The phase only beamforming synthesis via an accelerated coordinate descent method

Abstract

Phase-only (constant modulus) beamforming synthesis is a key issue in radar, communication and sonar systems. Due to the constant modulus constraint (CMC), the problem is non-convex and NP-hard. Most existing methods either indirectly solve the problem by relaxing with performance degrading, or by directly solve the problem in the high dimensional space with huge computational complexity. To address this problem, the low-complexity Accelerated Coordinate Descent (ACD) based method is proposed by directly solving the problem in the low dimensional space. First, the Coordinate Descent (CD) based method is proposed, where the high-dimensional problem is divided into multiple one-dimensional problems, to which the optimal solutions are found. Then, the ACD method is derived by the square iterative technique, which needs less computational complexity due to it only uses linear-complexity storage. Both the continuous and discrete phases are designed in the case of the uniform and random linear arrays. Compared with the existing methods, the proposed method achieves 4 dB beampattern sidelobe reduction and 1.5 magnitude complexity decreasing.