diff options
| -rw-r--r-- | Transceiver52M/laurent.m | 83 | ||||
| -rw-r--r-- | Transceiver52M/sigProcLib.cpp | 49 |
2 files changed, 123 insertions, 9 deletions
diff --git a/Transceiver52M/laurent.m b/Transceiver52M/laurent.m new file mode 100644 index 0000000..ef15428 --- /dev/null +++ b/Transceiver52M/laurent.m @@ -0,0 +1,83 @@ +% +% 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'); diff --git a/Transceiver52M/sigProcLib.cpp b/Transceiver52M/sigProcLib.cpp index b0ef21a..51584b7 100644 --- a/Transceiver52M/sigProcLib.cpp +++ b/Transceiver52M/sigProcLib.cpp @@ -422,11 +422,22 @@ void generateGSMPulse(int sps, int symbolLength) GSMPulse->empty->isRealOnly(true); *(GSMPulse->empty->begin()) = 1.0f; - len = sps * symbolLength; - if (len < 4) - len = 4; + /* + * For 4 samples-per-symbol use a precomputed single pulse Laurent + * approximation. This should yields below 2 degrees of phase error at + * the modulator output. Use the existing pulse approximation for all + * other oversampling factors. + */ + switch (sps) { + case 4: + len = 16; + break; + default: + len = sps * symbolLength; + if (len < 4) + len = 4; + } - /* GSM pulse approximation */ GSMPulse->buffer = convolve_h_alloc(len); GSMPulse->gaussian = new signalVector((complex *) GSMPulse->buffer, 0, len); @@ -435,12 +446,32 @@ void generateGSMPulse(int sps, int symbolLength) signalVector::iterator xP = GSMPulse->gaussian->begin(); - center = (float) (len - 1.0) / 2.0; + if (sps == 4) { + *xP++ = 4.46348606e-03; + *xP++ = 2.84385729e-02; + *xP++ = 1.03184855e-01; + *xP++ = 2.56065552e-01; + *xP++ = 4.76375085e-01; + *xP++ = 7.05961177e-01; + *xP++ = 8.71291644e-01; + *xP++ = 9.29453645e-01; + *xP++ = 8.71291644e-01; + *xP++ = 7.05961177e-01; + *xP++ = 4.76375085e-01; + *xP++ = 2.56065552e-01; + *xP++ = 1.03184855e-01; + *xP++ = 2.84385729e-02; + *xP++ = 4.46348606e-03; + *xP++ = 0.0; + } else { + center = (float) (len - 1.0) / 2.0; - for (int i = 0; i < len; i++) { - arg = ((float) i - center) / (float) sps; - *xP++ = 0.96 * exp(-1.1380 * arg * arg - - 0.527 * arg * arg * arg * arg); + /* GSM pulse approximation */ + for (int i = 0; i < len; i++) { + arg = ((float) i - center) / (float) sps; + *xP++ = 0.96 * exp(-1.1380 * arg * arg - + 0.527 * arg * arg * arg * arg); + } } float avgAbsval = sqrtf(vectorNorm2(*GSMPulse->gaussian)/sps); |