Over-relaxed ADMM-based Unitary Adaptive Beamforming Scheme with Lobe-level Constraints

The performance of adaptive beamforming may degrade dramatically in a highly dynamic environment, because the directions of arrival (DOAs) of targets and interferences can change rapidly. To address this problem, we propose here to introduce additional mainlobe-level and sidelobe-level constraints in the design problem, with the goal to broaden the mainlobe and the nulls of the beampattern. However, the solution of the resulting optimization problem with non-convex constraints has high computational complexity. To reduce it, we propose to transform the complex-valued non-convex constrained optimization problem into a real-valued convex constrained one by performing a unitary transformation, which is suitable for centro-symmetric arrays (CSA). Then, the problem is decomposed into multiple unconstrained optimization sub-problems that can be solved iteratively using the standard alternating direction method of multipliers (S-ADMM) method. To improve further the convergence speed, we then develop an over-relaxed ADMM (OR-ADMM) by exploiting the principle of relaxation. Numerical simulation demonstrates the robustness and the convergence speed improvements of the proposed OR-ADMM in a highly dynamic environment.