BCJR implementation

WDM code added (Pol Cont., Opt MUX/DEMUX, Opt Atten, DP_Fiber) -> the codebase is not optimized to always work with dp signals!

projects/ECOC_2025/theory/analytic_mpi_evaluation.m

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+% This script is used to evaluate Fig. 1b) in the paper "Adaptive Removal of Multipath Interference in Short Reach 112 GBd PAM-4 IM/DD Systems"
+
+%% Parameters
+df       = 1e6;%150e3;        % Laser linewidth [Hz]
+SIR_dB   = 20;                % Interference attenuation [dB]
+alpha    = 10^(-SIR_dB/20);   % Interference attenuation [linear]
+n_fiber  = 1.467;             % Refractive index
+c        = physconst('lightspeed'); % [m/s]
+
+L        = linspace(0,400,40); % Interference delay [m]  
+tau      = n_fiber./c.*L;       % Interference time (= tau) [s]
+
+tau_c = 1/(pi*df);              % laser coherence time [s]
+L_c   = (c/n_fiber)*tau_c;      % laser coherence length [m]
+
+var_sat = 2*alpha^2;            % Analytical saturation of variance
+
+%% Monte–Carlo Simulation
+fs               = 100e9;            % sampling rate [Hz]
+Tsim             = 50e-6;            % sim duration [s]
+N                = round(Tsim*fs);   % number of samples for each realization
+max_delay_samples  = round(max(tau)*fs); % largest delay that is evaluated (based on max. Interference delay)
+phase_noise_std   = sqrt(2*pi*df/fs); % standard dev. phase noise
+
+num_realizations = 10;             % number of parallel runs
+monte_carlo_variance = zeros(num_realizations, length(L));
+parfor r = 1:num_realizations
+
+    % generate a realization of phase noise random walk
+    dphi = phase_noise_std * randn(1, N + max_delay_samples); % matlab randn process has std = 1
+    phi  = cumsum(dphi);
+    phi_direct  = phi(max_delay_samples+1 : max_delay_samples+N);
+    var_k = zeros(1, length(L));
+    for t = 1:length(tau)
+
+        nd = round( tau(t)*fs ); % delay in samples for current interference time
+        phi_delayed = phi(max_delay_samples+1-nd : max_delay_samples+N-nd); %cut out interfering signal part (was earlier)
+
+        E = exp(1j*phi_direct) + alpha*exp(1j*phi_delayed); % E-fields combined
+        I = abs(E).^2; % photo current as magnitude square of E-field
+        var_k(t) = var(I);
+
+    end
+    monte_carlo_variance(r, :) = var_k;
+end
+
+avg_of_mc_variances = mean(monte_carlo_variance, 1);
+std_of_mc_variances = std(monte_carlo_variance, 0, 1);
+
+%% Analytic variance
+analytic_variance = 2*alpha^2 * (1 - exp(-2*pi*df.*tau)).^2;
+
+%% Plot 
+cols =     [0.3467    0.5360    0.6907
+            0.9153    0.2816    0.2878
+            0.4416    0.7490    0.4322];
+
+coherence_length_multiples = 0.5:0.5:ceil(L(end)/L_c);
+
+figure();
+hold on;
+plot(L, avg_of_mc_variances, 'LineWidth',2, 'DisplayName','Simulation','Color',cols(1,:),'LineStyle','-');
+errorbar(L, avg_of_mc_variances,std_of_mc_variances, 'LineWidth',0.7,'LineStyle','none', 'DisplayName','Simulation','Color',cols(1,:),'HandleVisibility','off');
+
+plot(L, analytic_variance, 'LineWidth',2, 'DisplayName','Analytic','Color',cols(2,:),'LineStyle','-');
+xticks(coherence_length_multiples.*L_c);
+xticklabels(round(coherence_length_multiples.*L_c));
+
+norm_to_coherence_len = 1;
+if norm_to_coherence_len
+    xticklabels(coherence_length_multiples);
+    xlabel('$\tau_c$', 'FontSize',12);
+end
+
+xline(L_c.*coherence_length_multiples, 'LineWidth',1.5, 'DisplayName','Coh. Length','HandleVisibility','off','Color',[0.7,0.7,0.7],'LineStyle','-');
+xlim([0,L(end)]);
+yline(var_sat, '-.k','LineWidth',1.5, 'DisplayName','Saturation: 2$\alpha ^2$');
+xlabel('Interference Delay [m]', 'FontSize',12);
+grid on;
+ylabel('Intensity Variance', 'FontSize',12);
+title(sprintf('MPI Variance; %d MHz; SIR: %d dB',df.*1e-6,SIR_dB), 'FontSize',14);
+legend('Location','southeast');

projects/ECOC_2025/theory/coherence_length_plot.m

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+%% Parameters
+df       = linspace(100e3,50e6,10000);   % Laser FWHM linewidth [Hz]
+n_fiber  = 1.467;                      % Fiber group index
+c        = 3e8;                        % Speed of light [m/s]
+
+% Compute coherence length (1/e of mean-fringe decay)
+tau_c = 1./(pi*df);
+L_c   = (c/n_fiber) .* tau_c;          % Coherence length [m]
+
+%% Plot
+figure('Color','w'); 
+loglog(df/1e6, L_c, 'LineWidth',2,'LineStyle','-'); % linewidth in MHz
+xticks([0.1, 1, 10, 50]);
+yticks([1, 10, 100, 1000]);
+yticklabels({'1','10','100','1000'})
+grid on; box on;
+xlabel('Laser linewidth [MHz]','FontSize',12,'Interpreter','none');
+ylabel('Coherence length [m]','FontSize',12,'Interpreter','none');
+title('Coherence Length vs. Laser Linewidth','FontSize',14,'Interpreter','none');
+
+%% Annotate some key points
+hold on;
+freqs = [150e3, 1e6, 10e6, 50e6]; % [Hz]
+for f = freqs
+    x = f/1e6;
+    y = (c/n_fiber) * (1/(pi*f));
+    scatter(x,y,'Marker','x','LineWidth',1,'MarkerEdgeColor','black');
+
+    text(x*1.1,y, sprintf('%.2f MHz', f/1e6), ...
+        'FontSize',10,'HorizontalAlignment','left');
+
+end