Journals: A Framework for Joint Design of Pilot Sequence and Linear Precoder
Pastore, Joham and J. Rodríguez Fonollosa

Abstract

Most performance measures of pilot-assisted multiple-input multiple-output (MIMO) systems are functions
that depend on both 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 a famous work by Hassibi and Hochwald. Our framework aims to extend 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 in [1]. 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.


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