On frequency hop synchronization in multipath Rayleigh fading

This paper is concerned with the effect of multipath fading on the performance of frequency hop (FH) time synchronization and the resultant bit-error rate (BER) performance. The expressions of the mean value and the variance of the estimated FH timing error and BER are derived for the case of multipath Rayleigh fading, which is characterized by a path-delay vector and a path-strength distribution vector. Somewhat surprisingly, our results show that in comparison with single-path fading, multipath fading does not degrade the mean and variance of the estimated timing error and BER performance, but rather improves them owing to multipath diversity. The significance of our results is to demonstrate quantitatively the robustness of FH in the presence of multipath fading as far as the establishment of hop timing is concerned. Furthermore, we identify the spectral estimator as a robust method for establishing FH timing.