Synchronization Scheme based on Pilot Sharing in Cell-Free Massive MIMO Systems

This paper analyzes the impact of pilot-sharing scheme on synchronization performance in a scenario where several slave access points (APs) with uncertain carrier frequency offsets (CFOs) and timing offsets (TOs) share a common pilot sequence. First, the Cramer-Rao bound (CRB) with pilot contamination is derived for pilot-pairing estimation. Furthermore, a maximum likelihood algorithm is presented to estimate the CFO and TO among the pairing APs. Then, to minimize the sum of CRBs, we devise a synchronization strategy based on a pilot-sharing scheme by jointly optimizing the cluster classification, synchronization overhead, and pilot-sharing scheme, while simultaneously considering the overhead and each AP's synchronization requirements. To solve this NP-hard problem, we simplify it into two sub-problems, namely cluster classification problem and the pilot sharing problem. To strike a balance between synchronization performance and overhead, we first classify the clusters by using the K-means algorithm, and propose a criteria to find a good set of master APs. Then, the pilot-sharing scheme is obtained by using the swap-matching operations. Simulation results validate the accuracy of our derivations and demonstrate the effectiveness of the proposed scheme over the benchmark schemes.