MLE for Receiver-to-Receiver Time Synchronization in Wireless Networks with Exponential Distributed Delays

Abstract

Receiver-to-receiver time synchronization in wireless networks is considered, and appropriate maximum-likelihood estimators (MLE) for environments with exponential distrusted reception delays are proposed. In the receiver-to-receiver synchronization approach, time at receivers should be directly related to one another without referring to the sender (reference), which permits to eliminate the sender's uncertainty from the variable delays (time critical-path). The models and estimators proposed for the sender-to-receiver approach are thus inappropriate for the receiver-to-receiver one. A model that accurately reflects the relative feature of the considered approach and eliminates the senders's uncertainty is used, where timestamps at the receivers are directly related without referring to the sender's time or timestamps. By directly relating time at two receivers with identical exponential reception delay, Exp(λ), it yields a Laplace(0,1/λ) distribution as the difference between the two delays. By using the log-likelihood function of the latter and the ML method, the offset estimator is analytically derived and a linear program is given for the joint offset/skew model. The accuracy of the proposed estimators has been numerically analyzed by simulation. Results show high precision of the proposed estimators, which can be integrated with any receiver-to-receiver synchronization protocol.