Co-Designing Statistical MIMO Radar and In-band Full-Duplex Multi-User MIMO Communications

We present a spectral co-design of a statistical multiple-input-multiple-output (MIMO) radar and an in-band full-duplex (IBFD) multi-user MIMO (MU-MIMO) communications system both of which concurrently operate within the same frequency band. Prior works on MIMO-radar-MIMO-communications (MRMC) problem either focus on colocated MIMO radars and half-duplex/single-user MIMO communications, seek coexistence solutions, do not jointly design waveforms and receiver processing or omit practical system constraints. Here, we jointly design statistical MIMO radar waveform, uplink (UL)/downlink (DL) precoders, and receive filters. To this end, we employ a novel performance measure, namely compounded-and-weighted sum mutual information (CWSM), that is subjected to multiple practical constraints of UL/DL transmit power, UL/DL quality of service, and peak-to-average-power-ratio. We solve the resulting non-convex problem by incorporating block coordinate descent (BCD) and alternating projection (AP) methods in a single algorithmic framework called BCD-AP MRMC. We achieve this by exploiting the relationship between mutual information and weighted minimum mean-squared-error (WMMSE), which allows use of the Lagrange dual problem in finding closed-form solutions for precoders and radar waveform. Numerical experiments show that our proposed WMMSE-based method quickly achieves monotonic convergence, improves target detection by $6$-$13$% compared to conventional radar coding, and provides $8.3$-$30$% higher rate in IBFD MU-MIMO system than other precoding strategies.