/* -*- c++ -*- */
/*
* Copyright 2010,2012 Free Software Foundation, Inc.
*
* GNU Radio is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3, or (at your option)
* any later version.
*
* GNU Radio is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Radio; see the file COPYING. If not, write to
* the Free Software Foundation, Inc., 51 Franklin Street,
* Boston, MA 02110-1301, USA.
*/
// Calculate the taps for the CPM phase responses
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <cmath>
#include <cfloat>
#include <analog/cpm.h>
//gives us erf on compilers without it
#include <boost/math/special_functions/erf.hpp>
namespace bm = boost::math;
namespace gr {
namespace analog {
#ifndef M_TWOPI
# define M_TWOPI (2*M_PI)
#endif
//! Normalised sinc function, sinc(x)=sin(pi*x)/pi*x
inline double
sinc(double x)
{
if(x == 0) {
return 1.0;
}
return sin(M_PI * x) / (M_PI * x);
}
//! Taps for L-RC CPM (Raised cosine of length L symbols)
std::vector<float>
generate_cpm_lrc_taps(unsigned samples_per_sym, unsigned L)
{
std::vector<float> taps(samples_per_sym * L, 1.0/L/samples_per_sym);
for(unsigned i = 0; i < samples_per_sym * L; i++) {
taps[i] *= 1 - cos(M_TWOPI * i / L / samples_per_sym);
}
return taps;
}
/*! Taps for L-SRC CPM (Spectral raised cosine of length L symbols).
*
* L-SRC has a time-continuous phase response function of
*
* g(t) = 1/LT * sinc(2t/LT) * cos(beta * 2pi t / LT) / (1 - (4beta / LT * t)^2)
*
* which is the Fourier transform of a cos-rolloff function with rolloff
* beta, and looks like a sinc-function, multiplied with a rolloff term.
* We return the main lobe of the sinc, i.e., everything between the
* zero crossings.
* The time-discrete IR is thus
*
* g(k) = 1/Ls * sinc(2k/Ls) * cos(beta * pi k / Ls) / (1 - (4beta / Ls * k)^2)
* where k = 0...Ls-1
* and s = samples per symbol.
*/
std::vector<float>
generate_cpm_lsrc_taps(unsigned samples_per_sym, unsigned L, double beta)
{
double Ls = (double) L * samples_per_sym;
std::vector<double> taps_d(L * samples_per_sym, 0.0);
std::vector<float> taps(L * samples_per_sym, 0.0);
double sum = 0;
for(unsigned i = 0; i < samples_per_sym * L; i++) {
double k = i - Ls/2; // Causal to acausal
taps_d[i] = 1.0 / Ls * sinc(2.0 * k / Ls);
// For k = +/-Ls/4*beta, the rolloff term's cos-function becomes zero
// and the whole thing converges to PI/4 (to prove this, use de
// l'hopital's rule).
if(fabs(fabs(k) - Ls/4/beta) < 2*DBL_EPSILON) {
taps_d[i] *= M_PI_4;
}
else {
double tmp = 4.0 * beta * k / Ls;
taps_d[i] *= cos(beta * M_TWOPI * k / Ls) / (1 - tmp * tmp);
}
sum += taps_d[i];
}
for(unsigned i = 0; i < samples_per_sym * L; i++) {
taps[i] = (float) taps_d[i] / sum;
}
return taps;
}
//! Taps for L-REC CPM (Rectangular pulse shape of length L symbols)
std::vector<float>
generate_cpm_lrec_taps(unsigned samples_per_sym, unsigned L)
{
return std::vector<float>(samples_per_sym * L, 1.0/L/samples_per_sym);
}
//! Helper function for TFM
double tfm_g0(double k, double sps)
{
if(fabs(k) < 2 * DBL_EPSILON) {
return 1.145393004159143; // 1 + pi^2/48 / sqrt(2)
}
const double pi2_24 = 0.411233516712057; // pi^2/24
double f = M_PI * k / sps;
return sinc(k/sps) - pi2_24 * (2 * sin(f) - 2*f*cos(f) - f*f*sin(f)) / (f*f*f);
}
//! Taps for TFM CPM (Tamed frequency modulation)
//
// See [2, Chapter 2.7.2].
//
// [2]: Anderson, Aulin and Sundberg; Digital Phase Modulation
std::vector<float>
generate_cpm_tfm_taps(unsigned sps, unsigned L)
{
unsigned causal_shift = sps * L / 2;
std::vector<double> taps_d(sps * L, 0.0);
std::vector<float> taps(sps * L, 0.0);
double sum = 0;
for(unsigned i = 0; i < sps * L; i++) {
double k = (double)(((int)i) - ((int)causal_shift)); // Causal to acausal
taps_d[i] = tfm_g0(k - sps, sps) +
2 * tfm_g0(k, sps) +
tfm_g0(k + sps, sps);
sum += taps_d[i];
}
for(unsigned i = 0; i < sps * L; i++) {
taps[i] = (float) taps_d[i] / sum;
}
return taps;
}
//! Taps for Gaussian CPM. Phase response is truncated after \p L symbols.
// \p bt sets the 3dB-time-bandwidth product.
//
// Note: for h = 0.5, this is the phase response for GMSK.
//
// This C99-compatible formula for the taps is taken straight
// from [1, Chapter 9.2.3].
// A version in Q-notation can be found in [2, Chapter 2.7.2].
//
// [1]: Karl-Dirk Kammeyer; Nachrichtenübertragung, 4th Edition.
// [2]: Anderson, Aulin and Sundberg; Digital Phase Modulation
//
std::vector<float>
generate_cpm_gaussian_taps(unsigned samples_per_sym, unsigned L, double bt)
{
double Ls = (double) L * samples_per_sym;
std::vector<double> taps_d(L * samples_per_sym, 0.0);
std::vector<float> taps(L * samples_per_sym, 0.0);
// alpha = sqrt(2/ln(2)) * pi * BT
double alpha = 5.336446256636997 * bt;
for(unsigned i = 0; i < samples_per_sym * L; i++) {
double k = i - Ls/2; // Causal to acausal
taps_d[i] = (bm::erf(alpha * (k / samples_per_sym + 0.5)) -
bm::erf(alpha * (k / samples_per_sym - 0.5)))
* 0.5 / samples_per_sym;
taps[i] = (float) taps_d[i];
}
return taps;
}
std::vector<float>
cpm::phase_response(cpm_type type, unsigned samples_per_sym, unsigned L, double beta)
{
switch(type) {
case LRC:
return generate_cpm_lrc_taps(samples_per_sym, L);
case LSRC:
return generate_cpm_lsrc_taps(samples_per_sym, L, beta);
case LREC:
return generate_cpm_lrec_taps(samples_per_sym, L);
case TFM:
return generate_cpm_tfm_taps(samples_per_sym, L);
case GAUSSIAN:
return generate_cpm_gaussian_taps(samples_per_sym, L, beta);
default:
return generate_cpm_lrec_taps(samples_per_sym, 1);
}
}
} // namespace analog
} // namespace gr