Identifiability of data-aided carrier-frequency offset estimation over frequency selective channels

Carrier-frequency offset (CFO) must be compensated before channel estimation and coherent detection. Several data-aided CFO estimation algorithms have been proposed recently. However, an improper selection of training sequences may cause the identifiability problem which results in failure of CFO estimation. In this correspondence, we present a detailed study on identifiability issue and derive two new theorems for data-aided CFO estimation. The first theorem is suitable for all training sequences. The second one mainly deals with a popular set of training sequences that is deemed as optimal for channel estimation. Simulation results are provided to validate the proposed study