Generalized Quadratic Matrix Programming: A Unified Approach for Linear Precoder Design

This paper investigates a new class of nonconvex optimization, which provides a unified framework for linear precoder design. The new optimization is called generalizedquadratic matrix programming (GQMP). Due to the non-deterministic polynomial time (NP)-hardness of GQMP problems, we provide a polynomial time algorithm that is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point. In terms of application, we consider the linear precoder design problem for spectrum-sharing secure broadcast channels. We design linear precoders to maximize the average secrecy sum rate with finite- alphabet inputs and statistical channel state information (CSI). The precoder design problem is a GQMP problem and we solve it efficiently by our proposed algorithm. A numerical example is also provided to show the efficacy of our algorithm.