Abstract
A cross-layer approach for routing messages in a multi-hop wireless sensor network tasked with the detection of a random signal field is presented. A routing metric that captures detection performance (in the application layer) is introduced based on classical concepts from signal processing theory and used to design the routing strategy (in the network layer). Under a Gaussian model for the signal field, it is shown that the logarithm of the variance of the innovation at each link can be used as a link metric for maximizing detection performance. A connection between this new link metric and the mutual information of a Gaussian channel is described, and the other properties of the new link metric are investigated. Finally, we show how the new link metric can be incorporated into conventional routing protocols.