import logging from datetime import datetime import numpy as np import numpy.typing as npt from ..config import config logger = logging.getLogger(__name__) class AoA: def __init__(self) -> None: self.historical_autocorr = np.array([]) self.N_subcarriers = -1 self.N_rx = -1 self.timestamp = datetime.now() pass def smooth(self, data: npt.NDArray[np.complex128]) -> npt.NDArray[np.complex128]: assert len(data.shape) == 3 M = data.shape[0] # Number of subcarriers N = data.shape[1] # Number of RX antennas T = data.shape[2] # Number of TX antennas self.N_subcarriers = M self.N_rx = N logger.debug(f"Smoothing: Subcarriers: {M}, RX antennas: {N}, TX antennas: {T}") # This only works with 1 TX antenna (i.e. no MIMO) - see #4 for more details assert T == 1, "The current implementation only supports 1 TX antenna" H_n = np.zeros((N, M // 2, M // 2 + 1), dtype=np.complex128) for i in range(N): for j in range(M // 2): H_n[i, j] = data[j : j + M // 2 + 1, i, 0] H_sm_rows = [np.hstack(H_n[i : i + N // 2 + 1]) for i in range(N // 2)] H_sm = np.vstack(H_sm_rows) logger.debug(f"Smoothed: {H_sm.shape}") return H_sm def update(self, data: npt.NDArray[np.complex128]) -> None: self.timestamp = datetime.now() H_sm = self.smooth(data) auto_corr = np.matmul(H_sm, np.conj(H_sm).T) # This matrix is by definition Hermitian. # Therefore, all of its eigenvectors are orthogonal. if self.historical_autocorr.size == 0: self.historical_autocorr = np.expand_dims(auto_corr, 0) else: self.historical_autocorr = np.append( self.historical_autocorr, np.expand_dims(auto_corr, 0), axis=0 ) WINDOW_SIZE = config.music.window_size if self.historical_autocorr.shape[0] > WINDOW_SIZE: self.historical_autocorr = self.historical_autocorr[-WINDOW_SIZE:] # Is the moving average also Hermitian? R = np.mean(self.historical_autocorr, axis=0) # The smallest eigenvectors span the noise subspace, # and the largest span the signal subspace. eigvals, eigvecs = np.linalg.eigh(R) self.E_n = eigvecs[:, np.abs(eigvals) < config.music.eigval_threshold] def steering_vector( self, theta: float, tof: float ) -> npt.NDArray[np.complexfloating]: omega_t: npt.NDArray[np.complex128] = np.exp(-2j * np.pi * config.delta_f * tof) phi_theta: npt.NDArray[np.complex128] = np.exp( 2j * np.pi * config.central_freq_hz * config.antennas.spacing * (1 - np.cos(theta)) / 299_792_458 ) omega_t = np.expand_dims(omega_t, axis=-1) phi_theta = np.expand_dims(phi_theta, axis=-1) antenna_v = omega_t ** np.arange(self.N_subcarriers // 2) phis = phi_theta ** np.arange(self.N_rx // 2) antenna_v = np.expand_dims(antenna_v, axis=-1) steering = antenna_v * phis return steering.T.reshape(-1) def evaluate(self, theta: float, tof: float) -> float: try: steering = self.steering_vector(theta, tof) steering_h = np.conj(steering).T except Exception as e: logger.exception(e) return 0 E_n = self.E_n E_n_H = np.conj(E_n).T c = 1 / (0.001 + (steering_h @ E_n @ E_n_H @ steering)) return np.abs(c.real) def test_smoothing() -> None: row, col = np.indices((4, 2)) data = row + 1j * col aoa = AoA() smoothed = aoa.smooth(data) H_0 = np.array([[0 + 0j, 0 + 1j, 0 + 2j], [0 + 1j, 0 + 2j, 0 + 3j]]) H_01 = np.vstack([H_0, H_0 + 1]) H_12 = np.vstack([H_0 + 1, H_0 + 2]) expected = np.hstack([H_01, H_12]) print(expected) assert np.allclose(smoothed, expected) def test_steering_vector() -> None: aoa = AoA() aoa.N_subcarriers = 10 aoa.N_rx = 2 tau = 1 theta = 0 print(aoa.steering_vector(theta, tau)) assert False