/* -*- c++ -*- */ /* * Copyright 2010,2012 Free Software Foundation, Inc. * * SPDX-License-Identifier: GPL-3.0-or-later * */ // Calculate the taps for the CPM phase responses #ifdef HAVE_CONFIG_H #include "config.h" #endif #include <gnuradio/analog/cpm.h> #include <gnuradio/math.h> #include <cfloat> #include <cmath> namespace gr { namespace analog { //! Normalised sinc function, sinc(x)=std::sin(pi*x)/pi*x inline double sinc(double x) { if (x == 0) { return 1.0; } return std::sin(GR_M_PI * x) / (GR_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 - std::cos((2.0 * GR_M_PI) * 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) * std::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) * std::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] *= std::cos(beta * (2.0 * GR_M_PI) * 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 = GR_M_PI * k / sps; return sinc(k / sps) - pi2_24 * (2 * std::sin(f) - 2 * f * std::cos(f) - f * f * std::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] = (std::erf(alpha * (k / samples_per_sym + 0.5)) - std::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