In this paper, resource allocation for energy-efficient uplink communications in cognitive small cell networks is studied. We formulate the entire network energy efficiency (EE) maximization problem for the joint allocation of small cell base stations (SCBSs), spectrum resources, and transmission power in an open access mode. Since the master optimization problem belong to integer combinatorial fractional program and is essentially NP-hard, we develop a low-complexity alternative as a suboptimal solution by decomposing the master optimization issue into two sub-problems: selection of SCBSs and spectrum resources, and power allocation. The selection sub-problem of SCBSs and spectrum resources for cognitive small cell users (CSCUs) is modeled as a potential game from the viewpoints of reducing system interference and improving received signal strength. We formulate the power allocation sub-problem as a non-cooperative game which can be solved in a distributed fashion. But it is also a non-convex optimization problem in fractional form to solve the optimal power strategies based on maximizing the EE on a specific channel. We transform the nonlinear fractional programming issue into an equivalent parametric programming in subtractive form. For obtaining a social optimum power Nash equilibrium (NE), we propose a novel price-based double-loop iteration algorithm to get the transmission power strategies, which take the form of water-filling structure among different CSCUs over a same channel. Simulation results show that the proposed algorithms can converge to NE, and polish up the EE of the overall system significantly.
['Yanan Jia', 'Dian-Wu Yue']
Energy-Efficient Uplink Resource Allocation Based on Game Theory in Cognitive Small Cell Networks