Added presentation; DE-QPSK; CD with FFT; split-step Fourier

[4yp.git] / kerr1Signal.m

diff --git a/kerr1Signal.m b/kerr1Signal.m
new file mode 100644 (file)
index 0000000..f4ea292
--- /dev/null
+++ b/kerr1Signal.m
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+numSymbs = 5e5;
+M = 4;
+
+Rsym = 2.5e10; % symbol rate (sym/sec)
+Tsym = 1 / Rsym; % symbol period (sec)
+
+rolloff = 0.25;
+span = 6; % filter span
+sps = 2; % samples per symbol
+
+fs = Rsym * sps; % sampling freq (Hz)
+Tsamp = 1 / fs;
+
+t = (0 : 1 / fs : numSymbs / Rsym + (1.5 * span * sps - 1) / fs).';
+
+
+%%power_dBm = -3:0.2:4;
+power_dBm = [0];
+power = 10 .^ (power_dBm / 10) * 1e-3; % watts
+
+Es = power * Tsym; % joules
+Eb = Es / log2(M); % joules
+
+N0ref_db = 10; % Eb/N0 at power = 1mW
+%% Fix N0, such that Eb/N0 = N0ref_db at power = 1mW
+N0 = 1e-3 * Tsym / (log2(M) * 10 ^ (N0ref_db / 10)); % joules
+
+
+plotlen = length(power);
+
+ber = zeros(1, plotlen);
+
+data = randi([0 M - 1], numSymbs, 1);
+modData = pskmod(data, M, pi / M, 'gray');
+
+
+%% Chromatic dispersion
+D = 17; % ps / (nm km)
+lambda = 1550; % nm
+z = 600; % km
+
+
+for i = 1:plotlen
+  snr = Es(i) / sps / N0;
+  snr_dB = 10 * log10(snr);
+
+  x = txFilter(modData, rolloff, span, sps);
+  %% Now, sum(abs(x) .^ 2) / length(x) should be 1.
+  %% We can set its power simply by multiplying.
+  x = sqrt(power(i)) * x;
+
+  %% We can now do split-step Fourier.
+  gamma = 1.2; % watt^-1 / km
+  %%stepnum = round(40 * z * gamma); % Nonlinear Fiber optics, App B
+  stepnum = 100;
+  xCD = splitstepfourier(x, D, lambda, z, Tsamp, gamma, stepnum);
+
+  y = awgn(xCD, snr, power(i), 'linear');
+  %%y = xCD;
+
+  r = rxFilter(y, rolloff, span, sps);
+  rCDComp = CDCompensation(r, D, lambda, z, Tsamp);
+  rCDComp = normalizeEnergy(rCDComp, numSymbs*sps, 1);
+
+  rSampled = rCDComp(sps*span/2+1:sps:(numSymbs+span/2)*sps);
+  rNoCompSampled = r(sps*span/2+1:sps:(numSymbs+span/2)*sps);
+
+  %% rotate rNoCompSampled to match original data
+  theta = angle(-sum(rNoCompSampled .^ M)) / M;
+  %% if theta approx +pi/M, wrap to -pi/M
+  if abs(theta - pi / M) / (pi / M) < 0.1
+    theta = -pi / M;
+  end
+  rNoCompSampled = rNoCompSampled .* exp(-j * theta);
+
+
+  %% Not entirely sure why, but after using FFT instead of time-domain
+  %% convolution for simulating CD, we now need to do the same rotation
+  %% for rSampled as well, but this time with a positive rotation.
+  theta = angle(-sum(rSampled .^ M)) / M;
+  if abs(theta + pi / M) / (pi / M) < 0.1
+    theta = +pi / M;
+  end
+  rSampled = rSampled .* exp(-1j * theta);
+
+  %% adaptive filter
+  adaptFilterOut = adaptiveCMA(rSampled);
+
+  demodAdapt = pskdemod(adaptFilterOut, M, pi / M, 'gray');
+  [~, ber(i)] = biterr(data, demodAdapt)
+end
+
+return
+
+
+figure(1);
+clf;
+
+%% Plot simulated results
+semilogy(power_dBm, ber, 'Color', [0, 0.6, 0], 'LineWidth', 2);
+hold on;
+
+title({'CD + Kerr + CD compensation', ...
+       strcat(['$D = 17$ ps/(nm km), $z = ', num2str(z), '$ km'])});
+grid on;
+%%xlabel('$E_b/N_0$ (dB)');
+xlabel('Optical power (dBm)');
+ylabel('BER');
+
+formatFigure;