On minimum energy routing in wireless multihop networks

A linear network between a source and destination pair in a wireless multihop network is considered. The performance metric is the total energy consumed in order for a bit to be successfully received by the destination. The energy includes transmitted energy and receiver processing energy. It is shown that a regular (equi-spaced) network is optimal in terms of minimizing the total energy consumption for an additive white Gaussian noise (AWGN) channel. Closed form expressions for the optimal rate and number of hops to minimize the total energy consumption are provided. The result is extended to general channels which satisfy sufficient conditions to guarantee convexness of the problem. The analysis demonstrates that the optimal rate and number of hops depend on the channel capacity characteristic, the amount of circuit processing energy, the end-to-end distance, and the path-loss exponent. Specifically, expressions for the optimal energy consumption are given for binary input AWGN channels and binary input hard decision AWGN channels.