Two-dimensional transmit beamforming for MIMO radar with sparse symmetric arrays

Multiple-input multiple-output (MIMO) radar using one-dimensional transmit arrays has been thoroughly investigated in the literature. In this paper, we consider the MIMO radar problem in the context of two-dimensional (2D) transmit arrays. In particular, we address the problem of transmit beamforming design using 2D arrays with symmetrically missing elements. This situation is encountered in practice when some of the array elements are assigned for a different purpose, e.g., for communication purposes. We cast the transmit beamforming problem as an optimization problem that minimizes the difference between a desired transmit beampattern and the actual one while satisfying constraints such as uniform transmit power across the array elements, sidelobe level control, etc. Moreover, different transmit beams can be enforced to have rotational invariance with respect to each other, a property that enables efficient computationally cheap 2D direction finding at the receiver. Semi-definite relaxation is used to recast the optimization problem as a convex one that can be solved efficiently using the interior point optimization methods. Simulations are used to validate the proposed method.