On the transport capacity of a broadcast Gaussian channel

The main question addressed in this paper is the problem of maximizing the "trans- port capacity" of a broadcast network in a Gaussian power-law channel, where by transport capacity we mean a generalization of the bandwidth-distance product as a means of assigning value to the information delivered by a communication network. This problem arises in areas such as cellular network coverage and ad-hoc network design, where the distance or area covered by a transmission is a critical consideration in the system design process. In the process of addressing this issue we also derive a transport-capacity maximizing resource allocation scheme for a general set of reward and channel penalty functions. The behavior of transport capacity for a very large network of receivers in a Gaussian power-law channel is also examined and a "large-scale" view of the optimal power allocation scheme for a given distance-payo function is provided. 1. Introduction and Problem Setup. In this paper we consider and general- ize the notion of transport capacity of a single-transmitter ad-hoc network. Transport capacity was originally defined in the work of Gupta and Kumar (5),(6) as the total bandwidth-distance product that a communication network is capable of supporting in a given area. In this paper we generalize this definition of the transport capacity to include more general payo functions and consider the resulting "transport capacity"