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针对方向图可重构天线阵列的稀疏布阵问题,提出一种基于扩展酉矩阵束算法的优化设计算法。首先建立以阵元位置和多组激励为变量的多方向图联合稀疏优化模型,并利用期望方向图采样数据构建Hankel块矩阵。然后通过centro-Hermitian化处理和酉变换将采样矩阵从复数域转换到实数域,舍弃实矩阵中较小的奇异值对可重构线阵进行稀疏。最后通过对等价矩阵束的广义特征值分解估计稀布阵元位置,进而得到每个方向图对应的激励。仿真验证了该方法能够以阵元非均匀稀疏分布的阵列形式有效实现多个方向图的精确重构。
Aiming at the problem of sparse arrangement of reconfigurable antenna arrays in directional pattern, an optimized design algorithm based on extended unitary matrix beam algorithm is proposed. Firstly, a joint sparse optimization model of multi-directional graph with array element location and multi-group motivation as variables is established, and the Hankel block matrix is constructed by using the expected pattern sample data. Then the centro-Hermitian processing and unitary transform are used to convert the sampling matrix from the complex number domain to the real number domain. The smaller singular value in the real matrix is discarded and the reconfigurable linear array is sparse. Finally, we estimate the position of sparse array element by using the generalized eigenvalue decomposition of the equivalent matrix beam, and then get the corresponding excitation of each pattern. The simulation results show that the proposed method can effectively reconstruct multiple directional patterns with an array of sparsely distributed array elements.