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. 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

5. 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

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 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)

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) = S ak 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 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

12. 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)

13. 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)

14. 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

15. 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

16. Reading
Carlson Ch. 11.1, 11.2, 11.3