Chapter 9 Detection of Signal in Noise

1. Chapter 9 Detection of Signal in Noise • Content • Detection of Known Signals in WGN • Receiver Performance • Detection of Random Signals in WGN • Signal Processing examples

2. 9.1 Detection of Known Signals in WGN Designa a receiver which operates on the reveiver signal z(t) Two possible hypotheses Or

3. Assume Where the moise is WGN,with mean zero and spectral density N0/2

4. In order for the noise samples to be independent,we must sample z(t) at intervals Then LRT is

6. Log LRT is So that the decision rule can be written as

7. + Threshold comparetor y1(t) z(t) -  y0(t) Correlation receiver for binary decision problem

8. Alterative form t=T h1(t)=y1(T-t) + TC z(t) - t=T decision h0(t)=y0(T-t) 

9. 9.2 Receiver Perfromance Decision rule in the following equivalent form: We note that I is a Gaussian variable under both hypotheses.Under H0

11. Similarly Let

13. For equally likely hypotheses and the minimum probability of error criterion, For =-1，that is y0(t)=-y1(t) ，The detector is optimum.The detector is known as a ideal binary comminication system.

14. Examples :We will determine the performance of the three commonly used communication systems in which the binary signals are sine waves.We will assume that the signals are phase-synchronized at the transmitting systems are reffered to as “coherent” systems .we will use the minimum probabilty of error criterion in all cases.

15. In coherent phase shift keying(CPSK),the signal In coherent Frquency (CFSK)，the binary signals are

16. In on-off keying(OOK)，