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This paper addresses optimal periodic training signal design for frequency offset estimation in frequency selective multipath Rayleigh fading channels. For a fixed transmitted training signal energy and within a fixed length block, the optimal periodic training signal structure (the optimal location 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 snap-shot CRB, the optimal periodic training structure is derived. The optimal training subblock signal is obtained by utilizing the average CRB and the received training signal statistics. The optimal training structure with optimal training signals achieves substantial performance improvement over nonoptimal training structure with nonoptimal training signals.