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EE354 : Communications System I

EE354 : Communications System I. Lecture 25,26,27: Digital communication Aliazam Abbasfar. Outline. Digital communication Baseband systems Optimum receiver. Digital communication. Transfer of digital messages from source to destination reliably Sometimes called signaling

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EE354 : Communications System I

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  1. EE354 : Communications System I Lecture 25,26,27: Digital communication Aliazam Abbasfar

  2. Outline • Digital communication • Baseband systems • Optimum receiver

  3. Digital communication • Transfer of digital messages from source to destination reliably • Sometimes called signaling • Digital message • Sequence of symbols (digits) • Symbols are chosen from an alphabet (M symbols) • Binary symbols : bits : alphabet {0,1} • Data rate • Symbol/Baud/Signaling rate (symbols per second) (r) • bit rate (bits per second) (rb) • Reliability is measured by probability of error • Symbol/Bit error rate (BER) • Packet error rate (PER) • BER targets • Voice : 10-5 • Data : 10-6 • Video : 10-7

  4. Channel decoder Demod Channel encoder Mod Digital systems message • Digital source • Digitized voice/images • Data • Source encoder and decoder • Data compression • Encryption • Channel encoder and decoder • Error detection/correction • Example : repetition code • Modulation/demodulation • Digital • Baseband/bandpass y(t) x(t) Source decoder Digital Source Source encoder Channel

  5. Pulse Amplitude Modulation (PAM) • A sequence of pulses with varying amplitudes • y(t) = Sak p(t- kT) + n(t) • T : symbol time • Inter-symbol interference (ISI) • y(kT) = ak p(0) + S am p(mT) + n(kT) • p(0) = 1; p(mT) = 0; for all m<>0 • Rectangular pulse • Sinc pulse • Symbols are mapped into pulse amplitudes (ak) • M-PAM has M levels  unipolar 2-PAM levels: {0, A} • Alphabet {0,1}  bipolar 2-PAM levels: {-A, A} • Alphabet {0,1}  bipolar 2-PAM levels: {-A, A} • Alphabet {0,1,2}  bipolar 3-PAM levels: {-A, 0, A} • Alphabet {0,1,2,3}  bipolar 4-PAM levels: {-3A, -A, A, 3A} • Data rate • Symbol rate : r= 1/T • Bit rate : rb = log2(M)/T • Example: binary signaling with rectangular pulse • Bipolar 2-PAM • RZ and NRZ y(t) T

  6. Performance with noise • AWGN with power s2 • E[n2(t)] = s2 • Sampled signal distribution • No ISI and p(0)=1 • z = y(kT) = ak + n(kT) • Symbol detection • Compare with thresholds • Slicer or A/D • Probability of error • Pe = S PiPe|i • Pe|i : probability of error for ith symbol • Unipolar binary : Pe = Q(A/2s) • Bipolar binary : Pe = Q(A/s) • Bipolar M-PAM : Pe = 2(1-1/M) Q(A/s) = 2(1-1/M) Q(Amax/(M-1)s)

  7. Analog vs Digital repeater • Digital (regenerative) repeater detects the symbols and regenerate them again • Pem = 1-(1-Pe)m m Pe • Accumulate errors • Analog repeater amplifies signal + noise • Accumulate noise • sm2 = m s2 • Pem = 2(1-1/M) Q(A/sm) • Hybrid repeater : A digital repeater after every m analog repeater • Pemxk = k Pem

  8. Pulse detector • x(t) = {0 or p(t)} + n(t) • p(t) is time-limited pulse • p(t) = 0; t<0 or t> T • AWGN with power spectral density of N0/2 • Rn(t) = N0/2 d(t) • Gn(f) = N0/2 • Filter x(t) with H(f) and sample at time T • Signal amplitude : • Noise power : • Maximize A/2s • Matched filter • H(f) = P(f)* e-j2pfT • h(t) = p(T-t) • Amax = Ep • s2 = EpN0/2 • Probability of error

  9. Correlator • Matched filter output is the correlation of the signal and the pulse • Detecting one out of two different pulses • y(t) = {p0(t) or p1(t)} + n(t) • y(t)-p0(t) = {0 or p1(t)-p0(t)} + n(t) • Correlate y(t) with p1(t)-p0(t) • Decision level : corr( [p1(t)+p0(t)]/2, p(t) ) • Error probability • Correlator receiver • Correlate y(t) with all pi(t) • Detected symbol based on the output of the correlators • If we have a series of pulses, each pulse is detected by correlation • y(t) = Sak p(t- kT) + n(t) • Correlate y(t) with p(t-kT)  ak

  10. ISI free matched filtering • ISI free : Matched filter output due to other pulses = 0 • Shifted versions of the pulse are orthogonal • combT(Rp(t))= Epd(t)  rep1/T(|P(f)|2) = Cte • Folded spectrum is flat • Band-limited pulses • Sinc pulse • Root raised cosine

  11. Power spectrum • x(t) = Sak p(t- kT) = [Sakd(t- kT)]  p(t) • Gx(f) = Ga(f) |P(f)|2 • Bipolar PAM : • Ga(f) = E[ak2]/T • Gx(f) = E[ak2]/T |P(f)|2 • Px = E[ak2] Ep/T = Es/T

  12. Bandpass modulations • Amplitude shift keying (ASK) • x(t) = Sak p(t- kT) • p(t) = cos(wct) • ak = 0 or A • Coherent detection • Down convert  unipolar 2-PAM • Envelope detector • Similar to AM (a strong carrier)

  13. PSK • Phase shift keying (PSK) • x(t) = S p(t- kT) • p(t) = cos(wct + Fk) • BPSK • Modulated bipolar 2-PAM • x(t) = Sak p(t- kT) • ak = -A or A • p(t) = cos(wct) • QPSK • x(t) = Sak p1(t- kT) + bk p2(t- kT) • ak = -A or A • p1(t) = cos(wct) • p2(t) = sin(wct)

  14. QAM • Quadrature amplitude modulation(QAM) • Amplitude and phase modulations • x(t) = Sak p1(t- kT) + bk p2(t- kT) • p1(t) = cos(wct) • p2(t) = sin(wct) • 2 independent PAM

  15. FSK • Frequency shift keying (FSK) • Two different frequencies fc1 and fc2 • x(t) = {A cos(wc1t) or A cos(wc2t)} • Coherent detection • Ep1-p2 = 2K Eb • K=1 when orthogonal pulses • Non-coherent detection • Use frequency detectors

  16. Reading • Carlson Ch. 11.1, 11.2, 11.3

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