BCJR implementation
WDM code added (Pol Cont., Opt MUX/DEMUX, Opt Atten, DP_Fiber) -> the codebase is not optimized to always work with dp signals!
This commit is contained in:
Silas Oettinghaus
171
test/minimal_example_bcjr.m
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171
test/minimal_example_bcjr.m
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M_format = [2,4,6,8];
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for m = 1:length(M_format)
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% --- Parameters ---
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M = M_format(m); % PAM order (e.g., 2,4,8)
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Nsym = 1e5; % number of symbols
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h = [1, 0.5]; % Impulse response to remove
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b = log2(M);
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if M == 6 b = 5; end
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rng(1);
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bits_tx = logical(randi([0 1], Nsym, b, 'uint8'));
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tx_symbols = pammap(bits_tx,M);
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if M == 6
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states = unique(tx_symbols);
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pam6transitions = combvec(states',states')'; % pam6transitions =
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bitmapping = pamdemap(reshape(pam6transitions',1,[])',M);
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else
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bitmapping = pamdemap(unique(tx_symbols),M);
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end
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scaling = sqrt(sum(unique(tx_symbols).^2)/numel(unique(tx_symbols)));
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tx_symbols = tx_symbols ./ scaling;
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% apply impulse response to signal
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y_filt = filter(h, 1, tx_symbols);
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sir = 10:25;
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for s = 1:length(sir)
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% apply noise
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y = awgn(y_filt,sir(s),"measured",1);
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% apply bcjr
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BCJR = bcjr_pam("DIR",h,"duobinary_output",0,"M",M,"trellis_states",unique(tx_symbols));
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[viterbi_estimate,LLR,GMI(m,s)] = BCJR.process(y,tx_symbols,bits_tx,bitmapping);
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% decode LLR's
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bits_LLR = LLR > 0;
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% demap viterbi symbols sequence
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rx_symbols = viterbi_estimate .* scaling;
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bits_rx = pamdemap(rx_symbols,M);
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% BER calc
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BER_vit(m,s) = nnz(bits_tx ~= bits_LLR) / numel(bits_tx);
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fprintf('BER LLR = %.2e \n', BER_vit);
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BER_llr(m,s) = nnz(bits_tx ~= bits_rx) / numel(bits_tx);
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fprintf('BER = %.2e \n', BER_llr);
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end
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end
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figure();hold on
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for m = 1:length(M_format)
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plot(sir,BER_llr(m,:),'DisplayName',sprintf('PAM %d',M_format(m)))
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% plot(sir,BER_vit(m,:),'DisplayName',sprintf('PAM %d',M_format(m)),'LineStyle',':','LineWidth',0.1,'HandleVisibility','off');
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end
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ylabel('BER');
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xlabel('SNR')
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title('BER vs. SNR');
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set(gca, 'XScale', 'linear', ...
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'YScale', 'log', ...
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'TickLabelInterpreter', 'latex', ...
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'FontSize', 11);
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figure();hold on
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for m = 1:length(M_format)
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plot(sir,GMI(m,:),'DisplayName',sprintf('GMI PAM %d',M_format(m)))
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end
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ylabel('GMI');
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xlabel('SNR')
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title('GMI vs. SNR');
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set(gca, 'XScale', 'linear', ...
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'YScale', 'linear', ...
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'TickLabelInterpreter', 'latex', ...
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'FontSize', 11);
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function symbols = pammap(bits,M)
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bits = logical(bits);
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if M == 2
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symbols = bits;
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elseif M == 4
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symbols= 2*bits(:,1) + (bits(:,1)==bits(:,2));
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symbols=2*symbols-3;
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elseif M == 6
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m = 1;
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if size(bits,2)>size(bits,1)
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bits = bits'; %vector aufrecht stellen
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end
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bits = reshape(bits',1,[])';
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thres = [-3 5;-1 5;-3 -5;-1 -5;-5 3;-5 1;-5 -3;-5 -1;-1 3;-1 1;-1 -3;-1 -1;-3 3;-3 1;-3 -3;-3 -1;3 5;1 5;3 -5;1 -5;5 3;5 1;5 -3;5 -1;1 3;1 1;1 -3;1 -1;3 3;3 1;3 -3;3 -1];
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% LUT based mapping
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for k = 1:5:fix(length(bits)/5)*5
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symbols(m:m+1,1) = thres(bin2dec(int2str(bits(k:k+4)'))+1,:);
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m = m+2;
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end
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elseif M == 8
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x1 = bits(:,1);
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x2 = (bits(:,1)==bits(:,3));
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x3 = x2~=bits(:,2);
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symbols = 4*x1 + 2*x2 + x3;
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symbols=2*symbols-7;
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end
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end
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function bits = pamdemap(symbols,M)
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if M == 2
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thres=0;
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elseif M == 4
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thres=[-2,0,2];
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elseif M == 6
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thres = [-3 5;-1 5;-3 -5;-1 -5;-5 3;-5 1;-5 -3;-5 -1;-1 3;-1 1;-1 -3;-1 -1;-3 3;-3 1;-3 -3;-3 -1;3 5;1 5;3 -5;1 -5;5 3;5 1;5 -3;5 -1;1 3;1 1;1 -3;1 -1;3 3;3 1;3 -3;3 -1];
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elseif M == 8
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thres=-6:2:6;
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end
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if M ~= 6
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symbols = symbols';
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a = squeeze(repmat(real(symbols),[1 1 length(thres)])); %Eingangssignal in 3 spalten
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b = squeeze(repmat(reshape(thres(:).',[1 1 length(thres)]),[1 length(symbols) 1])); %Threshold in 3 Spalten
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comp_real = a > b; %check for each symbol/ sampling if it exeeds the obj.thresholdseshold 1, 2 or 3
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comp_real=repmat(real(symbols),[1 1 length(thres)]) > repmat(reshape(thres(:).',[1 1 length(thres)]),[1 length(symbols) 1]);
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s1=size(comp_real,1);
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s2=size(comp_real,2);
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end
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if M == 2
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data_out=abs(comp_real(:,:,1));
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elseif M == 4
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data_out=[comp_real(:,:,2); ones(s1,s2) - comp_real(:,:,1) + comp_real(:,:,3)];
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elseif M == 6
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if size(symbols,2) > 1
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symbols = symbols.';
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end
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if length(symbols)/2 ~= round(length(symbols)/2)
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symbols = [symbols;0];
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end
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m = 1;
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for n = 1:2:length(symbols)
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dist = sqrt((symbols(n)-thres(:,1)).^2+(symbols(n+1)-thres(:,2)).^2);
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[~,dd_idx] = min(dist);
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% dec_out(n:n+1) = LUT(dd_idx,:);
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data_out(m:m+4) = bitget(dd_idx-1,5:-1:1);
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m = m+5;
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end
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data_out = reshape(data_out',5,[]);
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elseif M == 8
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data_out=[comp_real(:,:,4);
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comp_real(:,:,1)-comp_real(:,:,3)+comp_real(:,:,5)-comp_real(:,:,7);
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1-comp_real(:,:,2)+comp_real(:,:,6)];
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end
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bits = data_out';
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end
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