Training sequence selection for frequency offset estimation in frequency selective channels

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 Cramer-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. (C) 2002 Elsevier Science (USA). All rights reserved.