Radar and Communication Spectral Coexistence in Range-Dependent Interference

In this paper, we investigate the spectral coexistence between a multiple-input multiple-output (MIMO) communication system and a MIMO radar which inspects multiple range gates with non-homogeneous interference. We consider two formulations for joint resource allocation, aiming at minimizing the inverse of the harmonic mean of the signal-to-interference-plus noise ratio (SINR) across the range gates inspected by the radar under a constraint on the communication mutual information or at minimizing a properly-weighted difference between the inverse of the harmonic mean of the SINR's and the mutual information, respectively. The degrees of freedom for system design are the radar probing signal, the radar receive filters at each range gate, and the communication codebook, under the usual constraints on the transmit power and on the similarity of the radar waveform to a reference signal. We derive a sub-optimal procedure that allows to decompose the non-convex optimizations at the hand into a sequence of simpler sub-problems. Numerical examples are provided to assess the merits of the proposed solutions.