Utility Maximization via Power and Rate Allocation with Outage Constraints in Nakagami-Lognormal Channels

The problem of maximizing a utility function while limiting the outage probability below an appropriate threshold is investigated. A coded-division multi access wireless network under mixed Nakagami-lognormal fading is considered. Solving such a utility maximization problem is difficult because the problem is non-convex and non-geometric with mixed integer and real decision variables and no explicit functions of the constraints are available. In this paper, three methods for the solution of the utility maximization problem are proposed. By the first method, a simple explicit outage approximation is used and the constraint that rates are integers is relaxed yielding a standard convex programming optimization that can be solved quickly but at the price of a reduced accuracy. The second method uses a more accurate outage approximation, which allows one solving the utility maximization problem by the Lagrange duality for non-convex problems and contraction mapping theory. The third method is a combination of the first and the second one. Numerical results show that the first method performs well for average values of the outage requirements, whereas the second one is always more accurate, but is also more computationally expensive. Finally, the third method gives same accuracy as the second one, but has a lower computational complexity only for a small number of transmitters.

I. Introduction

THE advent of multimedia services over wireless and ad hoc communication networks is increasing the demand of communications with a high utility experienced by the end users. For instance, being able to maximize the typical utility measure given by the amount of data that can be transmitted with a given quality of service (QoS) is essential for typical services provided by these networks, as video streaming, surveillance, and industrial automation [1].