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

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.