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Burst transmission of digital data and voice has become commonplace, particularly in satellite communication systems employing time-division multiple-access (TI)MA) and packet demand-assignment multiple-access (DAMA) techniques. In TDMA systems particularly, phase estimation on each successive burst is a requirement, while bit timing and carrier frequency can be accurately tracked between bursts. A class of nonlinear estimation algorithms is described to estimate the unknown phase of a carrier which is fully modulated by -ary PSK modulation. Performance of the method is determined in closed form and compared to the Cramér-Rao lower bound for the variance of the estimation error in the phase of an unmodulated carrier. Results are also obtained when the carrier frequency is imprecisely known. Finally, the effect of quantization and finite read-only-memory (ROM) implementation of the nonlinearity are determined by computer simulation.