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