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

• Authors: Liang-Liang Xie;P. R. Kumar
• Venue: IEEE Transactions on Information Theory
• Year: 2004

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 ρmin0. II) A simplistic model of signal attenuation e-γρ/ρδ over a distance ρ, where γ≥0 is the absorption constant (usually positive, unless over a vacuum), and δ0 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 CT:=supΣonℓ=1mRℓ·ρℓ, where the supremum is taken over m, and vectors (R1,R2,...,Rm) of feasible rates for m source-destination pairs, and ρℓ 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 γ0 or δ3, 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