Antenna Selection and Receive Beamforming for Multi-Functional Sparse Linear Array via Consensus ADMM

Multi-functional antenna array has an ability to significantly simplify the antenna system in multi-functional radar or communication systems since it can work in multiple frequency bands simultaneously. To further reduce the system overhead, such as RF front-ends and digital processing channels, this paper discusses the joint design of antenna selection and receive beamforming for multi-functional antenna arrays. With the assistance of a RF switch network, $K$ antennas selected from an $N$-element linear array ($K< N$) only require $K$ RF front-ends and digital processing channels. To maximize the output signal-to-interference-plus-noise ratio (SINR) and control the sidelobe levels concurrently, the proposed multi-functional sparse array design can be formulated into a nonconvex constrained optimization problem with a $l_{2,0}$-mixed norm regularization. This problem ensures that the selected antenna positions are the same in all operating frequency bands while the beamforming weights of each frequency band are jointly optimized. In virtue of the consensus alternating direction method of multipliers (CADMM) and reweighted $l_{2,1}$-norm approximation techniques, a CADMM-based iteratively reweighted algorithm is proposed to handle this problem effectively, where the original problem is converted into a series of subproblems whose optimal solutions are all readily obtained. The convergence and computational complexity are also analysed. Numerical results show that the proposed multi-functional sparse array remarkably reduces the sidelobe level in all operating frequency bands concurrently while maintains the maximum output SINR, and thus has superior performance on interference suppression.