A least squares estimator of carrier phase and amplitude in a receiver in a communication system using a phase shift keying modulation scheme that uses both known pilot symbols and unknown data symbols is described. That is, the method exploits knowledge of pilot symbols in addition to the unknown data symbols to estimate carrier phase and amplitude. Further, an efficient recursion based estimation method is described that only requires O(L. log L) arithmetic operations where L is the number of received signals. This method uses the M-Ary rounded phase offsets to sort the data symbols and this sorted order is used to recursively calculate candidate values in an optimization process. Simulation results show that the estimation methods Using data and pilot symbols outperform estimation methods using only data symbols (ie non-coherent detection methods). Further, the system can be used for systems using multiple M-ary phase shift keying digital modulation schemes.