Synthesis of pattern reconfigurable sparse arrays via sequential convex optimizations for monopulse radar applications

In this paper, a new array synthesis approach is developed for the design of reconfigurable sparse arrays radiating sum and difference patterns. The proposed approach provides a significant reduction in the complexity of the beam forming network, which is fulfilled by reducing the number of antenna elements in the array and sharing some excitation weights for the sum and difference channels. An iterative scheme is used where the prescribed pattern response in the mainlobe is cast as a multi-convex problem at each step that the nonconvex lower bound constraint is relaxed while including a reweighted $l_{1} $l1-norm minimization based on the magnitudes of the elements. Thus a better performance of beam pattern (e.g. narrower 3-dB beamwidth, lower maximum sidelobe levels) and a smaller number of elements can be obtained compared with the case of uniformly spaced array. The practical array imperfections are also compensated in the optimization stage by using worst-case performance optimization technique. Numerical tests are presented and discussed to validate the versatility and effectiveness of the proposed approach.