A linear network between a source and destination pair in a wireless multihop network is considered.  
The performance metric is the total energy which 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, the optimal 
energy consumption constants are shown for binary input AWGN channels and binary input hard decision 
AWGN channels.