以最大稀疏化阵列得到所期望的方向图是稀疏阵列综合理论中的关键问题。由于阵列天线本身具有稀疏的物理特性，因此可将稀疏阵列综合归结为稀疏信号的重建过程。该文提出一种将阵列天线的波束形成问题等效为求解稀疏信号向量的最优化问题的方法，并利用FOCUSS算法快速准确地得到最大稀疏化的阵列，以及阵元位置和激励幅度。理论分析和数值仿真表明了该方法的有效性。%The use of maximally sparse array to achieve the desired radiation pattern is a key problem in sparse array synthesis theory. Since the array antenna has intrinsic character of sparsity, the sparse array synthesis problem can be seen as a process of sparse signal reconstruction. In this paper, the problem of beamforming with antenna array is proved to be the same as the optimization problem of solving sparse signal vector. By using the focal undetermined system solver (FOCUSS) algorithm, maximally sparse array as well as the elements’ locations and amplitudes are achieved quickly and accurately. The efficiency of this method is proved by theoretical analyses and numerical simulations.
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