Contents 16 Hrs Introduction Geometric rep.of the sig waveforms Pulse amplitude modulation 2-d signal waveforms M-d signal waveforms ■Opt.reception for the sig.in AWGN ■Optimal receivers and probs of err UESTC-Digital transmission through the AWGN channel Prof李晓峰 2
5.5 Opt.reception for the sig.In AWGN In the nth interval,the process is as follows, {,an,} {,an…} s(1) r(t) The topics are: 1)The Correlation-Demodulators 2)The MF-Demodulators 3)The Theory of Optimum Detectors 5.6 Typical Optimal Receivers ·Binary signals r(t) Carrier-amp(1-D signals) Carrier-phs (2-D signals) It is convenient to divide the receiv QAM (2-D signals) 1)Demodulator:produce an obse 。 FSK (M-D orthogonal signals) 2)Detector:estimate the sym from the observation UESTC-Digital transmission through the AWGN channel Prof李晓峰 3
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h(1)=Cs(T-1),where C is any non-zero constant and T is a given sample-time.. Consider a signal s(t)being corrupted as r(t)=s(t)+n(t),where n(t)is AWGN.Suppose that r(t)is measured as follows. Sampling r() y() (T) h(r) The filter h(t)is to reduce the noise and sampling is to obtain a measurement. We design the filter h(t)to obtain max-SNR in y(T),so that a GOOD measurement is obtained. UESTC-Digital transmission through the AWGN channel Prof李晓峰 4
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h(1)=Cs(T-1),where C is any non-zero constant and T is a given sample-time.. Consider a signal s(t)being corrupted as r(t)=s(t)+n(t),where n(t)is AWGN.Suppose that r(t)is measured as follows. Sampling r() y() y(I) h(r) Properties of MF: If a given signal is corrupted by AWGN,a matched filter to the signal maximizes the output SNR. Simply,MF is the optimal filter for this case UESTC-Digital transmission through the AWGN channel Prof李晓峰 5
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h(t)=Cs(T-1),where C is any non-zero constant and T is a given sample-time.. The SNR is defined as, Consider a signal s(t)b (h(r)s(T--)dr n(t)is AWGN.Suppose that r(t) E["h(t)n(T-t)dt Sampling r() y() y(T) h(r) Compute, )=h0）*ro0以lgA(ert-dr=∫lrrT-rdr =["h(c)s(-r)dr+["h(r)n(i-r)dr UESTC-Digital transmission through the AWGN channel Prof李晓峰 6
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h(1)=Cs(T-1),where C is any non-zero constant and T is a given sample-time.. The SNR is defined as, Consider a signal s(t)b 2GgE 2E, n(t)is AWGN.Suppose that r(t NoGE No Sampling r() y() (T) MF is the optimal filter h(r) when h(t)=Cs(T-t) Compute, T)=h0*r0lhr=∫h(r)rt-r)dr,=∫hr)rT-r)dr =∫h(r)s(T-x)dr+∫hr)n(T-x)dr UESTC-Digital transmission through the AWGN channel Prof李晓峰 7
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h()=Cs(T-1),where C is any non-zero constant and T is y(r) s(0 h(0=s(T-0l (T刀 A A corrupted as is easured as fo 0 Sampling 0 2T r() y() y(T) MF is the optimal filter h(r) whenh(t)=Cs(T-1) Compute, I)=h0*r0lhr=∫h(r)rt-r)dr,=∫hr)rT-r)dr =∫h(r)s(T-x)dr+∫h(r)n(T-t)dr UESTC-Digital transmission through the AWGN channel Prof李晓峰 8
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h()=Cs(T-1),where C is any non-zero constant and T is a given sample-time.. A MF to W(1) Sampling r(0) h(0)= y() x(I) MF is the optimal filter ”(T-) Compute, T)= h)*r(r =he)r(-)dr =∫he)r(T-rdr =h(r)s(T-r)dr+[h(r)n(T-r)dr UESTC-Digital transmission through the AWGN channel Prof李晓峰 9
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h()=Cs(T-1),where C is any non-zero constant and T is a given sample-time.. A MF tox(t) Sampling r() h(0)= y() y(T) MF is the optimal filter (T-) Compute, A matched filter is .0fr(rh-t)dr∫r(w[T equivalent to a correlator. An alternate demodulator S0, y(T=r(r)w(r)dr☑ is as Fig 5.35 on page 276. UESTC-Digital transmission through the AWGN channel Prof李晓峰 10
5.5.2 Matched-filter type demodulator A Matched Filter (MF)to s(t)is defined as a LTI filter whose impulse response is as h(1)=Cs(T-1),where C is any non-zero constant and T is a given sample-time.. 中() )dt (T-0 ()d 2(T-0 r(r) r(0 A matched filter is equivalent to a correlator. w(T-) An alternate demodulator is as Fig 5.35 on page 276. UESTC-Digital transmission through the AWGN channel Prof李晓峰 11