A Minimax Approach in Training Sequence Design for Carrier Frequency Offset Estimation in Frequency-Selective Channels

In this paper, the problem of carrier frequency offset estimation for frequency-selective channels in a data-aided context is considered. The channel is assumed to be contaminated with an unknown noise and the Cramér-Rao bound (CRB) is used as an estimation accuracy criterion. The minimax approach consists in minimizing the worst-case (maximum) CRB of the frequency offset. Under certain assumptions, it is shown that the worst-case CRB of the frequency offset is achieved when the noise is modeled as circularly symmetric complex-valued Gaussian. In addition, it is illustrated that a white training sequence minimizes the worst-case CRB, or equivalently, achieves the minimax optimality in this case.