Optimal Performance Versus Fairness Tradeoff for Resource Allocation in Wireless Systems

Resource allocation is a challenging issue in multiuser wireless systems. Since users are not all in the same conditions and do not achieve the same performance given the same amount of resources, resource allocation must typically deal with the following two conflicting objectives: on the one hand, the overall performance should be maximized, tending to prioritize few users in better conditions, and on the other hand, fairness among users should be maximized, consequently reducing the overall performance. Identifying the compromise that is somehow optimum is all but simple and this aspect is normally worsened by the absence of a curve describing how the maximum performance varies changing the accepted level of fairness. To cover this gap, in this paper, we propose a unified and general mathematical formulation of the optimal performance versus fairness tradeoff in multiuser wireless communication systems. Differently from the existing literature, our approach is based on the generalized Lagrange method and adopts general definitions for both performance and fairness. Besides the exact solving equations describing how the maximum performance varies with fairness, we also derive a simpler lower bound with reduced computational cost. Example results are provided for two case studies, respectively, concerning linear and logarithmic dependence of performance on resources.