1. Chapter 7 Error Probabilities for Binary Signalling
Error Probability for Binary Signalling
Probability of Error in Gaussian Noise
Optimum Binary Reception
Huseyin Bilgekul
EEE 461 Communication Systems II
Department of Electrical and Electronic Engineering
Eastern Mediterranean University

2. Homework Assignments Return date: 20-12-2005 Assignments: Problem 7-1

3. Error Probabilities for Binary Signaling
Develop the technique for finding the Bit-error-rate (BER) for binary signalling.
Noise is Gaussian

4. Error Probabilities for Binary Signaling
Symbols transmitted once every Tb seconds
To transmit
Send s1(t) for a “1”
Send s0(t) for a “0”
Noise is Gaussian
h(t)
H(f)
Threshold
Detector
t=to
r(t)=s(t)+n(t)
ro(t)=so(t)+no(t)
r(to)= ro
s0(t0)=s0
n0(t0)=n0
Decision:
1 if ro >VT
0 if ro < VT

5. Error Probabilities for Binary Signaling
Develop the technique for finding the Bit-error-rate (BER) for binary signaling.
Noise is Gaussian
Transmitted signal waveform over (0, T) is s(t)

6. Error Probabilities for Binary Signaling
After a linear processing receiver circuit, the noise is still Gaussian.
The sampled received signal is r0=s0+n0 r0(t0)=r0, s0(t0)=s0, n0(t0)=n0
The probability of error can be found if the pdf’s and the threshold are specified

7. Error Probabilities for Binary Signaling
P(Error/s2 sent)
P(Error/s1 sent)
Threshold

8. BER for Binary Signaling in Gaussian Noise
After a linear processing receiver circuit, the noise is still Gaussian.
Using Gaussian pdf’s,

9. BER for Binary Signaling in Gaussian Noise

10. BER for Binary Signaling in Gaussian Noise Using Matched Filter Reception

11. BER for Binary Signaling in Gaussian Noise Using Matched Filter Reception

12. BER for Binary Signaling in Gaussian Noise Using Matched Filter Reception
Error is expressed in terms of the difference signal energy at the receiver input (Ed).
Performance depends on pulse energy not pulse shape.
Probability axis usually on a log10 scale.