Modular carrier recovery

A receiver apparatus comprising:

• a communication interface configured to receive a communication signal conveying a plurality of symbols at a respective plurality of positions within a current clock cycle, wherein the plurality of symbols comprises a data set consisting of data symbols and a pilot set consisting of pilot symbols;
• circuitry configured to determine detected phases of the plurality of symbols based on the communication signal;
• circuitry configured to generate first phase estimates in linear space based on the detected phases of a subset of the pilot set, and reference phases of the subset of the pilot set, wherein the first phase estimates are associated with the positions of the pilot set, and wherein the first phase estimates track carrier frequency offset and are free of cycle slips;
• circuitry configured to generate second phase estimates based on the detected phases of the pilot set, reference phases of the pilot set, and the first phase estimates, wherein the second phase estimates are associated with the positions of the pilot set and the positions of at least a subset of the data set;
• and
• circuitry configured to apply rotations to the detected phases of the plurality of symbols based on the second phase estimates.