Time and Frequency Acquisition of FH-MFSK Signals with Random Data: Hopping Down the Most Likely Trail

A unified approach based on maximum likelihood estimation for time and frequency acquisition of frequency-hopped M-ary FSK signals with random data is presented. Algorithms for estimation of frequency and joint estimation of time and frequency are derived for the cases in which: (1) the data sequence is treated as a set of nuisance parameters; (2) the data sequence is estimated along with time and frequency. The performance of the frequency estimators is evaluated for typical cases of interest, and it is shown that the joint estimator of data and frequency is superior to a simplified estimator of frequency only, provided the signal-to-noise ratio is sufficiently high.