Timing-delay and frequency-offset estimations for initial synchronisation on time-varying Rayleigh fading channels

A technique for timing-delay and frequency-offset estimations that takes advantage of a single dual-chirp preamble burst operating in frequency-non-selective fading environments is proposed. As the shape of the autocorrelation function of the dual-chirp signal does not essentially change by different values of frequency offset, the proposed technique provides a maximum-likelihood (ML) timing-delay estimation by exploiting only one pair of pseudo-noise matched filters (PN MFs), instead of conventionally exploiting a continuum of MFs, therefore approaching the Miller-Chang bound (MCB) in the timing-delay estimation with a channel gain and an initial phase error as nuisance parameters. Using the transform invariance property of the dual-chirp signal, the proposed technique estimates a frequency offset by exploiting frequency-domain PN MFs, therefore approaching the MCB in the frequency-offset estimation. The proposed technique accomplishes ML timing-delay and frequency-offset estimations to attain the performance bounds. The advantages of the proposed technique are verified by rigorous statistical analysis in conjunction with comprehensive computer simulations.