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Estimate Turbo Code BER Performance in AWGN

Simulate an end-to-end communication link employing 16-QAM using turbo codes in an AWGN channel. Estimate the bit error rate.

Initialize Simulation

Set the modulation order and the range of Eb/No values to evaluate. Set the frame length to 500.

M = 16;
bps = log2(M); % bits per symbol
EbNo = (2:0.5:4);
frmLen = 500;

Initialize the bit error rate vector.

ber = zeros(size(EbNo));

Create a turbo encoder and decoder pair, where the interleaver indices are supplied as input arguments.

turboEnc = comm.TurboEncoder('InterleaverIndicesSource','Input port');

turboDec = comm.TurboDecoder('InterleaverIndicesSource','Input port', ...

Create a QAM modulator and demodulator pair, where the demodulator outputs soft bits determined by using a log-likelihood ratio method. The modulator and demodulator objects are normalized to use an average power of 1 W.

qamModulator = comm.RectangularQAMModulator('ModulationOrder',M, ...
    'BitInput',true, ...
    'NormalizationMethod','Average power');

qamDemodulator = comm.RectangularQAMDemodulator('ModulationOrder',M, ...
    'BitOutput',true, ...
    'NormalizationMethod','Average power', ...
    'DecisionMethod','Log-likelihood ratio', ...
    'VarianceSource','Input port');

Create an AWGN channel and an error rate counter.

awgnChannel = comm.AWGNChannel('NoiseMethod','Variance','Variance',1);
errorRate = comm.ErrorRate;

Use the frame length and turbo encoder settings to determine actual transmitted bit rate. The turbo-coding objects are initialized to use rate-1/2 trellis for their constituent convolutional codes, resulting in a turbo encoder output with 2 parity bit streams, (in addition to the systematic stream) and 12 tail bits for the input frame. The 12 tail bits are due to the specified constraint length of 4 per constituent encoder, which leads to 3-bit outputs per stream, for a total of 4 streams (S1 P1 S2 P2).

    rate = frmLen/(3*frmLen+4*3);

Main Processing Loop

The processing loop performs the following steps:

  • Generate random binary data

  • Generate random interleaver indices

  • Turbo encode the data

  • Apply 16-QAM modulation

  • Pass the modulated signal through an AWGN channel

  • Demodulate the noisy signal using an LLR algorithm

  • Turbo decode the data

  • Calculate the error statistics

for k = 1:length(EbNo)
    % Initialize error statistics vector, signal-to-noise ratio, and noise variance
    errorStats = zeros(1,3);

    EsNo = EbNo(k) + 10*log10(bps);       
    snrdB = EsNo + 10*log10(rate);      % in dB
    noiseVar = 1./(10.^(snrdB/10)); 

    awgnChannel.Variance = noiseVar;

    while errorStats(2) < 100 && errorStats(3) < 1e7

        % Generate random binary data
        data = randi([0 1],frmLen,1);

        % Interleaver indices
        intrlvrInd = randperm(frmLen);

        % Turbo encode the data
        encodedData = turboEnc(data,intrlvrInd);

        % Modulate the encoded data
        modSignal = qamModulator(encodedData);

        % Pass the signal through the AWGN channel
        receivedSignal = awgnChannel(modSignal);

        % Demodulate the received signal
        demodSignal = qamDemodulator(receivedSignal,noiseVar);

        % Turbo decode the demodulated signal. Because the bit mapping from the
        % demodulator is opposite that expected by the turbo decoder, the
        % decoder input must use the inverse of demodulated signal.
        receivedBits = turboDec(-demodSignal,intrlvrInd);

        % Calculate the error statistics
        errorStats = errorRate(data,receivedBits);
    % Save the BER data and reset the bit error rate object
    ber(k) = errorStats(1);

Plot the bit error rate and compare it to the uncoded bit error rate.

xlabel('Eb/No (dB)')
ylabel('Bit Error Rate')
uncodedBER = berawgn(EbNo,'qam',M);     % Estimate of uncoded BER
hold on

See Also