Wideband frequency-invariant beamforming with dynamic range ratio constraints

Abstract

This paper focuses on the optimization design of weighting coefficients of Frost-structural beamformer to obtain a frequency-invariant (FI) beampattern. To ensure the normal operation of beamformer in transmitting links with limited dynamic range, the design is modeled by minimizing the weighted sum of the beampattern matching error and spatial response variation under the constraints of dynamic range ratio (DRR) and linear phase. Next, we propose a novel iterative algorithm to solve the resulting high-dimensional non-convex optimization problems via alternately handling a tractable problem and a multi-constrained convex subproblem. To speed up, we reformulate this multi-constrained subproblem into a new alternating direction method of multipliers form with a series of low-dimensional and less-constrained subproblems, and deduce the closed-form solutions to each subproblem. Numerical results exhibit the good convergence of proposed algorithm and the excellent FI of obtained beampattern under the DRR constraints.