Sparse MIMO Array Design Using Uplink-Downlink Duality and Hole-Free Zone Co-Array Sensing

In this paper, we consider sparse MIMO transceiver array design for joint sensing and communications. We aim to optimally design uplink and downlink sparse arrays by selecting two disjoint subsets of antennas from an underlying uniform linear array. We optimize the signal-to-interference plus noise ratio (SINR) while ensuring the sensing identifiability of a specified number of sources by constraining the related sum co-array to have a specified hole-free zone. By leveraging the uplink-downlink duality theory, it is shown that the uplink and downlink array design problems without any sensing constraints are equivalent, with the same subset of antennas being optimal both for uplink and downlink. However, since we desire non-overlapping subsets of antennas for uplink and downlink with a certain hole-free zone in the related sum co-array, the proposed non-convex optimization problem yields an interesting trade-off between uplink and downlink SINRs. Numerical simulations demonstrate that with the proposed convex relaxation method, we obtain near-Pareto optimal sparse arrays.