Mutual Information based Co-Design for Coexisting MIMO Radar and Communication Systems

In this paper, we focus on the spectrum sharing between a colocated Multiple-Input Multiple-Output (MIMO) radar and MIMO communication system comprised of K users. Aiming to find the maximum data transmission strategy for communication and the optimal information extraction waveform for radar, we jointly maximize the sum-rate of the communication system and the mutual information (MI) between the target impulse response and the target echoes on radar system. The optimal solution is, simultaneously minimizing target parameter estimation error of radar and data estimation error of communication. However, the problem is non-convex and several variables are coupled, hence, the problem is NP-hard. Toward this end, we develop an alternating primal-dual subgradient ascent framework to efficiently find a sub-optimal solution. More specifically, the precoders and radar waveform are found iteratively through subgradient ascent on augmented Lagrange function. An optimal decoder for communication is found in a closed-form using Minimum Mean Square error criterion. To maintain Kronecker structure of radar decoder, it is obtained in a closed form approximation using joint generalized Rayleigh quotient and Kronecker product approximation. The simulation results show that interferences are suppressed efficiently by the jointly designed precoders and decoders. The total mutual information achieves a near linear growth with signal noise ratio increasing, especially in relative high SNR regime.