From ed7c68d78bb42d1c26eae699ef43d749cdc457b6 Mon Sep 17 00:00:00 2001 From: Silas Oettinghaus Date: Wed, 25 Mar 2026 10:26:50 +0100 Subject: [PATCH] PMD theory; S21 measures; NGMI theory --- Functions/Theory/NGMI/calculate_gmi_example.m | 49 + .../mutual_infomation_undertsanding_gpt.m | 43 + .../PMD_maxwellshape/dgd_considerations.m | 116 + .../Theory/PMD_maxwellshape/pmd_maxwell.m | 59 + projects/S21/ExampleDirectoryApp.mlapp | Bin 0 -> 59717 bytes projects/S21/HF Kabel/kabel-09z07001.s2p | 806 +++++ projects/S21/HF Kabel/kabel-09z07002.s2p | 806 +++++ projects/S21/HF Kabel/kabel-miniband-1.s2p | 806 +++++ projects/S21/HF Kabel/kabel-miniband-2.s2p | 806 +++++ projects/S21/HF Kabel/kabel-miniband-3.s2p | 806 +++++ projects/S21/HF Kabel/kabel-miniband-4.s2p | 806 +++++ .../S21/HF Kabel/kabel-miniband-5defekt.s2p | 806 +++++ projects/S21/HF Kabel/kabel-miniband-6.s2p | 806 +++++ projects/S21/HF Kabel/kabel-miniband-7.s2p | 806 +++++ projects/S21/HF Kabel/kabel-sn2830-2ea.s2p | 806 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mode 100644 projects/S21/precomp_opt_b2b_uxr1102A_loop1_1.mat create mode 100644 projects/S21/precomp_opt_b2b_uxr1102A_loop1_1_gut.mat create mode 100644 projects/S21/precomp_opt_b2b_uxr1102A_loop3_1.mat create mode 100644 projects/S21/precomp_opt_b2b_uxr1102A_loop5_1.mat create mode 100644 projects/S21/precomp_optical_120GAWG_256GScope_b2b_1.mat create mode 100644 projects/S21/precomp_optical_92G.mat diff --git a/Functions/Theory/NGMI/calculate_gmi_example.m b/Functions/Theory/NGMI/calculate_gmi_example.m new file mode 100644 index 0000000..bcd4d8f --- /dev/null +++ b/Functions/Theory/NGMI/calculate_gmi_example.m @@ -0,0 +1,49 @@ +% Parameters +symbols = [0, 1, 2, 3]; % PAM-4 symbols +P_X = [0.25, 0.25, 0.25, 0.25]; % Uniform probabilities +sigma2 = 0.1; % Noise variance +received_samples = [0.2, 1.1, 1.9, 2.8];% Received symbols (example) +gray_bits = [0 0; 0 1; 1 1; 1 0]; % Gray coding (bits per symbol) +m = size(gray_bits, 2); % Bits per symbol +N = length(received_samples); % Number of received samples + +% 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 = received_samples(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; + + +% Display the result +fprintf('GMI: %.4f bits\n', GMI); +fprintf('NGMI: %.4f bits\n', NGMI); \ No newline at end of file diff --git a/Functions/Theory/NGMI/mutual_infomation_undertsanding_gpt.m b/Functions/Theory/NGMI/mutual_infomation_undertsanding_gpt.m new file mode 100644 index 0000000..abb6c26 --- /dev/null +++ b/Functions/Theory/NGMI/mutual_infomation_undertsanding_gpt.m @@ -0,0 +1,43 @@ +% estimate_entropies.m +clear; rng(0); + +%% 1) Parameters +M = 1e5; % number of Monte-Carlo samples +EbNo_dB = 0; % SNR per bit in dB +EbNo = 10^(EbNo_dB/10); +sigma2 = 1/(2*EbNo); % noise variance per real dimension + +% 4-QAM constellation (row vector) +X = [1+1j, 1-1j, -1+1j, -1-1j]; +N = numel(X); +PX = ones(1,N)/N; % uniform PMF + +%% 2) Generate transmit symbols and AWGN +idx = randi(N,1,M); % 1×M random symbol indices +s = X(idx); % 1×M transmitted symbols +n = sqrt(sigma2)*(randn(1,M) + 1j*randn(1,M)); +y = s + n; % 1×M received samples + +%% 3) Compute p_{Y|X}(y|x) for each constellation point +% Create an N×M matrix where row n is |y - X(n)|^2 +d2 = abs(bsxfun(@minus, X(:), y)).^2; % N×M +pYgX = (1/(pi*sigma2)) * exp(-d2 / sigma2); % N×M + +%% 4) Estimate H(Y) = -E[ log2 p_Y(Y) ] +% Mixture density p_Y(y_m) = sum_n PX(n)*pYgX(n,m) +pY = PX * pYgX; % 1×M +HY = -mean(log2(pY)); % bits + +%% 5) Estimate H(Y|X) = -E[ log2 p(Y|X) ] +% For each m, pick the row corresponding to the true idx(m) +linearIdx = sub2ind([N, M], idx, 1:M); +pYgX_true = pYgX(linearIdx); % 1×M +HYgX = -mean(log2(pYgX_true)); % bits + +%% 6) Mutual information +I = HY - HYgX; + +%% 7) Display +fprintf('Estimated H(Y) = %.4f bits\n', HY); +fprintf('Estimated H(Y|X) = %.4f bits\n', HYgX); +fprintf('Estimated I(X;Y) = %.4f bits\n', I); diff --git a/Functions/Theory/PMD_maxwellshape/dgd_considerations.m b/Functions/Theory/PMD_maxwellshape/dgd_considerations.m new file mode 100644 index 0000000..fd998db --- /dev/null +++ b/Functions/Theory/PMD_maxwellshape/dgd_considerations.m @@ -0,0 +1,116 @@ + +if 0 +pmd = 0.2 * ( 1e-12 / sqrt(1e3) ) ; % 0.1 ps/sqrt(km) -> 1e-9 -> s/sqrt(m) +L = 1000; % m +corr_len = 100; +num_wave_plates = 100; +wp_len = L / num_wave_plates; %waveplate length +dgd = pmd * sqrt(L); +fdac = 120e9; % GHz + +fsim = fdac * 512 ; %oversampled simulation frequency +dt = 1/fsim; % sample time +nt = 4; % sampled signal length +omega = 2*pi*[(0:nt/2-1),(-nt/2:-1)]/(dt*nt) ; %angular frequency vector for optical signal of length nt +omega = 2*pi*fsim ; %angular frequency vector for optical signal of length nt + +for rlz = 1:20000 + + db0 = []; + db1 = []; + delta_beta = []; + + db0 = (rand(num_wave_plates,1)*2*pi - pi); % normal distr. between -pi <-> +pi + + db1 = sqrt(3*pi/8)*(dgd/fsim)/ num_wave_plates .* omega; % linear increasing delta beta 1 + + %loop over waveplates + for n_wp = 1:length(db0) + delta_beta(n_wp,:) = (db1+db0(n_wp))./corr_len; + end + + dphi = delta_beta*wp_len; %phase shift due to propagation constant = beta * L + + if rlz == 1 + figure() + plot(cumsum( delta_beta )); + end + + dphi_end(rlz) = sum( dphi ); + +end + +figure; +histogram((dphi_end),100); + +deltaT = mean(abs(dphi_end)); + +%H = exp(-1j*dphi); % Filter to apply phase shift in freq. domain +end + + +PMD = 0.1 * ( 1e-12 / sqrt(1e3) ); %PMD s/sqrt(m) +L = 10e3; %m +sigma_dgd = PMD * sqrt(L); % in sec. +disp(['variance of DGD in pico seconds: ',num2str(sigma_dgd*1e12)]); +disp(['variance of DGD in pico seconds: ',num2str(sigma_dgd*1e12)]); + +dgd = []; +for i = 1:4 + dgd(i,:) = DGD(sigma_dgd,10000); +end + +rms = PMD * sqrt(40e3) * 1e12 ; % in sec. +t = [0:0.01:100]; +z2 = sqrt(2/pi).*(t.^2)/(rms.^3).*exp(-t.^2/(2*rms^2)) ; +figure; +histogram(dgd*1e12,1000,"Normalization","pdf"); +hold on +plot(t(1:200),z2(1:200),'r'); +hold off + +function z = DGD(sigma_dgd,N) + + %PMD = 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If an error occurs for a different file, try regenerating the code from the Import Tool. +dataArray = textscan(fileID, formatSpec, 'Delimiter', '', 'WhiteSpace', '', 'TextType', 'string', 'HeaderLines' ,startRow-1, 'ReturnOnError', false, 'EndOfLine', '\r\n'); + +%% Close the text file. +fclose(fileID); + +%% Convert the contents of columns containing numeric text to numbers. +% Replace non-numeric text with NaN. +raw = repmat({''},length(dataArray{1}),length(dataArray)-1); +for col=1:length(dataArray)-1 + raw(1:length(dataArray{col}),col) = mat2cell(dataArray{col}, ones(length(dataArray{col}), 1)); +end +numericData = NaN(size(dataArray{1},1),size(dataArray,2)); + +for col=[1,2,3,4,5,6,7,8,9,10] + % Converts text in the input cell array to numbers. Replaced non-numeric text with NaN. + rawData = dataArray{col}; + for row=1:size(rawData, 1) + % Create a regular expression to detect and remove non-numeric prefixes and suffixes. + regexstr = '(?.*?)(?([-]*(\d+[\,]*)+[\.]{0,1}\d*[eEdD]{0,1}[-+]*\d*[i]{0,1})|([-]*(\d+[\,]*)*[\.]{1,1}\d+[eEdD]{0,1}[-+]*\d*[i]{0,1}))(?.*)'; + try + result = regexp(rawData(row), regexstr, 'names'); + numbers = result.numbers; + + % Detected commas in non-thousand locations. + invalidThousandsSeparator = false; + if numbers.contains(',') + thousandsRegExp = '^[-/+]*\d+?(\,\d{3})*\.{0,1}\d*$'; + if isempty(regexp(numbers, thousandsRegExp, 'once')) + numbers = NaN; + invalidThousandsSeparator = true; + end + end + % Convert numeric text to numbers. + if ~invalidThousandsSeparator + numbers = textscan(char(strrep(numbers, ',', '')), '%f'); + numericData(row, col) = numbers{1}; + raw{row, col} = numbers{1}; + end + catch + raw{row, col} = rawData{row}; + end + end +end + + +%% Replace non-numeric cells with NaN +R = cellfun(@(x) ~isnumeric(x) && ~islogical(x),raw); % Find non-numeric cells +raw(R) = {NaN}; % Replace non-numeric cells + +%% Create output variable +matrix = cell2mat(raw); +%% Clear temporary variables +clearvars filename startRow formatSpec fileID dataArray ans raw col numericData rawData row regexstr result numbers invalidThousandsSeparator thousandsRegExp R; + +end diff --git a/projects/S21/M8199B_Spara/M8199B_ch1_inverted_Scope_Ch4.s2p b/projects/S21/M8199B_Spara/M8199B_ch1_inverted_Scope_Ch4.s2p new file mode 100644 index 0000000..15aa6f6 --- /dev/null +++ b/projects/S21/M8199B_Spara/M8199B_ch1_inverted_Scope_Ch4.s2p @@ -0,0 +1,603 @@ +# GHz S RI R 50 +! S-Parameters data +! 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