1. A method for reducing phase noise in a communication receiver, the method comprising: receiving a first sequence of input values, each input value comprising an unknown data symbol corrupted by phase noise; determining a first sequence of data symbols from the first sequence of input values; determining a sequence of raw phase noise values from both the first sequence of input values and the first sequence of data symbols; filtering the sequence of raw phase noise values to provide a first sequence of filtered phase noise values; and compensating the first sequence of input values using the first sequence of filtered phase noise values to provide a sequence of compensated input values; for one or more iterations until a termination condition is met, performing the elements: determining a second sequence of data symbols from the sequence of compensated input values; determining a new sequence of raw phase noise values from both the sequence of compensated input values and the second sequence of data symbols; filtering the new sequence of raw phase noise values to provide a second sequence of filtered phase noise values; and compensating the first sequence of input values using the second sequence of filtered phase noise values to update the sequence of compensated input values; and outputting the updated sequence of compensated input values.