Identifiability of Training Based CFO Estimation over Frequency Selective Channels

Frequency synchronization is one of the most important issues for reliable transmission in most practical communication systems. Carrier frequency offset (CFO) must be compensated before channel estimation and coherent detection. Normally, training sequences are sent for CFO estimation and channel estimation before the data transmission. However, an improper selection of training sequences may cause failure in CFO estimation, resulting in the identifiability problem. In this paper, we present a detailed study on identifiability issue relate with data-aided CFO estimation. We firstly propose a theorem that is applicable for all training sequences. Then, the theorem is modified to deal with a popular set of training sequences that is deemed as optimal for channel estimation. Simulation results are provided to validate the proposed study.