84 lines
2.1 KiB
Mathematica
84 lines
2.1 KiB
Mathematica
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%
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% Laurent decomposition of GMSK signals
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% Generates C0, C1, and C2 pulse shapes
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%
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% Pierre Laurent, "Exact and Approximate Construction of Digital Phase
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% Modulations by Superposition of Amplitude Modulated Pulses", IEEE
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% Transactions of Communications, Vol. 34, No. 2, Feb 1986.
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%
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% Author: Thomas Tsou <tom@tsou.cc>
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%
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% Modulation parameters
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oversamp = 16;
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L = 3;
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f = 270.83333e3;
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T = 1/f;
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h = 0.5;
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BT = 0.30;
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B = BT / T;
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% Generate sampling points for L symbol periods
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t = -(L*T/2):T/oversamp:(L*T/2);
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t = t(1:end-1) + (T/oversamp/2);
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% Generate Gaussian pulse
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g = qfunc(2*pi*B*(t - T/2)/(log(2)^.5)) - qfunc(2*pi*B*(t + T/2)/(log(2)^.5));
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g = g / sum(g) * pi/2;
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g = [0 g];
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% Integrate phase
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q = 0;
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for i = 1:size(g,2);
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q(i) = sum(g(1:i));
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end
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% Compute two sided "generalized phase pulse" function
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s = 0;
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for i = 1:size(g,2);
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s(i) = sin(q(i)) / sin(pi*h);
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end
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for i = (size(g,2) + 1):(2 * size(g,2) - 1);
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s(i) = sin(pi*h - q(i - (size(g,2) - 1))) / sin(pi*h);
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end
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% Compute C0 pulse: valid for all L values
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c0 = s(1:end-(oversamp*(L-1)));
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for i = 1:L-1;
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c0 = c0 .* s((1 + i*oversamp):end-(oversamp*(L - 1 - i)));
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end
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% Compute C1 pulse: valid for L = 3 only!
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% C1 = S0 * S4 * S2
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c1 = s(1:end-(oversamp*(4)));
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c1 = c1 .* s((1 + 4*oversamp):end-(oversamp*(4 - 1 - 3)));
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c1 = c1 .* s((1 + 2*oversamp):end-(oversamp*(4 - 1 - 1)));
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% Compute C2 pulse: valid for L = 3 only!
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% C2 = S0 * S1 * S5
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c2 = s(1:end-(oversamp*(5)));
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c2 = c2 .* s((1 + 1*oversamp):end-(oversamp*(5 - 1 - 0)));
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c2 = c2 .* s((1 + 5*oversamp):end-(oversamp*(5 - 1 - 4)));
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% Plot C0, C1, C2 Laurent pulse series
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figure(1);
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hold off;
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plot((0:size(c0,2)-1)/oversamp - 2,c0, 'b');
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hold on;
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plot((0:size(c1,2)-1)/oversamp - 2,c1, 'r');
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plot((0:size(c2,2)-1)/oversamp - 2,c2, 'g');
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% Generate OpenBTS pulse
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numSamples = size(c0,2);
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centerPoint = (numSamples - 1)/2;
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i = ((0:numSamples) - centerPoint) / oversamp;
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xP = .96*exp(-1.1380*i.^2 - 0.527*i.^4);
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xP = xP / max(xP) * max(c0);
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% Plot C0 pulse compared to OpenBTS pulse
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figure(2);
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hold off;
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plot((0:size(c0,2)-1)/oversamp, c0, 'b');
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hold on;
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plot((0:size(xP,2)-1)/oversamp, xP, 'r');
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