Abstract — 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 sub-blocks) and the optimal training sub-block 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 sub-block 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 non-optimal training structure with non-optimal training signals. I.

Abstract—This paper addresses an optimal training-signal design for frequency-offset estimation. Based on minimizing the Cramer–Rao lower bound for frequency-offset estimation with constraints on the peak and the total training signal energies, and the training block length, the optimal training-signal structure is developed. An approximate version of the optimal training-signal structure is proposed, which has practically the same performance as the optimal one, and provides convenience in training-signal generation and estimator derivation. Two robust reduced-complexity frequency-offset estimation methods for the proposed training structures are presented. In order to handle larger frequency offsets, modified training-signal structures are proposed. Frequency-offset estimation methods suitable for these training signals are also derived, based on the best linear unbiased estimation principle. Analytical and simulation results show that the proposed training-signal structures improve the estimation performance significantly. Index Terms—Best linear unbiased estimation (BLUE), Cramer–Rao bound (CRB), frequency-offset estimation, peak-to-average sample energy ratio (PAR), training design. I.

For emerging high data-rate communication systems in highly dispersive channels such as ultra-wideband systems, possible frequency offsets could be larger than the estimation range of the existing methods using training signals with identical parts or repetitive training signals (i.e., the training signals are composed of several identical sub-blocks or are obtained by repeating a training sub-block for several times). This paper presents a novel improved maximum likelihood frequency offset estimator which can handle at least twice the estimation range of the existing methods using training signals with identical parts and achieves a better estimation performance. Based on the likelihood metric, a new design metric is introduced which is a pair-wise error probability (PEP) between the correct frequency offset point and a trial frequency offset point. The proposed PEP metric gives more theoretical insights on the performance of practical maximum likelihood estimators. How to design the PEP to achieve both a larger estimation range and a better estimation performance in fading channel environments is also presented and the corresponding estimator implementation is described.