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

Abstract

Receiver-to-receivertimesynchronizationinwirelessnetworksisconsidered,andappropriatemaximum-likelihoodestimators(MLE)forenvironmentswithexponentialdistrustedreceptiondelaysareproposed.Inthereceiver-to-receiversyn-chronizationapproach,timeatreceiversshouldbedirectlyrelatedtooneanotherwithoutrefereingtothesender(reference),whichpermitstoeliminatethesender’suncertaintyfromthevariabledelays(timecritical-path).Themodelsandestimatorsproposedforthesender-to-receiverapproacharethusinappro-priateforthereceiver-to-receiverone.Amodelthataccuratelyreflectstherelativefeatureoftheconsideredapproachandeliminatesthesenders’suncertaintyisused,wheretimestampsatthereceiversaredirectlyrelatedwithoutrefereingtothesender’stimeortimestamps.Bydirectlyrelatingtimeattworeceiverswithidenticalexponentialreceptiondelay,,ityieldsadistributionasthedifferencebetweenthetwodelays.TheyusetheloglikelihoodfunctionofthelatterandtheMLmethod,theoffsetestimatorhasbeenanalyticallyderived,wherealinearprogramisgivenforthejointoffset/skewmodel.Theaccuracyoftheproposedestimatorshasbeennumericallyanalyzedbysimulation.Resultsshowhighprecisionoftheproposedestimators,whichcanbeintegratedwithanyreceiver-to-receiversynchronizationprotocol.