Cramer-Rao Lower Bound for the clock offset of silent nodes synchronizing through a general sender-receiver protocol in wireless sensornets

Agreement on a common time reference among the nodes is one of the most critical issues in the successful operation of the Wireless Sensor Networks (WSNs). In a previous paper [1], the Maximum Likelihood Estimator (MLE) for the clock offset of the silent nodes overhearing a two-way timing message exchange between two nodes, assuming an exponential link delay model, was obtained. This paper targets the derivation of Cramer-Rao Lower Bound (CRLB) for any unbiased clock offset estimator of the silent nodes as a performance threshold. The CRLB is shown to be inversely proportional to the square of the number of observations, and hence the variance of the MLE decreases very rapidly with the increase in data points. However, it is proved that the MLE does not achieve the CRLB and hence it is not efficient for small number of observations (although MLE has optimal properties for a large number of observations, i.e., it tends to become unbiased and attains CRLB). In addition, the CRLB for the clock offset estimator of the active node, as estimated by the silent node, is also derived and shown to be slightly better, but on a similar scale as the CRLB for the clock offset of the inactive node.