diff --git a/examples/pcmfm_test.py b/examples/pcmfm_test.py index a4ad049..18b5f9b 100644 --- a/examples/pcmfm_test.py +++ b/examples/pcmfm_test.py @@ -4,11 +4,14 @@ import numpy as np from matplotlib.axes import Axes from matplotlib.ticker import MultipleLocator -from scipy.signal import besselap, impulse from waveforms.cpm.helpers import normalize_cpm_filter from waveforms.cpm.modulate import cpm_modulate -from waveforms.cpm.pcmfm import PCMFM_DENOM, PCMFM_NUMER +from waveforms.cpm.pcmfm import ( + PCMFM_DENOM, + PCMFM_NUMER, + freq_pulse_pcmfm, +) from waveforms.cpm.trellis.encoder import TrellisEncoder from waveforms.cpm.trellis.model import SimpleTrellis2 from waveforms.glfsr import PNSequence @@ -42,12 +45,7 @@ ["-", "--", "-", "--", "-."], [3, 3, 2, 2, 2], ): - t, y = impulse( - besselap(order, norm="mag"), - T=np.linspace(0, length * 2 / 0.7, num=(length - 1) * sps + 1), - ) - freq_pulse = normalize_cpm_filter(sps, np.convolve(y, np.ones(sps))) - + freq_pulse = freq_pulse_pcmfm(sps, order) normalized_time, modulated_signal = cpm_modulate( symbols=symbols, mod_index=mod_index, diff --git a/examples/soqpsk_detection.py b/examples/soqpsk_detection.py index 37fbe77..76bf2be 100644 --- a/examples/soqpsk_detection.py +++ b/examples/soqpsk_detection.py @@ -6,26 +6,33 @@ from matplotlib.axes import Axes from matplotlib.ticker import MultipleLocator from numpy.typing import NDArray +from scipy.signal import butter, filtfilt, firwin, lfilter from waveforms.cpm.modulate import cpm_modulate from waveforms.cpm.pamapprox import rho_pulses from waveforms.cpm.soqpsk import ( + RecursiveDD, + RecursiveDE, + SOQPSKDifferentialDecoder, + SOQPSKDifferentialEncoder, freq_pulse_soqpsk_mil, freq_pulse_soqpsk_tg, ) from waveforms.cpm.trellis.encoder import TrellisEncoder from waveforms.cpm.trellis.model import ( + SOQPSKTrellis4x2, SOQPSKTrellis4x2DiffEncoded, ) from waveforms.glfsr import PNSequence from waveforms.noise import generate_complex_awgn from waveforms.viterbi.algorithm import SOQPSKTrellisDetector +from waveforms.viz import plot_constellation # Set seeds so iterations on implementation can be compared better rng = np.random.Generator(np.random.PCG64(seed=1)) -PN_DEGREE = 15 +PN_DEGREE = 17 DATA_GEN = PNSequence(PN_DEGREE) DATA_BUFFER = np.packbits(DATA_GEN.generate_sequence()) @@ -34,22 +41,75 @@ if __name__ == "__main__": logging.basicConfig(level=logging.INFO) - # Constants + # Signal Processing Constants sps = 10 fft_size = 2**9 - pulse_pad = 0.5 - sigma = np.sqrt(2) / 2 - P = 4 + ebn0 = 10 # Quasonix RDMS has a 1e-5 BER for SOQPSK-TG @ Eb/N0 = 11.2 dB + sigma = np.sqrt(sps / np.power(10, ebn0 / 10) / 2) + filter_type = "hamming" + + # Encoding Constants + use_irig_diff_encoding = True + use_recursive_diff_encoding = False + use_standard_trellis = True + + if use_standard_trellis and not use_irig_diff_encoding and not use_recursive_diff_encoding: + _logger.warning( + "No differential encoding utilized. " + "Trellis detectors susceptible to initial state determining output sequence." + ) + + # Plotting Constants + t_min, t_max = 100, 120 + + # Pre-detector filter + filter_delay = 0 + filter_method = lfilter + + # IIR Filter options + if filter_type == "butter": + order = 5 + lpf = butter(order, 0.45, btype="low", fs=sps, analog=False) + filter_method = filtfilt + _logger.warning( + "Using filtfilt for IIR filter to linearize phase response. " + "This filtering method is non-trivial to implement in real-time systems." + ) + + # FIR Filter options - by default generate forward-reverse filter to linearize phase response + elif filter_type == "hamming": + fir_taps = firwin(sps * 8 + 1, 0.5, window="hamming", fs=sps) + forward_reverse_taps = np.convolve(fir_taps, fir_taps[::-1], mode="full") + lpf = forward_reverse_taps, [1] + filter_delay = int(len(forward_reverse_taps) / 2) + + elif filter_type == "kaiser": + fir_taps = firwin(sps * 8 + 1, 0.5, window=("kaiser", 8), fs=sps) + forward_reverse_taps = np.convolve(fir_taps, fir_taps[::-1], mode="full") + lpf = forward_reverse_taps, [1] + filter_delay = int(len(forward_reverse_taps) / 2) + + else: + lpf = None # Bits of information to transmit bit_array = np.unpackbits(DATA_BUFFER) + input_bits = bit_array[:] + + # Map bits of information to ternary symbols + symbol_precoder = TrellisEncoder( + SOQPSKTrellis4x2 if use_standard_trellis else SOQPSKTrellis4x2DiffEncoded + ) + if use_irig_diff_encoding: + bit_array = SOQPSKDifferentialEncoder()(bit_array) + + if use_recursive_diff_encoding and use_standard_trellis: + bit_array = RecursiveDE()(bit_array) - # Convert bits to symbols - symbol_precoder = TrellisEncoder(SOQPSKTrellis4x2DiffEncoded) symbols = symbol_precoder(bit_array) # Create plots and axes - fig_eye, iq_axes = plt.subplots(4, 2, figsize=(12, 10), dpi=100) + fig_eye, iq_axes = plt.subplots(4, 2, figsize=(12, 12), dpi=100) for ax in iq_axes.flatten(): ax.grid(which="both", linestyle=":") @@ -64,14 +124,14 @@ # Simulate the following SOQPSK Waveforms pulses_colors_labels = ( - (freq_pulse_soqpsk_mil(sps=sps), "MIL", 1 / P), - (freq_pulse_soqpsk_tg(sps=sps), "TG", 1 / P), + (freq_pulse_soqpsk_mil(sps=sps), "MIL", 1 / 4), + (freq_pulse_soqpsk_tg(sps=sps), "TG", 1 / 4), ) for i, (pulse_filter, label, mod_index) in enumerate(pulses_colors_labels): # Assign axes iq_ax: Axes = iq_axes[0, i] - psd_ax: Axes = iq_axes[1, i] - rho_ax: Axes = iq_axes[2, i] + mf_ax: Axes = iq_axes[1, i] + psd_ax: Axes = iq_axes[2, i] errors_ax: Axes = iq_axes[3, i] # Modulate the input symbols @@ -83,54 +143,92 @@ ) noise = generate_complex_awgn(sigma, modulated_signal.size, rng) modulated_signal[:] *= np.exp(-1j * np.pi / 4) - freq_pulses = np.angle(modulated_signal[1:] * modulated_signal.conj()[:-1]) * sps / np.pi # Received signal unfiltered_signal: NDArray[np.complex128] = modulated_signal + noise - received_signal = unfiltered_signal + received_signal: NDArray[np.complex128] + received_signal = filter_method(*lpf, unfiltered_signal) if lpf else unfiltered_signal[:] # Display transmitted and received signal in the time domain - iq_ax.plot(normalized_time, modulated_signal.real, "b-", alpha=1.0, label=r"Re[$s(t)]$") - iq_ax.plot(normalized_time, unfiltered_signal.real, "b-", alpha=0.4, label=r"$Re[s(t)+N]$") - iq_ax.plot(normalized_time, modulated_signal.imag, "r-", alpha=1.0, label=r"Im[$s(t)]$") - iq_ax.plot(normalized_time, unfiltered_signal.imag, "r-", alpha=0.4, label=r"$Im[s(t)+N]$") + iq_ax.plot( + normalized_time[t_min * sps : t_max * sps], + modulated_signal.real[t_min * sps : t_max * sps], + "b-", + alpha=1.0, + label=r"Re[$s(t)]$", + ) + iq_ax.plot( + normalized_time[t_min * sps : t_max * sps], + modulated_signal.imag[t_min * sps : t_max * sps], + "r-", + alpha=1.0, + label=r"Im[$s(t)]$", + ) + + # Unfiltered Signal + iq_ax.plot( + normalized_time[t_min * sps : t_max * sps], + unfiltered_signal.real[t_min * sps : t_max * sps], + "b-", + alpha=0.2, + label=r"$Re[s(t)+N]$", + ) + iq_ax.plot( + normalized_time[t_min * sps : t_max * sps], + unfiltered_signal.imag[t_min * sps : t_max * sps], + "r-", + alpha=0.2, + label=r"$Im[s(t)+N]$", + ) + + # Filtered Signal + iq_ax.plot( + normalized_time[: -filter_delay or None][t_min * sps : t_max * sps], + received_signal.real[filter_delay:][t_min * sps : t_max * sps], + "b-", + alpha=0.4, + ) + iq_ax.plot( + normalized_time[: -filter_delay or None][t_min * sps : t_max * sps], + received_signal.imag[filter_delay:][t_min * sps : t_max * sps], + "r-", + alpha=0.4, + ) pulse_ax = iq_ax.twinx() pulse_ax.stem( - normalized_time[sps::sps], - symbols / 2, + normalized_time[sps::sps][t_min:t_max], + symbols[t_min:t_max] / 2, markerfmt="ko", linefmt="k-", basefmt=" ", label="Symbol", ) - pulse_ax.plot( - normalized_time[:-1], - freq_pulses, - "k-", - alpha=0.4, - label="Frequency Pulses", - ) pulse_ax.set_ylim(-np.pi / 2, np.pi / 2) # Display transmitted and received signal PSD to illustrate SNR - pxx_tx, freqs = psd_ax.psd( - modulated_signal, + psd_ax.psd( + modulated_signal[: fft_size * 100], NFFT=fft_size, Fs=sps, label="$s(t)$", scale_by_freq=False, ) - pxx_specan, freqs = psd_ax.psd( - received_signal, + psd_ax.psd( + noise[: fft_size * 100], + NFFT=fft_size, + Fs=sps, + label="$N(t)$", + scale_by_freq=False, + ) + psd_ax.psd( + received_signal[: fft_size * 100], NFFT=fft_size, Fs=sps, label="$r(t)$", scale_by_freq=False, ) - ebn0_calc = 10 * np.log10(sps / (2 * sigma**2)) - # Pulse Truncation Filters L = int(pulse_filter.size / sps) truncation = 1 @@ -139,21 +237,12 @@ pt_end = int((L + truncation) * sps / 2) + 1 truncated_phase_pulse = q[pt_start:pt_end] mf_outputs_pt = np.zeros((3, received_signal.size), dtype=np.complex128) - mf_outputs_pt[0, :] = np.convolve( - received_signal, - np.exp(-2j * np.pi * mod_index * -2 * truncated_phase_pulse), - mode="same", - ) - mf_outputs_pt[1, :] = np.convolve( - received_signal, - np.exp(-2j * np.pi * mod_index * +0 * truncated_phase_pulse), - mode="same", - ) - mf_outputs_pt[2, :] = np.convolve( - received_signal, - np.exp(-2j * np.pi * mod_index * +2 * truncated_phase_pulse), - mode="same", - ) + for sym_idx in range(3): + mf_outputs_pt[sym_idx, :] = np.convolve( + received_signal, + np.exp(-2j * np.pi * mod_index * 2 * (sym_idx - 1) * truncated_phase_pulse), + mode="same", + ) # PAM De-composition rho pulses/matched filters rho = rho_pulses(pulse_filter, mod_index, sps, k_max=2) @@ -163,22 +252,80 @@ k_max, num_symbols = pseudo_symbols.shape mf_outputs_pam = np.zeros((num_symbols, received_signal.size), dtype=np.complex128) for sym_idx in range(num_symbols): + # Generate matched filter for ternary symbol + matched_filted = np.zeros(d_max, dtype=np.complex128) for k in range(k_max): # Zero-pad all to length d_max for alignment - rk = np.concatenate((rho[k], np.zeros(d_max - rho[k].size))) - mf_outputs_pam[sym_idx, :] += np.convolve( - received_signal, - rk, - mode="same", - ) * np.conj(pseudo_symbols[k, sym_idx]) + matched_filted[: rho[k].size] += rho[k] * np.conj(pseudo_symbols[k, sym_idx]) + + # Convolve received signal with matched filter + mf_outputs_pam[sym_idx, :] += np.convolve( + received_signal, + matched_filted, + mode="same", + ) + sym = 2 * (sym_idx - 1) + (line,) = mf_ax.plot( + normalized_time[t_min * sps : t_max * sps], + mf_outputs_pam[sym_idx, filter_delay:].real[t_min * sps : t_max * sps], + label=f"MF Re[{sym:+}]", + linestyle="-", + marker="s", + markevery=(0 if label == "TG" else sps, sps), + ) + mf_ax.plot( + normalized_time[t_min * sps : t_max * sps], + mf_outputs_pam[sym_idx, filter_delay:].imag[t_min * sps : t_max * sps], + label=f"MF Im[{sym:+}]", + color=line.get_color(), + linestyle="--", + marker="s", + markevery=(0 if label == "TG" else sps, sps), + ) + + # DETECTION METHODS + output_bits_dict = {} + + # SxS Detection + constellation_signal: NDArray[np.complex128] = np.zeros_like(received_signal) + constellation_signal[sps:] += (received_signal * np.exp(1j * np.pi / 4)).real[:-sps] + constellation_signal[:] += (received_signal * np.exp(1j * np.pi / 4)).imag * 1j + sxs_output = [] + sxs_delay = 2 + id_filter_n = sps + constellation_out = [] + + for n in range(filter_delay + sps, received_signal.size - sps, sps * 2): + # Integrate & Dump + soft_symbol: complex = constellation_signal[ + n - int(id_filter_n / 2) : n + id_filter_n - int(id_filter_n / 2) + ].sum() + constellation_out.append(soft_symbol / id_filter_n) + sxs_output.append(int(soft_symbol.real > 0)) + sxs_output.append(int(soft_symbol.imag > 0)) + + # Decoding Steps + sxs_output = np.array(sxs_output, dtype=np.uint8) + if use_recursive_diff_encoding or not use_standard_trellis: + sxs_output = RecursiveDD()(sxs_output) + + if use_irig_diff_encoding: + sxs_output = SOQPSKDifferentialDecoder()(sxs_output) + + # Align with input_bits + output_bits_dict["Single Symbol"] = sxs_output[sxs_delay:] # Initialize FSM # WIP - ATTEMPTS TO DO A VA TRACEBACK ON EACH SYMBOL - for mf_outputs, detector_type in zip((mf_outputs_pt, mf_outputs_pam), ("PT", "PAM")): - det = SOQPSKTrellisDetector(length=2, differantial_encoding=True) + va_delay = 2 + delay = int(filter_delay / sps) + for mf_outputs, detector_type in zip( + (mf_outputs_pt, mf_outputs_pam), + ("PT Viterbi", "PAM Viterbi"), + ): + det = SOQPSKTrellisDetector(length=4, differantial_encoding=not use_standard_trellis) output_symbols = [] output_bits = [] - delay = 0 # Should replace magic numbers. Ideally this gets solved with timing recovery. if detector_type == "PT": @@ -188,59 +335,69 @@ for n in range(received_signal.size - det.length * sps): # Placeholder timing recovery, will replace with Non-data-aided method - if (n + timing_offset) % sps: + if (n + timing_offset + filter_delay) % sps: continue # Perform Fixed Length VA Traceback sym_idx = int((n + timing_offset) / sps) rbits, rsyms = det.iteration(mf_outputs[:, n]) - output_symbols.append(rsyms[0]) - output_bits.append(rbits[0]) - - # Calculate number of errors, and visualize - iter_va_output_symbols = np.array(output_symbols[det.length :], dtype=np.int8) - iter_va_output_bits = np.array(output_bits[det.length :], dtype=np.uint8) - aligned_symbols = symbols[delay:] - min_size = min(aligned_symbols.size, iter_va_output_symbols.size) + output_symbols.append(rsyms[va_delay]) + output_bits.append(rbits[va_delay]) + + # Run decoding steps + output_bits = np.array(output_bits, dtype=np.uint8) + + if use_recursive_diff_encoding and use_standard_trellis: + output_bits = RecursiveDD()(output_bits) + + if use_irig_diff_encoding: + output_bits = SOQPSKDifferentialDecoder()(output_bits) + + # Align with input_bits + output_bits_dict[detector_type] = output_bits[det.length + delay - va_delay :] + + # Plot cumulative errors over time and log error metrics + for detector_type, output_bits in output_bits_dict.items(): + # Align input and output bitstreams, count errors, calculate error rate, plot errors + min_size = min(len(input_bits), len(output_bits)) t = np.linspace(0, min_size - 1, num=min_size) - (sym_err_idx,) = np.where( - iter_va_output_symbols[:min_size] - aligned_symbols[:min_size] - ) - (bit_err_idx,) = np.where(iter_va_output_bits[:min_size] - bit_array[:min_size]) - log_msg = ( - f"SOQPSK-{label} {detector_type}: " - f"Eb/N0 = {ebn0_calc:.2f} dB, " - f"SER = {len(sym_err_idx)/min_size:.3E} " - f"BER = {len(bit_err_idx)/min_size:.3E}" - ) + bit_err_idx = np.where(output_bits[:min_size] - input_bits[:min_size])[0] + ber = len(bit_err_idx) / min_size + + # Handle inverted output (frame sync is responsible for this) + if ber > (1 - ber): + ber = 1 - ber + output_bits[:] = 1 - output_bits[:] + bit_err_idx = np.where(output_bits[:min_size] - input_bits[:min_size])[0] + + # Log BER and plot cumulative errors + log_msg = f"SOQPSK-{label} {detector_type}: Eb/N0 = {ebn0:.2f} dB, BER = {ber:.3e}" _logger.info(log_msg) errors_ax.plot( t[bit_err_idx], np.cumsum(np.ones(bit_err_idx.shape)), marker="x", - label=detector_type, - ) - - # Plot Rho pulses used for PAM Approximation - for k, rho_k, fmt in zip(range(k_max), rho, ("b-", "g--")): - t = np.linspace(0, (rho_k.size - 1) / sps, num=rho_k.size) - rho_ax.plot( - t, - rho_k, - fmt, - label=rf"SOQPSK-{label} $\rho_{k}(t)$", + label=f"{detector_type} (BER = {ber:.3e})", ) - rho_ax.set_xlim(0, (max(rho, key=np.size).size - 1) / sps) - for ax in iq_axes[0, :]: ax: Axes - ax.set_xlim([100, 130]) + ax.grid(which="both", linestyle=":") + ax.set_xlim([t_min, t_max]) + ax.set_ylim([-4, 4]) ax.legend(loc="upper center", fontsize=8, ncols=4) ax.xaxis.set_major_locator(MultipleLocator(5)) ax.xaxis.set_minor_locator(MultipleLocator(1)) - for psd_ax in iq_axes[1, :]: + for ax in iq_axes[1, :]: + ax: Axes + ax.set_xlim([t_min, t_max]) + ax.set_ylim([-sps * 2, sps * 2]) + ax.legend(loc="upper center", fontsize=8, ncols=3) + ax.xaxis.set_major_locator(MultipleLocator(5)) + ax.xaxis.set_minor_locator(MultipleLocator(1)) + + for psd_ax in iq_axes[2, :]: psd_ax.set_title("Power Spectral Density") psd_ax.set_ylabel("Amplitude [dBc]") psd_ax.set_xlabel("Normalized Frequency [$T_b$ = 1]") @@ -251,10 +408,6 @@ psd_ax.xaxis.set_major_locator(MultipleLocator(0.5)) psd_ax.grid(which="both", linestyle=":") - for rho_ax in iq_axes[2, :]: - rho_ax.grid(which="both", linestyle=":") - rho_ax.legend() - for ax in iq_axes[3, :]: ax.grid(which="both", linestyle=":") ax.set_ylabel("Cumulative Bit Errors") @@ -263,6 +416,27 @@ ax.set_xlim(0, symbols.size - 1) ax.legend(loc="upper left", fontsize=8, ncol=1) + # Create and format constellation axis + fig_const, ax_const = plt.subplots(1, figsize=(5, 5), dpi=100) + ax_const.set_xlim([-1.5, +1.5]) + ax_const.set_ylim([-1.5, +1.5]) + ax_const.xaxis.set_major_locator(MultipleLocator(1)) + ax_const.xaxis.set_minor_locator(MultipleLocator(0.25)) + ax_const.yaxis.set_major_locator(MultipleLocator(1)) + ax_const.yaxis.set_minor_locator(MultipleLocator(0.25)) + + plot_constellation( + signal=np.array(constellation_out, dtype=np.complex128), + n=8192, + axis=ax_const, + linestyle=" ", + marker="s", + markersize=1, + color="b", + ) + ax_const.set_title(f"SOQPSK SxS I&D Constellation ($E_b/N_0 = {ebn0:.1f}$ dB)") + + images_dir = Path(__file__).parent.parent / "images" fig_eye.tight_layout() - fig_eye.savefig(Path(__file__).parent.parent / "images" / "soqpsk_pam.png") + fig_eye.savefig(images_dir / "soqpsk_detection.png") plt.show() diff --git a/examples/soqpsk_pam.py b/examples/soqpsk_pam.py new file mode 100644 index 0000000..4e2bba0 --- /dev/null +++ b/examples/soqpsk_pam.py @@ -0,0 +1,293 @@ +from __future__ import annotations + +import logging +from pathlib import Path +from typing import TYPE_CHECKING + +import matplotlib.pyplot as plt +import numpy as np +from matplotlib.ticker import MultipleLocator + +from waveforms.cpm.modulate import cpm_modulate +from waveforms.cpm.pamapprox import rho_pulses +from waveforms.cpm.soqpsk import ( + freq_pulse_soqpsk_mil, + freq_pulse_soqpsk_tg, +) +from waveforms.cpm.trellis.encoder import TrellisEncoder +from waveforms.cpm.trellis.model import ( + SOQPSKTrellis4x2DiffEncoded, +) +from waveforms.glfsr import PNSequence +from waveforms.viz import plot_constellation + + +if TYPE_CHECKING: + from matplotlib.axes import Axes + from numpy.typing import NDArray + + +# Set seeds so iterations on implementation can be compared better +rng = np.random.Generator(np.random.PCG64(seed=1)) + + +# PRBS sequence +PN_DEGREE = 13 +DATA_GEN = PNSequence(PN_DEGREE) +DATA_BUFFER = np.packbits(DATA_GEN.generate_sequence()) + + +# Logger +_logger = logging.getLogger(__name__) + + +if __name__ == "__main__": + logging.basicConfig(level=logging.INFO) + + # Constants + sps = 10 + pam_use_superposition = False # Switch between two equivalent methods of PAM superposition + theoretical_nsme = { # From E. Perrins Thesis, pg51 + "MIL": 0, + "TG": 4.26e-3, + } + + # Bits of information to transmit + bit_array = np.unpackbits(DATA_BUFFER) + + # Convert bits to symbols + symbol_precoder = TrellisEncoder(SOQPSKTrellis4x2DiffEncoded) + symbols = symbol_precoder(bit_array) + + # Create plots and axes + fig_eye, iq_axes = plt.subplots(3, 2, figsize=(12, 8), dpi=100) + + # Generate pseudo-symbols + pseudo_symbols = np.array( + [ + [-1j, 1, 1j], + [np.sqrt(2) / 2 * (1 - 1j), np.sqrt(2) / 2, np.sqrt(2) / 2 * (1 + 1j)], + ], + dtype=np.complex128, + ) + + # Simulate the following SOQPSK Waveforms + pulses_colors_labels = ( + (freq_pulse_soqpsk_mil(sps=sps), "MIL", 1 / 4), + (freq_pulse_soqpsk_tg(sps=sps), "TG", 1 / 4), + ) + for i, (pulse_filter, label, mod_index) in enumerate(pulses_colors_labels): + # Assign axes + iq_ax: Axes = iq_axes[0, i] + rho_ax: Axes = iq_axes[1, i] + mf_ax: Axes = iq_axes[2, i] + + # Modulate the input symbols + normalized_time, modulated_signal = cpm_modulate( + symbols=symbols, + mod_index=mod_index, + pulse_filter=pulse_filter, + sps=sps, + ) + modulated_signal[:] *= np.exp(+1j * np.pi / 4) + + # Display transmitted and received signal in the time domain + iq_ax.plot( + normalized_time, + modulated_signal.real, + "b-", + alpha=1.0, + label=r"CPM-I", + marker="o", + markersize=5, + markevery=(int(sps / 2), sps), + ) + iq_ax.plot( + normalized_time, + modulated_signal.imag, + "r-", + alpha=1.0, + label=r"CPM-Q", + marker="o", + markersize=5, + markevery=(int(sps / 2), sps), + ) + + pulse_ax = iq_ax.twinx() + pulse_ax.stem( + normalized_time[sps::sps], + symbols / 2, + bottom=0, + markerfmt="ko", + linefmt="k-", + basefmt="k", + label="Symbol", + ) + pulse_ax.set_ylim(-np.pi / 2, np.pi / 2) + + # Pulse Truncation Filters + L = int(pulse_filter.size / sps) + truncation = 1 + q = np.cumsum(pulse_filter) / sps + pt_start = int((L - truncation) * sps / 2) + pt_end = int((L + truncation) * sps / 2) + 1 + truncated_phase_pulse = q[pt_start:pt_end] + + # PAM De-composition rho pulses/matched filters + rho = rho_pulses(pulse_filter, mod_index, sps, k_max=2) + d_max = max([rho_k.size for rho_k in rho]) + k_max, num_symbols = pseudo_symbols.shape + + # Plot Rho pulses used for PAM Approximation + for k, rho_k, fmt in zip(range(k_max), rho, ("b-", "g--")): + t = np.linspace(0, (rho_k.size - 1) / sps, num=rho_k.size) + rho_ax.plot( + t, + rho_k, + fmt, + label=rf"SOQPSK-{label} $\rho_{k}(t)$", + ) + + rho_ax.set_xlim(0, (max(rho, key=np.size).size - 1) / sps) + + # Plot the matched filters + matched_filters: list[NDArray[np.complex128]] = [] + t = np.linspace(0, (d_max - 1) / sps, num=d_max) + for j in range(num_symbols): + matched_filter = np.zeros(d_max, dtype=np.complex128) + for k in range(k_max): + matched_filter[: rho[k].size] += np.conj(pseudo_symbols[k][j]) * rho[k] + + # Descending linewidth so we can see overlapping filter components + (line,) = mf_ax.plot( + t, + matched_filter.real, + label=rf"$H_{{{j-1:+}}}(t)$", + linestyle="-", + linewidth=3 - j, + ) + mf_ax.plot( + t, + matched_filter.imag, + linestyle="--", + linewidth=3 - j, + color=line.get_color(), + ) + matched_filters.append(matched_filter) + + # Re-construct signal from PAM pulses following Laurent Decomposition principles + # Cumulative phase state from symbol + phase_index = np.cumsum(np.concatenate([[2], symbols], dtype=np.int32)) + phase_state = np.exp(1j * phase_index * np.pi / 4).round() + + # CPM signal approximation by superposition of PAM pulses + # First symbol at index sps, zero-padded to sps, same as cpm_modulate + if pam_use_superposition: + pam_approx = np.zeros(len(symbols + 1) * sps + d_max + 1, dtype=np.complex128) + + # Account for delay of L / 2 due to filter peak being centered across L*sps samples + pam_delay = int(sps * L // 2) + truncate = sps * L + 2 + + for idx, symbol in enumerate(symbols, start=1): + symbol_idx = int(symbol / 2) + 1 + pam_approx[idx * sps : idx * sps + d_max] += ( + phase_state[idx - 1] * matched_filters[symbol_idx].conj() + ) + + else: + # Convolution of rho[k] against an array of pseudo symbols zero-filled to sps + num_points = (symbols.size + 1) * sps + pseudo_symbols_interpolated = np.zeros((k_max, num_points), dtype=np.complex128) + pam_approx = np.zeros(num_points, dtype=np.complex128) + symbol_indicies = (symbols / 2 + 1).astype(np.int8) + + pam_delay = 0 + truncate = 0 + conv_delay = int(sps // 2) + + for k in range(k_max): + delay = int((d_max - rho[k].size) / 2) + pseudo_symbols_interpolated[k, sps - delay : -1 - delay : sps] = ( + np.take(pseudo_symbols[k], symbol_indicies) * phase_state[:-1] + ) + pam_approx[conv_delay:] += np.convolve( + pseudo_symbols_interpolated[k, :-conv_delay], + rho[k], + mode="same", + ) + + # Plot PAM Approximation + pam_approx = pam_approx[pam_delay : -truncate or None] + pam_approx_error = np.power( + np.abs(pam_approx[:] - modulated_signal[: pam_approx.size]), + 2, + )[d_max:-d_max] # Crop "incomplete" approximated symbols. + nmse = pam_approx_error.sum() / pam_approx_error.size + msg = f"Calculated NMSE = {nmse:.3e}. " f"Theoretical NMSE = {theoretical_nsme[label]:.3e}." + _logger.info(msg) + + iq_ax.plot( + normalized_time[: -pam_delay or None], + pam_approx.real, + "b--", + alpha=0.5, + linewidth=3, + label=rf"PAM-I ($k_{{max}}={k_max}$)", + ) + iq_ax.plot( + normalized_time[: -pam_delay or None], + pam_approx.imag, + "r--", + alpha=0.5, + linewidth=3, + label=rf"PAM-Q ($k_{{max}}={k_max}$)", + ) + + for ax in iq_axes[0, :]: + ax: Axes + ax.grid(which="both", linestyle=":") + ax.set_xlim([0, 30]) + ax.legend(loc="upper center", fontsize=8, ncols=4) + ax.xaxis.set_major_locator(MultipleLocator(5)) + ax.xaxis.set_minor_locator(MultipleLocator(1)) + ax.set_ylim([-3, 3]) + + for rho_ax in iq_axes[1, :]: + rho_ax.grid(which="both", linestyle=":") + rho_ax.legend() + + for mf_ax in iq_axes[2, :]: + mf_ax.grid(which="both", linestyle=":") + mf_ax.legend() + + qpsk_esque_signal = np.zeros_like(pam_approx) + pam_approx[:] *= np.exp(1j * np.pi / 4) + qpsk_esque_signal[sps:] += pam_approx.real[:-sps] + qpsk_esque_signal[:] += pam_approx.imag * 1j + + # Create and format constellation axis + fig_const, ax_const = plt.subplots(1, figsize=(5, 5), dpi=100) + ax_const.set_xlim([-2, 2]) + ax_const.set_ylim([-2, 2]) + ax_const.xaxis.set_major_locator(MultipleLocator(1)) + ax_const.xaxis.set_minor_locator(MultipleLocator(0.25)) + ax_const.yaxis.set_major_locator(MultipleLocator(1)) + ax_const.yaxis.set_minor_locator(MultipleLocator(0.25)) + ax_const.set_title("SOQPSK PAM Approximation Constellation") + + plot_constellation( + signal=qpsk_esque_signal[:: sps * 2][L:-L], + n=8192, + axis=ax_const, + linestyle=" ", + marker="s", + color="g", + ) + + images_dir = Path(__file__).parent.parent / "images" + fig_eye.tight_layout() + fig_eye.savefig(images_dir / "soqpsk_laurent_decomp.png") + fig_const.tight_layout() + fig_const.savefig(images_dir / "soqpsk_pam_k2_constellation.png") + plt.show() diff --git a/images/soqpsk_detection.png b/images/soqpsk_detection.png new file mode 100644 index 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100644 --- a/waveforms/cpm/soqpsk/__init__.py +++ b/waveforms/cpm/soqpsk/__init__.py @@ -1,9 +1,33 @@ -from .precoder import SOQPSKPrecoder +from .precoder import ( + RecursiveDD, + RecursiveDE, + SOQPSKDifferentialDecoder, + SOQPSKDifferentialEncoder, + SOQPSKRecursivePrecoder, + SOQPSKStandardPrecoder, +) from .pulse_filters import ( SOQPSK_DENOM, SOQPSK_NUMER, - freq_pulse_soqpsk_a, + freq_pulse_soqpsk, freq_pulse_soqpsk_b, freq_pulse_soqpsk_mil, freq_pulse_soqpsk_tg, ) + + +__all__ = [ + "SOQPSK_DENOM", + "SOQPSK_NUMER", + "RecursiveDD", + "RecursiveDE", + "SOQPSKDifferentialDecoder", + "SOQPSKDifferentialEncoder", + "SOQPSKRecursivePrecoder", + "SOQPSKStandardPrecoder", + "freq_pulse_soqpsk", + "freq_pulse_soqpsk_a", + "freq_pulse_soqpsk_b", + "freq_pulse_soqpsk_mil", + "freq_pulse_soqpsk_tg", +] diff --git a/waveforms/cpm/soqpsk/precoder.py b/waveforms/cpm/soqpsk/precoder.py index 8e9eb04..8d1aa7b 100644 --- a/waveforms/cpm/soqpsk/precoder.py +++ b/waveforms/cpm/soqpsk/precoder.py @@ -2,9 +2,101 @@ from numpy.typing import NDArray -class SOQPSKPrecoder: +class RecursiveDE: def __init__(self) -> None: - self.i = 0 + self.memory = 0, 0 + + def __call__(self, bits: NDArray[np.uint8]) -> NDArray[np.uint8]: + """Recursive diff encoder.""" + out = np.zeros(len(bits) + 2, dtype=np.uint8) + out[:2] = self.memory + for i in range(2, len(bits) + 1): + out[i] = bits[i - 2] ^ out[i - 2] + self.memory = out[-2:] + return out[2:] + + +class RecursiveDD: + def __init__(self) -> None: + self.memory = 1, 0 + + def __call__(self, bits: NDArray[np.uint8]) -> NDArray[np.uint8]: + """Recursive diff encoder.""" + out = np.zeros(len(bits), dtype=np.uint8) + inp = np.concatenate((self.memory, bits), dtype=np.int8) + for i in range(len(bits)): + out[i] = inp[i + 2] ^ inp[i] + self.memory = inp[-2:] + return out + + +class SOQPSKDifferentialEncoder: + def __init__(self) -> None: + self.out_mem = 1, 1 + self.in_mem = 0 + + def __call__(self, bits: NDArray[np.uint8]) -> NDArray[np.int8]: + """SOQPSK Differential Encoder. + + From IRIG 106 Chapter 2 2-22: + 𝛿̅[2i] = b[2i] βŠ• 𝛿̅[2i-1] βŠ• 1 + 𝛿̅[2i+1] = b[2i+1] βŠ• 𝛿̅[2i] + + Simplified: + 𝛿̅[i] = b[i] βŠ• b[i-1] βŠ• 𝛿̅[i-2] βŠ• 1 + + Args: + bits (NDArray[np.uint8]): Input bit sequence. + + Returns: + NDArray[np.unt8]: Output bits. + + """ + out = np.zeros(len(bits) + 2, dtype=np.int8) + out[:2] = self.out_mem + inp = np.concatenate(([self.in_mem], bits), dtype=np.int8) + for i in range(2, len(bits) + 1): + out[i] = inp[i - 1] ^ inp[i - 2] ^ out[i - 2] ^ 1 + self.in_mem = bits[-1] + self.out_mem = out[-2:] + return out[2:] + + +class SOQPSKDifferentialDecoder: + def __init__(self) -> None: + self.out_mem = 1 + self.in_mem = 0, 0 + + def __call__(self, bits: NDArray[np.uint8]) -> NDArray[np.uint8]: + """SOQPSK Differential Decoder. + + From IRIG 106 Chapter 2 2-23: + b[2i] = Ξ΄[2i] βŠ• 𝛿̅[2i-1] βŠ• 1 + b[2i+1] = Ξ΄[2i+1] βŠ• 𝛿̅[2i] + + Simplified: + b[i] = b[i-1] βŠ• 𝛿[i] βŠ• 𝛿̅[i-2] βŠ• 1 + + Args: + bits (NDArray[np.uint8]): Input bit sequence. + + Returns: + NDArray[np.int8]: Output bits. + + """ + out = np.zeros(len(bits) + 1, dtype=np.uint8) + out[0] = self.out_mem + inp = np.concatenate((self.in_mem, bits), dtype=np.int8) + for i in range(1, len(bits) + 1): + out[i] = out[i - 1] ^ inp[i + 1] ^ inp[i - 1] ^ 1 + self.in_mem = bits[-2:] + self.out_mem = out[-1] + return out[1:] + + +class SOQPSKStandardPrecoder: + def __init__(self) -> None: + self.i = 1 self.mem = 0, 0 def __call__(self, bits: NDArray[np.uint8]) -> NDArray[np.int8]: @@ -15,10 +107,35 @@ def __call__(self, bits: NDArray[np.uint8]) -> NDArray[np.int8]: Returns: NDArray[np.int8]: Output symbols. + """ a = np.concatenate((self.mem, bits), dtype=np.int8) i_arr = np.ones(bits.shape, dtype=np.int8) i_arr[self.i :: 2] = -1 self.i = (self.i + len(bits)) % 2 self.mem = a[-2:] - return i_arr * (2 * a[1:-1] - 1) * (a[:-2] - a[2:]) + return i_arr * (2 * a[1:-1] - 1) * (a[:-2] - a[2:]) * 2 + + +class SOQPSKRecursivePrecoder: + def __init__(self) -> None: + self.i = 0 + self.sign = 0 + + def __call__(self, bits: NDArray[np.uint8]) -> NDArray[np.int8]: + """Encodes bits to symbols when instance is called. + + Args: + bits (NDArray[np.uint8]): Input bit sequence. + + Returns: + NDArray[np.int8]: Output symbols. + + """ + out = np.zeros_like(bits, dtype=np.int8) + for i, bit in enumerate(bits): + out[i] = (-1) ** self.sign * bit * 2 + self.sign = (self.sign + out[i] / 2 + 1) % 2 + + self.i = (self.i + len(bits)) % 2 + return out diff --git a/waveforms/viz/constellation.py b/waveforms/viz/constellation.py index 937d7b0..31da5a0 100644 --- a/waveforms/viz/constellation.py +++ b/waveforms/viz/constellation.py @@ -1,42 +1,78 @@ from __future__ import annotations -from typing import TYPE_CHECKING +from typing import TYPE_CHECKING, TypedDict import matplotlib.pyplot as plt if TYPE_CHECKING: + from typing import Annotated, Unpack + import numpy as np + from annotated_types import Doc from matplotlib.axes import Axes from matplotlib.figure import Figure + from matplotlib.markers import MarkerStyle from numpy.typing import NDArray -def constellation( +_CONSTELLATION_DEFAULT_KWARGS = { + "alpha": 0.2, + "marker": "s", + "color": "b", +} + + +class Line2DKwargs(TypedDict): + linewidth: float | None = None + linestyle: str | None = None + color: str | None = None + gapcolor: str | None = None + marker: str | MarkerStyle | None = None + markersize: float | None = None + markeredgewidth: str | None = None + markeredgecolor: str | None = None + markerfacecolor: str | None = None + markerfacecoloralt: str = "none" + fillstyle: str | None = None + antialiased: bool | None = None + dash_capstyle: str | None = None + solid_capstyle: str | None = None + dash_joinstyle: str | None = None + solid_joinstyle: str | None = None + pickradius: int = 5 + drawstyle: str = "default" + markevery: Annotated[ + int | tuple[int, int] | slice | list[int] | list[bool] | float | tuple[float, float] | None, + Doc( + "See: https://matplotlib.org/stable/gallery/lines_bars_and_markers/markevery_demo.html" + ), + ] = None + + +def plot_constellation( signal: NDArray[np.complex128], n: int = 1024, - color: str | None = None, axis: Axes | None = None, + **plot_kwargs: Unpack[Line2DKwargs], ) -> Figure: """Plots a constellation (In-phase vs Quadrature) graph. Args: signal: complex time-domain input signal. n: number of samples to plot (default=1024). - color: Color of the lines and points. axis: Optional axis if new figure is not desired. + plot_kwargs: Additional kw arguments for axis.plot(...). Returns: Figure of plotted constellation. """ axis = axis or plt.subplots(1)[-1] - axis.plot( - signal.real[:n], - signal.imag[:n], - color=color, - alpha=0.2, - marker="o", - ) + + for key, value in _CONSTELLATION_DEFAULT_KWARGS.items(): + plot_kwargs[key] = plot_kwargs.get(key, value) + + axis.plot(signal.real[:n], signal.imag[:n], **plot_kwargs) axis.set_title("Constellation") axis.set_ylabel("Quadrature [V]") axis.set_xlabel("In-phase [V]")