Frequency synchronization of Polynomial Cancellation Coding

In this paper we introduce a new method of carrier frequency offset estimation for Orthogonal Frequency Division Multiplexing (OFDM) communication systems. The method uses one or more pairs of adjacent subcarriers within an OFDM symbol. The pairs of subcarriers are modulated with equal amplitude and opposite polarity. In the absence of frequency offset, the received subcarrier pairs also have equal amplitude and opposite polarity. Frequency offset disrupts this balance in a predictable way. This is used as the basis for the new frequency offset estimator. When the normalized frequency offset is less than half of the subcarrier frequency spacing, the new estimator is shown to be an approximately linear function of carrier frequency offset. The method is particularly applicable to the technique of Polynomial Cancellation Coding (PCC) in which the data to be transmitted is mapped onto subcarrier pairs rather than individual subcarriers. A number of different implementations are possible depending on whether the basic modulation technique is ordinary OFDM, or PCC-OFDM. For use with ordinary OFDM pilot subcarrier pairs must be inserted. If the pilot pair is contained in a symbol that also carries data, when the frequency offset is not close to zero, inter-carrier interference (ICI) from the other subcarriers can result a large variance of the estimator. For PCC-OFDM the estimation can be based on the subcarrier pairs which are carrying data. The variance in this case is much reduced, both because of the reduced ICI of PCC-OFDM and because the estimate can be based on the average over a number of pairs. Simulation results are presented for a number of cases.