Constrained Least Squares, SDP, and QCQP Perspectives on Joint Biconvex Radar Receiver and Waveform design.

P. Setlur, Sean M. O’Rourke, M. Rangaswamy
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引用次数: 3

Abstract

Joint radar receive filter and waveform design is non-convex, but is individually convex for a fixed receiver filter while optimizing the waveform, and vice versa. Such classes of problems are fre- quently encountered in optimization, and are referred to biconvex programs. Alternating minimization (AM) is perhaps the most popu- lar, effective, and simplest algorithm that can deal with bi-convexity. In this paper we consider new perspectives on this problem via older, well established problems in the optimization literature. It is shown here specifically that the radar waveform optimization may be cast as constrained least squares, semi-definite programs (SDP), and quadratically constrained quadratic programs (QCQP). The bi-convex constraint introduces sets which vary for each iteration in the alternat- ing minimization. We prove convergence of alternating minimization for biconvex problems with biconvex constraints by showing the equivalence of this to a biconvex problem with constrained Cartesian product convex sets but for convex hulls of small diameter.
约束最小二乘,SDP和QCQP的观点联合双凸雷达接收机和波形设计。
联合雷达接收滤波器和波形设计为非凸型,而单独凸型对于固定接收滤波器同时优化波形,反之亦然。这类问题在优化中经常遇到,被称为双凸规划。交替极小化(AM)可能是处理双凸性的最流行、最有效和最简单的算法。在本文中,我们考虑了这个问题的新视角,通过旧的,完善的问题,在优化文献。具体来说,雷达波形优化可以被转换为约束最小二乘、半确定规划(SDP)和二次约束二次规划(QCQP)。双凸约束在交替最小化中引入了在每次迭代中变化的集合。我们证明了具有双凸约束的双凸问题的交替极小化的收敛性,证明了交替极小化与具有约束的笛卡尔积凸集的双凸问题的等价性,但凸包的直径较小。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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