Afrl-ry-wp-tp-2016-0197 Relaxed Bi-quadratic Optimization for Joint Filter-signal Design in Signal-dependent Space-time Adaptive Processing (stap)

We investigate an alterative 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 recieved 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.