A Framework for Joint Design of Pilot Sequence and Linear Precoder
  Most performance measures of pilot-assisted multiple-input multiple-output (MIMO) systems are functions that depend on both the linear precoding filter 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. The framework applies to a wide class of utility functions of said effective SNR matrix, most notably a well-known mutual information expression for Gaussian inputs, an upper bound on the minimum mean-square error (MMSE), as well as approximations thereof. The approach consists in decomposing the joint optimization problem into three subproblems: first, we describe how to reformulate the optimization of the linear precoder subject to a fixed pilot sequence as a convex problem. Second, we do likewise for the optimization of the pilot sequence subject to a fixed precoder. Third, we describe how to generate pairs of precoders and pilot sequences that are Pareto optimal in the sense that they attain the Pareto boundary of the set of feasible effective SNR matrices. By combining these three optimization problems into an iteration, we obtain an algorithm which allows to compute jointly optimal pairs of precoders and pilot sequences with respect to some generic utility function of the effective SNR. 
Adriano Pastore, Michael Joham, Javier Rodr\'iguez Fonollosa
cs.IT math.IT