Co-Design for Overlaid MIMO Radar and Downlink MISO Communication Systems via Cramér–Rao Bound Minimization

This paper considers the problem of co-existence of collocated multiple-input multiple-output (MIMO) radar and downlink multiple-input single-output (MISO) communication systems, which share the same frequency band. As the interference caused by the communication systems would degrade the accuracy of radar target localization, we formulate the co-design of radar waveform and communication transmit weights by minimizing the Cramér-Rao Bound (CRB) of direction-of-arrival (DOA) estimation, subject to a set of constraints accounting for the worst-case signal-to-noise-plus-interference ratio (SINR), similarity and energy. However, the objective is nonconvex and all variables are coupled together in the SINR constraints, the formulated problem is thus NP-hard. Towards that end, a decentralized block successive upper-bound minimization (D-BSUM) method based on the decomposition theory is developed. More specifically, at each iteration of this algorithm, the radar waveform is obtained with the aid of the alternating direction method of multipliers (ADMM) algorithm, and communication weights are obtained by exploiting the semidefinite programs (SDP). It is also proved that the proposed SDP-based method gives a rank-one solution. Numerical simulations are conducted to evaluate the effectiveness of the proposed algorithm.