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.