On the path-loss attenuation regime for positive cost and linear scaling of transport capacity in wireless networks

Abstract—Wireless networks with a minimum inter-node sep-aration distance are studied where the signal attenuation grows in magnitude as 1 with distance. Two performance measures of wireless networks are analyzed. The transport capacity is the supremum of the total distance–rate products that can be sup-ported by the network. The energy cost of information transport is the infimum of the ratio of the transmission energies used by all the nodes to the number of bit-meters of information thereby transported. If the phases of the attenuations between node pairs are uni-formly and independently distributed, it is shown that the expected transport capacity is upper-bounded by a multiple of the total of the transmission powers of all the nodes, whenever 2 for two-dimensional networks or 5