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This commit is contained in:
Silas Oettinghaus
2025-02-17 21:31:12 +01:00
parent becaf3f6c9
commit d099efea03
21 changed files with 1502 additions and 272 deletions
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177
Classes/04_DSP/Sequence Detection/MLSE_viterbi.m Normal file
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classdef MLSE_viterbi < handle
%MLSE calculates the most probable sequence for an input signal with given/ known channel impulse response of any length
properties(Access=public)
M %PAM-M
DIR
trellis_states
duobinary_output
end
methods (Access=public)
function obj = MLSE_viterbi(options)
%NAME Construct an instance of this class
% Detailed explanation goes here
arguments
options.M double = 4;
options.DIR double = [1];
options.trellis_states double = [-3 -1 1 3];
options.duobinary_output logical = false;
end
%
fn = fieldnames(options);
for n = 1:numel(fn)
try
obj.(fn{n}) = options.(fn{n});
end
end
% do more stuff
end
function signalclass = process(obj,signalclass)
data_in = signalclass.signal;
data_out = obj.process_(data_in);
signalclass.signal = data_out;
end
function data_out = process_(obj,data_in)
% remove unnecessary zeros at start of impulse response to keep
% number of trellis states minimal
DIR_nonzero = find(obj.DIR ~= 0);
if DIR_nonzero(1) > 1
obj.DIR(1:DIR_nonzero(1)-1) = [];
end
if isscalar(obj.DIR)
obj.DIR = [0 obj.DIR];
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%% WORKING
% impulse respnse i.e. [0.5, 1.0000]
obj.DIR = flip(obj.DIR);
% RMS normalization of input data
data_in = data_in ./ rms(data_in);
% seems to be the only way to use combvec for a flexible amount
% of vectors. 'combs' contains all trellis states
pre_comb_mat = repmat(obj.trellis_states,length(obj.DIR)-1,1);
pre_comb_cell = mat2cell(pre_comb_mat,ones(1,size(pre_comb_mat,1)),size(pre_comb_mat,2));
combs = fliplr(combvec(pre_comb_cell{:}).');
% Save first and last symbol of each state
first_sym = combs(:,1);
last_sym = combs(:,end);
states = sum(combs,2);
% Calculate all possible input symbols for the desired impulse
% response. Row number is the index of the previous state,
% column number is the index of the next state
% noise free received == branch metrics
noise_free_received = zeros(length(states),length(states));
count_row = 1;
count_col = 1;
for l1 = 1:length(states)
for l2 = 1:length(states)
if sum(combs(l2,2:end) == combs(l1,1:end-1)) == size(combs,2)-1
noise_free_received(count_row,count_col) = sum(combs(l2,:).*obj.DIR(end:-1:2)) + last_sym(l1)*obj.DIR(1);
else
noise_free_received(count_row,count_col) = inf;
end
count_row = count_row + 1;
end
count_col = count_col + 1;
count_row = 1;
end
% match amplitude levels of input signal to those of the calculated ideal symbols
% i.e. match the rms values of data_in to noise_free_received
if isreal(data_in)
if obj.M == round(obj.M)
data_in = data_in * rms(noise_free_received(noise_free_received ~= inf),'all','omitnan');
end
end
% OLD
% initilaize the output vector
data_out = NaN(size(data_in));
sum_path_metrics = zeros(length(states),length(states));
% first trellis path
% euclidian distance as path metric
path_metrics = (abs(repmat(data_in(1),size(noise_free_received)) - noise_free_received)).^2;
sum_path_metrics = sum_path_metrics + path_metrics; % calculation of all possible sum path metrics
[sum_path_metrics_res(:,1),path_idx(:,1)] = min(sum_path_metrics,[],2); % find the best path to each state, store sum path metric and predecessor for each state
% remaining trellis paths
for n = 2:length(data_in)
sum_path_metrics = repmat(sum_path_metrics_res(:,n-1).',length(states),1);
% path_metrics = (repmat(data_in(n),size(noise_free_received)) - noise_free_received).^2;%.*prob_mat;
path_metrics = (abs(repmat(data_in(n),size(noise_free_received)) - noise_free_received)).^2;
sum_path_metrics = sum_path_metrics + path_metrics;
[sum_path_metrics_res(:,n),path_idx(:,n)] = min(sum_path_metrics,[],2);
end
%% trace back
ideal_path = NaN(1,length(data_in)+1);
% find ideal trellis path by going through the trellis
% backwards
[~,ideal_path(length(data_in)+1)] = min(sum_path_metrics_res(:,length(data_in)));
% starting with the state that has the lowest sum path
% metric, follow the stored information about the
% predecessor
for h = length(data_in):-1:1
ideal_path(h) = path_idx(ideal_path(h+1),h);
end
idx_out = ideal_path(2:length(data_in)+1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%% WORKING
if obj.duobinary_output
%use duobinary encoder, output is already scaled inside this
%one
data_out = Duobinary().encode(first_sym(idx_out));
else
%
data_out(1:length(data_in)) = first_sym(idx_out);
% scale to rms = 1 using the standard sqrt() expressions
if obj.M == 4
data_out = data_out./sqrt(5);
elseif obj.M == 6
data_out = data_out./sqrt(10);
elseif obj.M == 8
data_out = data_out./sqrt(21);
end
end
end
end
methods (Access=private)
% Cant be seen from outside! So put all your functions here that can/
% shall not be called from outside
end
end

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Classes/04_DSP/TransmissionPerformance.m Normal file
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classdef TransmissionPerformance
% TransmissionPerformance
%
% This class calculates the best possible net data rate (in bits/s)
% from a given gross rate (bits/s) and a measured channel quality
% parameter (either bit error ratio (BER) or NGMI). The class uses
% lookup tables for three different FEC modes:
%
% 1. SD+HD concatenated (uses overall code rate and an NGMI threshold)
% 2. SD+HD concatenated with punctured LDPC (uses overall code rate and an NGMI threshold)
% 3. HD-only (uses a code rate and a BER threshold)
%
% The basic algorithm is as follows:
% 1. Given a measured quality (NGMI or BER) for each measurement, find in
% the table the first (i.e. “best”) entry that is satisfied by the
% measured value. For NGMI the condition is measured NGMI >= threshold,
% while for BER the condition is measured BER <= threshold.
% 2. Use the corresponding overall code rate to compute:
%
% net rate = gross rate * code rate.
%
% USAGE EXAMPLE (array inputs):
%
% tp = TransmissionPerformance;
% % Suppose we have 3 measurements:
% % Gross rates: 10, 15, and 20 Gbps
% % Measured NGMI: 0.92, 0.88, and 0.85
% % Measured BER: 1e-4, 7e-3, and 2e-2
% netrates = tp.calculatenetrate([10e9 15e9 20e9], ...
% 'NGMI', [0.92 0.88 0.85], ...
% 'BER', [1e-4 7e-3 2e-2]);
%
% The returned structure netrates will contain the net rates (and the
% used code rates and thresholds) for each mode in vector form.
properties (Constant)
%% Lookup Table for SD+HD concatenated (using NGMI)
% Overall code rate and NGMI threshold for each row.
OVERALLCODERATES_SDHD = [0.7519, 0.7602, 0.7684, 0.7766, 0.7850, ...
0.7932, 0.8014, 0.8098, 0.8180, 0.8262, ...
0.8345, 0.8428, 0.8510, 0.8593, 0.8676, ...
0.8733, 0.8790, 0.8848, 0.8905, 0.8962, ...
0.9019, 0.9077, 0.9134, 0.9191, 0.9248, ...
0.9306, 0.9363, 0.9420, 0.9477, 0.9535];
NGMITHRESHOLDS_SDHD = [0.8116, 0.8167, 0.8241, 0.8317, 0.8401, ...
0.8459, 0.8512, 0.8574, 0.8685, 0.8746, ...
0.8829, 0.8892, 0.8958, 0.9022, 0.9090,...
0.9150, 0.9210, 0.9270, 0.9330, 0.9390, ...
0.9450, 0.9510, 0.9570, 0.9630, 0.9690, ...
0.9750, 0.9810, 0.9870, 0.9930, 0.9990];
ISPUNCT_LDPI = [zeros(1,15),ones(1,15)];
%% Lookup Table for HD-only mode (using BER)
% For HD-only, the table gives the code rate and the maximum acceptable BER.
CODE_RATES_HD = [0.7500, 0.8000, 0.8123, 0.8333, 0.8571, ...
0.8750, 0.8889, 0.9000, 0.9091, 0.9167, 0.9412];
BERTHRESHOLDS_HD = [2.12e-2, 1.76e-2, 1.62e-2, 1.44e-2, 1.25e-2, ...
1.03e-2, 9.29e-3, 8.33e-3, 7.54e-3, 7.04e-3, 4.70e-3];
%% LUT for KP4-FEC and Inner Code https://grouper.ieee.org/groups/802/3/dj/public/23_03/patra_3dj_01b_2303.pdf
CODE_RATE_KP4_AND_INNER = [0.885799];
BERTHRESHOLDS_KP4_AND_INNER = 4.85e-3;
end
methods
function netrates = calculateNetRate(obj, grossRate, varargin)
% calculatenetrate Calculate the net data rate(s) from measured data.
%
% netrates = tp.calculatenetrate(grossRate, 'BER', berValue, 'NGMI', ngmiValue)
%
% INPUTS:
% grossRate - (scalar or vector) gross data rate(s) [bits/s]
%
% Optional name/value pairs:
% 'BER' - (scalar or vector) measured bit error ratio(s)
% 'NGMI' - (scalar or vector) measured NGMI value(s)
%
% At least one of 'BER' or 'NGMI' must be provided.
%
% OUTPUT:
% netrates - a structure with the following fields (if available):
% .SDHD - for SD+HD concatenated (using NGMI)
% .SDHD_LDPC - for SD+HD with punctured LDPC (using NGMI)
% .HD - for HD-only (using BER)
%
% Each sub-structure contains fields:
% .CodeRate - the chosen overall code rate from the table (vector)
% .Threshold - the threshold value used from the table (vector)
% .<BER/NGMI> - net rate computed as grossRate * CodeRate (vector)
% Parse inputs.
p = inputParser;
addRequired(p, 'grossRate', @(x) isnumeric(x));
addParameter(p, 'BER', [], @(x) isnumeric(x));
addParameter(p, 'NGMI', [], @(x) isnumeric(x));
parse(p, grossRate, varargin{:});
ber = p.Results.BER;
ngmi = p.Results.NGMI;
if isempty(ber) && isempty(ngmi)
error('At least one of ''BER'' or ''NGMI'' must be provided.');
end
% Determine the number of measurements.
numMeasurements = max([numel(grossRate), numel(ngmi), numel(ber)]);
% Broadcast scalars if needed.
if isscalar(grossRate) && numMeasurements > 1
grossRate = repmat(grossRate, 1, numMeasurements);
elseif numel(grossRate) ~= numMeasurements
error('grossRate must be scalar or have %d elements.', numMeasurements);
end
if ~isempty(ngmi)
if isscalar(ngmi) && numMeasurements > 1
ngmi = repmat(ngmi, 1, numMeasurements);
elseif numel(ngmi) ~= numMeasurements
error('NGMI must be scalar or have %d elements.', numMeasurements);
end
end
if ~isempty(ber)
if isscalar(ber) && numMeasurements > 1
ber = repmat(ber, 1, numMeasurements);
elseif numel(ber) ~= numMeasurements
error('BER must be scalar or have %d elements.', numMeasurements);
end
end
% Initialize the output structure.
netrates = struct;
if ~isempty(ngmi)
netrates.SDHD.GrossRate = NaN(1, numMeasurements);
netrates.SDHD.NetRate = NaN(1, numMeasurements);
netrates.SDHD.punctLDPI = NaN(1, numMeasurements);
netrates.SDHD.CodeRate = NaN(1, numMeasurements);
netrates.SDHD.Threshold = NaN(1, numMeasurements);
end
if ~isempty(ber)
netrates.HD.GrossRate = NaN(1, numMeasurements);
netrates.HD.NetRate = NaN(1, numMeasurements);
netrates.HD.CodeRate = NaN(1, numMeasurements);
netrates.HD.Threshold = NaN(1, numMeasurements);
netrates.KP4_hamming.GrossRate = NaN(1, numMeasurements);
netrates.KP4_hamming.NetRate = NaN(1, numMeasurements);
netrates.KP4_hamming.CodeRate = NaN(1, numMeasurements);
netrates.KP4_hamming.Threshold = NaN(1, numMeasurements);
end
% Process each measurement individually.
for i = 1:numMeasurements
% --- NGMI-based modes ---
if ~isempty(ngmi)
% SD+HD concatenated mode.
idx = find(obj.NGMITHRESHOLDS_SDHD <= ngmi(i), 1, 'last');
if ~isempty(idx)
codeRate = obj.OVERALLCODERATES_SDHD(idx);
netrates.SDHD.NetRate(i) = grossRate(i) * codeRate;
netrates.SDHD.GrossRate(i) = grossRate(i) ;
netrates.SDHD.CodeRate(i) = codeRate;
netrates.SDHD.Threshold(i) = obj.NGMITHRESHOLDS_SDHD(idx);
netrates.SDHD.punctLDPI(i) = obj.ISPUNCT_LDPI(idx);
end
end
% --- BER-based mode (HD-only) ---
if ~isempty(ber)
% Loop through the BER thresholds from the best (highest code rate)
% to the worst until the measured BER is acceptable.
idxBER = [];
for j = length(obj.BERTHRESHOLDS_HD):-1:1
if ber(i) <= obj.BERTHRESHOLDS_HD(j)
idxBER = j;
break;
end
end
if ~isempty(idxBER)
codeRate = obj.CODE_RATES_HD(idxBER);
netrates.HD.NetRate(i) = grossRate(i) * codeRate;
netrates.HD.GrossRate(i) = grossRate(i) ;
netrates.HD.CodeRate(i) = codeRate;
netrates.HD.Threshold(i) = obj.BERTHRESHOLDS_HD(idxBER);
end
idxBER = [];
for j = length(obj.BERTHRESHOLDS_KP4_AND_INNER):-1:1
if ber(i) <= obj.BERTHRESHOLDS_KP4_AND_INNER(j)
idxBER = j;
break;
end
end
if ~isempty(idxBER)
codeRate = obj.CODE_RATE_KP4_AND_INNER(idxBER);
netrates.KP4_hamming.NetRate(i) = grossRate(i) * codeRate;
netrates.KP4_hamming.GrossRate(i) = grossRate(i) ;
netrates.KP4_hamming.CodeRate(i) = codeRate;
netrates.KP4_hamming.Threshold(i) = obj.BERTHRESHOLDS_KP4_AND_INNER(idxBER);
end
end
end
end
end
end

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Classes/DataBaseHandler/copyStylingFrom.m Normal file
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function copyStylingFrom(figNumSource, figNumTgt)
% Get handles to the source and target figures
sourceFig = figure(figNumSource);
targetFig = figure(figNumTgt);
% Get axes of source and target figures
sourceAxes = findall(sourceFig, 'type', 'axes');
targetAxes = findall(targetFig, 'type', 'axes');
% Ensure the number of axes match
if length(sourceAxes) ~= length(targetAxes)
error('Number of axes in source and target figures must be the same.');
end
% Loop through each pair of axes and copy styling properties
for i = 1:length(sourceAxes)
copyAxesProperties(sourceAxes(i), targetAxes(i));
end
% Apply general figure properties if desired
targetFig.Color = sourceFig.Color; % Background color
end
function copyAxesProperties(sourceAx, targetAx)
% List of properties to copy from source to target axes
propsToCopy = {'XColor', 'YColor', 'ZColor', 'FontSize', 'FontName', ...
'GridColor', 'GridLineStyle', 'MinorGridColor', 'Box', ...
'XGrid', 'YGrid', 'ZGrid', 'XMinorGrid', 'YMinorGrid', 'ZMinorGrid', ...
'LineWidth', 'TitleFontSizeMultiplier', 'LabelFontSizeMultiplier'};
% Copy properties from source to target
for i = 1:length(propsToCopy)
try
targetAx.(propsToCopy{i}) = sourceAx.(propsToCopy{i});
catch
% Skip property if it doesn't exist or can't be copied
end
end
% Copy axis labels and titles
targetAx.Title.String = sourceAx.Title.String;
targetAx.XLabel.String = sourceAx.XLabel.String;
targetAx.YLabel.String = sourceAx.YLabel.String;
targetAx.ZLabel.String = sourceAx.ZLabel.String;
% Copy children elements like lines, patches, etc.
sourceChildren = allchild(sourceAx);
targetChildren = allchild(targetAx);
% Ensure the number of children elements match
if length(sourceChildren) ~= length(targetChildren)
warning('Number of elements in source and target axes differ. Styling may not be applied completely.');
end
% Copy properties of children (like lines, patches, etc.), except colors and legends
for i = 1:min(length(sourceChildren), length(targetChildren))
copyObjectProperties(sourceChildren(i), targetChildren(i));
end
end
function copyObjectProperties(sourceObj, targetObj)
% List of common properties to copy for plot elements (lines, patches, etc.)
propsToCopy = {'LineStyle', 'LineWidth', 'Marker', 'MarkerSize', ...
'MarkerEdgeColor', 'MarkerFaceColor', 'DisplayName'};
% Copy properties from source to target, excluding colors
for i = 1:length(propsToCopy)
try
if ~contains(propsToCopy{i}, 'Color') % Skip color properties
targetObj.(propsToCopy{i}) = sourceObj.(propsToCopy{i});
end
catch
% Skip property if it doesn't exist or can't be copied
end
end
end

150
Functions/EQ_visuals/analyzeEQperformance.m Normal file
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function analyzeEQperformance(ref_bits,ref_symbols,rx_signal,eq_signal,eq_decisions,fsym,M,options)
arguments
ref_bits
ref_symbols
rx_signal
eq_signal
eq_decisions
fsym
M
options.postfilterclass
options.eqclass
options.mlseclass
options.db_precoded
options.displayname
end
% toolkit to visualize stuff related to DSP of IM/DD
%%% Preps
if isempty(eq_decisions)
eq_decisions = PAMmapper(M,0).quantize(eq_signal);
end
%%% Demap eqlzd signal to determine BER
if options.db_precoded
eq_hd = PAMmapper(M,0).quantize(eq_signal);
eq_hd = Duobinary().encode(eq_hd);
eq_hd = Duobinary().decode(eq_hd,"M",M);
rx_bits = PAMmapper(M,0).demap(eq_hd);
else
rx_bits = PAMmapper(M,0).demap(eq_signal);
end
[~,numerr,ber_sd,errpos] = calc_ber(rx_bits.signal,ref_bits.signal,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
% fprintf('SD BER: %.2e \n',ber_sd);
%%% Demap provided decisions to determine BER
rx_bits = PAMmapper(M,0).demap(eq_decisions);
[~,numerr,ber_mlse,errpos] = calc_ber(rx_bits.signal,ref_bits.signal,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
% fprintf('MLSE BER: %.2e \n',ber_mlse);
%%% Noise prior to DSP (is thius accurate with resampling?)
rx_resampled = rx_signal.normalize("mode","rms").resample("fs_out",fsym);
rx_noise = rx_resampled-ref_symbols;
%%% Noise after to soft-decision DSP
eq_noise = eq_signal-ref_symbols;
col = cbrewer2('paired',12);
lines = numel(findall(figure(200), 'Type', 'Line'))+1;
darkcoloridx = max(mod(2*lines,12),2);
lightcoloridx = max(mod(2*lines-1,12),1);
%%% Separate Classes
constellation = unique(ref_symbols.signal);
received_sd = NaN(numel(constellation),length(ref_symbols));
received_hd = NaN(numel(constellation),length(ref_symbols));
lvlcol = cbrewer2('Set1',numel(constellation));
for lvl = 1:numel(constellation)
%Separate the equalized signal into the
%respective levels based on the actually
%transmitted level!
received_sd(lvl,ref_symbols.signal==constellation(lvl)) = eq_signal.signal(ref_symbols.signal==constellation(lvl));
received_hd(lvl,ref_symbols.signal==constellation(lvl)) = eq_decisions.signal(ref_symbols.signal==constellation(lvl));
end
%%% bursts
% Find differences between consecutive elements
diff_indices = diff(errpos);
% Identify the start of new sequences (when the difference is not 1)
sequence_starts = [1, find(diff_indices ~= 1) + 1]; % Include the first index
sequence_ends = [sequence_starts(2:end) - 1, length(errpos)]; % Calculate end indices
% Initialize burst count and print bursts longer than 10
burst_len = 1:10;
burst_count = zeros(length(burst_len),1);
for t = 1:numel(burst_len)
for i = 1:length(sequence_starts)
% Extract current sequence
current_burst = errpos(sequence_starts(i):sequence_ends(i));
% Check if the sequence length matches criterion
if length(current_burst) == burst_len(t)
burst_count(t) = burst_count(t) + 1;
end
end
end
burst_symbols = burst_count .* burst_len';
burst_rate = burst_symbols ;%./ length(rx_signal);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Rx Spectrum %200
rx_signal.spectrum("displayname",sprintf('Rx %d GBd PAM%d',fsym.*1e-9,M),'fignum',200,'normalizeTo0dB',1,'color',col(darkcoloridx,:));
xline([-fsym/2,fsym/2].*1e-9,'Color',col(mod(lines,12)+2,:),'HandleVisibility','off');
ylim([-20,3]);
%%% EQ Spectrum
%
%%% EQ Time Series %210
showEQTimeSignal(eq_signal,ref_symbols)
%%% EQ Noise Spectrum + inverted Postfilter %220
showEQNoisePSD(eq_noise,options.postfilterclass.burg_coeff,"fignum",220,"color",col(darkcoloridx,:));
%%% EQ SNR Spectrum %230
fft_length = 2^13;
[s_lin,w] = pwelch(eq_signal.signal,hanning(fft_length),fft_length/2,fft_length,eq_signal.fs,"centered","psd","mean");
[n_lin,w] = pwelch(eq_noise.signal,hanning(fft_length),fft_length/2,fft_length,eq_noise.fs,"centered","psd","mean");
w = w.*1e-9;
snr_dbm = 10*log10(s_lin./n_lin);
figure(230)
hold on
plot(w,snr_dbm,'DisplayName','SNR after EQ','LineWidth',1,'Color',col(darkcoloridx,:));
xlabel("Frequency in GHz");
edgetick = 2^(nextpow2(eq_signal.fs*1e-9));
xticks(-edgetick:16:edgetick);
xlim([-128 128]);
ylim([-20,35]);
grid minor
yticks(-200:10:100);
grid on; grid minor;
legend('Interpreter','none');
title('Noise of soft decision signal (not MLSE)');
%%% FFE histogram %240
showLevelHistogram(eq_signal,ref_symbols)
%%% Confusion Matrix
showLevelConfusionMatrix(eq_decisions,ref_symbols,"fignum",250)
%%% Burst Count
figure(260)
hold on
plot(burst_len,burst_rate,'Marker','x','Color',col(darkcoloridx,:),"displayname",sprintf('Rx %d GBd PAM%d; %s',fsym.*1e-9,M,options.displayname));
xlabel('length of error burst');
ylabel('occurences')
grid on
set(gca, 'YScale', 'log');
autoArrangeFigures
end

44
Functions/EQ_visuals/showEQNoisePSD.m Normal file
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function showEQNoisePSD(eq_noise, options)
arguments
eq_noise
options.postfilter_taps = NaN
options.fignum (1,1) double = NaN % Default to NaN if not provided
options.displayname (1,:) char = '' % Default to an empty string if not provided
options.color = [0.2157 0.4941 0.7216];
end
% Determine the figure number to use or create a new figure
if isnan(options.fignum)
fig = figure; % Create a new figure and get its handle
else
fig = figure(options.fignum); % Use the specified figure number
end
hold on
ax = gca;
% N = numel(ax.Children);
N = sum(arrayfun(@(x) strcmp(x.LineStyle, '-'), ax.Children));
cmap = linspecer(8);
options.color = cmap(mod(N, size(cmap, 1)) + 1, :);
% Ensure the figure is ready before calling spectrum
eq_noise.spectrum("displayname", options.displayname, "fignum", fig.Number, "normalizeTo0dB", 1,"color",options.color);
title('Noise of soft decision signal (not MLSE)')
if ~isnan(options.postfilter_taps)
% Hold on to the figure for further plotting
hold on;
% Compute the frequency response of the postfilter
[h, w] = freqz(1, options.postfilter_taps, length(eq_noise), "whole", eq_noise.fs);
h = h / max(abs(h)); % Normalize the filter response
% Adjust frequency axis to center at 0
w_ = (w - eq_noise.fs / 2);
% Plot the inverted postfilter response
plot(w_ * 1e-9, 20 * log10(fftshift(abs(h))), 'DisplayName', ['Burg Coeffs: ', num2str(round(options.postfilter_taps, 2)), ' '], 'LineWidth', 1,'Color',options.color,'LineStyle','--');
% Ensure a legend is displayed
legend('show');
end
end

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function showEQNoiseSNR(tx_signal, rx_signal, options)
arguments
tx_signal
rx_signal
options.fs_tx
options.fs_rx
options.fignum (1,1) double = NaN % Default to NaN if not provided
options.displayname (1,:) char = '' % Default to an empty string if not provided
options.color = [0.2157 0.4941 0.7216];
end
% Determine the figure number to use or create a new figure
if isnan(options.fignum)
fig = figure; % Create a new figure and get its handle
else
fig = figure(options.fignum); % Use the specified figure number
end
if isa(tx_signal,'Signal')
options.fs_tx = tx_signal.fs;
tx_signal = tx_signal.signal;
end
if isa(rx_signal,'Signal')
options.fs_rx = rx_signal.fs;
rx_signal = rx_signal.signal;
end
hold on
ax = gca;
% N = numel(ax.Children);
N = sum(arrayfun(@(x) strcmp(x.LineStyle, '-'), ax.Children));
cmap = linspecer(8);
options.color = cmap(mod(N, size(cmap, 1)) + 1, :);
% Ensure the figure is ready before calling spectrum
title('SNR of received Signal')
fft_length = 2^(nextpow2(length(tx_signal))-7);
[s_lin,w] = pwelch(tx_signal,hanning(fft_length),fft_length/2,fft_length,options.fs_tx,"centered","psd","mean");
[n_lin,w] = pwelch(rx_signal,hanning(fft_length),fft_length/2,fft_length,options.fs_rx,"centered","psd","mean");
w = w.*1e-9;
snr_dbm = 10*log10(s_lin./n_lin);
% figure(231)
hold on
plot(w,snr_dbm,'DisplayName','SNR','LineWidth',0.5,'Color',options.color);
xlabel("Frequency in GHz");
edgetick = 2^(nextpow2(options.fs_tx*1e-9));
ticks = -edgetick:16:edgetick;
xticks(ticks);
[~,b]=min(abs((-edgetick:16:edgetick)-max(w)));
xlim([-ticks(b+1) ticks(b+1)]);
max_snr = ceil(max(snr_dbm)/10)*10;
min_snr = floor(min(snr_dbm)/10)*10;
ylim([min_snr,max_snr]);
yticks(-200:10:100);
grid on; grid minor;
legend('Interpreter','none');
title('Noise of soft decision signal (not MLSE)');
end

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function showEQTimeSignal(eq_signal,ref_symbols,options)
arguments
eq_signal
ref_symbols
options.fignum (1,1) double = NaN % Default to NaN if not provided
options.displayname (1,:) char = '' % Default to an empty string if not provided
options.color = [0.2157 0.4941 0.7216];
end
% Determine the figure number to use or create a new figure
if isnan(options.fignum)
fig = figure; % Create a new figure and get its handle
else
fig = figure(options.fignum); % Use the specified figure number
end
M = numel(unique(ref_symbols.signal));
lvlcol = cbrewer2('Set1',M);
col = cbrewer2('paired',2);
eq_decisions = PAMmapper(M,0).quantize(eq_signal);
rx_bits = PAMmapper(M,0).demap(eq_signal);
ref_bits = PAMmapper(M,0).demap(ref_symbols);
%%% Separate Classes
constellation = unique(ref_symbols.signal);
received_sd = NaN(numel(constellation),length(ref_symbols));
received_hd = NaN(numel(constellation),length(ref_symbols));
lvlcol = cbrewer2('Set1',numel(constellation));
for lvl = 1:numel(constellation)
%Separate the equalized signal into the
%respective levels based on the actually
%transmitted level!
received_sd(lvl,ref_symbols.signal==constellation(lvl)) = eq_signal.signal(ref_symbols.signal==constellation(lvl));
received_hd(lvl,ref_symbols.signal==constellation(lvl)) = eq_decisions.signal(ref_symbols.signal==constellation(lvl));
end
[~,numerr,ber_sd,errpos] = calc_ber(rx_bits.signal,ref_bits.signal,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
%%% EQ Time Series %210
eq_signal.plot("fignum",fig.Number,"displayname",'Equalized Signal','color',col(1,:),'clear',1);
hold on
try
yline(PAMmapper(M,0).get_demodulation_thresholds,'HandleVisibility','off','LineStyle','--');
for c = 1:M
scatter(errpos./eq_signal.fs,received_sd(c,errpos),1,'x','MarkerEdgeColor',lvlcol(c,:),'LineWidth',2,'DisplayName',sprintf('Tx Lvl: %d',c));
end
end
end

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function showEQcoefficients(n1, n2, n3, options)
% Show filter coefficients as stem plot
% n1, n2, and n3 in different subplots
% Scale all y-axis to -1 and 1
arguments
n1
n2
n3
options.fignum (1,1) double = NaN % Default to NaN if not provided
options.displayname (1,:) char = '' % Default to an empty string if not provided
options.color = [0.2157, 0.4941, 0.7216];
options.clf = 0; % Clear figure before plotting new
end
% Determine the figure number to use or create a new figure
if isnan(options.fignum)
fig = figure; % Create a new figure and get its handle
else
fig = figure(options.fignum); % Use the specified figure number
end
if options.clf
clf(fig); % Clear the figure if requested
end
hold on
ax = gca;
N = numel(ax.Children);
% Set up a colormap for consistent coloring
cmap = linspecer(8);
options.color = cmap(mod(N, size(cmap, 1)) + 1, :);
% Create subplots for n1, n2, n3
for i = 1:3
subplot(3, 1, i);
switch i
case 1
stem(n1, 'Color', options.color, 'LineWidth', 1,'Marker','.','MarkerSize',10);
title(sprintf('1st order Filter Coefficients: %d',numel(n1)));
case 2
stem(n2, 'Color', options.color, 'LineWidth', 1,'Marker','.','MarkerSize',10);
title(sprintf('2nd order Filter Coefficients: %d',numel(n2)));
case 3
stem(n3, 'Color', options.color, 'LineWidth', 1,'Marker','.','MarkerSize',10);
title(sprintf('3rd order Filter Coefficients: %d',numel(n3)));
end
ylim([-1, 1]); % Scale y-axis to -1 and 1
grid on;
grid minor
xlabel('Coefficient Index');
ylabel('Amplitude');
end
% Ensure the layout is tight for better visibility
sgtitle('Filter Coefficients'); % Overall title
end

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function showErrorBurstCount(eq_signal,ref_symbols,options)
arguments
eq_signal
ref_symbols
options.fignum (1,1) double = NaN % Default to NaN if not provided
options.displayname (1,:) char = '' % Default to an empty string if not provided
end
% Determine the figure number to use or create a new figure
if isnan(options.fignum)
fig = figure; % Create a new figure and get its handle
else
fig = figure(options.fignum); % Use the specified figure number
end
if numel(unique(eq_signal.signal)) > 20
M = numel(unique(ref_symbols.signal));
eq_signal = PAMmapper(M,0).quantize(eq_signal);
end
diff_indices = eq_signal.signal == ref_symbols.signal;
% Identify the start of new sequences (when the difference is not 1)
sequence_starts = [1, find(diff_indices ~= 1) + 1]; % Include the first index
sequence_ends = [sequence_starts(2:end) - 1, length(errpos)]; % Calculate end indices
% Initialize burst count and print bursts longer than 10
burst_len = 1:10;
burst_count = zeros(length(burst_len),1);
for t = 1:numel(burst_len)
for i = 1:length(sequence_starts)
% Extract current sequence
current_burst = errpos(sequence_starts(i):sequence_ends(i));
% Check if the sequence length matches criterion
if length(current_burst) == burst_len(t)
burst_count(t) = burst_count(t) + 1;
end
end
end
burst_symbols = burst_count .* burst_len';
burst_rate = burst_symbols ;%./ length(rx_signal);
end

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function showLevelConfusionMatrix(decided_symbols,ref_symbols,options)
arguments
decided_symbols
ref_symbols
options.M = NaN
options.fignum (1,1) double = NaN % Default to NaN if not provided
options.displayname (1,:) char = '' % Default to an empty string if not provided
end
% Determine the figure number to use or create a new figure
if isnan(options.fignum)
fig = figure; % Create a new figure and get its handle
else
fig = figure(options.fignum); % Use the specified figure number
end
if length(unique(decided_symbols.signal))>20
assert(~isnan(options.M),'Provide either decided symbol sequence or modulation order M (PAM-4 -> M=4)');
decided_symbols = PAMmapper(options.M,0).quantize(decided_symbols);
end
%%% Confusion Matrix
cm = confusionchart(ref_symbols.signal,decided_symbols.signal,'RowSummary','row-normalized','ColumnSummary','column-normalized','Title','Confusion Matrix','XLabel','Decisions','YLabel','Transmitted');
end

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function showLevelHistogram(eq_signal,ref_symbols,options)
arguments
eq_signal
ref_symbols
options.fignum (1,1) double = NaN % Default to NaN if not provided
options.displayname (1,:) char = '' % Default to an empty string if not provided
end
if isa(eq_signal,'Signal')
eq_signal = eq_signal.signal;
end
if isa(ref_symbols,'Signal')
ref_symbols = ref_symbols.signal;
end
% Determine the figure number to use or create a new figure
if isnan(options.fignum)
fig = figure; % Create a new figure and get its handle
else
fig = figure(options.fignum); % Use the specified figure number
end
%%% Separate Classes
constellation = unique(ref_symbols);
received_sd = NaN(numel(constellation),length(ref_symbols));
lvlcol = cbrewer2('Set1',numel(constellation));
for lvl = 1:numel(constellation)
%Separate the equalized signal into the
%respective levels based on the actually
%transmitted level!
received_sd(lvl,ref_symbols==constellation(lvl)) = eq_signal(ref_symbols==constellation(lvl));
end
%%% FFE histogram
clf
for lvl = 1:numel(constellation)
intermediate = received_sd(lvl,:);
cnt(lvl) = round(numel(intermediate(~isnan(intermediate)))./length(eq_signal),3).*100;
hold on
histogram(received_sd(lvl,:),1000,"EdgeAlpha",0,'DisplayName',['Lvl ',num2str(lvl),' | ',num2str(cnt(lvl)),' %'],'FaceColor',lvlcol(lvl,:),'Normalization','pdf');
end
legend
grid on
end

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function air = air_garcia_implementation(x,r,idx_tx,Px,M_training)
MAX_MEMORY = 200e6; % maximum allowed size for a matrix
if nargin == 3
Px = [];
M_training = [];
end
if nargin == 4
M_training = [];
end
% if input is complex, separate into real and imaginary parts
if any(imag(x(:))~=0) || any(imag(r(:))~=0)
x = [real(x); imag(x)];
r = [real(r); imag(r)];
end
D = size(x, 1); % D = 2 if complex x
N = size(x, 2); % number of constellation points
M = size(r, 2); % number of samples
% set default training set size
if isempty(M_training)
M_training = ceil(0.3*M);
end
M_testing = M - M_training;
% Training: estimate parameters of the conditionally Gaussian model
% sort according to transmit index
[idx_tx_training, idx_sort] = sort(idx_tx(1:M_training));
r_training = r(:, idx_sort);
i_bounds = zeros(1, N+1);
% compute conditional means and covariance matrices
C_n = zeros(D, D, N);
det_n = zeros(1, N);
for n=1:N
% find how many times x(:, n) was transmitted and update i_bounds
N_current_x = find(idx_tx_training((i_bounds(n)+1):end)==n, 1, 'last');
if isempty(N_current_x), N_current_x=0; end
i_bounds(n+1) = i_bounds(n) + N_current_x;
if N_current_x > 0
% Compute mu_n=E[Y|X=x_n] according to Eq. (14) and store it in
% x(:, n) to save space
x(:, n) = sum(r_training(:, (i_bounds(n)+1):i_bounds(n+1)), 2)/(i_bounds(n+1)-i_bounds(n));
% compute C_n=cov[Y|X=x_n] according to Eq. (15)
r_meanfree = r_training(:, (i_bounds(n)+1):i_bounds(n+1)) - x(:, n);
C_n(:, :, n) = (r_meanfree*r_meanfree')/(i_bounds(n+1)-i_bounds(n));
% store also the determinant of C(:, :, n)
det_n(n) = det(C_n(:, :, n));
% if the determinant is 0, or if the matrix is badly conditioned,
% regularize by adding a small identity matrix. Note that we do
% need the check for 0 determinant, in case a cloud has exactly 0
% variance according to the training set
if det_n(n)==0 || cond(C_n(:, :, n))>1e16
C_n(:, :, n) = C_n(:, :, n) + 5 * eps * eye(D);
det_n(n) = (5*eps)^D;
end
end
end
% uniform input pmf Px if not provided
if isempty(Px)
Px = repmat(1/N, [1, N]);
end
% extract testing set and sort it according to transmit index
[idx_tx_testing, idx_sort] = sort(idx_tx((M_training+1):M));
r_testing = r(:, M_training+idx_sort);
% computation of h(Y|X)
h_Y_X = 0;
i_bounds_testing = zeros(1, N+1);
% loop over constellation points to compute h(Y|X)
for n = 1:N
% find how many times x(:, n) was transmitted and update
% i_bounds_testing
N_current_x = find(idx_tx_testing((i_bounds_testing(n)+1):end)==n, 1, 'last');
if isempty(N_current_x), N_current_x=0; end
i_bounds_testing(n+1) = i_bounds_testing(n) + N_current_x;
% add the corresponding contribution to the mutual information (two
% first lines of Eq. (17)). This, together with
% D/2*log2(2*pi) after the end of the loop, gives h(Y|X)
h_Y_X = h_Y_X + N_current_x * log2(det_n(n))/2+...
sum(sum(conj(r_testing(:, (i_bounds_testing(n)+1):i_bounds_testing(n+1))-x(:, n)).*(C_n(:, :, n)\(r_testing(:, (i_bounds_testing(n)+1):i_bounds_testing(n+1))-x(:, n)))))/2/log(2);
end
h_Y_X = D/2*log2(2*pi) + h_Y_X/M_testing;
% When computing log(py), we might run out of memory. If necessary, we
% doe the computation in blocks
logpy = zeros(1, M_testing);
BLOCK_SIZE = floor(MAX_MEMORY/N);
N_blocks = ceil(M_testing/BLOCK_SIZE);
% loop over blocks of symbols. This loop can be replaced by parfor to allow
% parallel computation
for i_block = 1:N_blocks
logpy_cur = zeros(1, M_testing);
% beginning of block
i_start = (i_block-1) * BLOCK_SIZE + 1;
% end of block
i_end = min(M_testing, i_block*BLOCK_SIZE);
% block size
current_block_size = i_end-i_start+1;
% compute exponents of third line of (17)
exponents = zeros(N, current_block_size);
for n = 1:N
exponents(n, :) = -log(det_n(n))/2-real(sum(conj(r_testing(:, i_start:i_end)-x(:, n)).*(C_n(:, :, n)\(r_testing(:, i_start:i_end)-x(:, n))), 1))/2;
%sum über 2 einträge von r
end
% compute third line of Eq. (17). Use a custom function
% that computes log(sum(exp(x))) avoiding overflow errors
logpy_cur(i_start:i_end) = math_logsumexp(log(Px(:))+exponents, 1);
logpy = logpy + logpy_cur;
end
% output entropy h(Y)
h_Y = D/2*log2(2*pi) - mean(logpy)/log(2);%log basis change
% compute mutual information
air = h_Y - h_Y_X;
end
function [y] = math_logsumexp(x, dim)
%[y] = math_logsumexp(x, dim)
% Computes log(sum(exp(x), dim)), avoiding overflow errors when one of the
% x is large.
if nargin<2 || isempty(dim)
m = max(x);
y = m + log(sum(exp(x-m)));
else
m = max(x, [], dim);
y = m + log(sum(exp(x-m), dim));
end
end

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function [ach_inf_rate] = calc_air(test_signal,reference_signal,options)
% Calculation of AIR acc. to J. Kozesnik, „Numerically Computing Achievable Rates of Memoryless Channels“, Francisco Javier Garcıa-Gomez, doi: 10.1007/978-94-009-9857-5.
% Implementation is not accessible, I mailed TUM to get the code...
arguments(Input)
test_signal;
reference_signal;
options.skip_front = 0;
options.skip_end = 0;
options.returnErrorLocation = 0;
end
options.skip_end = abs(options.skip_end);
options.skip_front = abs(options.skip_front);
assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
if isa(reference_signal,'Signal')
reference_signal = reference_signal.signal;
end
if isa(test_signal,'Signal')
test_signal = test_signal.signal;
end
% TRIM
[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
% CALC EVM
%%% new implementation of AIR
constellation = unique(reference_signal);
reference_idx = arrayfun(@(x) find(constellation == x, 1), reference_signal);
ach_inf_rate = air_garcia_implementation(constellation',test_signal',reference_idx');
function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
data_ = data(skipstart+1:end-skip_end,:);
delta_bits = length(reference) - length(data);
skip_end = delta_bits + skip_end;
reference_ = reference(skipstart+1:end-skip_end,:);
end
end

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function [bits,errors,ber,errorIndice] = calc_ber(data_in,data_ref,options)
arguments(Input)
data_in;
data_ref;
options.skip_front = 0;
options.skip_end = 0;
options.returnErrorLocation = 0;
end
options.skip_end = abs(options.skip_end);
options.skip_front = abs(options.skip_front);
assert((options.skip_end+options.skip_front)<length(data_in),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
errorIndice= [];
% trim sequence to given start; stop. trim reference if signal is shorter
[data_in,data_ref]=trimseq(data_in,data_ref,options.skip_front,options.skip_end);
if length(data_ref) == length(data_in)
bits = numel(data_in(:,options.skip_front+1:end));
if options.returnErrorLocation == 0
errors = sum( data_in ~= data_ref,"all" );
else
errorIndice = sum(data_in ~= data_ref,1);
errors = sum(errorIndice ,"all" );
[~,errorIndice] = find(errorIndice~=0);
errorIndice = errorIndice+options.skip_front;
end
% Determine BER
ber = sum(errors)/sum(bits);
else
error('Sequence length does not match');
end
function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
data_ = logical(data(skipstart+1:end-skip_end,:))';
delta_bits = length(reference) - length(data);
skip_end = delta_bits + skip_end;
reference_ = logical(reference(skipstart+1:end-skip_end,:))';
end
end

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function [evm_total,evm_lvl] = calc_evm(test_signal,reference_signal,options)
arguments(Input)
test_signal;
reference_signal;
options.skip_front = 0;
options.skip_end = 0;
options.returnErrorLocation = 0;
end
options.skip_end = abs(options.skip_end);
options.skip_front = abs(options.skip_front);
assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
if isa(reference_signal,'Signal')
reference_signal = reference_signal.signal;
end
if isa(test_signal,'Signal')
test_signal = test_signal.signal;
end
% TRIM
[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
% CALC EVM
[evm_total,evm_lvl] = calc_evm_(test_signal,reference_signal);
function [evm_total,evm_lvl] = calc_evm_(test_signal,reference_signal)
assert(length(test_signal) == length(reference_signal),"Sequence length does not match");
error_vector = (test_signal-reference_signal);
%%% Overall EVM
evm_total = rms(error_vector);
try
%%% Per Level EVM
k = unique(reference_signal);
for lvl = 1:length(k)
lvl_errors = error_vector(reference_signal==k(lvl));
evm_lvl(lvl) = rms(lvl_errors);
end
catch
evm_lvl = NaN;
warning('No EVM per level calculated')
end
end
function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
data_ = data(skipstart+1:end-skip_end,:);
delta_bits = length(reference) - length(data);
skip_end = delta_bits + skip_end;
reference_ = reference(skipstart+1:end-skip_end,:);
end
end

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function [GMI,NGMI] = calc_ngmi(test_signal,reference_signal,options)
% Silas implementation of (N)GMI calculation according to: J. Cho, L. Schmalen, und P. J. Winzer,
% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, doi: 10.1109/ECOC.2017.8345872.
% This implementation assumes the same normal distributed noise for each
% channel (sigma2 is calculated once for the whole signal)
arguments(Input)
test_signal;
reference_signal;
options.skip_front = 0;
options.skip_end = 0;
options.returnErrorLocation = 0;
end
options.skip_end = abs(options.skip_end);
options.skip_front = abs(options.skip_front);
assert((options.skip_end+options.skip_front)<length(test_signal),"You can not skip more bits than overall length of data! Set skip_front or skip_end to lower value or check data_in");
if isa(reference_signal,'Signal')
reference_signal = reference_signal.signal;
end
if isa(test_signal,'Signal')
test_signal = test_signal.signal;
end
% TRIM
[test_signal,reference_signal]=trimseq(test_signal,reference_signal,options.skip_front,options.skip_end);
% CALC EVM
[GMI,NGMI] = calc_ngmi_(test_signal,reference_signal);
function [GMI,NGMI] = calc_ngmi_(test_signal,reference_signal)
assert(length(test_signal) == length(reference_signal),"Sequence length does not match");
%%% implemented according to [1] J. Cho, L. Schmalen, und P. J. Winzer,
% „Normalized Generalized Mutual Information as a Forward Error Correction Threshold for Probabilistically Shaped QAM“,
% in 2017 European Conference on Optical Communication (ECOC), Sep. 2017, S. 1–3. doi: 10.1109/ECOC.2017.8345872.
error_vector = (test_signal-reference_signal);
sigma2 = var(error_vector); %noise variance
%%% Separate Classes
constellation = unique(reference_signal);
received_sd = NaN(numel(constellation),length(reference_signal));
lvlcol = cbrewer2('Set1',numel(constellation));
for lvl = 1:numel(constellation)
%Separate the equalized signal into the
%respective levels based on the actually
%transmitted level!
received_sd(lvl,reference_signal==constellation(lvl)) = test_signal(reference_signal==constellation(lvl));
end
N = length(test_signal); % Number of received samples
M = length(constellation); %P
m = log2(M); %bits per symbol
entries = sum(~isnan(received_sd),2)';
P_X = entries./N;
% Parameters
symbols = constellation'; % PAM-4 symbols
gray_bits = PAMmapper(M,0).demap_(constellation); % Gray coding (bits per symbol)
% Conditional probability function for AWGN
q_Y_given_X = @(y, x) (1 / sqrt(2 * pi * sigma2)) * exp(-(y - x).^2 / (2 * sigma2));
% Entropy term
H_X = -sum(P_X .* log2(P_X)); % Entropy of input distribution
% GMI computation
noise_impact_term = 0;
for k = 1:N
y_k = test_signal(k); % Current received sample
[~, closest_symbol_idx] = min(abs(symbols - y_k)); % Closest symbol index
closest_symbol = symbols(closest_symbol_idx); % Closest symbol
for i = 1:m
% Extract i-th bit for each symbol
bit_mask = gray_bits(:, i); % Binary column for i-th bit of all symbols
matching_symbols = symbols(bit_mask == gray_bits(closest_symbol_idx, i));
% Numerator: Sum over x in x_{b_{k, i}}
numerator = sum(q_Y_given_X(y_k, matching_symbols) .* P_X(ismember(symbols, matching_symbols)));
% Denominator: Sum over all x
denominator = sum(q_Y_given_X(y_k, symbols) .* P_X);
% Logarithmic contribution
noise_impact_term = noise_impact_term + log2(numerator / denominator);
end
end
% Normalize the noise impact term by N
noise_impact_term = noise_impact_term / N;
% GMI
GMI = H_X + noise_impact_term;
NGMI = GMI / m;
end
function [data_,reference_]=trimseq(data,reference,skipstart,skip_end)
data_ = data(skipstart+1:end-skip_end,:);
delta_bits = length(reference) - length(data);
skip_end = delta_bits + skip_end;
reference_ = reference(skipstart+1:end-skip_end,:);
end
end

176
projects/A_minimal_example/imdd_simulation_minimal.m
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@@ -1,176 +0,0 @@
function [ber] = imdd_simulation_minimal(varargin)
% BASIC IMDD Model...
% varargin is either empty or a struct, i.e.:
% optionalvars = struct('bitrate',300e9,'M',6);
% then:
% imdd_simulation_minimal(optionalvars)
% replaces the respective variables -> nice for looping parameter sets
curFolder = pwd;
funcFolder=fileparts(mfilename('fullpath'));
if ~isempty(funcFolder)
cd(funcFolder);
end
% TX
M = 4;
fsym = 112e9;
bitrate = 224e9;
apply_pulsef = 1;
fdac = 256e9;
fadc = 256e9;
random_key = 1;
db_precode = 0;
db_encode = 0;
rcalpha = 0.05;
kover = 16;
vbias_rel = 0.5;
u_pi = 2.9;
vbias = -vbias_rel*u_pi;
laser_wavelength = 1310;
laser_linewidth = 0;
tx_bw_nyquist = 0.95;
% Channel
link_length = 1; %km
% RX
rop = -7;
rx_bw_nyquist = 0.9;
% EQ
vnle_order=[50,7,7];
dfe_order = [2 0 0];
len_tr = 4096*2;
mu_ffe = [0.0004 0.0004 0.0004];
mu_dfe = 0.0004;
mu_dc = 0.00;
% Replace optional input arguments if there are any
if ~isempty(varargin)
var_s = varargin{1};
if isstruct(var_s)
fields = fieldnames(var_s);
for i = 1:numel(fields)
eval([fields{i}, ' = ', num2str( var_s.(fields{i}) ), ';']);
fprintf("%s <-- %.2f \n", fields{i}, var_s.(fields{i}));
end
else
error('Optional variables should be passed as a struct.');
end
end
fsym_ = floor( bitrate*1e-9./log2(M) ).*1e9;
if fsym_ ~= fsym
fsym = fsym_;
fprintf('Adapted symbolrate to %d GBd, to match provided bitrate of %d GBit/s using PAM %d \n',fsym.*1e-9,bitrate.*1e-9, M);
end
f_nyquist = fsym/2;
%%%% TX Signal
Pform = Pulseformer("fsym",fsym,"fdac",4*fsym,"pulse","rrc","pulselength",16,"rrcalpha",rcalpha);
[Digi_sig,Tx_symbols,Tx_bits] = PAMsource(...
"fsym",fsym,"M",M,"order",18,"useprbs",1,...
"fs_out",fdac,...
"applyclipping",0,"clipfactor",1.5,...
"applypulseform",apply_pulsef,"pulseformer",Pform,...
"randkey",random_key,...
"db_precode",db_precode,"db_encode",db_encode,...
"mrds_code",0,"mrds_blocklength",512).process();
Digi_sig.spectrum("displayname",'Digital Spectrum at TX','fignum',10,'normalizeTo0dB',1);
%%%%% AWG
% El_sig = M8199A("kover",kover).process(Digi_sig);
El_sig = AWG("fdac",fdac,"f_cutoff",fsym,"lpf_active",1,"kover",kover,"bit_resolution",12).process(Digi_sig);
% El_sig.spectrum("displayname",'Digi Spectrum','fignum',100,'normalizeTo0dB',0);
El_sig = El_sig.setPower(0,"dBm");
El_sig.eye(fsym,M,"fignum",11,'displayname','Rx Eye');
%%%%% Low-pass el. components %%%%%%
El_sig = Filter('filtdegree',4,"f_cutoff",75e9,"fs",fdac*kover,"filterType",filtertypes.butterworth,"active",true).process(El_sig);
%%%%% Electrical Driver Amplifier %%%%%%
El_sig = Amplifier("amp_mode","ideal_no_noise","gain_mode","gain","amplification_db",3).process(El_sig);
%%%%% MODULATE E/O CONVERSION %%%%%%
[Opt_sig] = EML("mode",eml_mode.im_cosinus,"power",3,"fsimu",El_sig.fs,"lambda",laser_wavelength,"bias",vbias,"u_pi",u_pi,"linewidth",laser_linewidth,"randomkey",random_key+1).process(El_sig);
%%%%%% Fiber %%%%%%
Opt_sig = Fiber("fsimu",Opt_sig.fs,"fiber_length",link_length/1000,"alpha",0.3,"D",0,"lambda0",1310,"gamma",0,"Dslope",0.07).process(Opt_sig);
%%%%%% ROP %%%%%%
Rx_sig = Amplifier("amp_mode","ideal_no_noise","gain_mode","output_power","amplification_db",rop).process(Opt_sig);
%%%%%% PD Square Law %%%%%%
Rx_sig = Photodiode("fsimu",fdac*kover,"dark_current",2e-08,"responsivity",1,"temperature",20,"nep",1.8e-11).process(Rx_sig);
Rx_sig.eye(fsym,M,"fignum",30,'displayname','Rx Eye');
%%%%%% Low-pass RX (PD, El. Connectors and Scope %%%%%%
Rx_sig = Filter('filtdegree',4,"f_cutoff",75e9,"fs",fdac*kover,"filterType",filtertypes.butterworth,"active",true).process(Rx_sig);
%%%%%% Low-pass inside Scope %%%%%%
Lp_scpe = Filter('filtdegree',4,"f_cutoff",110e9,"fs",fadc,"filterType",filtertypes.butterworth,"active",true);
%%%%%% Scope %%%%%%
Scpe_sig = Scope("fsimu",fdac*kover,"fadc",fadc,...
"delay",0,"fixed_delay",0,"filtertype",filtertypes.butterworth,...
"samplingdelay",0,"rand_samplingdelay",0,"freq_offset",0,"samp_jitter",0,...
"adcresolution",8,"quantbuffer",0.1,'block_dc',1,'lpf_active',1,'H_lpf',Lp_scpe).process(Rx_sig);
Scpe_sig.spectrum("displayname",'Digital (256 GSa/s) Rx Spectrum','fignum',10,'normalizeTo0dB',1);
Scpe_sig.normalize("mode","rms").plot("displayname",'Digital (256 GSa/s) Rx Spectrum','fignum',21,'clear',1);
%%%%%% Sample to 2x fsym %%%%%%
Scpe_sig = Scpe_sig.resample("fs_in",fadc,"fs_out",2*fsym);
%%%%%% Sync Rx signal with reference %%%%%%
[Scpe_sig,S] = Scpe_sig.tsynch("reference",Tx_symbols,"fs_ref",fsym);
%%% EQUALIZING
%FFE or VNLE
[Eq_signal,Eq_noise] = EQ("Ne",vnle_order,"Nb",dfe_order,"training_length",len_tr,"training_loops",5,"dd_loops",5,"K",2,"DCmu",mu_dc,"DDmu",[mu_ffe mu_dfe],"DFEmu",0.005,"FFEmu",0,"plotfinal",0,"ideal_dfe",1).process(Scpe_sig,Tx_symbols);
Rx_bits = PAMmapper(M,0).demap(Eq_signal);
[~,numErrors,ber,~] = calc_ber(Rx_bits.signal,Tx_bits.signal,"skip_front",100,"skip_end",150,"returnErrorLocation",1);
Eq_signal.normalize("mode","rms").plot("displayname",'Digital (256 GSa/s) Rx Spectrum','fignum',21,'clear',0);
%%% Visualize EQ Stuff
figure(40);
clf
title(sprintf('PAM %d after EQ ; BER: %1.2e',M, ber ));
constellation = unique(Tx_symbols.signal);
received = NaN(numel(constellation),length(Tx_symbols));
for lvl = 1:numel(constellation)
%Separate the equalized signal into the
%respective levels based on the actually
%transmitted level!
received(lvl,Tx_symbols.signal==constellation(lvl)) = Eq_signal.signal(Tx_symbols.signal==constellation(lvl));
intermediate = received(lvl,:);
cnt(lvl) = numel(intermediate(~isnan(intermediate)));
hold on
histogram(received(lvl,:),1000,"EdgeAlpha",0,'DisplayName',['Lvl ',num2str(lvl),' | ',num2str(cnt(lvl)),' entries']);
end
legend
fprintf('BER: %.2e \n',ber);
autoArrangeFigures;
if ~isempty(curFolder)
cd(curFolder);
end
end

23
projects/A_minimal_example/run_loops.m
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@@ -1,23 +0,0 @@
uloops = struct;
uloops.bitrate = [300,330,360,390,420,450,480].*1e9;
uloops.M = [4,6,8];
wh = DataStorage(uloops);
wh.addStorage("ber");
fprintf("Let's simulate %d configuratiuons! \n",wh.getLastLinIndice);
wh = submit_simulations(wh,"parallel",1);
for m_ = uloops.M
ber_row = wh.getStoValue('ber', uloops.bitrate,m_);
figure(2024)
hold on
plot(uloops.bitrate.*1e-9,ber_row,'DisplayName',sprintf('PAM %d',m_));
end
yline(3.8e-3,'LineWidth',2,'DisplayName','3.8e-3');
yline(2e-2,'LineWidth',2,'LineStyle','--','DisplayName','2e-2');
beautifyBERplot()
legend

72
projects/A_minimal_example/submit_simulations.m
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@@ -1,72 +0,0 @@
function wh = submit_simulations(wh,options)
arguments
wh
options.parallel = 1;
end
%%% 2) SUBMIT SIMULATION
% Initialize job results
if options.parallel
if isempty(gcp('nocreate'))
parpool;
end
results = parallel.FevalFuture.empty();
else
results = [];
end
lin_idx = 1;
for lin_idx = 1:wh.getLastLinIndice
optionalVars = struct();
if ~isempty(wh.getDimension)
% Build the optionalVars struct
[parametervalues,parameternames]=wh.getPhysIndicesByLinIndex(lin_idx);
for pidx = 1:numel(parameternames)
optionalVars.(parameternames{pidx}) = parametervalues{pidx};
end
end
%%% SIMULATION HERE
if options.parallel
numOutputs = 1;
results(lin_idx) = parfeval(@imdd_simulation_minimal, numOutputs, optionalVars);
else
finalresults{lin_idx} = imdd_simulation_minimal(optionalVars);
wh.addValueToStorageByLinIdx(finalresults{lin_idx}, 'ber', lin_idx);
end
end
if options.parallel
%%% 4) Setup waitbar
h = waitbar(0, 'Processing Simulations...');
% Helper function to compute progress
updateWaitbar = @(~) waitbar(mean(arrayfun(@(f) strcmp(f.State, 'finished'), results)), h);
fprintf('Fetching results... \n');
% Update the waitbar after each simulation
updateWaitbarFutures = afterEach(results, updateWaitbar, 0);
% Close the waitbar after all simulations complete
afterAll(updateWaitbarFutures, @(~) delete(h), 0);
%%% 7) Fetch final results after all computations
fetchOutputs(results);
for ridx = 1:length(results)
wh.addValueToStorageByLinIdx(results(ridx).OutputArguments{1}, 'ber', ridx);
end
end
end

89
projects/HighSpeedExperiment_2024/auswertung/analyze_mu_dc.m Normal file
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@@ -0,0 +1,89 @@
if 0
uloops = struct;
uloops.precomp = [0,1];
uloops.db_precode = [0,1];
uloops.bitrate = [300,330,360,390,420,450,480].*1e9; %[300,330,360,390,420,450,480]
uloops.laser_wavelength = [1293,1302,1310,1318,1327.4];
uloops.M = [4,6,8];
uloops.link_length = [2]; % 1,2,3,5,6,8,10
wh = DataStorage(uloops);
wh.addStorage("ber");
wh = submit_simulations(wh,"parallel",1,"simulation_mode",0);
save('wh_2km',"wh");
end
for wavelength = wh.parameter.laser_wavelength.values
cols = linspecer(6);%cbrewer2('Set2',10);
figcnt = 0;
figWidth = 21; % Full-width for IEEE double-column papers (~7 inches)
figHeight = 6; % Adjust height as needed (~3.5 inches)
figure('Units','centimeters','Position', [1 1 figWidth figHeight],'PaperUnits','centimeters','PaperPosition', [0 0 figWidth figHeight])
tiledlayout(1,3, 'Padding', 'compact', 'TileSpacing', 'compact');
for m = uloops.M
figcnt = figcnt+1;
% subplot(1,3,figcnt)
nexttile
hold on
title(sprintf('%d km | %d nm | PAM %d',uloops.link_length,wavelength,m));
precomp = 1;
db_precode = 0;
a = wh.getStoValue('ber',precomp, db_precode, uloops.bitrate , wavelength, m, uloops.link_length);
ber_vnle = cellfun(@(x) x.vnle_pf_package{1,1}.ber_vnle, a);
ber_vnle_cell = cellfun(@(s) cellfun(@(p) p.ber_vnle, s.vnle_pf_package, 'UniformOutput', true), a, 'UniformOutput', false);
ber_vnle_best = cellfun(@(c) min(c), ber_vnle_cell);
plot(uloops.bitrate.*1e-9,ber_vnle_best,'DisplayName',sprintf('Tx precomp + VNLE'),'Color',cols(3,:),'LineStyle','-','HandleVisibility','on');
xticks(uloops.bitrate.*1e-9);
xlim([min(uloops.bitrate.*1e-9) max(uloops.bitrate.*1e-9)]);
precomp = 0; %0
db_precode = 1;
a = wh.getStoValue('ber',precomp, db_precode, uloops.bitrate , wavelength, m, uloops.link_length);
% ber_db = cellfun(@(x) x.dbtgt_package{1,1}.ber, a);
ber_db_cell = cellfun(@(s) cellfun(@(p) p.ber, s.dbtgt_package, 'UniformOutput', true), a, 'UniformOutput', false);
ber_db_best = cellfun(@(c) min(c), ber_db_cell);
plot(uloops.bitrate.*1e-9,ber_db_best,'DisplayName',sprintf('DB tgt. + MLSE',uloops.link_length,uloops.M),'Color',cols(1,:),'LineStyle','-','HandleVisibility','on');
xticks(uloops.bitrate.*1e-9);
xlim([min(uloops.bitrate.*1e-9) max(uloops.bitrate.*1e-9)]);
precomp = 0; %0
db_precode = 0; %1
a = wh.getStoValue('ber',precomp, db_precode, uloops.bitrate , wavelength, m, uloops.link_length);
% ber_mlse = cellfun(@(x) x.vnle_pf_package{1,1}.ber_mlse, a);
ber_mlse_cell = cellfun(@(s) cellfun(@(p) p.ber_mlse, s.vnle_pf_package, 'UniformOutput', true), a, 'UniformOutput', false);
ber_mlse_best = cellfun(@(c) min(c), ber_mlse_cell);
plot(uloops.bitrate.*1e-9,ber_mlse_best,'DisplayName',sprintf('VNLE + 1 tap post-filter + MLSE',uloops.link_length,uloops.M),'Color',cols(4,:),'LineStyle','-','HandleVisibility','on');
xticks(uloops.bitrate.*1e-9);
xlim([min(uloops.bitrate.*1e-9) max(uloops.bitrate.*1e-9)]);
set(gca, 'YScale', 'log');
ylim([8e-5 0.3]);
yline([4.8e-3, 2e-2],'HandleVisibility','off','LineWidth',1,'LineStyle','--','Color',[0.1 0.1 0.1]);
% legend
beautifyBERplot()
xlabel('Bit Rate in Gbps');
ylabel('BER');
if m ==4
text(310,6.8e-3,"4.8e-3","FontSize",10,"Interpreter","latex")
text(310,3e-2,"2e-2","FontSize",10,"Interpreter","latex")
end
% text(0.5,1,sprintf('%d km %d nm PAM %d',uloops.link_length,wavelength,m),...
% 'Units', 'normalized',"FontSize",10,"Interpreter","latex","BackgroundColor",[1 1 1],"EdgeColor",[0 0 0],'HorizontalAlignment','center','VerticalAlignment','top')
end
lgd = legend;
% Place the legend underneath the tiled layout
lgd.NumColumns = 3;
lgd.Layout.Tile = 'south';
end

2
projects/IMDD_base_system/imdd_it.m
View File

@@ -14,7 +14,7 @@ if 1
wh = DataStorage(uloops);
wh.addStorage("ber");
wh = submit_simulations(wh,"parallel",1,"simulation_mode",0);
wh = submit_simulations(wh,"parallel",0,"simulation_mode",1);
end
wh_ana = wh;