Radar Waveform Design Using Lagrangian Dynamics for Co-Channel Interference Mitigation

In this paper, a novel radar waveform phase function design is presented that constructs a radar waveform that spectrally manuevers around in-band co-channel interference (CCI) from active communications users that are co-channel with the radar system. The design approach treats the CCI problem as the physical interpretable problem of optical refraction where the time-frequency (TF) signature of the radar waveform is made to be analogous to a light ray propagating from a start time and position (frequency) to an end time and position (frequency) and will naturally accelerate through the CCI as if the equivalent light ray accelerated in through different mediums (with an index of refraction related to CCI power spectral density (PSD)). Using the Euler-Lagrange equations, we design the radar phase function that is used to modulate a constant modulus (CM) waveform. The radar waveform design will generally result in a nonlinear-frequency modulated (NLFM) waveform that provides improved signal-to-interference-plus-noise-ratio (SINR) on a potential target in the presence of CCI leading to improved probability of detection performance. We provide theoretical analysis and simulation results for the proposed waveform design.