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.