A method decodes an optical signal transmitted over an optical channel from a transmitter to a receiver. The method produces, from the transmitted optical signal, a digital signal including received data symbols and received pilot symbols and determines phase noise on the pilot symbols using a statistical probability distribution of phase noise on the optical channel and errors between phases of the received pilot symbols and the transmitted pilot signals. The method estimates phase noise on the data symbols using an interpolation of the phase noise on the pilot symbols and compensates the digital signal with the phase noise on the data symbols to produce a filtered signal with an equalized phase. The method demodulates and decodes the filtered signal to produce an estimate of the transmitted optical signal.