In one embodiment, a receiver of the invention has a detector coupled to a digital processor. The detector is adapted to mix the received PSK signal with a local oscillator (LO) signal having a time-varying phase offset with respect to the carrier frequency of the PSK signal to produce a digital measure of the PSK signal. The digital processor is adapted to: (i) estimate a frequency offset between the carrier frequency of the PSK signal and the LO signal; (ii) remove from an angular component of the digital measure a component corresponding to the frequency offset to generate a frequency-offset-adjusted signal; (iii) for each time slot of the PSK signal, estimate the phase of a respective PSK constellation symbol based on an angular component of the frequency-offset-adjusted signal and an angular component of a recursive function; (iv) estimate a phase differential for a PSK-symbol transition based on two consecutive phase estimates; (v) map each estimated phase differential onto a phase increment corresponding to a symbol transition in the PSK constellation; and (vi) recover a data sequence encoded in the PSK signal based on the mapping results.