Relaxed Bi-quadratic Optimization for Joint Filter-Signal Design in Signal-Dependent STAP
Provides a theoretical and practical solution for optimizing radar systems in signal-dependent environments, though incremental as it builds on prior work.
The paper addresses the non-convex joint filter-signal design problem in signal-dependent STAP, demonstrating its non-convexity and proposing a convex relaxation via biquadratic optimization and semidefinite relaxations, with analytical and numerical solutions.
We investigate an alternative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy[1]. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and clutter power under a minimum variance distortionless response (MVDR) constraint, is generally non-convex and provide concrete insight into the nature of the nonconvexity. Second, we employ the theory of biquadratic optimization and semidefinite relaxations to produce a relaxed version of the problem, which we show to be convex. The optimality conditions of this relaxed problem are examined and a variety of potential solutions are found, both analytically and numerically.