Harmonic mean SINR maximization in a cognitive radar with communication spectrum sharing

We investigate the shared spectrum access between a communication system and a radar which inspects multiple range gates with non-homogeneous interference. The degrees of freedom for system design are the radar waveform, the radar receive filters at each range gate, and the communication codebook. Assuming some cognition of the environment, we propose to maximize the harmonic mean of the signal-to-interference-plus-noise ratio across the range gates inspected by the radar under semi-definite constraints on the communication mutual information, the transmitted power, and the similarity of the radar code to a desired reference signal. Numerical examples are provided to assess the merits of the proposed solution.