In energy limited wireless sensor networks, both local quantization andmultihop transmission are essential to save transmission energy and thus prolong the network lifetime. The goal is to maximize the network lifetime, defined as the estimation task cycles accomplished before the network becomes nonfunctional.The network lifetime optimization problem includes three components: Optimizing source coding at each sensor node, optimizing source throughput at each sensor node.Optimizing multihop routing path. Source coding optimization can be decoupled from source throughput and multihop routing path optimization and is solved by introducing a concept of equivalent 1-bit Mean Square Error (MSE) function. Based on optimal source coding, multihop routing path optimization is formulated as a linear programming problem, which suggests a new notion of character based routing. It is also seen that optimal multihop routing improves the network lifetime bound significantly compared with single-hop routing for heterogeneous networks. Furthermore, the gain is more significant when the network is denser since there are more opportunities for multihop routing. Also the gain is more significant when the observation noise variances are more diverse.
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