Modulate an 8-PSK signal, add white Gaussian noise, and plot the signal to visualize the effects of the noise.

Create a M-PSK modulator System object™. The default modulation order for the object is 8.

pskModulator = comm.PSKModulator;

Modulate the signal.

modData = pskModulator(randi([0 7],2000,1));

Add white Gaussian noise to the modulated signal by passing the signal through an additive white Gaussian noise (AWGN) channel.

channel = comm.AWGNChannel('EbNo',20,'BitsPerSymbol',3);

Transmit the signal through the AWGN channel.

channelOutput = channel(modData);

Plot the noiseless and noisy data by using scatter plots to visualize the effects of the noise.

scatterplot(modData)

scatterplot(channelOutput)

Change the EbNo property to 10 dB to increase the noise.

channel.EbNo = 10;

Pass the modulated data through the AWGN channel.

channelOutput = channel(modData);

Plot the channel output. You can see the effects of increased noise.

scatterplot(channelOutput)

Create 16-PSK modulator and demodulator System objects™ which use custom symbol mapping. Estimate the BER in an AWGN channel and compare the performance to a theoretical Gray-coded PSK system.

Create a custom symbol mapping for the 16-PSK modulation scheme. The 16 integer symbols must have values which fall between 0 and 15.

custMap = [0 2 4 6 8 10 12 14 15 13 11 9 7 5 3 1];

Create a 16-PSK modulator and demodulator pair having custom symbol mapping defined by the array, custMap.

pskModulator = comm.PSKModulator(16,'BitInput',true, ...
    'SymbolMapping','Custom','CustomSymbolMapping',custMap);
pskDemodulator = comm.PSKDemodulator(16,'BitOutput',true, ...
    'SymbolMapping','Custom','CustomSymbolMapping',custMap);

Display the modulator constellation.

constellation(pskModulator)

Create an AWGN channel System object for use with 16-ary data.

awgnChannel = comm.AWGNChannel('BitsPerSymbol',log2(16));

Create an error rate object to track the BER statistics.

errorRate = comm.ErrorRate;

Initialize the simulation vectors. The ${\mathit{E}}_{\mathrm{b}}/{\mathit{N}}_0$ is varied from 6 to 18 dB in 1 dB steps.

ebnoVec = 6:18;
ber = zeros(size(ebnoVec));

Estimate the BER by modulating binary data, passing it through an AWGN channel, demodulating the received signal, and collecting the error statistics.

for k = 1:length(ebnoVec)
    
    % Reset the error counter for each Eb/No value
    reset(errorRate)
    % Reset the array used to collect the error statistics
    errVec = [0 0 0];
    % Set the channel Eb/No
    awgnChannel.EbNo = ebnoVec(k);
    
    while errVec(2) < 200 && errVec(3) < 1e7
        % Generate a 1000-symbol frame
        data = randi([0 1],4000,1);
        % Modulate the binary data
        modData = pskModulator(data);
        % Pass the modulated data through the AWGN channel
        rxSig = awgnChannel(modData);
        % Demodulate the received signal
        rxData = pskDemodulator(rxSig);
        % Collect the error statistics
        errVec = errorRate(data,rxData);
    end
    
    % Save the BER data
    ber(k) = errVec(1);
end

Generate theoretical BER data for an AWGN channel using the berawgn function.

berTheory = berawgn(ebnoVec,'psk',16,'nondiff');

Plot the simulated and theoretical results. The 16-PSK modulation BER performance of the simulated custom symbol mapping is not as good as the theoretical prediction curve for Gray codes.

figure
semilogy(ebnoVec,[ber; berTheory])
xlabel('Eb/No (dB)')
ylabel('BER')
grid
legend('Simulation','Theory','location','ne')