Joint maximum-likelihood timing and data estimation for MSK signals from matched-filter samples

We derive the joint likelihood function for estimating jointly data sequences and timing error for minimum shift keying signalling. The likelihood function utilizes samples taken in a free-running mode at some arbitrary sampling rate. Lower bounds on both the error-probability and mean-square timing-error are presented and seen to approach closely the optimum performance for sampling rates of two or more samples per symbol. Simulation results show that when the sampling rate is two samples per symbol the performance of our joint estimation algorithm approaches the performance of binary phase-shift-keying with perfect synchronization