Range and Doppler processing

This page covers the range and Doppler stage of witwin.radar.processing. Frame.range_profile() and Frame.range_doppler() call these functions for you. Call them directly when you need the typed records in your own pipeline.

from witwin.radar.processing import ProcessingCube, RangeDopplerMap, RangeProfile, range_doppler_map, range_profile

Two conventions hold for every waveform:

• Amplitude. Each transform is amplitude normalized, so an isolated row on a bin peaks at abs(C) · window_coherent_gain, where C is its transfer coefficient and window_coherent_gain is the mean of the window.
• Doppler sign. A positive Doppler bin is a closing target. range_doppler_map is the only place the sign is reconciled with the cube's phasor.

Windows are named: "rectangular" (all ones), "hann", "hamming" and "blackman". None means rectangular.

ProcessingCube#

class ProcessingCube(data, axes)

A complex [TX, RX, slow, fast] tensor with the ProcessingAxes that describe it. Bare tensors are refused by range_profile, because the fast axis alone cannot tell an FMCW spectrum from a beat signal.

Get one with frame.processing_cube().

range_profile#

range_profile(cube, *, window=None, remove_dc=False) -> RangeProfile

Transform the fast axis to range. The method depends on cube.axes.waveform:

• FMCW: an FFT over fast time. For output="spectrum" the cube is already range-transformed, so only the rectangular window is accepted.
• OFDM: an inverse FFT over subcarriers, which gives the channel impulse response.
• Pulsed: a matched filter that correlates the train against the analytic pulse replica.

Returns RangeProfile.

Raises TypeError for a bare tensor. ValueError for a fast-time window on an FMCW spectrum cube or an unknown window name.

profile = range_profile(frame.processing_cube())
print(profile.data.shape, profile.range_axis[:3])

RangeProfile#

class RangeProfile(data, axes, window, window_coherent_gain)

Complex [..., C, R]: one range profile per slow-time sample.

range_doppler_map#

range_doppler_map(profile, *, window=None) -> RangeDopplerMap

Transform the slow axis to Doppler. The output is fftshifted and in the closing-positive convention for every waveform. The transform carries a 1 / D factor, so the coherent integration gain is not in the amplitude.

Returns RangeDopplerMap.

rd = range_doppler_map(range_profile(frame.processing_cube()), window="hann")
power = rd.data.abs().square().sum(dim=(0, 1))       # [doppler, range]
d, r = divmod(int(power.argmax()), power.shape[1])
print(float(rd.doppler_axis[d]), float(rd.range_axis[r]))

RangeDopplerMap#

class RangeDopplerMap(data, axes, window, window_coherent_gain)

Complex [..., D, R].

Both functions are differentiable; see Differentiability.