PMD theory; S21 measures; NGMI theory

Functions/Theory/PMD_maxwellshape/pmd_maxwell.m

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+
+PMDcoeff    = 0.1 * ( 1e-12 / sqrt(1e3) ); %PMD s/sqrt(m)
+
+
+L_40        = 40e3;                   %m
+mean_dgd    = PMDcoeff * sqrt(L_40);       % in sec. E(tau) == PMD value 
+
+disp(['defined mean of DGD in pico seconds: ',num2str(mean_dgd*1e12)]);
+
+dgd_40km = [];
+for i = 1:4000
+    dgd_40km(i,:) = getDGDrealization(mean_dgd,1);
+end
+
+disp(['simulated mean of DGD in pico seconds: ',num2str(mean(dgd_40km)*1e12)]);
+
+%%% 2 test for segmented link %%%%
+
+L_10        = 10e3;                   %m
+mean_dgd    = PMDcoeff * sqrt(L_10);       % in sec. E(tau) == PMD value 
+
+dgd_10km = [];
+for j = 1:4
+    for i = 1:1000
+        dgd_10km(i,j) = getDGDrealization(mean_dgd,1);
+    end
+end
+
+a = sum(dgd_10km,2) ;
+
+%%% calc maxwell curve
+mean_dgd =  PMDcoeff * sqrt(L_40) * 1e12 ; % in sec.
+q = sqrt(pi/8) * mean_dgd;
+t = [0:0.01:100];
+
+maxwell = sqrt(2/pi).* (t.^2)/(q.^3) .* exp(-t.^2/(2*q^2)) ;
+
+
+%%% plot everything 
+
+figure;
+histogram(dgd_40km*1e12,1000,"Normalization","pdf",'EdgeColor','none','FaceColor','b','FaceAlpha',0.6);
+hold on
+histogram(a*1e12,1000,"Normalization","pdf",'EdgeColor','none','FaceColor','g','FaceAlpha',0.6);
+plot(t(1:200),maxwell(1:200),'r','LineWidth',3);
+xline(mean_dgd,'LineWidth',3,'Color','magenta')
+hold off
+
+function z = getDGDrealization(mean_dgd,N)
+
+    mean_dgd = mean_dgd; %to pico seconds
+    q = sqrt(pi/8) * mean_dgd;
+    threenormaldists = randn(3,N)*q; %3x normal dist around [-1,1] with a deviation of mean_dgd 
+
+    y = threenormaldists.^2;
+
+    z = sqrt(sum(y,1));
+  
+end