Training sequence selection for frequency offset estimation in frequency selective channels

Abstract

We consider the problem of optimal training sequence selection for frequency offset estimation in frequency-selective channels. Since it is desired that the optimal training sequence does not depend on a particular estimation method, we examine the Cramér–Rao bound (CRB) for the problem at hand. For a fairly large class of training sequences, an expression for the asymptotic CRB is derived which depends in a simple way on the channel impulse response and the training sequence correlation. Based on the asymptotic CRB, two methods are presented to select an optimal training sequence. First, we consider a minmax problem which consists in minimizing the worst-case asymptotic CRB and whose solution is shown to be a white training sequence. Next, an expression for the training sequence that minimizes the asymptotic CRB is derived. Numerical simulations illustrate the estimation performance obtained with these training sequences.