Sparse Array Design for Adaptive Beamforming via Semidefinite Relaxation

In this letter, we propose a sparse array design method for adaptive beamforming in the presence of interferences. Our solution is based on finding the beamformer weight vector such that maximum output signal-to-interference-plus-noise ratio is attained. To control the sidelobes of the beampattern, quadratic fractional constraints are also introduced to optimize the beamformer weights. We formulate the array design problem as real-valued quadratically constrained quadratic program (QCQP) with reweighted $l_1$-norm to promote sparsity. Moreover, we adopt semidefinite relaxation (SDR) and linear fractional SDR together to solve the QCQP problem. The resulting array yields excellent beamforming performance and a beampattern with low sidelobes. Numerical results demonstrate the effectiveness of the proposed sparse array design.

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