New metric for routing in multi-hop wireless sensor networks for detection of correlated random fields

The problem of combining task performance and routing for the detection of correlated random fields using multi-hop wireless sensor networks is considered. Under the assumption of Gauss-Markov structure along a liven route. a link metric that captures the detection performance associated with a route is derived. Under Bayesian formulation Chernoff information is used as a performance criterion. It is shown that at high SNR Chernoff information is approximately given by a sum of the logarithm of the innovation variance at each link, which thus provides a link metric to determine the optimal route for the detection application. The value of the proposed metric is equivalent to the mutual information for Gaussian channel with signal power defined as the variance of signal innovation. The properties of the proposed metric are also investigated. It is shown that for SNR > 1. as a function of link length, the metric is 1) strictly increasing, 2) strictly concave. 3) bounded from above and the maximum information that a link can provide is (1)/(2) log(1 + SNR) achieved by independent and, identically distributed samples. It is also shown that the proposed link metric is well approximated by a function of the length of the corresponding link only.