Resource Allocation for Cognitive Small Cell Networks: A Cooperative Bargaining Game Theoretic Approach

Cognitive small cell networks have been envisioned as a promising technique for meeting the exponentially increasing mobile traffic demand. Recently, many technological issues pertaining to cognitive small cell networks have been studied, including resource allocation and interference mitigation, but most studies assume non-cooperative schemes or perfect channel state information (CSI). Different from the existing works, we investigate the joint uplink subchannel and power allocation problem in cognitive small cells using cooperative Nash bargaining game theory, where the cross-tier interference mitigation, minimum outage probability requirement, imperfect CSI and fairness in terms of minimum rate requirement are considered. A unified analytical framework is proposed for the optimization problem, where the near optimal cooperative bargaining resource allocation strategy is derived based on Lagrangian dual decomposition by introducing time-sharing variables and recalling the Lambert-W function. The existence, uniqueness, and fairness of the solution to this game model are proved. A cooperative Nash bargaining resource allocation algorithm is developed, and is shown to converge to a Pareto-optimal equilibrium for the cooperative game. Simulation results are provided to verify the effectiveness of the proposed cooperative game algorithm for efficient and fair resource allocation in cognitive small cell networks

Shapley Meets Shapley

This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a coalition of vertices is the weight of the maximum size matching in the subgraph induced by the coalition. The Shapley value is one of the most important solution concepts in cooperative game theory. After establishing some general insights, we show that the Shapley value of matching games can be computed in polynomial time for some special cases: graphs with maximum degree two, and graphs that have a small modular decomposition into cliques or cocliques (complete k-partite graphs are a notable special case of this). The latter result extends to various other well-known classes of graph-based cooperative games. We continue by showing that computing the Shapley value of unweighted matching games is #P-complete in general. Finally, a fully polynomial-time randomized approximation scheme (FPRAS) is presented. This FPRAS can be considered the best positive result conceivable, in view of the #P-completeness result.Comment: 17 page

Cooperative Precoding/Resource Allocation Games under Spectral Mask and Total Power Constraints

The use of orthogonal signaling schemes such as time-, frequency-, or code-division multiplexing (T-, F-, CDM) in multi-user systems allows for power-efficient simple receivers. It is shown in this paper that by using orthogonal signaling on frequency selective fading channels, the cooperative Nash bargaining (NB)-based precoding games for multi-user systems, which aim at maximizing the information rates of all users, are simplified to the corresponding cooperative resource allocation games. The latter provides additional practically desired simplifications to transmitter design and significantly reduces the overhead during user cooperation. The complexity of the corresponding precoding/resource allocation games, however, depends on the constraints imposed on the users. If only spectral mask constraints are present, the corresponding cooperative NB problem can be formulated as a convex optimization problem and solved efficiently in a distributed manner using dual decomposition based algorithm. However, the NB problem is non-convex if total power constraints are also imposed on the users. In this case, the complexity associate with finding the NB solution is unacceptably high. Therefore, the multi-user systems are categorized into bandwidth- and power-dominant based on a bottleneck resource, and different manners of cooperation are developed for each type of systems for the case of two-users. Such classification guarantees that the solution obtained in each case is Pareto-optimal and actually can be identical to the optimal solution, while the complexity is significantly reduced. Simulation results demonstrate the efficiency of the proposed cooperative precoding/resource allocation strategies and the reduced complexity of the proposed algorithms.Comment: 33 pages, 8 figures, Submitted to the IEEE Trans. Signal Processing in Oct. 200