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Diffstat (limited to 'gr-analog/lib/cpm.cc')
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1 files changed, 221 insertions, 0 deletions
diff --git a/gr-analog/lib/cpm.cc b/gr-analog/lib/cpm.cc new file mode 100644 index 000000000..618475cec --- /dev/null +++ b/gr-analog/lib/cpm.cc @@ -0,0 +1,221 @@ +/* -*- 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 + |