Chapter 7 Error Probabilities for Binary Signalling Error

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

Homework Assignments • Return date: 20 -12 -2005 • Assignments: Problem 7 -1 Problem 7 -5 Problem 7 -7 Problem 7 -10 Problem 7 -14 EEE 461 2

Error Probabilities for Binary Signaling • Develop the technique for finding the Bit-error-rate (BER) for binary signalling. • Noise is Gaussian EEE 461 3

Error Probabilities for Binary Signaling • Symbols transmitted once every Tb seconds • To transmit – Send s 1(t) for a “ 1” – Send s 0(t) for a “ 0” • Noise is Gaussian r(t)=s(t)+n(t) h(t) H(f) ro(t)=so(t)+no(t) t=to r(to)= ro s 0(t 0)=s 0 n 0(t 0)=n 0 Threshold Detector Decision: 1 if ro >VT 0 if ro < VT EEE 461 4

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) EEE 461 5

Error Probabilities for Binary Signaling • After a linear processing receiver circuit, the noise is still Gaussian. • The sampled received signal is r 0=s 0+n 0 r 0(t 0)=r 0, s 0(t 0)=s 0, n 0(t 0)=n 0 The probability of error can be found if the pdf’s and the threshold are specified EEE 461 6

Error Probabilities for Binary Signaling P(Error/s sent) 1 P(Error/s sent) 2 Threshold EEE 461 7

BER for Binary Signaling in Gaussian Noise • After a linear processing receiver circuit, the noise is still Gaussian. • Using Gaussian pdf’s, EEE 461 8

BER for Binary Signaling in Gaussian Noise EEE 461 9

BER for Binary Signaling in Gaussian Noise Using Matched Filter Reception EEE 461 10

BER for Binary Signaling in Gaussian Noise Using Matched Filter Reception EEE 461 11

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 log 10 scale. EEE 461 12