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QPSK and OFDM with MATLAB System Objects

This example shows how to simulate a basic communication system in which the signal is first QPSK modulated and then subjected to Orthogonal Frequency Division Multiplexing. The signal is then passed through an additive white Gaussian noise channel prior to being demultiplexed and demodulated. Lastly, the number of bit errors are calculated. The example showcases the use of MATLAB® System objects™.

Set the simulation parameters.

M = 4;                 % Modulation alphabet
k = log2(M);           % Bits/symbol
numSC = 128;           % Number of OFDM subcarriers
cpLen = 32;            % OFDM cyclic prefix length
maxBitErrors = 100;    % Maximum number of bit errors
maxNumBits = 1e7;      % Maximum number of bits transmitted

Construct System objects needed for the simulation: QPSK modulator, QPSK demodulator, OFDM modulator, OFDM demodulator, AWGN channel, and an error rate calculator. Use name-value pairs to set the object properties.

Set the QPSK modulator and demodulator so that they accept binary inputs.

qpskMod = comm.QPSKModulator('BitInput',true);
qpskDemod = comm.QPSKDemodulator('BitOutput',true);

Set the OFDM modulator and demodulator pair according to the simulation parameters.

ofdmMod = comm.OFDMModulator('FFTLength',numSC,'CyclicPrefixLength',cpLen);
ofdmDemod = comm.OFDMDemodulator('FFTLength',numSC,'CyclicPrefixLength',cpLen);

Set the NoiseMethod property of the AWGN channel object to Variance and define the VarianceSource property so that the noise power can be set from an input port.

channel = comm.AWGNChannel('NoiseMethod','Variance', ...
    'VarianceSource','Input port');

Set the ResetInputPort property to true to enable the error rate calculator to be reset during the simulation.

errorRate = comm.ErrorRate('ResetInputPort',true);

Use the info function of the ofdmMod object to determine the input and output dimensions of the OFDM modulator.

ofdmDims = info(ofdmMod)
ofdmDims = struct with fields:
    DataInputSize: [117 1]
       OutputSize: [160 1]

Determine the number of data subcarriers from the ofdmDims structure variable.

numDC = ofdmDims.DataInputSize(1)
numDC = 117

Determine the OFDM frame size (in bits) from the number of data subcarriers and the number of bits per symbol.

frameSize = [k*numDC 1];

Set the SNR vector based on the desired Eb/No range, the number of bits per symbol, and the ratio of the number of data subcarriers to the total number of subcarriers.

EbNoVec = (0:10)';
snrVec = EbNoVec + 10*log10(k) + 10*log10(numDC/numSC);

Initialize the BER and error statistics arrays.

berVec = zeros(length(EbNoVec),3);
errorStats = zeros(1,3);

Simulate the communication link over the range of Eb/No values. For each Eb/No value, the simulation runs until either maxBitErrors are recorded or the total number of transmitted bits exceeds maxNumBits.

for m = 1:length(EbNoVec)
    snr = snrVec(m);
    while errorStats(2) <= maxBitErrors && errorStats(3) <= maxNumBits
        dataIn = randi([0,1],frameSize);              % Generate binary data
        qpskTx = qpskMod(dataIn);                     % Apply QPSK modulation
        txSig = ofdmMod(qpskTx);                      % Apply OFDM modulation
        powerDB = 10*log10(var(txSig));               % Calculate Tx signal power
        noiseVar = 10.^(0.1*(powerDB-snr));           % Calculate the noise variance
        rxSig = channel(txSig,noiseVar);              % Pass the signal through a noisy channel
        qpskRx = ofdmDemod(rxSig);                    % Apply OFDM demodulation
        dataOut = qpskDemod(qpskRx);                  % Apply QPSK demodulation
        errorStats = errorRate(dataIn,dataOut,0);     % Collect error statistics
    berVec(m,:) = errorStats;                         % Save BER data
    errorStats = errorRate(dataIn,dataOut,1);         % Reset the error rate calculator

Use the berawgn function to determine the theoretical BER for a QPSK system.

berTheory = berawgn(EbNoVec,'psk',M,'nondiff');

Plot the theoretical and simulated data on the same graph to compare results.

hold on
xlabel('Eb/No (dB)')
ylabel('Bit Error Rate')
grid on
hold off

Figure contains an axes object. The axes object with xlabel Eb/No (dB), ylabel Bit Error Rate contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Simulation, Theory.

Observe that there is good agreement between the simulated and theoretical data.