Estimate BER of 8-PSK in AWGN with Reed-Solomon Coding

Transmit Reed-Solomon encoded data using 8-PSK over an AWGN channel. Demodulate and decode the received signal and collect error statistics. Plot the bit error rate estimate.

Define the example parameters.

M = 8;  % Modulation order
bps = log2(M); % Bits per symbol
N = 7; % RS codeword length
K = 5; % RS message length

Create modulator, demodulator, AWGN channel, and error rate objects.

pskModulator = comm.PSKModulator('ModulationOrder',M,'BitInput',true);
pskDemodulator = comm.PSKDemodulator('ModulationOrder',M,'BitOutput',true);
awgnChannel = comm.AWGNChannel('BitsPerSymbol',bps);
errorRate = comm.ErrorRate;

Create a (7,5) Reed-Solomon encoder and decoder pair which accepts bit inputs.

rsEncoder = comm.RSEncoder('BitInput',true,'CodewordLength',N,'MessageLength',K);
rsDecoder = comm.RSDecoder('BitInput',true,'CodewordLength',N,'MessageLength',K);

Set the range of $$E_b/N_0$$ values. Initialize the error statistics matrix.

ebnoVec = (3:0.5:8)';
errorStats = zeros(length(ebnoVec),3);

Estimate the bit error rate for each $$E_b/N_0$$ value. The simulation runs until either 100 errors or $$10^7$$ bits is encountered. The main simulation loop processing includes encoding, modulation, demodulation, and decoding.

for i = 1:length(ebnoVec)
    awgnChannel.EbNo = ebnoVec(i);
    reset(errorRate)
    while errorStats(i,2) < 100 && errorStats(i,3) < 1e7
        data = randi([0 1],1500,1); % Generate binary data
        encData = rsEncoder(data); % RS encode
        modData = pskModulator(encData); % Modulate
        rxSig = awgnChannel(modData); % Pass signal through AWGN
        rxData = pskDemodulator(rxSig); % Demodulate
        decData = rsDecoder(rxData); % RS decode
        errorStats(i,:) = errorRate(data,decData); % Collect error statistics
    end
end

Fit a curve to the BER data using berfit. Generate an estimate of 8-PSK performance without coding using the berawgn function.

berCurveFit = berfit(ebnoVec,errorStats(:,1));
berNoCoding = berawgn(ebnoVec,'psk',8,'nondiff');

Plot the BER data, the BER curve fit, and the estimated performance without RS coding.

semilogy(ebnoVec,errorStats(:,1),'b*', ...
ebnoVec,berCurveFit,'c-',ebnoVec,berNoCoding,'r')
ylabel('BER')
xlabel('Eb/No (dB)')
legend('Data','Curve Fit','No Coding')
grid

The (7,5) RS code improves the $$E_b/N_0$$ required to achieve a $$10^{-2}$$ bit error rate by, approximately, 1.4 dB.

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