Estimators for RBS-based time synchronization in heterogeneous wireless networks

A general scenario for using reference broadcast synchronization (RBS) in heterogeneous multi-hop wireless networks is defined, together with an appropriate model allowing to directly derive maximum likelihood estimators (MLE) to the skew and offset between communicating nodes. The model captures nodes heterogeneity that may cause differences in the reception delays. It also eliminates the need for synchronizing to the reference and enables direct relative synchronization. This accurately eliminates sender´s delays from the critical path, which faithfully reflects RBS features and the receiver/receiver paradigm. It will be shown that state-of-the-art RBS estimators for the joint skew/offset problem fail to eliminate sender´s delay. Appropriate MLEs are accordingly proposed. The Cramer-Rao lower bounds (CRLBs) are calculated, then the proposed estimators are numerically analyzed. Results show the estimators quadratically converge to the CRLB as the sample size rises, and that the precession is uninfluenced by the degree of heterogeneity (increase of delay differences). In a summary, the contribution of this paper is threefold; i) considering usage of RBS in heterogeneous and multi-hop networks, ii) defining an appropriate model and - accordingly - the maximum likelihood estimators for relative skew/offset between communicating nodes, iii) defining theoretical bounds for the estimators and numerically analyzing their convergence.