Code design for correlated MIMO channels

Abstract

This paper describes a numerical design procedure for the design ofoptimal (in the minimum mean square channel estimation error sense)precoders for diversity systems with unitary codes where temporalcorrelation in the channel is present. The paper describes the usematrix differential calculus to derive the Jacobian (first derivative)of trace of the optimal (MMSE) estimation error covariance matrix with respect to the channel precoder matrix. This is used to define a gradient descent algorithm to minimise this error over all unit normprecoders. Simulation results using a per-survivor processing basedreceiver illustrate the improvement gained over unitary codes. Thepaper also shows by example that this does not necessarily lead on its own to optimal symbol detection error probability performance.