Relaxed Biquadratic Optimization for Joint Filter-Signal Design in Signal-Dependent STAP

We investigate an alternative solution method to the joint signal-beamformer optimization problem considered in a recent publication devoted to this topic. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and clutter power under a minimum variance distortionless response constraint, is generally nonconvex and we provide 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 beconvex. The optimality conditions of this relaxed problem are examined and a variety of potential solutions are found, both analytically and numerically. These solutions are then compared to existing alternating minimization schemes.