""" Some of the functions defined here were ported directly from CuSignal under terms of the MIT license, under the following notice: Copyright (c) 2019-2023 NVIDIA CORPORATION & AFFILIATES. All rights reserved. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ import cupy from cupyx.scipy.signal import windows def _pulse_preprocess(x, normalize, window): if window is not None: n = x.shape[-1] if callable(window): w = window(cupy.fft.fftfreq(n).astype(x.dtype)) elif isinstance(window, cupy.ndarray): if window.shape != (n,): raise ValueError("window must have the same length as data") w = window else: w = windows.get_window(window, n, False).astype(x.dtype) x = x * w if normalize: x = x / cupy.linalg.norm(x) return x def pulse_compression(x, template, normalize=False, window=None, nfft=None): """ Pulse Compression is used to increase the range resolution and SNR by performing matched filtering of the transmitted pulse (template) with the received signal (x) Parameters ---------- x : ndarray Received signal, assume 2D array with [num_pulses, sample_per_pulse] template : ndarray Transmitted signal, assume 1D array normalize : bool Normalize transmitted signal window : array_like, callable, string, float, or tuple, optional Specifies the window applied to the signal in the Fourier domain. nfft : int, size of FFT for pulse compression. Default is number of samples per pulse Returns ------- compressedIQ : ndarray Pulse compressed output """ num_pulses, samples_per_pulse = x.shape dtype = cupy.result_type(x, template) if nfft is None: nfft = samples_per_pulse t = _pulse_preprocess(template, normalize, window) fft_x = cupy.fft.fft(x, nfft) fft_t = cupy.fft.fft(t, nfft) out = cupy.fft.ifft(fft_x * fft_t.conj(), nfft) if dtype.kind != 'c': out = out.real return out def pulse_doppler(x, window=None, nfft=None): """ Pulse doppler processing yields a range/doppler data matrix that represents moving target data that's separated from clutter. An estimation of the doppler shift can also be obtained from pulse doppler processing. FFT taken across slow-time (pulse) dimension. Parameters ---------- x : ndarray Received signal, assume 2D array with [num_pulses, sample_per_pulse] window : array_like, callable, string, float, or tuple, optional Specifies the window applied to the signal in the Fourier domain. nfft : int, size of FFT for pulse compression. Default is number of samples per pulse Returns ------- pd_dataMatrix : ndarray Pulse-doppler output (range/doppler matrix) """ num_pulses, samples_per_pulse = x.shape if nfft is None: nfft = num_pulses xT = _pulse_preprocess(x.T, False, window) return cupy.fft.fft(xT, nfft).T def cfar_alpha(pfa, N): """ Computes the value of alpha corresponding to a given probability of false alarm and number of reference cells N. Parameters ---------- pfa : float Probability of false alarm. N : int Number of reference cells. Returns ------- alpha : float Alpha value. """ return N * (pfa ** (-1.0 / N) - 1) def ca_cfar(array, guard_cells, reference_cells, pfa=1e-3): """ Computes the cell-averaged constant false alarm rate (CA CFAR) detector threshold and returns for a given array. Parameters ---------- array : ndarray Array containing data to be processed. guard_cells_x : int One-sided guard cell count in the first dimension. guard_cells_y : int One-sided guard cell count in the second dimension. reference_cells_x : int one-sided reference cell count in the first dimension. reference_cells_y : int one-sided reference cell count in the second dimension. pfa : float Probability of false alarm. Returns ------- threshold : ndarray CFAR threshold return : ndarray CFAR detections """ shape = array.shape if len(shape) > 2: raise TypeError('Only 1D and 2D arrays are currently supported.') mask = cupy.zeros(shape, dtype=cupy.float32) if len(shape) == 1: if len(array) <= 2 * guard_cells + 2 * reference_cells: raise ValueError('Array too small for given parameters') intermediate = cupy.cumsum(array, axis=0, dtype=cupy.float32) N = 2 * reference_cells alpha = cfar_alpha(pfa, N) tpb = (32,) bpg = ((len(array) - 2 * reference_cells - 2 * guard_cells + tpb[0] - 1) // tpb[0],) _ca_cfar_1d_kernel(bpg, tpb, (array, intermediate, mask, len(array), N, cupy.float32(alpha), guard_cells, reference_cells)) elif len(shape) == 2: if len(guard_cells) != 2 or len(reference_cells) != 2: raise TypeError('Guard and reference cells must be two ' 'dimensional.') guard_cells_x, guard_cells_y = guard_cells reference_cells_x, reference_cells_y = reference_cells if shape[0] - 2 * guard_cells_x - 2 * reference_cells_x <= 0: raise ValueError('Array first dimension too small for given ' 'parameters.') if shape[1] - 2 * guard_cells_y - 2 * reference_cells_y <= 0: raise ValueError('Array second dimension too small for given ' 'parameters.') intermediate = cupy.cumsum(array, axis=0, dtype=cupy.float32) intermediate = cupy.cumsum(intermediate, axis=1, dtype=cupy.float32) N = 2 * reference_cells_x * (2 * reference_cells_y + 2 * guard_cells_y + 1) N += 2 * (2 * guard_cells_x + 1) * reference_cells_y alpha = cfar_alpha(pfa, N) tpb = (8, 8) bpg_x = (shape[0] - 2 * (reference_cells_x + guard_cells_x) + tpb[0] - 1) // tpb[0] bpg_y = (shape[1] - 2 * (reference_cells_y + guard_cells_y) + tpb[1] - 1) // tpb[1] bpg = (bpg_x, bpg_y) _ca_cfar_2d_kernel(bpg, tpb, (array, intermediate, mask, shape[0], shape[1], N, cupy.float32(alpha), guard_cells_x, guard_cells_y, reference_cells_x, reference_cells_y)) return (mask, array - mask > 0) _ca_cfar_2d_kernel = cupy.RawKernel(r''' extern "C" __global__ void _ca_cfar_2d_kernel(float * array, float * intermediate, float * mask, int width, int height, int N, float alpha, int guard_cells_x, int guard_cells_y, int reference_cells_x, int reference_cells_y) { int i_init = threadIdx.x+blockIdx.x*blockDim.x; int j_init = threadIdx.y+blockIdx.y*blockDim.y; int i, j, x, y, offset; int tro, tlo, blo, bro, tri, tli, bli, bri; float outer_area, inner_area, T; for (i=i_init; i0 && j>0){ outer_area = intermediate[tro]-intermediate[tlo]- intermediate[bro]+intermediate[blo]; } else if (i == 0 && j > 0){ outer_area = intermediate[tro]-intermediate[bro]; } else if (i > 0 && j == 0){ outer_area = intermediate[tro]-intermediate[tlo]; } else if (i == 0 && j == 0){ outer_area = intermediate[tro]; } inner_area = intermediate[tri]-intermediate[tli]- intermediate[bri]+intermediate[bli]; T = outer_area-inner_area; T = alpha/N*T; mask[offset] = T; } } } ''', '_ca_cfar_2d_kernel') _ca_cfar_1d_kernel = cupy.RawKernel(r''' extern "C" __global__ void _ca_cfar_1d_kernel(float * array, float * intermediate, float * mask, int width, int N, float alpha, int guard_cells, int reference_cells) { int i_init = threadIdx.x+blockIdx.x*blockDim.x; int i, x; int br, bl, sr, sl; float big_area, small_area, T; for (i=i_init; i0){ big_area = intermediate[br]-intermediate[bl]; } else{ big_area = intermediate[br]; } small_area = intermediate[sr]-intermediate[sl]; T = big_area-small_area; T = alpha/N*T; mask[x] = T; } } ''', '_ca_cfar_1d_kernel')