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
Homework Assignments Return date: 20-12-2005 Assignments: Problem 7-1
Error Probabilities for Binary Signaling Develop the technique for finding the Bit-error-rate (BER) for binary signalling. Noise is Gaussian
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
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)
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
Error Probabilities for Binary Signaling P(Error/s2 sent) P(Error/s1 sent) Threshold
BER for Binary Signaling in Gaussian Noise After a linear processing receiver circuit, the noise is still Gaussian. Using Gaussian pdf’s,
BER for Binary Signaling in Gaussian Noise
BER for Binary Signaling in Gaussian Noise Using Matched Filter Reception
BER for Binary Signaling in Gaussian Noise Using Matched Filter Reception
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.