Dr. David Johnson Profile

Dr. David Johnson

at Australian Ctr for Field Robotics USYD

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Proceedings Article | 12 April 2021 Presentation + Paper

Millimetre wave ray tracing simulator with phase and beam effects using the Wigner distribution function

Jacob Mackay, David Johnson

Proceedings Volume 11745, 1174508 (2021) https://doi.org/10.1117/12.2585861

KEYWORDS: Wigner distribution functions, Ray tracing, Optical simulations, Extremely high frequency, Transmitters, Temporal coherence, Radar, Phased array optics, Modeling, Data modeling

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Scene reconstruction through simulation with millimetre wave radar can allow for autonomous perception in poor weather, but requires an accurate forward and inverse propagation model. Ray-based light-transport is computationally efficient but generally neglects wave effects relevant to millimetre imaging. Challenges of note are the temporal coherence of signals and resulting multi-path interference glint and fade; and the spatial coherence of antennas resulting in beam patterns and phased arrays. We propose Wigner phasor signal rendering, an enhanced geometric-optics simulation framework which includes spatial and temporal coherence for modelling the response of a scene for a given input signal. This method is based on the coherent summation of waves and the representation of a wavefront as rays of constant phase. By studying the phase-space representation of a signal in separable time and space and applying appropriate transforms for propagation and interaction, we find that ray-based transport and evaluation of the transport integral yields results capturing expected wave behaviour. Using the phase-space formulation we develop three concepts for coherent signal rendering. First, the antennas radiance function is described in both position and direction via its Wigner Distribution Function. This allows for accurate and simple modelling without the imposition of beam-width or side-lobe assumptions. Second, we introduce the concept of virtual elements, locations in the phase-space of phased-arrays which contribute no energy but carry information about interference. Third, we present phasor channels and coherence kernels as a way to evaluate temporal interference as a sum of relative phases without keeping a list of all interactions. We demonstrate the validity of our framework through simulation, comparisons against the incoherent case, and measured field data.

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