Build out MATLAB test framework and core integration coverage
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Silas Oettinghaus
212
Functions/Minimal_examples/pam_6_states_analysis.m
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212
Functions/Minimal_examples/pam_6_states_analysis.m
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M = 6;
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bitpattern = [];
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s = RandStream('twister','Seed',1);
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for i = 1:log2(M)
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N = 2^(17-1); %length of prbs
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bitpattern(:,i) = randi(s,[0 1], N, 1);
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end
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if M == 6
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bitpattern = reshape(bitpattern',[],1);
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bitpattern = bitpattern(1:end-mod(length(bitpattern),5));
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end
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bits = Informationsignal(bitpattern);
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symbols = PAMmapper(M,0).map(bits);
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bits_rx = PAMmapper(M,0).demap(symbols);
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[~,~,ber_direct,~] = calc_ber(bits.signal,bits_rx.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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assert(ber_direct==0,'Mapping is wrong');
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nBursts = 0;
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% No Precoding %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%SEND DIRECTLY
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symbols_tx = symbols;
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symbols_rx = introduce_symbol_errors(symbols_tx, 1, 10, nBursts, 42);
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%RECEIVE BRANCH (do nothing special)
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bits_rx = PAMmapper(M,0).demap(symbols_rx);
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[~,~,ber,errpos] = calc_ber(bits.signal,bits_rx.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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disp(['BER normal: - ',sprintf('%.1E',ber),' - - PAM-',num2str(M)]);
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bursts_normal = count_error_bursts(errpos, 20);
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% Precode Emulation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%SEND DIRECTLY
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symbols_tx = symbols;
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symbols_rx = introduce_symbol_errors(symbols_tx, 1, 10, nBursts, 42);
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%REFERENCE BRACH
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symbols_db = Duobinary().encode(symbols_tx);
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symbols_tx_emu = Duobinary().decode(symbols_db);
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bits_tx_emu = PAMmapper(M,0).demap(symbols_tx_emu);
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% symbols_rx = introduce_symbol_errors(symbols_tx, 1, 10, 200, 42);
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%RECEIVE BRANCH
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symbols_db = Duobinary().encode(symbols_rx);
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symbols_rx_emu = Duobinary().decode(symbols_db);
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bits_rx = PAMmapper(M,0).demap(symbols_rx_emu);
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[~,~,ber_precode_emulation,errpos_precode_emulation] = calc_ber(bits_tx_emu.signal,bits_rx.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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disp(['BER precode emulation: ',sprintf('%.1E',ber_precode_emulation),' - - PAM-',num2str(M)]);
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bursts_precode_emulation = count_error_bursts(errpos_precode_emulation, 20);
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% Precode at Tx %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%SEND PRECODED DATA
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symbols_tx_prec = Duobinary().precode(symbols);
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symbols_rx_prec = introduce_symbol_errors(symbols_tx_prec, 1, 10, nBursts, 42);
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%RECEIVE BRANCH
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symbols_db = Duobinary().encode(symbols_rx_prec);
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symbols_rx_prec = Duobinary().decode(symbols_db);
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bits_rx = PAMmapper(M,0).demap(symbols_rx_prec);
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[~,~,ber_precoded,errpos_precoded] = calc_ber(bits.signal,bits_rx.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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disp(['BER precoded: ',sprintf('%.1E',ber_precoded),' - - PAM-',num2str(M)]);
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burst_precoded = count_error_bursts(errpos_precoded, 20);
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% Precode at Tx but omit at Rx %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%SEND PRECODED DATA
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symbols_tx_prec = Duobinary().precode(symbols);
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bits_tx_prec = PAMmapper(M,0).demap(symbols_tx_prec);
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symbols_rx_omit = introduce_symbol_errors(symbols_tx_prec, 1, 10, nBursts, 42);
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%RECEIVE BRANCH
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bits_rx = PAMmapper(M,0).demap(symbols_rx_omit);
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[~,~,ber_omit,errpos_omit] = calc_ber(bits_tx_prec.signal,bits_rx.signal,"skip_front",0,"skip_end",0,"returnErrorLocation",1);
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disp(['BER (omit precode): ',sprintf('%.1E',ber_omit),' - - PAM-',num2str(M)]);
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burst_omit = count_error_bursts(errpos_omit, 20);
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if 0
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cols = linspecer(8);
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figure();hold on;
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stem(1:20,bursts_normal,'LineWidth',2,'Color',cols(4,:),'Marker','_','DisplayName','w/o diff. precoder');
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stem(1:20,bursts_precode_emulation,'LineWidth',2,'Color',cols(3,:),'Marker','.','LineStyle','-','DisplayName','emulated precoder');
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stem(1:20,burst_precoded,'LineWidth',1,'Color',cols(6,:),'Marker','_','DisplayName','w/ diff. precoder');
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stem(1:20,burst_omit,'LineWidth',1,'Color',cols(5,:),'Marker','.','LineStyle',':','DisplayName','omit precoder');
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xlabel('Bit Error Burst Length')
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ylabel('Occurence')
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set(gca, 'yscale', 'log');
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end
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%% State Analysis
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signal_to_analyze = symbols_tx_emu;
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x = signal_to_analyze.signal(:);
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levels = sort(unique(x)).'; % or provide known 1x6 level values
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[~,ix] = min(abs(x - levels),[],2);
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x = levels(ix); % snapped/quantized
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%% TRANSITION COUNTS & PROBABILITIES
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K = numel(levels);
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% map to state indices 1..K
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[tf, idx] = ismember(x, levels);
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idx = idx(:);
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from = idx(1:end-1);
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to = idx(2:end);
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from = idx(1:2:end);
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to = idx(2:2:end);
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% counts C(from,to)
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C = accumarray([from,to], 1, [K K], @sum, 0);
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% row-stochastic transition matrix P(to|from)
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rowSums = sum(C,2);
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P = C ./ max(rowSums,1);
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%% 1) HEATMAP (which transitions are more probable?)
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figure('Name','Transition Probabilities (to | from)');
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h = heatmap(levels, levels, P, 'Colormap', parula, 'ColorbarVisible','on');
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colormap(gca,[[1,1,1];flip(cbrewer2('Spectral',100))]);clim([0,ceil(max(P(:))*10)/10]);
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h.XLabel = 'From state (level)';
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h.YLabel = 'To state (level)';
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h.Title = 'P(to | from)';
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%% 2) WEIGHTED TRANSITION GRAPH
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% Use dtmc if you have Econometrics Toolbox:
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mc = dtmc(P, 'StateNames', string(levels.*PAMmapper(M,0).get_scaling));
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figure('Name','Markov Graph (dtmc)');
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gp = graphplot(mc, 'ColorEdges',true, 'LabelEdges',true);
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function symbols = introduce_symbol_errors(symbols, j, maxBurstLen, nBursts, seed)
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%INTRODUCE_SYMBOL_ERRORS injects bursty level errors into symbols.signal.
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% symbols.signal : column/row vector of quantized levels (exactly one of 6 values)
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% j : max level step per sample (default 1)
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% maxBurstLen : maximum burst length (default 8)
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% nBursts : number of bursts to insert (default ~1% of length)
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% seed : RNG seed (optional)
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if nargin < 2 || isempty(j), j = 1; end
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if nargin < 3 || isempty(maxBurstLen), maxBurstLen = 8; end
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x = symbols.signal(:);
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N = numel(x);
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if nargin < 4 || isempty(nBursts), nBursts = max(1, round(0.01*N)); end
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if nargin >= 5 && ~isempty(seed), rng(seed); end
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% known levels and index mapping
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lvls = sort(unique(x)).';
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K = numel(lvls);
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[~, idx] = ismember(x, lvls); % idx in 1..6
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used = false(N,1); % avoid overlapping bursts
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burst_ranges = zeros(nBursts,2);
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for b = 1:nBursts
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% pick start not inside an existing burst
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s = randi(N);
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while used(s), s = randi(N); end
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L = randi(maxBurstLen);
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e = min(N, s+L-1);
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% mark used range
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used(s:e) = true;
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burst_ranges(b,:) = [s e];
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% choose one direction for the whole burst: -1 (down) or +1 (up)
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dir = randi([0 1])*2 - 1;
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% apply level errors within the burst
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for t = s:e
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k = idx(t); % current level index (1..6)
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% force inward movement at edges; prevents "flipping" to opposite edge
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if k == 1 && dir == -1, dir = +1; end
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if k == K && dir == +1, dir = -1; end
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step = randi([1 j]); % 1..j steps
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kNew = k + dir*step;
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% clamp to [1,K], no wrap-around
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if kNew < 1, kNew = 1; elseif kNew > K, kNew = K; end
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% if clamped to the same edge repeatedly, flip direction to keep changing
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if kNew == k
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dir = -dir;
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kNew = max(1, min(K, k + dir*step));
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end
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idx(t) = kNew;
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end
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end
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x_err = lvls(idx);
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symbols.signal = reshape(x_err, size(symbols.signal)); % preserve original shape
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end
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