ECE 6640 Digital Communications Dr. Bradley J. Bazuin Assistant Professor Department of Electrical and Computer Engineering College of Engineering and Applied Sciences
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