Theoretical estimators and lower-bounds for receiver-to-receiver time synchronization in multi-hop wireless networks

Maximum likelihood estimators (MLE) for time synchronization parameters of receiver-to-receiver protocols are derived. The MLE are first provided for a single-hop model, then generalized to a multi-hop model. The appropriate Cramer-Rao lower bounds (CRLB) for the estimators are then derived, which serves as a theoretical lower bound to any unbiased estimator. The proposed estimators are compared with their respective CRLB through simulation in multi-hop scenarios of up-to eight hops. The results show fast convergence of the estimation precision to the CRLB and demonstrate a high precision, where the mean square error (MSE) does not exceed 10^-6 for the skew, and 10^-5 for the offset.