Add partial response symbol mapping and IM/DD system example
- Implemented a new MATLAB script for partial response symbol mapping using Duobinary precoding. - Added functions for printing constellation bit mapping and partial response state tables. - Created a minimal example for an IM/DD system, including signal generation, modulation, and equalization processes. - Integrated various components such as pulse shaping, optical modulation, and receiver processing. - Included detailed configurations for parameters like bias, link length, and filter settings.
This commit is contained in:
Silas Oettinghaus
@@ -1,23 +1,21 @@
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for M = [2 4 8]
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bits = Signalgenerator("form", signalform.prms,"M", M,"order", 15).process();
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bits = Signalgenerator("form", signalform.prms,"M", M,"order", 16).process();
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mapper = PAMmapper(M,0);
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symbols = mapper.map(bits);
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symbols_pre = Duobinary().precode(symbols);
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symbols_db = Duobinary().encode(symbols_pre);
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symbols_rx = Duobinary().decode(symbols_db);
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db = Duobinary();
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pr1 = Partialresponse();
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symbols_pre = db.precode(symbols);
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symbols_db = db.encode(symbols_pre);
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symbols_rx = db.decode(symbols_db);
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bits_rx = PAMmapper(M,0).demap(symbols_rx);
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[~,~,ber,~] = calc_ber(bits.signal,bits_rx.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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disp(['Class BER: ',sprintf('%.1E',ber),' - PAM-',num2str(M)]);
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symbols_pre_pr = Partialresponse("order",1).precode(symbols,"M",M);
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symbols_db_pr = Partialresponse("order",1).encode(symbols_pre_pr,"M",M);
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symbols_rx_pr = Partialresponse("order",1).decode(symbols_db_pr,"M",M);
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symbols_pre_pr = pr1.precode(symbols,"M",M);
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symbols_db_pr = pr1.encode(symbols_pre_pr,"M",M);
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symbols_rx_pr = pr1.decode(symbols_db_pr,"M",M);
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bits_rx_pr = mapper.demap(symbols_rx_pr);
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[~,~,ber_pr,~] = calc_ber(bits.signal,bits_rx_pr.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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disp(['Partialresponse BER: ',sprintf('%.1E',ber_pr),' - PAM-',num2str(M)]);
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@@ -37,4 +35,43 @@ for M = [2 4 8]
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disp(['Decode match: ',num2str(dec_match), ...
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' | max abs diff: ',sprintf('%.3g',dec_maxdiff)]);
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disp('---');
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f = figure("Name",sprintf("PAM-%d Partial-Response Histograms",M));
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t = tiledlayout(f,1,4,"TileSpacing","compact","Padding","compact");
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title(t,sprintf("PAM-%d Symbol Histograms",M));
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nexttile;
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plotDiscreteHistogram(symbols.signal,sprintf("PAM-%d",M));
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nexttile;
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plotDiscreteHistogram(symbols_db_pr.signal,"Duobinary 1st Order");
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nexttile;
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plotDiscreteHistogram(getEncodedSymbols(symbols,M,2),"Duobinary 2nd Order");
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nexttile;
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plotDiscreteHistogram(getEncodedSymbols(symbols,M,3),"Duobinary 3rd Order");
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end
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function y = getEncodedSymbols(symbols, M, order)
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pr = Partialresponse("order",order);
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y = pr.encode(pr.precode(symbols,"M",M),"M",M).signal;
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end
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function plotDiscreteHistogram(x, plot_title)
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levels = unique(x(:)).';
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counts = zeros(size(levels));
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for idx = 1:numel(levels)
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counts(idx) = sum(abs(x - levels(idx)) < 1e-12);
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end
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bar(levels, counts, 0.9, "FaceColor", [0.2 0.45 0.75], "EdgeColor", "none");
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grid on;
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box on;
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xlabel("Level");
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ylabel("Count");
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title(plot_title);
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xticks(levels);
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end
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@@ -1,122 +0,0 @@
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useprbs = 1;
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M = 2;
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randkey = 1;
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datarate = 448e9;
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fsym = round(datarate / log2(M)) ;
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Tx_bits = Signalgenerator( ...
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"form", signalform.prms, ...
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"M", M, ...
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"order", 15).process();
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Symbols_tx = PAMmapper(M,0,"eth_style",0).map(Tx_bits);
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Symbols_tx.fs = fsym;
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precode = db_mode.db_precoded;
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%%% precode
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switch precode
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case db_mode.db_precoded
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Symbols_tx = Duobinary().precode(Symbols_tx);
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case db_mode.db_encoded
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Symbols_tx = Duobinary().precode(Symbols_tx);
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Symbols_tx = Duobinary().encode(Symbols_tx);
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case db_mode.no_db
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end
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for n = 10
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% Start from the transmitted symbol sequence for this impairment case.
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Symbols_rx = Symbols_tx;
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% Insert n deterministic symbol errors near the beginning of the sequence.
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% Each replacement is chosen from another symbol position with a different
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% amplitude, so this produces actual symbol decisions errors.
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pos = 1;
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if n~=0
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for pos = 1:n
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po = randi(100);
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a = Symbols_rx.signal(100+pos) == Symbols_tx.signal(100+po);
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while a == 1
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po = po+1;
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po = randi(100);
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a = Symbols_rx.signal(100+pos) == Symbols_tx.signal(100+po);
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end
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Symbols_rx.signal(100+pos) = Symbols_tx.signal(100+po);
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end
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end
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% Keep track of the positions where the artificial symbol errors were
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% inserted before duobinary encoding/decoding is applied.
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error_positions = ~(Symbols_rx.signal == Symbols_tx.signal);
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error_positions = find(error_positions==1);
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% Receiver-side duobinary processing depends on what was already done at
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% the transmitter side:
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% - db_precoded: the sequence is precoded only, so emulate the channel PR
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% encoder first and then apply memoryless duobinary decoding.
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% - db_encoded: the sequence already contains duobinary levels, so only
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% the memoryless duobinary decoder is applied.
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switch precode
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case db_mode.db_precoded
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Symbols_rx = Duobinary().encode(Symbols_rx);
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Symbols_rx = Duobinary().decode(Symbols_rx);
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case db_mode.db_encoded
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Symbols_rx = Duobinary().decode(Symbols_rx);
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end
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% Convert the recovered PAM symbols back to bits with the framework mapper.
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Rx_bits = PAMmapper(M,0).demap(Symbols_rx);
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%%%%% Check BER of Bit Sequence %%%%%
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% Skip a few edge samples because the first/last symbols can include
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% state/transient effects from the duobinary recursion.
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[~,error_num(n+1),ber,error_pos] = calc_ber(Tx_bits.signal,Rx_bits.signal,"skip_front",10,"skip_end",10,"returnErrorLocation",1);
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% disp(['BER: ',sprintf('%.1E',ber),sprintf(' - Num. Err: %.1d',error_num(n+1)-2),' - - PAM-',num2str(M)]);
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fprintf('n: %d - Num. Err: %.1d \n',n,error_num(n+1));
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end
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% Plot bit-level and symbol-level comparisons for a quick visual sanity check.
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figure(3);
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clf
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%sgtitle(['BER: ',num2str(ber),' // Error is at position: ',num2str(error_pos),''])
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% Compare the first few transmitted and received bits.
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subplot(2,2,1)
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hold on
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title('First Bits')
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stairs(Tx_bits.signal(100:150,1),'LineStyle','-','LineWidth',2,'DisplayName','Tx Bits');
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stairs(Rx_bits.signal(100:150,1),'LineWidth',2,'DisplayName','Rx Bits','LineStyle',':')
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legend
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% Compare the last few transmitted and received bits.
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subplot(2,2,2)
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title('Last Bits')
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hold on
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stairs(Tx_bits.signal(end-50:end,1),'LineStyle','-','LineWidth',2,'DisplayName','Tx Bits');
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stairs(Rx_bits.signal(end-50:end,1),'LineWidth',2,'DisplayName','Rx Bits','LineStyle',':')
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legend
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% Compare the first few symbol decisions after the duobinary processing chain.
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subplot(2,2,3)
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hold on
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title('First Symbols Compare')
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stairs(Symbols_tx.signal(1:100,1),'LineWidth',2,'DisplayName','Tx Symbols','LineStyle','-')
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stairs(Symbols_rx.signal(1:100,1),'LineStyle',':','LineWidth',2,'DisplayName','Rx Symbols');
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legend
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% Compare the last few symbol decisions after the duobinary processing chain.
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subplot(2,2,4)
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hold on
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title('Last Symbols Compare')
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stairs(Symbols_tx.signal(end-50:end,1),'LineWidth',2,'DisplayName','Tx Symbols','LineStyle','-')
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stairs(Symbols_rx.signal(end-50:end,1),'LineStyle',':','LineWidth',2,'DisplayName','Rx Symbols');
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legend
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@@ -0,0 +1,147 @@
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M = 4;
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useUnitRmsScaling = false;
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bits = Signalgenerator("form", signalform.prms,"M", M,"order", 16).process();
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mapper = PAMmapper(M,0);
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symbols = mapper.map(bits);
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[constellation, bitmap] = mapper.getConstellationBitMapping();
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printConstellationBitMapping(M, constellation, bitmap);
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printPartialResponseStateTable(M, bitmap, "Duobinary", 1, useUnitRmsScaling);
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db = Duobinary();
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pr1 = Partialresponse();
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symbols_pre = db.precode(symbols);
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symbols_db = db.encode(symbols_pre);
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symbols_rx = db.decode(symbols_db);
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bits_rx = PAMmapper(M,0).demap(symbols_rx);
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[~,~,ber,~] = calc_ber(bits.signal,bits_rx.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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disp(['Class BER: ',sprintf('%.1E',ber),' - PAM-',num2str(M)]);
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function printConstellationBitMapping(M, constellation, bitmap)
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fprintf("\n=== PAM-%d Bit Mapping ===\n", M);
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bitLabels = string(cellstr(char(bitmap + '0')));
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if size(constellation, 2) == 1
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mappingTable = table(constellation(:), bitLabels, ...
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'VariableNames', {'Symbol', 'Bits'});
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else
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mappingTable = table(constellation(:,1), constellation(:,2), bitLabels, ...
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'VariableNames', {'Symbol_1', 'Symbol_2', 'Bits'});
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end
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disp(mappingTable);
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fprintf("Number of constellation points: %d\n\n", size(constellation, 1));
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end
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function printPartialResponseStateTable(M, bitmap, label, order, useUnitRmsScaling)
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if useUnitRmsScaling
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scalingLabel = "unit-RMS scaling";
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encodedScaling = getEncodedScaling(M, order);
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else
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scalingLabel = "raw encoder levels";
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encodedScaling = 1;
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end
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fprintf("=== %s Effective State Table (order = %d, %s) ===\n", label, order, scalingLabel);
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mapper = PAMmapper(M, 0);
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h = arrayfun(@(k) nchoosek(order, k), 0:order);
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center = ((M - 1) * sum(h)) / 2;
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if useUnitRmsScaling
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pamScaling = mapper.scaling;
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else
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pamScaling = 1;
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end
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numStates = M^order;
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numInputs = M;
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prevStateLabels = strings(numStates * numInputs, 1);
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bitLabels = strings(numStates * numInputs, 1);
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aAmp = zeros(numStates * numInputs, 1);
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uIdx = zeros(numStates * numInputs, 1);
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uAmp = zeros(numStates * numInputs, 1);
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yAmp = zeros(numStates * numInputs, 1);
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nextStateLabels = strings(numStates * numInputs, 1);
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row = 1;
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for stateIdx = 0:(numStates - 1)
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state = indexToState(stateIdx, M, order);
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for a = 0:(numInputs - 1)
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u = mod(a - sum(h(2:end) .* state), M);
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y = (sum(h .* [u, state]) - center) / encodedScaling;
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prevStateLabels(row) = formatState(state);
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bitLabels(row) = bitsFromIndex(bitmap, a + 1);
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aAmp(row) = indexToPamAmplitude(a, pamScaling, M);
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uIdx(row) = u;
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uAmp(row) = indexToPamAmplitude(u, pamScaling, M);
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yAmp(row) = y;
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nextStateLabels(row) = formatState([u, state(1:end-1)]);
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row = row + 1;
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end
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end
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stateTable = table(prevStateLabels, bitLabels, aAmp, uIdx, uAmp, yAmp, nextStateLabels, ...
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'VariableNames', {'PrevState', 'Bits', 'InputSymbol', 'PrecodedIndex', 'PrecodedSymbol', 'EncodedLevel', 'NextState'});
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disp(stateTable);
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fprintf("States: %d, transitions: %d\n\n", numStates, height(stateTable));
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end
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function state = indexToState(stateIdx, M, order)
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state = zeros(1, order);
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tmp = stateIdx;
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for k = 1:order
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state(k) = mod(tmp, M);
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tmp = floor(tmp / M);
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end
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end
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function label = formatState(state)
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if isempty(state)
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label = "[]";
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else
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label = "[" + join(string(state), " ") + "]";
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end
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end
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function bitLabel = bitsFromIndex(bitmap, idx)
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bitLabel = string(char(bitmap(idx, :) + '0'));
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end
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function amplitude = indexToPamAmplitude(a, scaling, M)
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amplitude = (2 * a - (M - 1)) / scaling;
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end
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function scaling = getEncodedScaling(M, order)
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h = arrayfun(@(k) nchoosek(order, k), 0:order);
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numCombinations = M^(order + 1);
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y = zeros(numCombinations, 1);
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for n = 0:(numCombinations - 1)
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state = zeros(1, order + 1);
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tmp = n;
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for k = 1:numel(state)
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state(k) = mod(tmp, M);
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tmp = floor(tmp / M);
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end
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y(n + 1) = sum(h .* state);
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end
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center = ((M - 1) * sum(h)) / 2;
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scaling = sqrt(mean((y - center).^2));
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end
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@@ -1,55 +0,0 @@
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M = 8;
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apply_precode_at_tx = 1;
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bits = Signalgenerator( ...
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"form", signalform.prms, ...
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"M", M, ...
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"order", 15).process();
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symbols = PAMmapper(M,0).map(bits);
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if apply_precode_at_tx
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symbols_tx = Duobinary().precode(symbols);
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else
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symbols_tx = symbols;
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end
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disp(['Tx Sequenz: -- RMS:',sprintf('%.1f',rms(symbols_tx.signal)),' - - Levels -',num2str(numel(unique(symbols_tx.signal)))]);
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unique(symbols_tx.signal)
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disp('- - - - - - - - - -');
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show2Dconstellation(symbols_tx,symbols_tx,"displayname",'VNLE Out','fignum',2241);
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if apply_precode_at_tx
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% Entschiedene Symbole codieren: d_DB(n) = d(n) + d(n-1) (im Fall von PAM4 7 level [0 1 2 3 4 5 6])
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symbols_db = Duobinary().encode(symbols_tx);
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disp(['DB encoded -- RMS:',sprintf('%.1f',rms(symbols_db.signal)),' - - Levels -',num2str(numel(unique(symbols_db.signal)))]);
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unique(symbols_db.signal)
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disp('- - - - - - - - - -');
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% Entschiedene codierte Symbole decodieren: d_dec(n) = d_DB(n) mod4
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symbols_rx = Duobinary().decode(symbols_db);
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else
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symbols_db = Duobinary().encode(symbols_tx);
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symbols_rx = Duobinary().decode(symbols_db);
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end
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% Vergleichen von b(n) und d_dec(n)
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bits_rx = PAMmapper(M,0).demap(symbols_rx);
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disp(['Wieder normal -- RMS:',sprintf('%.1f',rms(symbols_rx.signal)),' - - Levels -',num2str(numel(unique(symbols_rx.signal)))]);
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unique(symbols_rx.signal)
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disp('- - - - - - - - - -');
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[~,~,ber,~] = calc_ber(bits.signal,bits_rx.signal,"skip_front",10,"skip_end",10,"returnErrorLocation",1);
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disp(['BER: ',sprintf('%.1E',ber),' - - PAM-',num2str(M)]);
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figure()
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subplot(1,2,1)
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histogram(symbols_tx.signal,100,'Normalization','count')
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subplot(1,2,2)
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histogram(symbols_db.signal,100,'Normalization','count')
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