Convolutional_codes_PSK_QAM_LLR.svg
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Summary
Description Convolutional codes PSK QAM LLR.svg | |
Date | |
Source | Own work |
Author | Kirlf |
SVG development
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Source code
InfoField
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MATLAB codeclear; close all; clc
rng default
M = [4, 8, 16, 64]; % Modulation order
EbNoVec = (0:5)'; % Eb/No values (dB)
numSymPerFrame = 100000; % Number of QAM symbols per frame
berEstSoft = zeros(size(EbNoVec));
trellis = poly2trellis(7,[171 133]);
tbl = 32;
rate = 1/2;
decoders = comm.ViterbiDecoder(trellis,'TracebackDepth',tbl,...
'TerminationMethod','Continuous','InputFormat','Unquantized');
for m = 1:length(M)
k = log2(M(m)); % Bits per symbol
if M(m) <= 8
modul = comm.PSKModulator(M(m), 'BitInput', true);
end
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_exact, numErrsHard, numBits] = deal(0);
[numErrsSoft_approx, numErrsHard, numBits] = deal(0);
while (numErrsSoft_exact < 100 OR numErrsSoft_approx < 100)...
&& numBits < 1e8
% Generate binary data and convert to symbols
dataIn = randi([0 1], numSymPerFrame*k, 1);
% Convolutionally encode the data
dataEnc = convenc(dataIn, trellis);
% QAM modulate
if M(m) <= 8
txSig = step(modul, dataEnc);
else
txSig = qammod(dataEnc, M(m), 'InputType','bit',...
'UnitAveragePower',true);
end
% Pass through AWGN channel
rxSig = awgn(txSig, snrdB, 'measured');
% Demodulate the noisy signal using hard decision (bit) and
% soft decision (approximate LLR) approaches.
if M(m) <= 8
demods_approx = comm.PSKDemodulator(M(m), ...
'BitOutput', true, ...
'DecisionMethod', ...
'Approximate log-likelihood ratio',...
'VarianceSource', 'Property', 'Variance', noiseVar);
demods_exact = comm.PSKDemodulator(M(m), ...
'BitOutput', true, ...
'DecisionMethod', 'Log-likelihood ratio',...
'VarianceSource', 'Property', 'Variance', noiseVar);
rxDataSoft_exact = step(demods_exact, rxSig);
rxDataSoft_approx = step(demods_approx, rxSig);
else
rxDataSoft_exact = qamdemod(rxSig, M(m), ...
'OutputType','llr', ...
'UnitAveragePower',true,'NoiseVariance',noiseVar);
rxDataSoft_approx = qamdemod(rxSig, M(m), ...
'OutputType','approxllr', ...
'UnitAveragePower',true,'NoiseVariance',noiseVar);
end
% Viterbi decode the demodulated data
dataSoft_exact = step(decoders, rxDataSoft_exact );
dataSoft_approx = step(decoders, rxDataSoft_approx);
% Calculate the number of bit errors in the frame.
% Adjust for the decoding delay,
% which is equal to the traceback depth.
numErrsInFrameSoft_exact = biterr(dataIn(1:end-tbl), ...
dataSoft_exact(tbl+1:end));
numErrsInFrameSoft_approx = biterr(dataIn(1:end-tbl), ...
dataSoft_approx(tbl+1:end));
% Increment the error and bit counters
numErrsSoft_exact = numErrsSoft_exact + ...
numErrsInFrameSoft_exact;
numErrsSoft_approx = numErrsSoft_approx + ...
numErrsInFrameSoft_approx;
numBits = numBits + numSymPerFrame*k;
end
% Estimate the BER for both methods
berEstSoft_exact(n, m) = numErrsSoft_exact/numBits;
berEstSoft_approx(n, m) = numErrsSoft_approx/numBits;
end
end
semilogy(EbNoVec, berEstSoft_exact(:, 1),'r-o', ...
EbNoVec, berEstSoft_exact(:, 2),'k-o',...
EbNoVec, berEstSoft_exact(:, 3),'b-o', ...
EbNoVec, berEstSoft_exact(:, 4),'c-o',...
EbNoVec, berEstSoft_approx(:, 1),'r->', ...
EbNoVec, berEstSoft_approx(:, 2),'k->',...
EbNoVec, berEstSoft_approx(:, 3),'b->', ...
EbNoVec, berEstSoft_approx(:, 4),'c->','LineWidth', 1.5)
hold on
legend('QPSK, Exact LLR', ...
'8PSK, Exact LLR', ...
'16-QAM, Exact LLR', ...
'64-QAM, Exact LLR',...
'QPSK, Approx. LLR', ...
'8PSK, Approx. LLR', ...
'16-QAM, Approx. LLR', ...
'64-QAM, Approx. LLR', ...
'location','best')
grid
title('Convolutional codes 1/2, AWGN')
xlabel('Eb/No (dB)')
ylabel('Bit Error Rate')
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Attribution-Share Alike 4.0 International
license.
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- ↑ Digital modulation: Exact LLR Algorithm (MathWorks)
- ↑ Digital modulation: Approximate LLR Algorithm (MathWorks)