Design criteria of preamble sequence for multipath fading channels with Doppler shift

The timing synchronization method proposed by Shmidl and Cox uses a reference block consisting of two identical parts, while the one proposed by Shi and Serpedin uses a reference block consisting of four parts with the third part being multiplied by -1. The accuracy of estimated delays of the latter method is higher than the former. In this paper, the number of division is generalized as an integer number M. Optimal M is investigated for single- and multi-path channels. We conclude that a recommended M value is approximately given by √(N/2) for both single- and muti-path channels, irrespectively of signal-to-noise ratio, where N is a length of the reference block.