Joint Sparsity-Based Range-Angle-Dependent Beampattern Synthesis for Frequency Diverse Array

For frequency diverse array (FDA) range-angle-dependent beampattern synthesis, the objective is to obtain the desired beampattern performance using fewer antenna elements or smaller aperture. This paper proposes a FDA single-beam pattern synthesis by joint $\ell _{1}$ -norm minimization and convex optimization in the beginning. A virtual uniform FDA array with small element spacing and corresponding frequency increment is created first. Then, we formulate the array pattern synthesis (APS) problem as finding a joint sparse weight vector, which can be obtained by solving a convex optimization problem with the joint sparse constraint between angle dimension weight vector and range dimension weight vector, where some small entries of the vector can be regarded as zeros without significantly changing the array pattern performance. The antenna elements corresponding to the mapping positions of nonzero values of the joint sparse weight vector are placed to form a non-uniform FDA. Finally, convex optimization is further conducted to obtain the optimal weight vector of the non-uniform FDA. Besides, we expand the idea to FDA multi-beam pattern synthesis based on the convex optimization problem with joint sparse constraint between angle dimension weight matrix and range dimension weight matrix. Numerical examples are provided to verify the efficiency of achieving the desired radiation pattern with the fewer antenna elements, and better APS performance for given array elements.