Add new functions

Functions/Metrics/calc_ngmi.m

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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