Joint Optimization of Sparse FDAs for Time Invariant Transmit Beampattern Synthesis

Abstract

Beampattern synthesis of frequency diverse arrays (FDAs) has recently raised increased attention attributed to their range-dependent beampattern. The transmit beampattern of uniform FDA appears <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S$</tex-math></inline-formula> -shaped, which implies coupling in the range-angle domain and thus causing unwanted energy leakage into the area of non-interest. In this work, we propose a joint optimization of sparse FDAs to synthesize a decoupled transmit beampattern from the perspective of spatial-frequency virtual array. Specifically, both spatial and spectral configuration of FDAs are optimized via joint antenna-frequency selection. In order to solve the resultant NP-hard combinatorial optimization problem, we propose an iterative reweighting strategy to transform the original problem into a convex optimization. Further, we proceed to synthesize a time-invariant decoupled beampattern by designing a time-varying unit frequency step. Comparative simulations are provided to manifest the superior performance of the proposed FDA in the metric of normalized peak sidelobe level (NPSLL) of transmit beampatterns.