Fast Pattern Synthesis for Large-Scale Time-Modulated Planar Arrays With a Novel Two-Stage Iterative Convex Optimization Method

Owing to the new design degree of freedom in the time dimension, the design variables for a time-modulated array synthesis problem usually include antenna element positions in a 3-D space, the ON–OFF time instant and duration time in each period, and probably will also include the amplitude and phase excitations. To improve the radiation pattern synthesis efficiency for large-scale time-modulated planar arrays (TMPAs), a novel two-stage iterative convex optimization (CVX) method is developed. The proposed method decomposes the complicated large-scale TMPAs optimization problem into two convex subarray optimization problems with much smaller scales. The switch-on time instant for each subarray is optimized in the first stage, while the radiation pattern of the entire array is further optimized in the second stage. Consequently, the time consumption for pattern synthesis is significantly reduced owing to a small number of optimization variables, which makes the proposed method especially attractive for real-time beamforming in large-scale arrays. Numerical example for a 10 000-element TMPA synthesis solution shows that high-precision scanning beams with low sidelobe levels (SLL = −20.0 dB) and low sideband levels (SBL < −30.0 dB) can be efficiently synthesized. The time consumption also demonstrates the effectiveness of the proposed method.