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 /spl rho//sub min/>0. II) A simplistic model of signal attenuation e/sup -/spl gamma//spl rho///spl rho//sup /spl delta// over a distance /spl rho/, where /spl gamma//spl ges/0 is the absorption constant (usually positive, unless over a vacuum), and /spl delta/>0 is the path loss exponent. III) All receptions subject to additive Gaussian noise of variance /spl sigma//sup 2/. The performance measure we mainly, but not exclusively, study is the transport capacity C/sub T/:=sup/spl Sigma/on/sub /spl lscr/=1//sup m/R/sub /spl lscr///spl middot//spl rho//sub /spl lscr//, where the supremum is taken over m, and vectors (R/sub 1/,R/sub 2/,...,R/sub m/) of feasible rates for m source-destination pairs, and /spl rho//sub /spl lscr// is the distance between the /spl lscr/th 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 /spl gamma/>0 or /spl delta/>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 /spl gamma/=0 and /spl delta/