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EE354 : Communications System I

EE354 : Communications System I. Lecture 22-23: Performance with AWGN Aliazam Abbasfar. Outline. Performance metrics Performance of different modulations. Signal to noise ratio (SNR). Baseband SNR SNR B = S R / N B = P R / P NB Band-limited signal:

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EE354 : Communications System I

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  1. EE354 : Communications System I Lecture 22-23: Performance with AWGN Aliazam Abbasfar

  2. Outline • Performance metrics • Performance of different modulations

  3. Signal to noise ratio (SNR) • Baseband SNR • SNRB = SR / NB = PR / PNB • Band-limited signal: • SNRB = g= PR / N0 W • (Received) Bandpass SNR • SNRR = SR / NR = PR / PNR = PR / N0 BT • Post-detection SNR • SNR = S/N = PS / PN • Detection gain = SNR/SNRR

  4. DSB • Transmitted signal • xo(t) = Ac x(t) cos(wct) • SNRB = PC PX /(N0W) • Received signal • v(t) = Ac x(t) cos(wct) + n(t) • SNRR = PC PX /(2N0W) • PR = PC PX • PNR = N0 (2W) • Coherent detection • y(t) = 2A cos(wct) [ Ac x(t) cos(wct) + nI(t) cos(wct) - nQ(t) sin(wct)] • SNR = PC PX /(N0W) = SNRB = 2 SNRR • PS = 2 A2 PC PX • PN = 2 A2 N0 W • Detection gain = 3 dB • nQ(t) was removed

  5. AM • Transmitted signal • xo(t) = Ac [1+m x(t)] cos(wct) • SNRB = PC (1 + m2 PX)/(N0W) • Received signal • v(t) = Ac [1+m x(t)] x(t) cos(wct) + n(t) • SNRR = PC (1 + m2 PX) /(2 N0W) • PR = PC (1 + m2 PX) • PNR = N0 (2W) • Coherent detection • y(t) = 2A cos(wct) [ Ac (1+m x(t)) cos(wct) + nI(t) cos(wct) - nQ(t) sin(wct)] • SNR = m2 PC PX /(N0W) = hAM SNRB = 2hAM SNRR • PS = 2 A2 m2 PC PX • PNR = 2 A2 N0 W • Detection gain = 2hAM < 1 • nQ(t) was removed • Much of TX power is wasted

  6. AM • Envelope detection • v(t) = Ac (1+m x(t)) cos(wct) + nI(t) cos(wct) - nQ(t) sin(wct) • Av(t) = | Ac(1+m x(t))+nI(t) + j nQ(t) | • Ac >> An(t) • Av(t) = Ac(1+m x(t))+nI(t) • SNR = m2 PC PX /(N0W) = hAM SNRB = 2hAM SNRR • PS = 2 m2 PC PX • PNR = 2 N0 W • Similar to coherent detection • Ac << An(t) • Av(t) = An(t) + Ac(1+m x(t)) cos(fn(t)) • Signal mutilation • Threshold effect • SNRRth = 10 = 10dB • Ac > An(t) in 99% of time • SNRR > SNR > Required SNR > SNRRth • Threshold effect is not a serious limitation

  7. SSB • Transmitted signal • xo(t) = Ac x(t) cos(wct) - Ac x(t) sin(wct) • SNRB = 2 PC PX /(N0W) • Received signal • r(t) = Ac x(t) cos(wct) - Ac x(t) sin(wct) + n(t) • SNRR = 2 PC PX /(N0W) • PR = 2 PC PX • PNR = N0 (W) • Coherent detection • y(t) = 2A cos(wct) [ Ac x(t) cos(wct) - Ac x(t) sin(wct) + nI(t) cos(wct) - nQ(t) sin(wct)] • SNR = 2 PC PX /(N0W) = SNRB = SNRR • PS = 2 A2 PC PX • PN = A2 N0 W • Detection gain = 0 dB • Cannot do better than baseband

  8. FM • Transmitted signal • xo(t) = Accos(wct + f(t)) • SNRB = Pc /(N0W) • Received signal • v(t) = Accos(wct + f(t)) + An(t) cos(wct + fn(t)) • fv(t) = f(t) + fe(t) • SNRR = Pc /(N0 BT) = (W/BT) SNRB • Discriminator detection • Ac >> An(t) • fv(t) = f(t) + nQ(t)/Ac • z(t) = 1/2p d fv(t) /dt = fDx(t) + n’(t) • SNR = 3 D2 PX PC /(N0W) = 3 D2 PX SNRB • PS = fD2 PX • PN = N0 W3/(3Ac2) • D= fD/W • Detection gain = 3 D2 (D+1) PX • Needs post-detection filtering • Can do better than baseband • Bandwidth and SNR trade-off • Example : Radio FM • fD = 75KHz, W=15KHz  D=5, Px=0.5  SNR = 38 SNRB

  9. FM • Ac < An(t) (Low SNRR ) • Spikes • SNR drop • Threshold effect • SNRRth = 10 = 10dB • SNRBth = 20(D+1) • SNRth = 60 D2(D+1) PX • SNR > Required SNR • SNRR > SNRRth • Threshold effect may be the system limitation (SNRR < SNR) • Example : • SNR > 50dB, Px = 0.5, W= 15 KHz • minimum D = 15  SNRBth = 20(15+1)=320 • minimum PR = 320 (N0W)

  10. Reading • Carlson Ch. 10.1, 10.2, 10.3 • Proakis & Salehi 5.1, 5.3

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