Pricing radio resources for utility maximization in the context of channel capacity region per unit cost

Distributed rate-and-power control are considered for a wireless data network where users maximize their utilities (QoS) measured in bits per Joule. The outcome of the distributed algorithm (a non-cooperative game) is a Nash equilibrium which is Pareto inefficient. Pricing of resources (rate and power) are used to effect Pareto improvements in the system. Numerical results show that pricing improves the utilities of all users while reducing their transmit powers. Specifically, we present these results in the context of Verdu's (1990) capacity region per unit cost where we observe that pricing of resources results in moving the vector of users' utilities closer to the boundary of the capacity region per unit cost-which is also the ultimate boundary for utility vectors measured in bits per Joule. This connects the concept of utility (measured in bits per Joule) and that of capacity per unit cost. In the absence of reliable decoding, pricing under heavy system loads moves the Nash equilibrium very close to the Pareto frontier, which is the practical boundary of utility possibilities.