Adaptive Sparse Array Beamformer Design by Regularized Complementary Antenna Switching

In this work, we propose a novel strategy of adaptive sparse array beamformer design, referred to as regularized complementary antenna switching (RCAS), to swiftly adapt both array configuration and excitation weights in accordance to the dynamic environment for enhancing interference suppression. In order to achieve an implementable design of array reconfiguration, the RCAS is conducted in the framework of regularized antenna switching, whereby the full array aperture is collectively divided into separate groups and only one antenna in each group is switched on to connect with the processing channel. A set of deterministic complementary sparse arrays with good quiescent beampatterns is first designed by RCAS and full array data is collected by switching among them while maintaining resilient interference suppression. Subsequently, adaptive sparse array tailored for the specific environment is calculated and reconfigured based on the information extracted from the full array data. The RCAS is devised as an exclusive cardinality-constrained optimization, which is reformulated by introducing an auxiliary variable combined with a piece-wise linear function to approximate the $l_0$-norm function. A regularization formulation is proposed to solve the problem iteratively and eliminate the requirement of feasible initial search point. A rigorous theoretical analysis is conducted, which proves that the proposed algorithm is essentially an equivalent transformation of the original cardinality-constrained optimization. Simulation results validate the effectiveness of the proposed RCAS strategy.