Cooperative resource allocation games under spectral mask and total power constraints

Abstract—Resource allocation problems in multi-user systems, modeled as Nash bargaining (NB) cooperative games, are inves-tigated under different constraints. Using the joint time division multiplexing and frequency division multiplexing (TDM/FDM) scheme as a manner of cooperation in the NB resource allocation game with only spectrum mask constraints (SMCs), it is shown that the efficiency of the corresponding solution depends on both the interference-to-signal and interference-to-noise ratios of the users. Sufficient conditions under which the joint TDM/FDM based NB solution outperforms a noncooperative Nash equilibrium solution are derived and shown to be mild. A semi-distributed algorithm is proposed for finding the NB solution of the corresponding game with SMCs only. The NB based resource allocation game with both SMCs and total power constraints (TPCs) is shown to be a nonconvex optimization problem of high complexity. For such a game, a classification of two-user systems into bandwidth- and power-dominant systems is proposed based on the concept of Pareto-optimality. This classification gives insights to the resource allocation problem by showing that the benefits of both users are guaranteed to increase simultaneously only when the dom-inant resource in the system increases. Using this classification, efficient suboptimal algorithms of low complexity are derived based on the idea of optimally allocating the dominant resource and suboptimally allocating the other resource. Simulation re-sults demonstrate the efficiency of the proposed cooperative NB resource allocation strategies. Index Terms—Cooperative games, multi-user systems, Nash bar-gaining, Pareto-optimality, spectral mask constraints, total power constraints. I