The Capacity Per Unit Energy Of Large Wireless Networks

We study the scaling of the capacity per unit energy of a wireless network as a function of the number of nodes and the deployment area. We show that in a network of n nodes located randomly in a region of area scaling linearly with n and communicating over Gaussian fading channels with power path-loss exponent alpha, the per-node capacity per unit energy scales essentially as Theta(n(1 alpha/2)) in the low path-loss regime (2 <= alpha <= 3) and essentially as Theta(n(-1/2)) in the high path-loss regime (alpha >= 3); while if the area is held constant, it scales essentially as Theta(n) and Theta(n((alpha-1)/2)) in the low and high path-loss regimes, respectively. We propose a novel communication scheme, phasealigned amplify-and-forward, which is shown to be order-optimal in the low path-loss regime-no other known scheme achieves the same scaling. We show that the well-known multi-hop scheme is order-optimal in the high path-loss regime.