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# Estimate BER for Hard and Soft Decision Viterbi Decoding

Estimate bit error rate (BER) performance for hard-decision and soft-decision Viterbi decoders in AWGN. Compare the performance to that of an uncoded 64-QAM link.

Set the simulation parameters.

```clear; close all rng default M = 64; % Modulation order k = log2(M); % Bits per symbol EbNoVec = (4:10)'; % Eb/No values (dB) numSymPerFrame = 1000; % Number of QAM symbols per frame```

Initialize the BER results vectors.

```berEstSoft = zeros(size(EbNoVec)); berEstHard = zeros(size(EbNoVec));```

Set the trellis structure and traceback depth for a rate `1/2`, constraint length `7`, convolutional code.

```trellis = poly2trellis(7,[171 133]); tbl = 32; rate = 1/2;```

The main processing loops performs these steps:

• Generate binary data

• Convolutionally encode the data

• Apply QAM modulation to the data symbols. Specify unit average power for the transmitted signal

• Pass the modulated signal through an AWGN channel

• Demodulate the received signal using hard decision and approximate LLR methods. Specify unit average power for the received signal

• Viterbi decode the signals using hard and unquantized methods

• Calculate the number of bit errors

The `while` loop continues to process data until either 100 errors are encountered or ${10}^{7}$ bits are transmitted.

```for n = 1:length(EbNoVec) % Convert Eb/No to SNR snrdB = EbNoVec(n) + 10*log10(k*rate); % Noise variance calculation for unity average signal power. noiseVar = 10.^(-snrdB/10); % Reset the error and bit counters [numErrsSoft,numErrsHard,numBits] = deal(0); while numErrsSoft < 100 && numBits < 1e7 % Generate binary data and convert to symbols dataIn = randi([0 1],numSymPerFrame*k,1); % Convolutionally encode the data dataEnc = convenc(dataIn,trellis); % QAM modulate txSig = qammod(dataEnc,M,'InputType','bit','UnitAveragePower',true); % Pass through AWGN channel rxSig = awgn(txSig,snrdB,'measured'); % Demodulate the noisy signal using hard decision (bit) and % soft decision (approximate LLR) approaches. rxDataHard = qamdemod(rxSig,M,'OutputType','bit','UnitAveragePower',true); rxDataSoft = qamdemod(rxSig,M,'OutputType','approxllr', ... 'UnitAveragePower',true,'NoiseVariance',noiseVar); % Viterbi decode the demodulated data dataHard = vitdec(rxDataHard,trellis,tbl,'cont','hard'); dataSoft = vitdec(rxDataSoft,trellis,tbl,'cont','unquant'); % Calculate the number of bit errors in the frame. Adjust for the % decoding delay, which is equal to the traceback depth. numErrsInFrameHard = biterr(dataIn(1:end-tbl),dataHard(tbl+1:end)); numErrsInFrameSoft = biterr(dataIn(1:end-tbl),dataSoft(tbl+1:end)); % Increment the error and bit counters numErrsHard = numErrsHard + numErrsInFrameHard; numErrsSoft = numErrsSoft + numErrsInFrameSoft; numBits = numBits + numSymPerFrame*k; end % Estimate the BER for both methods berEstSoft(n) = numErrsSoft/numBits; berEstHard(n) = numErrsHard/numBits; end```

Plot the estimated hard and soft BER data. Plot the theoretical performance for an uncoded 64-QAM channel.

```semilogy(EbNoVec,[berEstSoft berEstHard],'-*') hold on semilogy(EbNoVec,berawgn(EbNoVec,'qam',M)) legend('Soft','Hard','Uncoded','location','best') grid xlabel('Eb/No (dB)') ylabel('Bit Error Rate')```

As expected, the soft decision decoding produces the best results.

## Support

#### Bridging Wireless Communications Design and Testing with MATLAB

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