Pilot-aided digital coherent reception of high-order QAM signal detection using a continuous short pilot preamble and subsequent pilot symbols that are periodically distributed with payload data resulting in low-complexity and fast-convergence signal detection for continuous mode coherent reception of high-order QAM signals. A digital signal processor is configured to demodulate a transmitted data stream from digital stream of measurements of light mixtures produced in a receiver for coherent optical communications in response to receiving modulated optical carriers. The digital signal processor includes one circuit stage for providing corrections to the digital stream to compensate first effects on the light mixtures due to a frequency shift of a local optical oscillator of the receiver and another circuit stage for correcting the digital stream to compensate for second effects on the light mixtures due to polarization dependent channel modification of the modulated optical carriers.