmission
BER vs. SNR
theoretical 10 -1
simulation
unipolar 10 -2
BER
antipodal 10 -3 10 -4 -2 2 4 6 8 10

14. Assume h is Gaussian random:
Flat Fading Channel
Assume h is Gaussian random:
BPSK:
Conditional on h,
6.154, 6.155
Averaged over h, which follows chi-square distribution
at high SNR.

15. Effects of Fading
Other modulation 15

16. Simulation of Fading and Multipath16

17. Irreducible Bit Error Rate due to multipath
Error floor 17

18. Irreducible BER due to fading18

19. Irreducible BER due to fading19

20. BER due to fading & multipath20

21. Homework 4
5.4, 5.5,5.9, 5.17,5.18, 6.1, 6.12, 6.16
Due 4/10
ECE6331 Spring 2009