The PS-BCJR Algorithm for Joint Frequency Synchronization and Data Decoding in TCM systems

This study proposes a per-survivor based BCJR algorthm for joint frequency synchronization and data decoding in trellis coded modulation (TCM) systems. The proposed algorithm uses two probing signals and a carrier frequency offset (CFO) tracker to calculate the modified gamma factor involved in the BCJR algorithm. To track the CFO, a state-time process recursively updates the CFO tracker using the soft-information provided by the modified gamma factor. The state-time process consists of a state-process and a time-process. The state-process takes advantage of the state-diversity in the TCM signals to choose the most probable CFO update corresponding to the state with the maximal modified gamma factor. Based on this CFO value, and in conjunction with the tentatively selected probing signals, the succeeding time-process can iteratively track the CFO using the trellis structure of the TCM signals. This study also develops a least-square-linear-fitting (LSLF) approach based on the CFO trace to dynamically adjust the step-size for the CFO tracker. Computer simulations show that unlike the conventional augmented a posteriori probability (A2P2) method having a small CFO tracking range, the proposed approach can handle a significantly larger CFO because of its ML-based CFO estimate. In addition, the proposed LSLF step-size determination ensures the PS-BCJR a higher accuracy in CFO estimation than the A2P2.