A network information theory for wireless communication: scaling laws and optimal operation

How much information can be carried over a wireless network with a multiplicity of nodes, and how should the nodes cooperate to transfer information? To study these questions, we formulate a model of wireless networks that particularly takes into account the distances between nodes, and the resulting attenuation of radio signals, and study a performance measure that weights information by the distance over which it is transported. Consider a network with the following features. I) n nodes located on a plane, with minimum separation distance ρ_min>0. II) A simplistic model of signal attenuation e^-γρ/ρ^δ over a distance ρ, where γ≥0 is the absorption constant (usually positive, unless over a vacuum), and δ>0 is the path loss exponent. III) All receptions subject to additive Gaussian noise of variance σ². The performance measure we mainly, but not exclusively, study is the transport capacity C_T:=supΣon_ℓ=1^mR_ℓ·ρ_ℓ, where the supremum is taken over m, and vectors (R₁,R₂,...,R_m) of feasible rates for m source-destination pairs, and ρ_ℓ is the distance between the ℓth source and its destination. It is the supremum distance-weighted sum of rates that the wireless network can deliver. We show that there is a dichotomy between the cases of relatively high and relatively low attenuation. When γ>0 or δ>3, the relatively high attenuation case, the transport capacity is bounded by a constant multiple of the sum of the transmit powers of the nodes in the network. However, when γ=0 and δ<3/2, the low-attenuation case, we show that there exist networks that can provide unbounded transport capacity for fixed total power, yielding zero energy priced communication. Examples show that nodes can profitably cooperate over large distances using coherence and multiuser estimation when the attenuation is low. These results are established by developing a coding scheme and an achievable rate for Gaussian multiple-relay channels, a result that may be of interest in its own right.