Optimal design of constant-modulus channel training sequences

Abstract

Unimodular sequences have been widely used in communications and radars, for which some numerical algorithms have been proposed recently to obtain autocorrelation properties [1,2]. Design of such good sequences, however, does not take into account any prior information of the channel to be estimated. Although shaping the autocorrelation of a training sequence may imply a performance, it may be advantageous to directly optimize the performance measure of interest. In this paper, we consider the problem of optimal constant-modulus training sequence design for MMSE estimation of the channel impulse response and conditional mutual information maximization. Efficient iterative algorithms based on the majorization-minorization framework are proposed for each formulation. Numerical examples show that our proposed training sequences achieve better performances than that of low sidelobes or random phases.