Cramér-Rao Bound and Antenna Selection Optimization for Dual Radar-Communication Design

We consider multi-input multi-output (MIMO) dual function radar communication (DFRC) systems, and design a transmit beamforming matrix that optimizes a weighted combination of the radar estimate Cramer-Rao bound (CRB) and the communication rate. A hybrid beamforming structure is considered, with fewer RF chains than antennas, to achieve the benefits of MIMO systems while maintaining low cost. However, such a structure may have a rank-deficient beamforming matrix, resulting in degraded estimation performance. We propose antenna selection as means to ensure a full-rank beamforming matrix, and also select the communication channels so that high communication rate can be achieved. A learning approach is employed to optimally select antennas and design the corresponding beamforming matrix. By leveraging a combination of softmax neural networks, the proposed solution is able to optimize the joint performance metric for a DFRC system.