freq_est: implement L&R-based symbol-independent frequency estimation
The RX chain uses this to acquire an initial estimate of the carrier frequency. The estimate is adjusted on every incoming symbol until a preamble is found.
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@ -2,6 +2,8 @@
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#include "freq_est.h"
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#include "utils.h"
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// Fits a line y' = m*x' + t to the given points (x, y), where x is the
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// zero-based index in the array.
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static void linear_regression(size_t nx, const float *y, float *m, float *t)
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@ -25,28 +27,104 @@ static void linear_regression(size_t nx, const float *y, float *m, float *t)
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*t = mean_y - (*m) * mean_x;
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}
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#if 0
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// Calculates an estimation of the true peak frequency in the signal by
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// calculating the FFT und interpolating around the bin with the highest value.
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static float fft_true_peak(const float complex *recv, size_t n)
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{
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float complex *out = fft_malloc(n * sizeof(float complex));
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fft_run(n, (float complex*)recv, out, LIQUID_FFT_FORWARD, 0);
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fft_shift(out, n); // shifts by n/2
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// search for the maximum-amplitude bin
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size_t peak_pos = 0;
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float peak_amplitude = 0.0f;
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float amp[n];
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for(size_t i = 0; i < n; i++) {
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amp[i] = cabsf(out[i]);
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if(amp[i] > peak_amplitude) {
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peak_amplitude = amp[i];
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peak_pos = i;
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}
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}
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dump_array_f(amp, n, 1.0f, "/tmp/fft_amp.f32");
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// interpolation does not work at the first and last bin
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if(peak_pos == 0 || peak_pos == (n-1)) {
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return (peak_pos - n/2) / n;
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}
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float a1 = amp[peak_pos - 1];
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float a2 = amp[peak_pos];
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float a3 = amp[peak_pos + 1];
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// find fractional offset to peak_pos by quadratic interpolation.
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// Source: https://dspguru.com/dsp/howtos/how-to-interpolate-fft-peak/
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float d = (a3 - a1) / (2 * (2 * a2 - a1 - a3));
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fft_free(out);
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return ((float)peak_pos + d - (float)(n/2)) / n;
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}
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#endif
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// Frequency estimation algorithm by Luise & Reggiannini
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float freq_est_lr(const float complex *recv, size_t l0)
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{
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const size_t N = l0/2;
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float complex R[N];
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// calculate R[kappa]
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for(size_t kappa = 1; kappa <= N; kappa++) {
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R[kappa-1] = 0.0f;
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for(size_t k = 0; k < l0 - kappa; k++) {
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R[kappa-1] += recv[k + kappa] * conjf(recv[k]);
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}
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R[kappa-1] /= l0 - kappa;
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}
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// sum over R[kappa]
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float complex R_total = 0.0f;
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for(size_t kappa = 1; kappa <= N; kappa++) {
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R_total += R[kappa-1];
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}
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// calculate phase angle of summed R
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float arg = cargf(R_total);
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// convert to frequency offset in radians per sample
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float freq_offset = arg / (N+1) / 2.0f; /* FIXME: not sure where the factor 2 comes from. */
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return freq_offset;
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}
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float freq_est_unknown_bpsk(const float complex *recv, size_t n, float *final_phase)
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{
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float phases[n];
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float complex recv_sq[n];
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// square the symbols and calculate phase
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for(size_t i = 0; i < n; i++) {
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float complex s = recv[i];
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phases[i] = cargf(s * s);
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recv_sq[i] = s * s;
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}
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liquid_unwrap_phase(phases, n);
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float freq, phi0;
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linear_regression(n, phases, &freq, &phi0);
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float freq_est = freq_est_lr(recv_sq, n);
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float phi0 = cargf(recv[0]);
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// outputs must be divided by 2 because squaring the symbols doubles their phase.
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if(final_phase) {
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*final_phase = (phi0 + n * freq) / 2;
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*final_phase = (phi0 + n * freq_est) / 2;
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}
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return freq/2;
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return freq_est/2;
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}
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@ -48,7 +48,7 @@ static bool acquire_preamble(layer1_rx_t *rx, const float complex sample)
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// preamble search
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float complex corr_out = correlator_step(&rx->preamble_correlator, sample);
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if(cabsf(corr_out) > 0.9f * preamble_get_symbol_count()) {
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if(cabsf(corr_out) > 0.5f * preamble_get_symbol_count()) {
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// Preamble found!
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DEBUG_LOG("Preamble found: %.3f > %.3f\n", cabsf(corr_out), 0.5f * preamble_get_symbol_count());
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@ -80,33 +80,36 @@ static bool acquire_preamble(layer1_rx_t *rx, const float complex sample)
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} else {
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// preamble not found.
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// Run the frequency estimator in blocks of FREQ_EST_L samples.
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// This is an implementation that works with unknown BPSK symbols
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// and therefore can be used during ramp-up and preamble.
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if(freq_est_history_write_idx == FREQ_EST_L) {
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float freq_est = freq_est_unknown_bpsk(freq_est_history, FREQ_EST_L, NULL);
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// Run the frequency estimator for every incoming sample overy the last
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// FREQ_EST_L samples. This is an implementation that works with unknown
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// BPSK symbols and therefore can be used during ramp-up and preamble.
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float freq_adjustment = (freq_est / RRC_SPS) * 0.3f;
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nco_crcf_adjust_frequency(rx->carrier_coarse_nco, freq_adjustment);
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float actual_freq = nco_crcf_get_frequency(rx->carrier_coarse_nco);
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if(actual_freq > MAX_COARSE_FREQ_OFFSET) {
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fprintf(stderr, ">");
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nco_crcf_set_frequency(rx->carrier_coarse_nco, MAX_COARSE_FREQ_OFFSET);
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} else if(actual_freq < -MAX_COARSE_FREQ_OFFSET) {
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fprintf(stderr, "<");
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nco_crcf_set_frequency(rx->carrier_coarse_nco, -MAX_COARSE_FREQ_OFFSET);
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}
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DEBUG_LOG("Frequency adjustment: %.6f - carrier frequency: %.6f\n", freq_adjustment, nco_crcf_get_frequency(rx->carrier_coarse_nco));
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freq_est_history_write_idx = 0;
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float complex linearized_history[FREQ_EST_L];
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for(size_t i = 0; i < FREQ_EST_L; i++) {
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linearized_history[i] = freq_est_history[(i + freq_est_history_write_idx) % FREQ_EST_L];
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}
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float freq_est = freq_est_unknown_bpsk(linearized_history, FREQ_EST_L, NULL);
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float freq_adjustment = freq_est / 32.0f;
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nco_crcf_adjust_frequency(rx->carrier_coarse_nco, freq_adjustment);
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float actual_freq = nco_crcf_get_frequency(rx->carrier_coarse_nco);
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if(actual_freq > MAX_COARSE_FREQ_OFFSET) {
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//fprintf(stderr, ">");
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nco_crcf_set_frequency(rx->carrier_coarse_nco, MAX_COARSE_FREQ_OFFSET);
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} else if(actual_freq < -MAX_COARSE_FREQ_OFFSET) {
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//fprintf(stderr, "<");
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nco_crcf_set_frequency(rx->carrier_coarse_nco, -MAX_COARSE_FREQ_OFFSET);
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}
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DEBUG_LOG("Freq. est: %0.6f - Adj: %.6f - carrier frequency: %.6f\n", freq_est, freq_adjustment, nco_crcf_get_frequency(rx->carrier_coarse_nco));
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assert(freq_est_history_write_idx < FREQ_EST_L);
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freq_est_history[freq_est_history_write_idx] = sample;
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freq_est_history_write_idx++;
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freq_est_history_write_idx %= FREQ_EST_L;
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return false; // preamble not found
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}
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