Closed-Form Expression for the Exact Cramer-Rao Bound of Timing Recovery Estimators from MSK Transmissions

This paper addresses the problem of time delay estimation of minimum shift keying (MSK)-modulated signals. We derive for the first time the analytical expression of the stochastic Cramer-Rao lower bound (CRLB) for non-data-aided (NDA) timing recovery, from which the effects of the shaping pulse are easily observed. It is assumed that the transmitted symbols are completely unknown at the receiver. Moreover, the carrier phase and frequency are considered as unknown nuisance parameters.We emphasize the penalty resulting from considering the transmitted data as unknown in the estimation of the time delay.