Blind Carrier Frequency Offset Estimator for Cross QAM Based on CPS Hierarchical Search

For cross quadrature amplitude modulation (QAM) signals, the carrier frequency offset can be determined by identifying the normalized frequency corresponding to the peak of the cumulant function, leveraging the signal's feature which called constellation phase signature (CPS). However, the estimation accuracy of this method is limited. This paper improves the CPS carrier frequency estimation algorithm by proposing an enhanced CPS frequency synchronization method based on hierarchical search. This approach selectively refines the search only in the local region surrounding the target frequency estimate, focusing on extracting the desired information while disregarding other areas. Specifically, the proposed algorithm enhances resolution around the initial peak identified by the frequency search. It constructs new interpolated search sequences neighboring the original peak of the cumulant function. Using these sequences, the local cumulant function is recalculated to find a refined peak. The process may iterate, with the decision for further refinement potentially based on the order of the cross QAM signal, ultimately yielding a precise carrier frequency offset estimate. The proposed hierarchical search-based CPS algorithm maintains high estimation accuracy even for high-order cross QAM signals, at the cost of only a marginal increase in computational load. In contrast, achieving the same level of accuracy with the original CPS algorithm would require significantly higher computational effort. A detailed comparison between the two methods will be presented later in this paper.