  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.
