A Framework for Joint Design of Pilot Sequence and Linear Precoder

Most performance measures of pilot-assisted multiple-input multiple-output systems are functions of the linear precoder and the pilot sequence. A framework for the optimization of these two parameters is proposed, based on a matrix-valued generalization of the concept of effective signal-to-noise ratio (SNR) introduced in the famous work by Hassibi and Hochwald. Our framework aims to extend the work of Hassibi and Hochwald by allowing for transmit-side fading correlations, and by considering a class of utility functions of said effective SNR matrix, most notably including the well-known capacity lower bound used by Hassibi and Hochwald. We tackle the joint optimization problem by recasting the optimization of the precoder (resp. pilot sequence) subject to a fixed pilot sequence (resp. precoder) into a convex problem. Furthermore, we prove that joint optimality requires that the eigenbases of the precoder and pilot sequence be both aligned along the eigenbasis of the channel correlation matrix. We finally describe how to wrap all studied subproblems into an iteration that converges to a local optimum of the joint optimization.