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Chapter 7 Error Probabilities for Binary Signalling

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

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Chapter 7 Error Probabilities for Binary Signalling

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  1. Chapter 7Error 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 Problem 7-5 Problem 7-7 Problem 7-10 Problem 7-14

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

  4. t=to ro(t)=so(t)+no(t) h(t) H(f) r(t)=s(t)+n(t) Threshold Detector 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 Decision: 1if ro >VT 0if ro < VT r(to)= ro s0(t0)=s0 n0(t0)=n0

  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 NoiseUsing Matched Filter Reception

  11. BER for Binary Signaling in Gaussian NoiseUsing Matched Filter Reception

  12. BER for Binary Signaling in Gaussian NoiseUsing 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.

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