| 1 | function [x, y] = pdm_adaptiveCMA(rx, ry) |
| 2 | %% Perform adaptive equalization using CMA. |
| 3 | %% Input: rx, ry: Both polarizations of received signal |
| 4 | %% Output: x, y: Equalizaed signal |
| 5 | |
| 6 | taps = 15; % Number of taps. Should be odd. |
| 7 | mu = 1e-3; % Convergence parameter for gradient descent. |
| 8 | |
| 9 | hxx = zeros(taps, 1); |
| 10 | hxy = zeros(taps, 1); |
| 11 | hyx = zeros(taps, 1); |
| 12 | hyy = zeros(taps, 1); |
| 13 | %% hxx: real indices -K, ..., 0, ..., K. K = floor(taps/2) |
| 14 | %% MATLAB indices 1 1+K taps |
| 15 | |
| 16 | %% Initialize hxx, hxx[0] = 1, hxx[k] = hxx[-k] = 0 |
| 17 | hxx(ceil(taps/2)) = 1; |
| 18 | hxy(ceil(taps/2)) = 1; |
| 19 | hyx(ceil(taps/2)) = 1; |
| 20 | hyy(ceil(taps/2)) = 1; |
| 21 | |
| 22 | numSymbs = length(rx); |
| 23 | |
| 24 | %% Normalize to unit power. |
| 25 | rx = rx / sqrt(mean(abs(rx) .^ 2)); |
| 26 | ry = ry / sqrt(mean(abs(ry) .^ 2)); |
| 27 | |
| 28 | x = zeros(numSymbs, 1); |
| 29 | y = zeros(numSymbs, 1); |
| 30 | |
| 31 | %% Run CMA twice so that the first symbols were also equalized |
| 32 | for loops = 1:2 |
| 33 | %% Loop through each symbol |
| 34 | for it = 1:numSymbs |
| 35 | %% Construct block of length equal to filter length (taps) |
| 36 | if it <= (taps - 1) / 2; |
| 37 | %% If near the start, prepend zeros |
| 38 | xp = [zeros((taps - 1) / 2 - it + 1, 1); rx(1:it + (taps - 1) / 2)]; |
| 39 | yp = [zeros((taps - 1) / 2 - it + 1, 1); ry(1:it + (taps - 1) / 2)]; |
| 40 | elseif it + (taps - 1) / 2 > numSymbs |
| 41 | %% If near the end, append zeros |
| 42 | xp = [rx(it - (taps - 1) / 2 : end); ... |
| 43 | zeros(it + (taps - 1) / 2 - numSymbs, 1)]; |
| 44 | yp = [ry(it - (taps - 1) / 2 : end); ... |
| 45 | zeros(it + (taps - 1) / 2 - numSymbs, 1)]; |
| 46 | else |
| 47 | %% Just slice the signal |
| 48 | xp = rx(it - (taps - 1) / 2 : it + (taps - 1) / 2); |
| 49 | yp = ry(it - (taps - 1) / 2 : it + (taps - 1) / 2); |
| 50 | end |
| 51 | |
| 52 | %% Filtering |
| 53 | xout = sum(hxx .* xp) + sum(hxy .* yp); |
| 54 | yout = sum(hyx .* xp) + sum(hyy .* yp); |
| 55 | x(it) = xout; |
| 56 | y(it) = yout; |
| 57 | |
| 58 | %% Caculate error |
| 59 | ex = 1 - abs(xout) ^ 2; |
| 60 | ey = 1 - abs(yout) ^ 2; |
| 61 | |
| 62 | %% Update filter by gradient descent |
| 63 | hxx = hxx + mu * ex * xout * conj(xp); |
| 64 | hxy = hxy + mu * ex * xout * conj(yp); |
| 65 | hyx = hyx + mu * ey * yout * conj(xp); |
| 66 | hyy = hyy + mu * ey * yout * conj(yp); |
| 67 | |
| 68 | %% If both filters converge to the same polarization, |
| 69 | % re-initialize the filters. |
| 70 | if sum(abs(hxx - hyx)) < 0.01 && sum(abs(hxy - hyy)) < 0.01 |
| 71 | hxx = 0.5 * (hxx + flipud(conj(hyy))); |
| 72 | hyy = conj(flipud(hxx)); |
| 73 | hxy = 0.5 * (hxy - conj(flipud(hyx))); |
| 74 | hyx = -conj(flipud(hxy)); |
| 75 | end |
| 76 | end |
| 77 | end |
| 78 | end |