Maximum likelihood synchronization and frequency measurements

All coherent communications systems need a way to regenerate the transmitter's carrier at the receiver. The article presents a maximum likelihood algorithm for estimating the phase and frequency of a carrier coming from burst transmitters, when the carrier is observed against a background of white Gaussian noise and for enough time for the variance of the maximum likelihood estimate to be low. It analyses the performance of the maximum likelihood algorithm. Simulations of the algorithm's operation at a moderate signal ratio are compared with the high SNR bound. It outlines a similar algorithm to estimate the phase and frequency of the decaying sinusoids characteristic of physical measurements.