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

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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

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MPSK Nyquist Filter BERSER vs SNR

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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