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 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

Digital systems Channel encoder Mod Digital Source Source encoder message Channel encoder Mod x(t) y(t) Digital Source Source encoder Channel decoder Demod Source decoder Channel 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

Pulse Amplitude Modulation (PAM) A sequence of pulses with varying amplitudes y(t) = S ak 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 {0,1,2}  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

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 Pi Pe|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)

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

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

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) = S ak p(t- kT) + n(t) Correlate y(t) with p(t-kT)  ak

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

Power spectrum Gx(f) = Ga(f) |P(f)|2 Bipolar PAM : x(t) = S ak p(t- kT) = [S ak d(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

Bandpass modulations Envelope detector Amplitude shift keying (ASK) x(t) = S ak 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)

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

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

FSK Non-coherent detection 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

Reading Carlson Ch. 11.1, 11.2, 11.3