In one embodiment, a receiver of the invention has an optical detector coupled to a digital processor. The optical detector is adapted to mix the received optical quadrature-amplitude modulation (QAM) signal with an optical local oscillator (LO) signal having a time-varying phase offset with respect to the carrier frequency of the QAM signal to produce two digital measures of the QAM signal. The digital processor is adapted to: (i) determine the amplitude and phase differentials for each QAM-symbol transition based on these digital measures; (ii) adjust each phase differential for an amount of phase drift associated with the time-varying phase offset; (iii) map each QAM-symbol transition onto a constellation point of a 2D decision map using the transition's amplitude differential and adjusted phase differential; and (iv) based on the mapping results, recover the data encoded in the optical QAM signal.