86 lines
3.5 KiB
Matlab
86 lines
3.5 KiB
Matlab
% 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"
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%% Parameters
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df = 1e6; % Laser linewidth [Hz]
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SIR_dB = 20; % Interference attenuation [dB]
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alpha = 10^(-SIR_dB/20); % Interference attenuation [linear]
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n_fiber = 1.467; % Refractive index
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c = physconst('lightspeed'); % [m/s]
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L = linspace(0,250,50); % Interference delay [m]
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tau = n_fiber./c.*L; % Interference time (= tau) [s]
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tau_c = 1/(pi*df); % laser coherence time [s]
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L_c = (c/n_fiber)*tau_c; % laser coherence length [m]
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var_sat = 2*alpha^2; % Analytical saturation of variance
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%% Monte–Carlo Simulation
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fs = 100e9; % sampling rate [Hz]
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Tsim = 50e-6; % sim duration [s]
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N = round(Tsim*fs); % number of samples for each realization
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max_delay_samples = round(max(tau)*fs); % largest delay that is evaluated (based on max. Interference delay)
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phase_noise_std = sqrt(2*pi*df/fs); % standard dev. phase noise
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num_realizations = 50; % number of parallel runs
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monte_carlo_variance = zeros(num_realizations, length(L));
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parfor r = 1:num_realizations
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% generate a realization of phase noise random walk
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dphi = phase_noise_std * randn(1, N + max_delay_samples); % matlab randn process has std = 1
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phi = cumsum(dphi);
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phi_direct = phi(max_delay_samples+1 : max_delay_samples+N);
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var_k = zeros(1, length(L));
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for t = 1:length(tau)
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nd = round( tau(t)*fs ); % delay in samples for current interference time
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phi_delayed = phi(max_delay_samples+1-nd : max_delay_samples+N-nd); %cut out interfering signal part (was earlier)
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E = exp(1j*phi_direct) + alpha*exp(1j*phi_delayed); % E-fields combined
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I = abs(E).^2; % photo current as magnitude square of E-field
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var_k(t) = var(I);
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end
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monte_carlo_variance(r, :) = var_k;
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end
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avg_of_mc_variances = mean(monte_carlo_variance, 1);
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std_of_mc_variances = std(monte_carlo_variance, 0, 1);
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%% Analytic variance
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L_ = linspace(0,250,500); % Interference delay [m]
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tau_ = n_fiber./c.*L_;
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analytic_variance = 2*alpha^2 * (1 - exp(-2*pi*df.*tau_)).^2;
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%% Plot
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cols = [0.3467 0.5360 0.6907
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0.9153 0.2816 0.2878
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0.4416 0.7490 0.4322];
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coherence_length_multiples = 0.5:0.5:ceil(L(end)/L_c);
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figure();
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hold on;
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plot(L, avg_of_mc_variances, 'LineWidth',2, 'DisplayName','Simulation','Color',cols(1,:),'LineStyle','-');
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errorbar(L, avg_of_mc_variances,std_of_mc_variances, 'LineWidth',0.7,'LineStyle','none', 'DisplayName','Simulation','Color',cols(1,:),'HandleVisibility','off');
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plot(L_, analytic_variance, 'LineWidth',2, 'DisplayName','Analytic','Color',cols(2,:),'LineStyle','-');
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xticks(coherence_length_multiples.*L_c);
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xticklabels(round(coherence_length_multiples.*L_c,1));
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norm_to_coherence_len = 1;
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if norm_to_coherence_len
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xticklabels(coherence_length_multiples);
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xlabel('$n \cdot L_c$', 'FontSize',12);
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else
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xlabel('Interference Delay [m]', 'FontSize',12);
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end
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xline(L_c.*coherence_length_multiples, 'LineWidth',1.5, 'DisplayName','Coh. Length','HandleVisibility','off','Color',[0.7,0.7,0.7],'LineStyle','-');
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xlim([0,L(end)]);
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yline(var_sat, '-.k','LineWidth',1.5, 'DisplayName','Saturation: 2$\alpha ^2$');
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grid on;
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ylabel('Intensity Variance', 'FontSize',12);
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title(sprintf('MPI Variance; %d MHz; SIR: %d dB',df.*1e-6,SIR_dB), 'FontSize',14);
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legend('Location','southeast');
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