Maximally Sparse Arrays Via Sequential Convex Optimizations
Maximally Sparse Arrays Via Sequential Convex Optimizations
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DOI：
10.1109/lawp.2012.2186626
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发表时间：
2012-01-01
影响因子：
4.2
通讯作者：
D'Urso, Michele
中科院分区：
文献类型：
--
作者：
Prisco, Giancarlo;D'Urso, Michele
稀疏阵列的设计能够满足给定的上界功率掩模和最小的源数，是一个越来越受关注的研究领域。相关的综合问题可以用对解空间的基数的适当约束来表示，即它的l(0)范数。不幸的是，这种非凸约束要求解决np困难问题。已经成功地提出了以凸方式放松上述约束的有趣想法。一个可能的解决方案是基于l(1)-范数的最小化。这种策略并不总是能够获得最稀疏的解决方案。在下面，一个创新的综合方案，优化激发权和传感器位置的阵列辐射铅笔束模式进行了讨论。求解算法基于序列凸优化，包括重新加权的l(1)范数最小化。参考基准问题的数值测试表明，所提出的综合方法能够实现最大稀疏线性阵列，并与文献报道的采用全局优化方案获得的最佳结果相比较。
The design of sparse arrays able to radiate focused beam patterns satisfying a given upper-bound power mask with the minimum number of sources is a research area of increasing interest. The related synthesis problem can be formulated with proper constraints on the cardinality of the solution space, i.e., its l(0)-norm. Unfortunately, such a nonconvex constraint requires to solve an NP-hard problem. Interesting ideas to relax the above constraint in a convex way have been successfully proposed. A possible solution is based on the minimization of the l(1)-norm. This strategy is not always able to achieve a maximally sparse solution. In the following, an innovative synthesis scheme that optimizes both excitation weights and sensor positions of an array radiating pencil beam-patterns is discussed. The solution algorithm is based on sequential convex optimizations including a reweighted l(1)-norm minimization. Numerical tests, referred to benchmark problems, show that the proposed synthesis method is able to achieve maximally sparse linear arrays, also compared to the best results reported in the literature, obtained by means of global optimization schemes.