Nonlinear Beamforming via Convex Optimization for Phased Array Weather Radar

In this paper, we propose a nonlinear beamforming method for a phased array weather radar (PAWR). Conventional beamforming methods are linear in the sense that a signal arriving from each elevation is reconstructed by computing a weighted sum of the received signals. For distributed targets such as raindrops, however, the number of backscattered signals is very large differently from the case for point targets. Thus, the spatial resolution of the linear methods is limited. To improve the spatial resolution, we focus on two characteristics of the signals from the distributed targets. One is the continuity of the reflection intensity in the time and spatial domains. The other is the narrow bandwidth in the frequency domain. These can be expressed as group-sparsity of certain matrices, and we reconstruct the signals by solving a convex optimization problem based on the group-sparsity. Simulations using real PAWR data show that the proposed method captures fine variation of precipitation profile with high precision.