Design and analysis of linear precoders under a mean square error criterion, Part I: Foundations and worst case designs

Abstract

Much debate surrounds the pros and cons of linear precoders in wireless communication systems. This two-part paper contributes to the debate by formulating the precoder design problem as an optimisation problem and studying the optimal solutions, thereby gaining a better understanding of how precoders work and what they can do. Part I builds a mathematical foundation for the study of linear precoders. It is shown that under a mean square error criterion, a natural convex geometry arises. This geometry facilitates the derivation of a necessary and sufficient condition for a linear precoder to be maximally robust, meaning the precoder's worst case performance is no worse than that of any other..