Phase-only beampattern synthesis for maximizing mainlobe gain via Riemannian Newton method

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Beampattern synthesis with phase-only weights is extensively utilized in phased-array systems due to the virtue of low-cost and high power efficiency. It is always a non-convex optimization problem having constant modulus constraints (CMCs) and the performance significantly depends on the employed solvers. This paper discusses the phase-only beampattern synthesis for maximizing the mainlobe gain with the constraints on the mainlobe ripple and the relative sidelobe level. As CMC is equivalent to a complex circle manifold, the proposed beampattern synthesis is considered as a manifold optimization problem, and then decomposed into several subproblems under the framework of manifold alternating direction method of multipliers (ADMM). In particular, the subproblem for updating phase-only weights is efficiently tackled by a second-order Riemannian Newton method, which has faster convergence speed and no requirement on line search compared to widely-used first-order Riemannian manifold methods. The explicit convergence condition is derived and the computational complexity is also analyzed. Numerical results show that the proposed method has better performance on the mainlobe gain and sidelobe control accuracy, or less computational cost compared to several representative approaches, such as convex relaxation, standard ADMM, Riemannian gradient descent-based ADMM and Riemannian conjugate gradient methods.