Sparse Array Design for Transmit Beamforming

Sparse arrays are favored due to their inherent capability of optimizing the hardware and computational resources in executing the prescribed performance. The main emphasis on sparse array design thus far has been from the perspective of sparse receiver optimization. In this paper, we examine sparse array design for transmit beamforming. The main task is to design the beamformer to direct the bulk of the transmitted power to target locations. This, in turn, enables improved receiver performance which strives to maximize the signal-to-interference plus noise ratio (MaxSINR) of the radar returns. In order to realize an environmental-dependent adaptive design, it is incumbent that the directed signals towards different targets are maximally mutually independent. The optimum sparse active array design problem is formulated as quadratically constraint quadratic program (QCQP) alongside the regularization term. The semidefinite relaxation (SDR) of QCQP is used to enhance the sparsity of the beamformer through iterative re-weighting based on prior iterations. It is shown that the proposed approach can efficiently utilize the available array aperture to achieve the desired transmitted beampattern characteristics.