PMD theory; S21 measures; NGMI theory

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);