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ECE 6640Digital Communications
Dr. Bradley J. BazuinAssistant Professor
Department of Electrical and Computer EngineeringCollege of Engineering and Applied Sciences
ECE 6640 2
Chapter 4
4. Bandpass Modulation and Demodulation/Detection.1. Why Modulate? 2. Digital Bandpass Modulation Techniques. 3. Detection of Signals in Gaussian Noise. 4. Coherent Detection. 5. Noncoherent Detection. 6. Complex Envelope. 7. Error Performance for Binary Systems. 8. M-ary Signaling and Performance. 9. Symbol Error Performance for M-ary Systems (M>>2).
ECE 6640 3
Sklar’s Communications System
Notes and figures are based on or taken from materials in the course textbook: Bernard Sklar, Digital Communications, Fundamentals and Applications,
Prentice Hall PTR, Second Edition, 2001.
Notes on BER
• For MPSK and QAM– Sklar
• QAM p. 565• MPSK p. 229-230
– J.G. Proakis & M. Salehi, Digital Communications, 5th ed.• QAM p. 196-200• MPSK p. 190-195
– Jianhua Lu; Letaief, K.B.; Chuang, J. C-I; Liou, M.-L., "M-PSK and M-QAM BER computation using signal-space concepts," Communications, IEEE Transactions on , vol.47, no.2, pp.181,184, Feb 1999.
ECE 6640 4
MPSK BER Computations
ECE 6640 5
% Sklar (symbol error rate)PB1(:,ii) = 2*Q_fn(sqrt(2*Es_No)*sin(pi/M));PB1(:,ii) = PB1(:,ii)/bitpersym;
% Proakis (symbol error rate)PS(:,ii) = 2*Q_fn(sqrt(2*log2(M)*(Es_No/bitpersym)*sin(pi/M)^2));PB2(:,ii) = PS(:,ii)/bitpersym;
% Lu, Lataief, Chuang, and Liou (bit error rate)Qsum = 0;for jj=1:M/4
Qsum=Qsum+Q_fn(sqrt(2*Es_No)*sin((2*jj-1)*pi/M));endPB3(:,ii) = (2/log2(M))*Qsum;
MPSK BER Curves
ECE 6640 6-5 0 5 10 15 20 25 30 35 40
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100BER Composite Plot
Bit
Erro
r Rat
e
Eb/No (dB)
4 PSK8 PSK16 PSK32 PSK64 PSK128 PSK256 PSK
QAM BER Computation
ECE 6640 7
% Sklar (bit error rate)PB1(:,ii) = 2*((1-L^-1)/log2(L))*Q_fn(sqrt(3*log2(L)*2*Es_No/((M-1)*bitpersym)) );
% Proakis (symbol error rate)PB2(:,ii) = 2*(1-L^-1)*Q_fn(sqrt(3*log2(M)*Es_No/((M-1)*bitpersym)));PB2(:,ii) = 2*PB2(:,ii).*(1-0.5*PB2(:,ii));PB2(:,ii) = PB2(:,ii)/bitpersym;
% Lu, Lataief, Chuang, and Liou (bit error rate)Qsum = 0;for jj=1:L/2
Qsum=Qsum+Q_fn((2*jj-1)*sqrt(3*log2(M)*Es_No/((M-1)*bitpersym)));endPB3(:,ii) = 4*((1-L^-1)/log2(M))*Qsum;
QAM BER Curves
ECE 6640 8
0 5 10 15 20 25 3010-7
10-6
10-5
10-4
10-3
10-2
10-1
100BER Composite Plot
Bit
Erro
r Rat
e
Eb/No (dB)
4 QMA16 QAM64 QAM256 QAM
QAM BER Curves Detail/Differences
ECE 6640 9
-1 0 1 2 3 4 5 6 7 8 9 1010-2
10-1
100BER Composite Plot
Bit
Erro
r Rat
e
Eb/No (dB)
4 QMA16 QAM64 QAM256 QAM
Matlab Simulation
• MPSK_Filtered_TXRX_wNoise.m• QAM_Filtered_TXRX_wNoise.m
• Required Functions– Square Root Nyquist Filter
• nyq_fharris_odd.m• firrcos.m
ECE 6640 10
MPSK Nyquist Filter BERSER vs SNR
ECE 6640 11
0 5 10 15 20 25 30 35 40 45 50 5510-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
SNR (dB)
Sym
bol E
rror R
ate
MPSK Simulation: Theory vs. Simulation
T4S4T8S8T16S16T32S32T64S64T128S128T256S256
SklarTheory Plot
MPSK Nyquist Filter BERBER vs Eb/No
ECE 6640 12
-5 0 5 10 15 20 25 30 35 40 4510-7
10-6
10-5
10-4
10-3
10-2
10-1
100
EbNo (dB)
Bit
Erro
r Rat
eMPSK Simulation: Theory vs. Simulation
T4S4T8S8T16S16T32S32T64S64T128S128T256S256
SklarTheory Plot
QAM Nyquist Filter BERSER vs. SNR
ECE 6640 130 5 10 15 20 25 30 35
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
101
SNR (dB)
Sym
bol E
rror R
ateQAM Simulation: Theory vs. Simulation
T4S4T16S16T64S64T256S256
SklarTheory Plot
QAM Nyquist Filter BERBER vs Eb/No
ECE 6640 14
SklarTheory Plot
-5 0 5 10 15 20 2510-7
10-6
10-5
10-4
10-3
10-2
10-1
100
EbNo (dB)
Bit
Erro
r Rat
eQAM Simulation: Theory vs. Simulation
T4S4T16S16T64S64T256S256