Phase-only transmit beampattern design for large phased array antennas with multi-point nulling

In this paper, we investigate the problem of the phase-only transmit beampattern design for phased array system with large antennas. The goal of this paper is to maximize the mainlobe gain while nulling in multiple interference directions and keeping the shape of mainlobe similar to the quiescent beampattern. To this end, we formulate our optimization problem by maximizing mainlobe gain under the constraints of constant modulus, nulling levels as well as similarity between the designed beampattern and the quiescent one. To solve the resultant problem, an efficient iterative algorithm based on alternating direction method of multipliers (ADMM) framework is proposed. Concretely, two auxiliary variables are first introduced to modify the original problem, and then the primal variable in the ADMM framework is updated by utilizing the majorization–minimization and proximal algorithms. In addition, to facilitate the low-cost implementation of the transmit beampattern, we consider the problem of the one-bit transmit beampattern design, and propose an efficient ADMM algorithm to solve this problem. Numerical simulations are provided to demonstrate the effectiveness of the proposed algorithms.