Merge branch 'main' of cau-git.rz.uni-kiel.de:nt/mitarbeiter/silas/imdd_simulation
This commit is contained in:
Silas Oettinghaus
@@ -925,9 +925,10 @@ classdef Signal
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M
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M
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options.fignum = 100;
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options.fignum = 100;
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options.displayname = "";
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options.displayname = "";
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options.mode = 1; %1= histogram method; 2= intuitive "line based" eye
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end
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end
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mode = 2;
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mode = options.mode;
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histpoints = 2048; %% verticale resolution
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histpoints = 2048; %% verticale resolution
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histpoints = floor(histpoints/2)*2+1; %% to have the eye digram centered around one point make the vertical resolution uneven
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histpoints = floor(histpoints/2)*2+1; %% to have the eye digram centered around one point make the vertical resolution uneven
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@@ -966,8 +967,9 @@ classdef Signal
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col = cbrewer2('Set1',2);
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col = cbrewer2('Set1',2);
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for n=1:1000
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for n=1:1000
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hold on
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hold on
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plot(eye_mat(:,n),'LineStyle',':','LineWidth',0.1,'Color',col(2,:));
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plot(eye_mat(:,n),'LineStyle','-','LineWidth',0.1,'Color',col(2,:));
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end
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end
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xlabel('Samples','Interpreter','latex')
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xlabel('Samples','Interpreter','latex')
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ylabel('Amplitude of Signal','Interpreter','latex');
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ylabel('Amplitude of Signal','Interpreter','latex');
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xlim([0 histpoints_horizontal])
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xlim([0 histpoints_horizontal])
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@@ -52,11 +52,17 @@ symbols = PAMmapper(M,0).map(bits);
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symbols.fs = fsym;
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symbols.fs = fsym;
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symbols.spectrum("displayname",'Symbols','fignum',1);
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symbols.spectrum("displayname",'Symbols','fignum',1);
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%% RRC Shaping
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%% RRC Shaping
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rcalpha = 1;
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Pform = Pulseformer("fsym",fsym,"fdac",4*fsym,"pulse","rrc","pulselength",16,"alpha",rcalpha);
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for rcalpha = 0.1:0.2:1
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% rcalpha = 0.5;
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Pform = Pulseformer("fsym",fsym,"fdac",4*fsym,"pulse","rc","pulselength",16,"alpha",rcalpha);
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Digi_sig = Pform.process(symbols);
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Digi_sig = Pform.process(symbols);
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Digi_sig.spectrum("displayname",'Signal after pluse shaping','fignum',1);
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% Digi_sig.spectrum("displayname",'Signal after pluse shaping','fignum',1);
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Digi_sig.eye(fsym,M,"fignum",0.1*10,"mode",1);
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end
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%% RRC Matched Filtering
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%% RRC Matched Filtering
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Pform = Pulseformer("fsym",fsym,"fdac",4*fsym,"pulse","rrc","pulselength",16,"alpha",rcalpha);
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Pform = Pulseformer("fsym",fsym,"fdac",4*fsym,"pulse","rrc","pulselength",16,"alpha",rcalpha);
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@@ -49,6 +49,14 @@ for k = 1:size(scenarios, 1)
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% 'HandleVisibility', 'off'); % Hide from legend
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% 'HandleVisibility', 'off'); % Hide from legend
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% Capture Wide Spec (k=1) bounds for the TikZ measurement lines
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% Capture Wide Spec (k=1) bounds for the TikZ measurement lines
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hp.FaceAlpha = 0.5;
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hp.FaceAlpha = 0.5;
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% ho = outlinebounds(hl, hp);
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% % Change properties
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% set(ho, 'Color', 'k', ... % Make it black
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% 'LineStyle', '--', ... % Make it dashed
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% 'LineWidth', 1, ... % Make it thin
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% 'HandleVisibility', 'off'); % Hide from legend
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% Capture Wide Spec (k=1) bounds for the TikZ measurement lines
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hp.FaceAlpha = 0.5;
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else
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else
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hp.FaceAlpha = 0.8;
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hp.FaceAlpha = 0.8;
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end
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end
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116
Functions/Theory/Dissertation/pmd_vs_length.m
Normal file
116
Functions/Theory/Dissertation/pmd_vs_length.m
Normal file
@@ -0,0 +1,116 @@
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% pmd_vs_length.m
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% ------------------------------------------------------------
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% Plots the Foschini-Poole (1991) analytical variance formula for PMD:
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%
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% sigma_T^2(z) = 2*(Delta_beta1)^2 * lc^2
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% * [ exp(-z/lc) + z/lc - 1 ]
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%
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% and overlays the two asymptotic regimes:
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% - Short-reach (z << lc) : sigma_T(z) ~ (Delta_beta1) * z
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% - Long-haul (z >> lc) : sigma_T(z) ~ Dp * sqrt(z)
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%
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% Parameters follow typical SMF values from the literature.
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% ------------------------------------------------------------
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clear; clc;
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%% ── Parameters ──────────────────────────────────────────────────────────────
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% Intrinsic local birefringence [ps/km]
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Delta_beta1 = 1e-1; % typical value, adjust as needed
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% Correlation length [km]
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lc = 0.01; % ~50 m, typical for G.652 SMF
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% PMD parameter [ps / sqrt(km)] — derived from the two above
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Dp = Delta_beta1 * sqrt(2 * lc);
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% Distance axis [km]
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z_max = 10; % maximum distance
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z = linspace(0.001, z_max, 10000); % avoid z = 0 in log plot
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%% ── Exact Foschini-Poole formula (sigma_T in ps) ────────────────────────────
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sigma_T_sq = 2 .* Delta_beta1.^2 .* lc.^2 ...
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.* (exp(-z ./ lc) + z ./ lc - 1);
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sigma_T = sqrt(sigma_T_sq); % RMS DGD [ps]
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%% ── Asymptotic regimes ───────────────────────────────────────────────────────
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% Short-reach: linear growth (z << lc)
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sigma_T_short = Delta_beta1 .* z; % [ps]
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% Long-haul: square-root growth (z >> lc)
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sigma_T_long = Dp .* sqrt(z); % [ps]
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%% ── Plot ─────────────────────────────────────────────────────────────────────
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figure('Color','w','Position',[100 100 760 480]);
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hold on;
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% Color palette (matching dissertation style)
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c_exact = [0.1216, 0.4706, 0.7059]; % blue – exact
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c_short = [0.8392, 0.1529, 0.1569]; % red – short-reach asymptote
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c_long = [0.1961, 0.6314, 0.1725]; % green – long-haul asymptote
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% Exact solution
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h_exact = plot(z, sigma_T, ...
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'Color', c_exact, 'LineWidth', 2.0, ...
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'DisplayName', 'Exact (Foschini \& Poole)');
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% Short-reach asymptote σ_T ≈ Δβ₁ · z
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h_short = plot(z, sigma_T_short, ...
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'Color', c_short, 'LineWidth', 1.4, 'LineStyle', '--', ...
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'DisplayName', '$\sigma_T \approx \Delta\beta_1 \cdot z$ \quad ($z \ll l_c$)');
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% Long-haul asymptote σ_T ≈ D_p √z
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h_long = plot(z, sigma_T_long, ...
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'Color', c_long, 'LineWidth', 1.4, 'LineStyle', ':', ...
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'DisplayName', '$\sigma_T \approx D_p \sqrt{z}$ \quad ($z \gg l_c$)');
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%% ── Axes & decoration ────────────────────────────────────────────────────────
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ax = gca;
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set(ax, 'XScale', 'log', 'YScale', 'log');
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% ── X-axis: linear-style tick labels on log scale ────────────────────────
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x_ticks = [1e-3, 1e-2, 1e-1, 1, 10];
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ax.XTick = x_ticks;
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ax.XTickLabel = arrayfun(@(v) sprintf('%g km', v), x_ticks, 'UniformOutput', false);
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% ── Y-axis: linear-style tick labels on log scale ────────────────────────
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y_ticks = [1e-3, 1e-2, 1e-1, 1, 10];
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ax.YTick = y_ticks;
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ax.YTickLabel = arrayfun(@(v) sprintf('%g ps', v), y_ticks, 'UniformOutput', false);
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xlabel('Fiber length $z$ [km]', 'Interpreter', 'latex');
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ylabel('RMS DGD $\sigma_T$ [ps]', 'Interpreter', 'latex');
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grid on; box on;
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xlim([min(z) z_max]);
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legend([h_exact, h_short, h_long], ...
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'Location', 'northwest', 'Interpreter', 'latex', 'FontSize', 9);
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% Parameter annotation
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anno_str = sprintf( ...
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['$\\Delta\\beta_1 = %.3g$ ps/km\n' ...
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'$l_c = %.0f$ m\n' ...
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'$D_p = \\Delta\\beta_1\\sqrt{2l_c} = %.4g$ ps/$\\sqrt{\\mathrm{km}}$'], ...
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Delta_beta1, lc*1e3, Dp);
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annotation('textbox', [0.57 0.14 0.38 0.22], ...
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'String', anno_str, ...
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'Interpreter', 'latex', ...
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'FontSize', 8.5, ...
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'BackgroundColor','w', ...
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'EdgeColor', [0.5 0.5 0.5], ...
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'LineWidth', 0.8, ...
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'FitBoxToText', 'on');
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%% ── Regime transition marker ─────────────────────────────────────────────────
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% Mark the crossover region around z = lc
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xline(lc, '--', ...
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'Color', [0.5 0.5 0.5], 'LineWidth', 0.8, ...
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'HandleVisibility', 'off');
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text(lc * 1.15, min(sigma_T)*3, '$l_c$', ...
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'Interpreter', 'latex', 'Color', [0.4 0.4 0.4], 'FontSize', 9);
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%% ── Export (uncomment to use) ────────────────────────────────────────────────
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% mat2tikz_improved('C:\...\tikz\pmd\pmd_vs_length.tikz')
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25
Libs/mutual information rate TUM/LICENSE.txt
Normal file
25
Libs/mutual information rate TUM/LICENSE.txt
Normal file
@@ -0,0 +1,25 @@
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|
Copyright (c) 2019 Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
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|
Institute for Communications Engineering (LNT)
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|
Technical University of Munich, Germany
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|
www.lnt.ei.tum.de
|
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|
|
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|
All rights reserved.
|
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|
|
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|
Permission is hereby granted, free of charge, to any person obtaining a
|
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|
copy of this software and associated documentation files (the
|
||||||
|
"Software"), to deal in the Software without restriction, including
|
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|
without limitation the rights to use, copy, modify, merge, publish,
|
||||||
|
distribute, sublicense, and/or sell copies of the Software, and to permit
|
||||||
|
persons to whom the Software is furnished to do so, subject to the
|
||||||
|
following conditions:
|
||||||
|
|
||||||
|
The above copyright notice and this permission notice shall be included
|
||||||
|
in all copies or substantial portions of the Software.
|
||||||
|
|
||||||
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
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|
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
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|
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
|
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|
NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
|
||||||
|
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
|
||||||
|
OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
|
||||||
|
USE OR OTHER DEALINGS IN THE SOFTWARE.
|
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24
Libs/mutual information rate TUM/README.md
Normal file
24
Libs/mutual information rate TUM/README.md
Normal file
@@ -0,0 +1,24 @@
|
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|
## MI-CG: Numerically Computing Achievable Rates of Memoryless Channels
|
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|
|
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|
This repository provides a MATLAB function mi_cg.m to numerically compute achievable rates for memoryless channels. The function uses a conditionally-Gaussian (CG) channel model to obtain a lower bound on the achievable rate of the true channel. The method is well-known, and it is explained in [this short document](https://mediatum.ub.tum.de/node?id=1533663). Two example scripts that compute several achievable rate curves are also provided.
|
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|
|
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|
### Citation
|
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|
|
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|
This software and the accompanying document are meant as a tutorial to get started with mutual information as a numerical figure of merit for a communications channel. The software is provided under the open-source [MIT license](https://opensource.org/licenses/MIT). If you use the software in your academic work, please cite the accompanying [document](https://mediatum.ub.tum.de/node?id=1533663) as follows:
|
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|
|
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|
> F. J. Garcia-Gomez, “Numerically computing achievable rates of memoryless channels,” TUM University Library, 2019. [Online]. Available: https://mediatum.ub.tum.de/node?id=1533663
|
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|
|
||||||
|
The corresponding BibTeX entry is
|
||||||
|
```
|
||||||
|
@article{garcia2019numerically,
|
||||||
|
author = "Francisco Javier Garcia-Gomez",
|
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|
title = "Numerically Computing Achievable Rates of Memoryless Channels",
|
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|
year = "2019",
|
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|
journal="TUM University Library",
|
||||||
|
url={https://mediatum.ub.tum.de/node?id=1533663}
|
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|
}
|
||||||
|
```
|
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|
|
||||||
|
### Acknowledgment
|
||||||
|
|
||||||
|
This work was supported by the German Research Foundation (DFG) under Grant KR 3517/8-2.
|
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156
Libs/mutual information rate TUM/air.m
Normal file
156
Libs/mutual information rate TUM/air.m
Normal file
@@ -0,0 +1,156 @@
|
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|
function air = air(x,r,idx_tx,Px,M_training)
|
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|
|
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|
MAX_MEMORY = 200e6; % maximum allowed size for a matrix
|
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|
|
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|
if nargin == 3
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|
Px = [];
|
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|
M_training = [];
|
||||||
|
end
|
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|
|
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|
if nargin == 4
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||||||
|
M_training = [];
|
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|
end
|
||||||
|
|
||||||
|
|
||||||
|
% if input is complex, separate into real and imaginary parts
|
||||||
|
if any(imag(x(:))~=0) || any(imag(r(:))~=0)
|
||||||
|
x = [real(x); imag(x)];
|
||||||
|
r = [real(r); imag(r)];
|
||||||
|
end
|
||||||
|
|
||||||
|
D = size(x, 1); % D = 2 if complex x
|
||||||
|
N = size(x, 2); % number of constellation points
|
||||||
|
M = size(r, 2); % number of samples
|
||||||
|
|
||||||
|
% set default training set size
|
||||||
|
if isempty(M_training)
|
||||||
|
M_training = ceil(0.3*M);
|
||||||
|
end
|
||||||
|
|
||||||
|
M_testing = M - M_training;
|
||||||
|
|
||||||
|
% Training: estimate parameters of the conditionally Gaussian model
|
||||||
|
% sort according to transmit index
|
||||||
|
[idx_tx_training, idx_sort] = sort(idx_tx(1:M_training));
|
||||||
|
r_training = r(:, idx_sort);
|
||||||
|
i_bounds = zeros(1, N+1);
|
||||||
|
|
||||||
|
% compute conditional means and covariance matrices
|
||||||
|
C_n = zeros(D, D, N);
|
||||||
|
det_n = zeros(1, N);
|
||||||
|
|
||||||
|
for n=1:N
|
||||||
|
% find how many times x(:, n) was transmitted and update i_bounds
|
||||||
|
N_current_x = find(idx_tx_training((i_bounds(n)+1):end)==n, 1, 'last');
|
||||||
|
if isempty(N_current_x), N_current_x=0; end
|
||||||
|
i_bounds(n+1) = i_bounds(n) + N_current_x;
|
||||||
|
|
||||||
|
if N_current_x > 0
|
||||||
|
% Compute mu_n=E[Y|X=x_n] according to Eq. (14) and store it in
|
||||||
|
% x(:, n) to save space
|
||||||
|
x(:, n) = sum(r_training(:, (i_bounds(n)+1):i_bounds(n+1)), 2)/(i_bounds(n+1)-i_bounds(n));
|
||||||
|
|
||||||
|
% compute C_n=cov[Y|X=x_n] according to Eq. (15)
|
||||||
|
r_meanfree = r_training(:, (i_bounds(n)+1):i_bounds(n+1)) - x(:, n);
|
||||||
|
C_n(:, :, n) = (r_meanfree*r_meanfree')/(i_bounds(n+1)-i_bounds(n));
|
||||||
|
% store also the determinant of C(:, :, n)
|
||||||
|
det_n(n) = det(C_n(:, :, n));
|
||||||
|
|
||||||
|
% if the determinant is 0, or if the matrix is badly conditioned,
|
||||||
|
% regularize by adding a small identity matrix. Note that we do
|
||||||
|
% need the check for 0 determinant, in case a cloud has exactly 0
|
||||||
|
% variance according to the training set
|
||||||
|
if det_n(n)==0 || cond(C_n(:, :, n))>1e16
|
||||||
|
C_n(:, :, n) = C_n(:, :, n) + 5 * eps * eye(D);
|
||||||
|
det_n(n) = (5*eps)^D;
|
||||||
|
end
|
||||||
|
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
% uniform input pmf Px if not provided
|
||||||
|
if isempty(Px)
|
||||||
|
Px = repmat(1/N, [1, N]);
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
% extract testing set and sort it according to transmit index
|
||||||
|
[idx_tx_testing, idx_sort] = sort(idx_tx((M_training+1):M));
|
||||||
|
r_testing = r(:, M_training+idx_sort);
|
||||||
|
|
||||||
|
% computation of h(Y|X)
|
||||||
|
h_Y_X = 0;
|
||||||
|
i_bounds_testing = zeros(1, N+1);
|
||||||
|
% loop over constellation points to compute h(Y|X)
|
||||||
|
for n = 1:N
|
||||||
|
% find how many times x(:, n) was transmitted and update
|
||||||
|
% i_bounds_testing
|
||||||
|
N_current_x = find(idx_tx_testing((i_bounds_testing(n)+1):end)==n, 1, 'last');
|
||||||
|
if isempty(N_current_x), N_current_x=0; end
|
||||||
|
i_bounds_testing(n+1) = i_bounds_testing(n) + N_current_x;
|
||||||
|
% add the corresponding contribution to the mutual information (two
|
||||||
|
% first lines of Eq. (17)). This, together with
|
||||||
|
% D/2*log2(2*pi) after the end of the loop, gives h(Y|X)
|
||||||
|
h_Y_X = h_Y_X + N_current_x * log2(det_n(n))/2+...
|
||||||
|
sum(sum(conj(r_testing(:, (i_bounds_testing(n)+1):i_bounds_testing(n+1))-x(:, n)).*(C_n(:, :, n)\(r_testing(:, (i_bounds_testing(n)+1):i_bounds_testing(n+1))-x(:, n)))))/2/log(2);
|
||||||
|
|
||||||
|
|
||||||
|
end
|
||||||
|
h_Y_X = D/2*log2(2*pi) + h_Y_X/M_testing;
|
||||||
|
|
||||||
|
% When computing log(py), we might run out of memory. If necessary, we
|
||||||
|
% doe the computation in blocks
|
||||||
|
logpy = zeros(1, M_testing);
|
||||||
|
BLOCK_SIZE = floor(MAX_MEMORY/N);
|
||||||
|
N_blocks = ceil(M_testing/BLOCK_SIZE);
|
||||||
|
|
||||||
|
% loop over blocks of symbols. This loop can be replaced by parfor to allow
|
||||||
|
% parallel computation
|
||||||
|
for i_block = 1:N_blocks
|
||||||
|
|
||||||
|
logpy_cur = zeros(1, M_testing);
|
||||||
|
|
||||||
|
% beginning of block
|
||||||
|
i_start = (i_block-1) * BLOCK_SIZE + 1;
|
||||||
|
% end of block
|
||||||
|
i_end = min(M_testing, i_block*BLOCK_SIZE);
|
||||||
|
% block size
|
||||||
|
current_block_size = i_end-i_start+1;
|
||||||
|
|
||||||
|
% compute exponents of third line of (17)
|
||||||
|
exponents = zeros(N, current_block_size);
|
||||||
|
for n = 1:N
|
||||||
|
exponents(n, :) = -log(det_n(n))/2-real(sum(conj(r_testing(:, i_start:i_end)-x(:, n)).*(C_n(:, :, n)\(r_testing(:, i_start:i_end)-x(:, n))), 1))/2;
|
||||||
|
%sum über 2 einträge von r
|
||||||
|
end
|
||||||
|
|
||||||
|
% compute third line of Eq. (17). Use a custom function
|
||||||
|
% that computes log(sum(exp(x))) avoiding overflow errors
|
||||||
|
logpy_cur(i_start:i_end) = math_logsumexp(log(Px(:))+exponents, 1);
|
||||||
|
logpy = logpy + logpy_cur;
|
||||||
|
end
|
||||||
|
|
||||||
|
% output entropy h(Y)
|
||||||
|
h_Y = D/2*log2(2*pi) - mean(logpy)/log(2);%log basis change
|
||||||
|
|
||||||
|
% compute mutual information
|
||||||
|
air = h_Y - h_Y_X;
|
||||||
|
|
||||||
|
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
function [y] = math_logsumexp(x, dim)
|
||||||
|
%[y] = math_logsumexp(x, dim)
|
||||||
|
% Computes log(sum(exp(x), dim)), avoiding overflow errors when one of the
|
||||||
|
% x is large.
|
||||||
|
|
||||||
|
if nargin<2 || isempty(dim)
|
||||||
|
m = max(x);
|
||||||
|
y = m + log(sum(exp(x-m)));
|
||||||
|
else
|
||||||
|
m = max(x, [], dim);
|
||||||
|
y = m + log(sum(exp(x-m), dim));
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
124
Libs/mutual information rate TUM/example_mi_cg_complex_16qam.m
Normal file
124
Libs/mutual information rate TUM/example_mi_cg_complex_16qam.m
Normal file
@@ -0,0 +1,124 @@
|
|||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
% Copyright (c) 2019 Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
|
||||||
|
% Institute for Communications Engineering (LNT)
|
||||||
|
% Technical University of Munich, Germany
|
||||||
|
% www.lnt.ei.tum.de
|
||||||
|
%
|
||||||
|
% All rights reserved.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
%
|
||||||
|
% Permission is hereby granted, free of charge, to any person obtaining a
|
||||||
|
% copy of this software and associated documentation files (the
|
||||||
|
% "Software"), to deal in the Software without restriction, including
|
||||||
|
% without limitation the rights to use, copy, modify, merge, publish,
|
||||||
|
% distribute, sublicense, and/or sell copies of the Software, and to permit
|
||||||
|
% persons to whom the Software is furnished to do so, subject to the
|
||||||
|
% following conditions:
|
||||||
|
%
|
||||||
|
% The above copyright notice and this permission notice shall be included
|
||||||
|
% in all copies or substantial portions of the Software.
|
||||||
|
%
|
||||||
|
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
||||||
|
% OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||||
|
% MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
|
||||||
|
% NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
|
||||||
|
% DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
|
||||||
|
% OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
|
||||||
|
% USE OR OTHER DEALINGS IN THE SOFTWARE.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%% example_mi_cg_complex_16qam.m %%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
%
|
||||||
|
% Example usage of the function mi_cg to numerically compute mutual
|
||||||
|
% information between two complex sequences. This file simulates a
|
||||||
|
% one-dimensional complex AWGN channel with 16-QAM constellation for
|
||||||
|
% different SNRs, and then plots the achievable rate, which is equal to two
|
||||||
|
% times the 4-PAM curve of Fig. 1 of [1].
|
||||||
|
%
|
||||||
|
% Note that using mi_cg with complex sequences assumes that the channel
|
||||||
|
% model q(Y|X) is circularly symmetric for a given X=x (i.e., that the
|
||||||
|
% received clouds are circular). This is not the case in a channel with
|
||||||
|
% phase noise: see example_it_mi_cg.m for an example of how to deal with
|
||||||
|
% non-circularly-symmetric channels.
|
||||||
|
%
|
||||||
|
% [1] G. David Forney and Gottfried Ungerboeck, "Modulation and Coding for
|
||||||
|
% Linear Gaussian Channels", IEEE Trans. Inf. Theory vol. 44, no. 6, pp.
|
||||||
|
% 2384-2415, October 1998
|
||||||
|
%
|
||||||
|
% Technische Universitaet Muenchen - Lehrstuhl fuer Nachrichtentechnik
|
||||||
|
% Date: 12.12.2019
|
||||||
|
% Author: Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
|
||||||
|
%
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
clear;
|
||||||
|
% close all;
|
||||||
|
|
||||||
|
%%% Simulation parameters
|
||||||
|
M_QAM=16; % QAM size
|
||||||
|
var_w=1; % noise variance
|
||||||
|
SNR_dB_values=(-5):2:25; % SNR values in dB
|
||||||
|
N=8000; % number of Monte-Carlo points
|
||||||
|
|
||||||
|
%%% Derived parameters
|
||||||
|
n_SNR=length(SNR_dB_values);
|
||||||
|
SNR_values=10.^(SNR_dB_values/10);
|
||||||
|
|
||||||
|
%%% Generation of QAM constellation with power 1
|
||||||
|
M_PAM=sqrt(M_QAM); % number of points per real dimension
|
||||||
|
X_1d=-(M_PAM-1)+2*(0:(M_PAM-1)); % generate PAM
|
||||||
|
X=X_1d+1i*X_1d.'; % transform to QAM
|
||||||
|
X=X(:).'*sqrt(3/2/(M_QAM-1)); % set to unit power
|
||||||
|
X=[real(X); imag(X)]; % separate real and imaginary parts
|
||||||
|
|
||||||
|
%%% Uniformly choose transmit indices
|
||||||
|
idx_tx=randi(M_QAM, [1, N]);
|
||||||
|
|
||||||
|
%%% AWGN noise
|
||||||
|
w=sqrt(var_w)*(randn([2, N]));%+1i*randn([1, N]));
|
||||||
|
|
||||||
|
%%% Loop over the SNR values
|
||||||
|
|
||||||
|
MI_awgn=zeros(1, n_SNR);
|
||||||
|
fig = figure(1);
|
||||||
|
for i_SNR=1:n_SNR
|
||||||
|
|
||||||
|
% transmitted points
|
||||||
|
s=sqrt(SNR_values(i_SNR)*var_w)*X(:, idx_tx);
|
||||||
|
|
||||||
|
% AWGN channel
|
||||||
|
r_awgn = s+w;
|
||||||
|
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
clf
|
||||||
|
hold on
|
||||||
|
xlim([-20, 20]);
|
||||||
|
ylim([-20, 20]);
|
||||||
|
%received signal
|
||||||
|
scatter(r_awgn(1,:),r_awgn(2,:),1,"red",'.');
|
||||||
|
%tx signal constellation
|
||||||
|
scatter(s(1,:),s(2,:),4,"black",'o','filled');
|
||||||
|
%uni power transmit constallation
|
||||||
|
scatter(X(1,:),X(2,:),5,'blue','o','filled');
|
||||||
|
drawnow
|
||||||
|
pause(0.1)
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
|
||||||
|
% Compute MI
|
||||||
|
MI_awgn(i_SNR)=air(X, r_awgn, idx_tx);
|
||||||
|
% The following also works but is slower
|
||||||
|
% MI_awgn(i_SNR)=mi_cg(s, r_awgn);
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
I_shannon=log2(1+SNR_values);
|
||||||
|
|
||||||
|
figure(2);
|
||||||
|
hold on
|
||||||
|
plot(SNR_dB_values, I_shannon, '-', 'DisplayName', 'log_2 (1+SNR)');
|
||||||
|
hold on;
|
||||||
|
plot(SNR_dB_values, MI_awgn, '--', 'DisplayName', [num2str(M_QAM) '-QAM, AWGN']);
|
||||||
|
hold off;
|
||||||
|
xlabel('SNR (dB)'); ylabel('Achievable rate (bits/complex dimension)');
|
||||||
|
title(['Achievable rate of ' num2str(M_QAM) '-QAM in AWGN']);
|
||||||
|
legend('Location', 'NorthWest');
|
||||||
@@ -0,0 +1,140 @@
|
|||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
% Copyright (c) 2019 Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
|
||||||
|
% Institute for Communications Engineering (LNT)
|
||||||
|
% Technical University of Munich, Germany
|
||||||
|
% www.lnt.ei.tum.de
|
||||||
|
%
|
||||||
|
% All rights reserved.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
%
|
||||||
|
% Permission is hereby granted, free of charge, to any person obtaining a
|
||||||
|
% copy of this software and associated documentation files (the
|
||||||
|
% "Software"), to deal in the Software without restriction, including
|
||||||
|
% without limitation the rights to use, copy, modify, merge, publish,
|
||||||
|
% distribute, sublicense, and/or sell copies of the Software, and to permit
|
||||||
|
% persons to whom the Software is furnished to do so, subject to the
|
||||||
|
% following conditions:
|
||||||
|
%
|
||||||
|
% The above copyright notice and this permission notice shall be included
|
||||||
|
% in all copies or substantial portions of the Software.
|
||||||
|
%
|
||||||
|
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
||||||
|
% OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||||
|
% MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
|
||||||
|
% NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
|
||||||
|
% DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
|
||||||
|
% OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
|
||||||
|
% USE OR OTHER DEALINGS IN THE SOFTWARE.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%% example_mi_cg_real_2D_awgn_vs_phasenoise %%%%%%%%%%%%%%%%%
|
||||||
|
%
|
||||||
|
% Example usage of the function mi_cg to numerically compute mutual
|
||||||
|
% information between two sequences. This file simulates a two-dimensional
|
||||||
|
% AWGN channel with 4-PAM constellation (or, equivalently, a complex AWGN
|
||||||
|
% channel with 16-QAM constellation) for different SNRs, and then plots
|
||||||
|
% the achievable rate, reproducing the 4-PAM curve of Fig. 1 of [1]. Note
|
||||||
|
% that this curve can also be reproduced by simulating a 1-dimensional
|
||||||
|
% channel with 4-PAM: this file is an example of how to deal with multiple
|
||||||
|
% dimensions.
|
||||||
|
%
|
||||||
|
% This file also simulates a complex phase-noise channel:
|
||||||
|
% r=s.*exp(1i*theta)+w
|
||||||
|
% where w is complex AWGN and theta is i.i.d. real Gaussian. As q(Y|X) for
|
||||||
|
% this channel is not circularly-symmetric, this complex channel needs to
|
||||||
|
% be separated into two real dimensions to compute the mutual information.
|
||||||
|
% The resulting achievable rate is, as expected, below the rate for the
|
||||||
|
% AWGN channel.
|
||||||
|
%
|
||||||
|
% [1] G. David Forney and Gottfried Ungerboeck, "Modulation and Coding for
|
||||||
|
% Linear Gaussian Channels", IEEE Trans. Inf. Theory vol. 44, no. 6, pp.
|
||||||
|
% 2384-2415, October 1998
|
||||||
|
%
|
||||||
|
% [2]
|
||||||
|
%
|
||||||
|
% Technische Universitaet Muenchen - Lehrstuhl fuer Nachrichtentechnik
|
||||||
|
% Date: 12.12.2019
|
||||||
|
% Author: Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
|
||||||
|
%
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
clear;
|
||||||
|
close all;
|
||||||
|
|
||||||
|
%%% Simulation parameters
|
||||||
|
D=1; % number of complex dimensions
|
||||||
|
M_QAM=16; % QAM size
|
||||||
|
var_w=1; % noise variance
|
||||||
|
E_theta=0.2; % phase offset for the phase noise channel
|
||||||
|
var_theta=0.05; % phase noise variance
|
||||||
|
SNR_dB_values=(-5):2:25; % SNR values in dB
|
||||||
|
N=8000; % number of Monte-Carlo points
|
||||||
|
|
||||||
|
%%% Derived parameters
|
||||||
|
n_SNR=length(SNR_dB_values);
|
||||||
|
SNR_values=10.^(SNR_dB_values/10);
|
||||||
|
|
||||||
|
%%% Generation QAM constellation with power 1
|
||||||
|
M_PAM=sqrt(M_QAM); % number of points per real dimension
|
||||||
|
X_1d=-(M_PAM-1)+2*(0:(M_PAM-1)); % generate PAM
|
||||||
|
X=X_1d+1i*X_1d.'; % transform to QAM
|
||||||
|
X=X(:).'*sqrt(3/2/(M_QAM-1)); % set to unit power
|
||||||
|
X=[real(X); imag(X)]; % separate real and imaginary parts
|
||||||
|
|
||||||
|
%%% Uniformly choose transmit indices
|
||||||
|
idx_tx=randi(M_QAM^D, [1, N]);
|
||||||
|
|
||||||
|
%%% AWGN noise (real and imaginary parts)
|
||||||
|
w=sqrt(var_w/2)*randn([2*D, N]);
|
||||||
|
%%% phase noise
|
||||||
|
theta=E_theta+sqrt(var_theta)*randn([D, N]);
|
||||||
|
|
||||||
|
%%% Loop over the SNR values
|
||||||
|
MI_awgn=zeros(1, n_SNR);
|
||||||
|
MI_phasenoise=zeros(1, n_SNR);
|
||||||
|
fig = figure(1);
|
||||||
|
for i_SNR=1:n_SNR
|
||||||
|
% transmitted points
|
||||||
|
s=sqrt(SNR_values(i_SNR)*var_w)*X(:, idx_tx);
|
||||||
|
|
||||||
|
% AWGN channel
|
||||||
|
r_awgn=s+w;
|
||||||
|
|
||||||
|
% Compute MI
|
||||||
|
MI_awgn(i_SNR)=air(X, r_awgn, idx_tx)/D;
|
||||||
|
% The following also works but is slower
|
||||||
|
% MI_awgn(i_SNR)=air(s, r_awgn)/D;
|
||||||
|
|
||||||
|
% Phase-noise channel
|
||||||
|
s_complex=s(1:2:end, :)+1i*s(2:2:end, :); % transform to complex
|
||||||
|
r_phasenoise_complex=s_complex.*exp(1i*theta); % phase noise and AWGN
|
||||||
|
r_phasenoise=zeros(2*D, N); % transform to real
|
||||||
|
r_phasenoise(1:2:end, :)=real(r_phasenoise_complex);
|
||||||
|
r_phasenoise(2:2:end, :)=imag(r_phasenoise_complex);
|
||||||
|
r_phasenoise=r_phasenoise+w; % add AWGN
|
||||||
|
|
||||||
|
clf
|
||||||
|
fig = scatter(r_phasenoise(1,:),r_phasenoise(2,:),1,'.');
|
||||||
|
xlim([-20, 20]);
|
||||||
|
ylim([-20, 20]);
|
||||||
|
drawnow
|
||||||
|
pause(0.1)
|
||||||
|
|
||||||
|
% Compute MI
|
||||||
|
MI_phasenoise(i_SNR)=air(X, r_phasenoise, idx_tx)/D;
|
||||||
|
% The following also works but is slower
|
||||||
|
% MI_phasenoise(i_SNR)=air(s, r_phasenoise)/D;
|
||||||
|
end
|
||||||
|
|
||||||
|
% Shannon capacity of the AWGN channel
|
||||||
|
I_shannon=log2(1+SNR_values);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(SNR_dB_values, I_shannon, '-', 'DisplayName', 'log_2 (1+SNR)');
|
||||||
|
hold on;
|
||||||
|
plot(SNR_dB_values, MI_awgn, '--', 'DisplayName', '16-QAM, AWGN');
|
||||||
|
plot(SNR_dB_values, MI_phasenoise, '-.', 'DisplayName', ['16-QAM, Phase noise, \sigma_\Theta^2=' num2str(var_theta)]);
|
||||||
|
hold off;
|
||||||
|
xlabel('SNR (dB)'); ylabel('Achievable rate (bits/complex dimension)');
|
||||||
|
title(['Achievable rate of 16-QAM in AWGN and in a phase noise channel with \theta~N(' num2str(E_theta) ', ' num2str(var_theta) ')']);
|
||||||
|
legend('Location', 'NorthWest');
|
||||||
164
Libs/mutual information rate TUM/example_silas.m
Normal file
164
Libs/mutual information rate TUM/example_silas.m
Normal file
@@ -0,0 +1,164 @@
|
|||||||
|
colored_noise = true;
|
||||||
|
I_shannon=[];
|
||||||
|
for cmplx = [0,1]
|
||||||
|
cnt = 1;
|
||||||
|
for M_PAM = [4,8,16]
|
||||||
|
|
||||||
|
|
||||||
|
complex_constellation = cmplx;
|
||||||
|
|
||||||
|
%%% Simulation parameters
|
||||||
|
% M_PAM=2; % QAM size
|
||||||
|
var_w=1; % noise variance
|
||||||
|
SNR_dB_values=(-5):1:35; % SNR values in dB
|
||||||
|
N=8000; % number of Monte-Carlo points
|
||||||
|
|
||||||
|
%%% Derived parameters
|
||||||
|
n_SNR=length(SNR_dB_values);
|
||||||
|
SNR_values=10.^(SNR_dB_values/10);
|
||||||
|
|
||||||
|
%%% Generation of QAM constellation with power 1
|
||||||
|
M=sqrt(M_PAM); % number of points per real dimension
|
||||||
|
|
||||||
|
if complex_constellation
|
||||||
|
X_ = qammod(0:M_PAM-1,M_PAM,"gray");
|
||||||
|
else
|
||||||
|
X_ = pammod(0:M_PAM-1,M_PAM,0,'gray');
|
||||||
|
end
|
||||||
|
|
||||||
|
X_ = X_ ./ rms(unique(X_));
|
||||||
|
X_=[real(X_); imag(X_)];
|
||||||
|
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
figure(10);
|
||||||
|
clf
|
||||||
|
hold on
|
||||||
|
scatter(X_(1,:),X_(2,:),15,'red','x','DisplayName','Matlab');
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
|
||||||
|
%%% Uniformly choose transmit indices
|
||||||
|
idx_tx=randi(M_PAM, [1, N]);
|
||||||
|
|
||||||
|
%%% AWGN noise
|
||||||
|
w=sqrt(var_w)*(randn([2, N]));
|
||||||
|
|
||||||
|
%%% Loop over the SNR values
|
||||||
|
|
||||||
|
MI_awgn=zeros(1, n_SNR);
|
||||||
|
fig = figure(2);
|
||||||
|
|
||||||
|
if colored_noise
|
||||||
|
for i_SNR = 1:n_SNR
|
||||||
|
% Transmitted signal for the given indices
|
||||||
|
signal = X_(:, idx_tx);
|
||||||
|
|
||||||
|
% Generate white Gaussian noise of the same size as the signal
|
||||||
|
noise_white = randn(size(signal));
|
||||||
|
|
||||||
|
% Define the filter coefficient for colored noise (adjust as needed)
|
||||||
|
a = 0; % A higher value gives more correlation
|
||||||
|
|
||||||
|
% Filter the white noise to create colored noise.
|
||||||
|
% Here we filter each row (dimension) independently.
|
||||||
|
noise_colored = zeros(size(signal));
|
||||||
|
noise_colored(1,:) = filter(1, [1, -a], noise_white(1,:));
|
||||||
|
noise_colored(2,:) = filter(1, [1, -a], noise_white(2,:));
|
||||||
|
|
||||||
|
% Compute signal and unscaled noise power for proper scaling.
|
||||||
|
signal_power = mean(abs(signal(:)).^2);
|
||||||
|
noise_power = mean(abs(noise_colored(:)).^2);
|
||||||
|
|
||||||
|
% Convert desired SNR from dB to linear scale.
|
||||||
|
SNR_linear = 10^(SNR_dB_values(i_SNR)/10);
|
||||||
|
|
||||||
|
% Scale the colored noise so that signal_power / noise_power equals SNR_linear.
|
||||||
|
scaling_factor = sqrt(signal_power / (SNR_linear * noise_power));
|
||||||
|
noise_colored_scaled = scaling_factor * noise_colored;
|
||||||
|
|
||||||
|
% Received signal is the sum of the signal and the scaled colored noise.
|
||||||
|
r_colored = signal + noise_colored_scaled;
|
||||||
|
|
||||||
|
% For SNR measurement, compute the noise actually added.
|
||||||
|
measured_noise = r_colored - signal;
|
||||||
|
snr_meas_(i_SNR) = snr(signal(1,:) + 1i*signal(2,:), ...
|
||||||
|
measured_noise(1,:) + 1i*measured_noise(2,:));
|
||||||
|
|
||||||
|
% Plotting the transmitted and received signal
|
||||||
|
clf;
|
||||||
|
hold on;
|
||||||
|
xlim([-4, 4]);
|
||||||
|
ylim([-4, 4]);
|
||||||
|
scatter(signal(1,:), signal(2,:), 3, "black", 'o', 'DisplayName','Tx Constellation');
|
||||||
|
scatter(r_colored(1,:), r_colored(2,:), 1, "red", 'x', 'DisplayName', 'Colored Noise Mapping');
|
||||||
|
drawnow;
|
||||||
|
|
||||||
|
% Compute Mutual Information (or any other metric) with the new channel
|
||||||
|
MI_awgn_(i_SNR) = air(X_, r_colored, idx_tx);
|
||||||
|
end
|
||||||
|
else
|
||||||
|
|
||||||
|
|
||||||
|
for i_SNR=1:n_SNR
|
||||||
|
|
||||||
|
|
||||||
|
s_ = sqrt(SNR_values(i_SNR)*var_w) * X_(:, idx_tx);
|
||||||
|
% r_awgn_ = s_ + w;
|
||||||
|
|
||||||
|
r_awgn_ = awgn(X_(:, idx_tx),SNR_dB_values(i_SNR),"measured",10);
|
||||||
|
|
||||||
|
w_awgn_matlab = r_awgn_ - X_(:,idx_tx);
|
||||||
|
snr_meas_(i_SNR) = snr(X_(1, idx_tx)+1i*X_(2, idx_tx) , w_awgn_matlab(1,:)+1i*w_awgn_matlab(2,:));
|
||||||
|
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
clf
|
||||||
|
hold on
|
||||||
|
xlim([-4, 4]);
|
||||||
|
ylim([-4, 4]);
|
||||||
|
%received signal
|
||||||
|
scatter(X_(1, idx_tx),X_(2, idx_tx),3,"black",'o','DisplayName','Tx Constellation');
|
||||||
|
|
||||||
|
|
||||||
|
scatter(r_awgn_(1,:),r_awgn_(2,:),1,"red",'x','DisplayName','Matlab Mapping');
|
||||||
|
|
||||||
|
drawnow
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
|
||||||
|
MI_awgn_(i_SNR)=air(X_, r_awgn_, idx_tx);
|
||||||
|
% The following also works but is slower
|
||||||
|
% MI_awgn(i_SNR)=mi_cg(s, r_awgn);
|
||||||
|
end
|
||||||
|
end
|
||||||
|
|
||||||
|
figure(3);
|
||||||
|
hold on
|
||||||
|
|
||||||
|
if isempty(I_shannon)
|
||||||
|
I_shannon=log2(1+db2pow(snr_meas_));
|
||||||
|
plot(snr_meas_, I_shannon, '-', 'DisplayName', 'log_2 (1+SNR)','Color','black');
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
cols = [ 0.9047 0.1918 0.1988
|
||||||
|
0.2941 0.5447 0.7494
|
||||||
|
0.3718 0.7176 0.3612
|
||||||
|
1.0000 0.5482 0.1000
|
||||||
|
0.8650 0.8110 0.4330
|
||||||
|
0.6859 0.4035 0.2412];
|
||||||
|
if complex_constellation
|
||||||
|
plot(snr_meas_, MI_awgn_, ':', 'DisplayName', ['',num2str(M_PAM) '-QAM, AWGN'],'LineWidth',1,'Color',cols(cnt,:));
|
||||||
|
else
|
||||||
|
plot(snr_meas_, MI_awgn_, '-', 'DisplayName', ['',num2str(M_PAM) '-PAM, AWGN'],'LineWidth',1,'Color',cols(cnt,:));
|
||||||
|
end
|
||||||
|
|
||||||
|
hold off;
|
||||||
|
ylim([0,8]);
|
||||||
|
xlim([min(SNR_dB_values) max(SNR_dB_values)])
|
||||||
|
xlabel('SNR (dB)'); ylabel('Achievable rate (bits/complex dimension)');
|
||||||
|
title(['Achievable rate of ' num2str(M_PAM) '-QAM in AWGN']);
|
||||||
|
legend('Location', 'NorthWest');
|
||||||
|
yline(log2(M_PAM),'LineStyle',':','HandleVisibility','off','Color','black');
|
||||||
|
|
||||||
|
cnt = cnt+1;
|
||||||
|
|
||||||
|
end
|
||||||
|
end
|
||||||
104
Libs/mutual information rate TUM/mi_cg.m
Normal file
104
Libs/mutual information rate TUM/mi_cg.m
Normal file
@@ -0,0 +1,104 @@
|
|||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
% Copyright (c) 2019 Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
|
||||||
|
% Institute for Communications Engineering (LNT)
|
||||||
|
% Technical University of Munich, Germany
|
||||||
|
% www.lnt.ei.tum.de
|
||||||
|
%
|
||||||
|
% All rights reserved.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
%
|
||||||
|
% Permission is hereby granted, free of charge, to any person obtaining a
|
||||||
|
% copy of this software and associated documentation files (the
|
||||||
|
% "Software"), to deal in the Software without restriction, including
|
||||||
|
% without limitation the rights to use, copy, modify, merge, publish,
|
||||||
|
% distribute, sublicense, and/or sell copies of the Software, and to permit
|
||||||
|
% persons to whom the Software is furnished to do so, subject to the
|
||||||
|
% following conditions:
|
||||||
|
%
|
||||||
|
% The above copyright notice and this permission notice shall be included
|
||||||
|
% in all copies or substantial portions of the Software.
|
||||||
|
%
|
||||||
|
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
|
||||||
|
% OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
|
||||||
|
% MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
|
||||||
|
% NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
|
||||||
|
% DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
|
||||||
|
% OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
|
||||||
|
% USE OR OTHER DEALINGS IN THE SOFTWARE.
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%% example_mi_cg_complex_16qam.m %%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
%
|
||||||
|
% Example usage of the function mi_cg to numerically compute mutual
|
||||||
|
% information between two complex sequences. This file simulates a
|
||||||
|
% one-dimensional complex AWGN channel with 16-QAM constellation for
|
||||||
|
% different SNRs, and then plots the achievable rate, which is equal to two
|
||||||
|
% times the 4-PAM curve of Fig. 1 of [1].
|
||||||
|
%
|
||||||
|
% Note that using mi_cg with complex sequences assumes that the channel
|
||||||
|
% model q(Y|X) is circularly symmetric for a given X=x (i.e., that the
|
||||||
|
% received clouds are circular). This is not the case in a channel with
|
||||||
|
% phase noise: see example_it_mi_cg.m for an example of how to deal with
|
||||||
|
% non-circularly-symmetric channels.
|
||||||
|
%
|
||||||
|
% [1] G. David Forney and Gottfried Ungerboeck, "Modulation and Coding for
|
||||||
|
% Linear Gaussian Channels", IEEE Trans. Inf. Theory vol. 44, no. 6, pp.
|
||||||
|
% 2384-2415, October 1998
|
||||||
|
%
|
||||||
|
% Technische Universitaet Muenchen - Lehrstuhl fuer Nachrichtentechnik
|
||||||
|
% Date: 12.12.2019
|
||||||
|
% Author: Francisco Javier Garcia-Gomez <javier.garcia@tum.de>
|
||||||
|
%
|
||||||
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
|
|
||||||
|
clear;
|
||||||
|
close all;
|
||||||
|
|
||||||
|
%%% Simulation parameters
|
||||||
|
M_QAM=16; % QAM size
|
||||||
|
var_w=1; % noise variance
|
||||||
|
SNR_dB_values=(-5):2:25; % SNR values in dB
|
||||||
|
N=8000; % number of Monte-Carlo points
|
||||||
|
|
||||||
|
%%% Derived parameters
|
||||||
|
n_SNR=length(SNR_dB_values);
|
||||||
|
SNR_values=10.^(SNR_dB_values/10);
|
||||||
|
|
||||||
|
%%% Generation of QAM constellation with power 1
|
||||||
|
M_PAM=sqrt(M_QAM); % number of points per real dimension
|
||||||
|
X_1d=-(M_PAM-1)+2*(0:(M_PAM-1)); % generate PAM
|
||||||
|
X=X_1d+1i*X_1d.'; % transform to QAM
|
||||||
|
X=X(:).'*sqrt(3/2/(M_QAM-1)); % set to unit power
|
||||||
|
|
||||||
|
%%% Uniformly choose transmit indices
|
||||||
|
idx_tx=randi(M_QAM, [1, N]);
|
||||||
|
|
||||||
|
%%% AWGN noise
|
||||||
|
w=sqrt(var_w/2)*(randn([1, N])+1i*randn([1, N]));
|
||||||
|
|
||||||
|
%%% Loop over the SNR values
|
||||||
|
MI_awgn=zeros(1, n_SNR);
|
||||||
|
for i_SNR=1:n_SNR
|
||||||
|
% transmitted points
|
||||||
|
|
||||||
|
s=sqrt(SNR_values(i_SNR)*var_w)*X(:, idx_tx);
|
||||||
|
|
||||||
|
% AWGN channel
|
||||||
|
r_awgn = s+w;
|
||||||
|
|
||||||
|
% Compute MI
|
||||||
|
MI_awgn(i_SNR)=air(X, r_awgn, idx_tx);
|
||||||
|
% The following also works but is slower: MI_awgn(i_SNR)=air(s, r_awgn);
|
||||||
|
end
|
||||||
|
|
||||||
|
|
||||||
|
I_shannon=log2(1+SNR_values);
|
||||||
|
|
||||||
|
figure;
|
||||||
|
plot(SNR_dB_values, I_shannon, '-', 'DisplayName', 'log_2 (1+SNR)');
|
||||||
|
hold on;
|
||||||
|
plot(SNR_dB_values, MI_awgn, '--', 'DisplayName', [num2str(M_QAM) '-QAM, AWGN']);
|
||||||
|
hold off;
|
||||||
|
xlabel('SNR (dB)'); ylabel('Achievable rate (bits/complex dimension)');
|
||||||
|
title(['Achievable rate of ' num2str(M_QAM) '-QAM in AWGN']);
|
||||||
|
legend('Location', 'NorthWest');
|
||||||
135
Libs/mutual information rate TUM/silas_example_mi_cg_pam.m
Normal file
135
Libs/mutual information rate TUM/silas_example_mi_cg_pam.m
Normal file
@@ -0,0 +1,135 @@
|
|||||||
|
|
||||||
|
clear;
|
||||||
|
I_shannon=[];
|
||||||
|
for cmplx = [1,0]
|
||||||
|
cnt = 1;
|
||||||
|
for M_PAM = [2,4,8,16]
|
||||||
|
|
||||||
|
% close all;
|
||||||
|
usegarcia = 0;
|
||||||
|
|
||||||
|
complex_constellation = cmplx;
|
||||||
|
|
||||||
|
%%% Simulation parameters
|
||||||
|
% M_PAM=2; % QAM size
|
||||||
|
var_w=1; % noise variance
|
||||||
|
SNR_dB_values=(-5):1:35; % SNR values in dB
|
||||||
|
N=8000; % number of Monte-Carlo points
|
||||||
|
|
||||||
|
%%% Derived parameters
|
||||||
|
n_SNR=length(SNR_dB_values);
|
||||||
|
SNR_values=10.^(SNR_dB_values/10);
|
||||||
|
|
||||||
|
%%% Generation of QAM constellation with power 1
|
||||||
|
M=sqrt(M_PAM); % number of points per real dimension
|
||||||
|
|
||||||
|
if complex_constellation
|
||||||
|
X_ = qammod(0:M_PAM-1,M_PAM,"gray");
|
||||||
|
else
|
||||||
|
X_ = pammod(0:M_PAM-1,M_PAM,0,'gray');
|
||||||
|
end
|
||||||
|
|
||||||
|
X_ = X_ ./ rms(unique(X_));
|
||||||
|
X_=[real(X_); imag(X_)];
|
||||||
|
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
figure(10);
|
||||||
|
clf
|
||||||
|
hold on
|
||||||
|
scatter(X_(1,:),X_(2,:),15,'red','x','DisplayName','Matlab');
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
|
||||||
|
%%% Uniformly choose transmit indices
|
||||||
|
idx_tx=randi(M_PAM, [1, N]);
|
||||||
|
|
||||||
|
%%% AWGN noise
|
||||||
|
w=sqrt(var_w)*(randn([2, N]));
|
||||||
|
|
||||||
|
%%% Loop over the SNR values
|
||||||
|
|
||||||
|
MI_awgn=zeros(1, n_SNR);
|
||||||
|
fig = figure(2);
|
||||||
|
for i_SNR=1:n_SNR
|
||||||
|
|
||||||
|
if usegarcia
|
||||||
|
|
||||||
|
|
||||||
|
%scale transmitted points acc. to SNR condition (this is not correct I think, the papaer also show diff results)
|
||||||
|
% s=sqrt(SNR_values(i_SNR)*var_w)*X(:, idx_tx);
|
||||||
|
|
||||||
|
%scale nosie acc. to snr condition
|
||||||
|
noise_power = mean(abs(X_(1, idx_tx)+1i*X_(2, idx_tx)).^2) / SNR_values(i_SNR); % Noise power
|
||||||
|
w_ = sqrt(noise_power) .* w / sqrt(2);
|
||||||
|
|
||||||
|
% AWGN channel
|
||||||
|
r_awgn = X(:, idx_tx)+w_;
|
||||||
|
% snr_meas(i_SNR) = snr(s(1,:)+1i*s(2,:),w(1,:)+1i*w(2,:));
|
||||||
|
snr_meas(i_SNR) = snr(X_(1, idx_tx)+1i*X_(2, idx_tx),w_(1,:)+1i*w_(2,:));
|
||||||
|
end
|
||||||
|
|
||||||
|
s_ = sqrt(SNR_values(i_SNR)*var_w) * X_(:, idx_tx);
|
||||||
|
% r_awgn_ = s_ + w;
|
||||||
|
|
||||||
|
if cmplx
|
||||||
|
r_awgn_ = awgn(X_(:, idx_tx),SNR_dB_values(i_SNR),"measured",10);
|
||||||
|
w_awgn_matlab = r_awgn_ - X_(:,idx_tx);
|
||||||
|
snr_meas_(i_SNR) = snr(X_(1, idx_tx)+1i*X_(2, idx_tx) , w_awgn_matlab(1,:)+1i*w_awgn_matlab(2,:));
|
||||||
|
else
|
||||||
|
r_awgn_ = awgn(X_(1, idx_tx),SNR_dB_values(i_SNR),"measured",10);
|
||||||
|
w_awgn_matlab = r_awgn_ - X_(1,idx_tx);
|
||||||
|
snr_meas_(i_SNR) = snr(X_(1, idx_tx) , w_awgn_matlab(1,:));
|
||||||
|
end
|
||||||
|
|
||||||
|
%%%%%%%%%%%%
|
||||||
|
clf
|
||||||
|
hold on
|
||||||
|
xlim([-4, 4]);
|
||||||
|
ylim([-4, 4]);
|
||||||
|
%received signal
|
||||||
|
scatter(X_(1, idx_tx),X_(2, idx_tx),3,"black",'o','DisplayName','Tx Constellation');
|
||||||
|
|
||||||
|
|
||||||
|
if cmplx
|
||||||
|
scatter(r_awgn_(1,:),r_awgn_(2,:),1,"red",'x','DisplayName','Matlab Mapping');
|
||||||
|
else
|
||||||
|
scatter(r_awgn_,zeros(size(r_awgn_)),1,"red",'x','DisplayName','Matlab Mapping');
|
||||||
|
end
|
||||||
|
drawnow
|
||||||
|
|
||||||
|
MI_awgn_(i_SNR)=air(X_, r_awgn_, idx_tx);
|
||||||
|
% The following also works but is slower
|
||||||
|
% MI_awgn(i_SNR)=mi_cg(s, r_awgn);
|
||||||
|
end
|
||||||
|
|
||||||
|
figure(4);
|
||||||
|
hold on
|
||||||
|
|
||||||
|
if isempty(I_shannon)
|
||||||
|
I_shannon=log2(1+db2pow(snr_meas_));
|
||||||
|
plot(snr_meas_, I_shannon, '-', 'DisplayName', 'log_2 (1+SNR)','Color','black');
|
||||||
|
end
|
||||||
|
|
||||||
|
if usegarcia
|
||||||
|
plot(SNR_dB_values, MI_awgn, '--', 'DisplayName', ['GARCIA ',num2str(M_PAM) '-QAM, AWGN']);
|
||||||
|
end
|
||||||
|
|
||||||
|
cols = linspecer(6);
|
||||||
|
if complex_constellation
|
||||||
|
plot(snr_meas_, MI_awgn_, ':', 'DisplayName', ['',num2str(M_PAM) '-QAM, AWGN'],'LineWidth',1,'Color',cols(cnt,:));
|
||||||
|
else
|
||||||
|
plot(snr_meas_, MI_awgn_, '-', 'DisplayName', ['',num2str(M_PAM) '-PAM, AWGN'],'LineWidth',1,'Color',cols(cnt,:));
|
||||||
|
end
|
||||||
|
|
||||||
|
hold off;
|
||||||
|
ylim([0,8]);
|
||||||
|
xlim([min(SNR_dB_values) max(SNR_dB_values)])
|
||||||
|
xlabel('SNR (dB)'); ylabel('Achievable rate (bits/complex dimension)');
|
||||||
|
title(['Achievable rate of ' num2str(M_PAM) '-QAM in AWGN']);
|
||||||
|
legend('Location', 'NorthWest');
|
||||||
|
yline(log2(M_PAM),'LineStyle',':','HandleVisibility','off','Color','black');
|
||||||
|
|
||||||
|
autoArrangeFigures;
|
||||||
|
cnt = cnt+1;
|
||||||
|
|
||||||
|
end
|
||||||
|
end
|
||||||
@@ -61,8 +61,10 @@ coherence_length_multiples = 0.5:0.5:ceil(L(end)/L_c);
|
|||||||
|
|
||||||
figure();
|
figure();
|
||||||
hold on;
|
hold on;
|
||||||
plot(L, avg_of_mc_variances, 'LineWidth',2, 'DisplayName','Simulation','Color',cols(1,:),'LineStyle','-');
|
[hl, hp] = boundedline(L, avg_of_mc_variances, std_of_mc_variances, 'alpha', 'cmap', cols(1,:));
|
||||||
errorbar(L, avg_of_mc_variances,std_of_mc_variances, 'LineWidth',0.7,'LineStyle','none', 'DisplayName','Simulation','Color',cols(1,:),'HandleVisibility','off');
|
set(hl, 'LineWidth', 2, 'DisplayName', 'Simulation');
|
||||||
|
set(hp, 'HandleVisibility', 'off', 'FaceAlpha', 0.8); % Hide patch from legend to match original behavior
|
||||||
|
|
||||||
|
|
||||||
plot(L_, analytic_variance, 'LineWidth',2, 'DisplayName','Analytic','Color',cols(2,:),'LineStyle','-');
|
plot(L_, analytic_variance, 'LineWidth',2, 'DisplayName','Analytic','Color',cols(2,:),'LineStyle','-');
|
||||||
xticks(coherence_length_multiples.*L_c);
|
xticks(coherence_length_multiples.*L_c);
|
||||||
@@ -76,10 +78,12 @@ else
|
|||||||
xlabel('Interference Delay [m]', 'FontSize',12);
|
xlabel('Interference Delay [m]', 'FontSize',12);
|
||||||
end
|
end
|
||||||
|
|
||||||
xline(L_c.*coherence_length_multiples, 'LineWidth',1.5, 'DisplayName','Coh. Length','HandleVisibility','off','Color',[0.7,0.7,0.7],'LineStyle','-');
|
%xline(L_c.*coherence_length_multiples, 'LineWidth',1.5,'HandleVisibility','off','Color',[0.7,0.7,0.7],'LineStyle','-');
|
||||||
xlim([0,L(end)]);
|
xlim([0,L(end)]);
|
||||||
yline(var_sat, '-.k','LineWidth',1.5, 'DisplayName','Saturation: 2$\alpha ^2$');
|
yline(var_sat, '-.k','LineWidth',1.5, 'DisplayName','Saturation: 2$\alpha ^2$');
|
||||||
grid on;
|
grid on;
|
||||||
ylabel('Intensity Variance', 'FontSize',12);
|
ylabel('Intensity Variance', 'FontSize',12);
|
||||||
title(sprintf('MPI Variance; %d MHz; SIR: %d dB',df.*1e-6,SIR_dB), 'FontSize',14);
|
title(sprintf('MPI Variance; %d MHz; SIR: %d dB',df.*1e-6,SIR_dB), 'FontSize',14);
|
||||||
legend('Location','southeast');
|
legend('Location','southeast');
|
||||||
|
|
||||||
|
% mat2tikz_improved("C:\Users\Silas\Documents\6971e0b65b380ca6d71c837f\02_IMDD_System\tikz\mpi\analytical_mpi_variance2.tikz");
|
||||||
@@ -18,6 +18,7 @@ xlabel('Laser linewidth [MHz]','FontSize',12,'Interpreter','latex');
|
|||||||
ylabel('Coherence length [m]','FontSize',12,'Interpreter','latex');
|
ylabel('Coherence length [m]','FontSize',12,'Interpreter','latex');
|
||||||
title('Coherence Length vs. Laser Linewidth','FontSize',14,'Interpreter','latex');
|
title('Coherence Length vs. Laser Linewidth','FontSize',14,'Interpreter','latex');
|
||||||
|
|
||||||
|
mat2tikz_improved("C:\Users\Silas\Documents\6971e0b65b380ca6d71c837f\02_IMDD_System\tikz\mpi\laser_linewidth_vs_coherence.tikz");
|
||||||
%% Annotate some key points
|
%% Annotate some key points
|
||||||
% hold on;
|
% hold on;
|
||||||
% freqs = [150e3, 1e6, 10e6, 50e6]; % [Hz]
|
% freqs = [150e3, 1e6, 10e6, 50e6]; % [Hz]
|
||||||
|
|||||||
Reference in New Issue
Block a user