The capacity per unit energy of large wireless networks

Abstract—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 α, the per-node capacity per unit energy scales essentially as Θ(n1−α/2) in the low path-loss regime (2 ≤ α ≤ 3) and essentially as Θ(n−1/2) in the high path-loss regime (α ≥ 3); while if the area is held constant, it scales essentially as Θ(n) and Θ(n(α−1)/2) in the low and high path-loss regimes, respectively. We propose a novel communication scheme, phase-aligned 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. I