Optimal periodic training signal for frequency offset estimation in frequency-selective fading channels

This paper addresses an optimal periodic training signal design for frequency offset estimation in frequency-selective multipath Rayleigh fading channels. For a fixed transmitted training signal energy within a fixed-length block, the optimal periodic training signal structure (the optimal locations of identical training subblocks) and the optimal training subblock signal are presented. The optimality is based on the minimum Cramer-Rao bound (CRB) criterion. Based on the CRB for joint estimation of frequency offset and channel, the optimal periodic training structure (optimality only in frequency offset estimation, not necessarily in joint frequency offset and channel estimation) is derived. The optimal training subblock signal is obtained by using the average CRB (averaged over the channel fading) and the received training signal statistics. A robust training structure design is also presented in order to reduce the occurrence of outliers at low signal-to-noise ratio values. The proposed training structures and subblock signals achieve substantial performance improvement.