# Relaxed Bi-quadratic Optimization for Joint Filter-Signal Design in Signal-Dependent STAP

## TL;DR

This paper introduces a convex relaxation approach to a non-convex joint filter-signal optimization problem in signal-dependent STAP, providing insights and potential solutions for improved radar signal processing.

## Contribution

It applies biquadratic optimization and semidefinite relaxation techniques to transform a non-convex problem into a convex one, offering new analytical and numerical solution methods.

## Key findings

- The original problem is generally non-convex.
- The relaxed problem is convex and solvable.
- Potential solutions are identified both analytically and numerically.

## Abstract

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.