Hierarchic Power Allocation for Spectrum Sharing in OFDM-Based Cognitive   Radio Networks
  In this paper, a Stackelberg game is built to model the hierarchic power allocation of primary user (PU) network and secondary user (SU) network in OFDM-based cognitive radio (CR) networks. We formulate the PU and the SUs as the leader and the followers, respectively. We consider two constraints: the total power constraint and the interference-to-signal ratio (ISR) constraint, in which the ratio between the accumulated interference and the received signal power at each PU should not exceed certain threshold. Firstly, we focus on the single-PU and multi-SU scenario. Based on the analysis of the Stackelberg Equilibrium (SE) for the proposed Stackelberg game, an analytical hierarchic power allocation method is proposed when the PU can acquire the additional information to anticipate SUs' reaction. The analytical algorithm has two steps: 1) The PU optimizes its power allocation with considering the reaction of SUs to its action. In the power optimization of the PU, there is a sub-game for power allocation of SUs given fixed transmit power of the PU. The existence and uniqueness for the Nash Equilibrium (NE) of the sub-game are investigated. We also propose an iterative algorithm to obtain the NE, and derive the closed-form solutions of NE for the perfectly symmetric channel. 2) The SUs allocate the power according to the NE of the sub-game given PU's optimal power allocation. Furthermore, we design two distributed iterative algorithms for the general channel even when private information of the SUs is unavailable at the PU. The first iterative algorithm has a guaranteed convergence performance, and the second iterative algorithm employs asynchronous power update to improve time efficiency. Finally, we extend to the multi-PU and multi-SU scenario, and a distributed iterative algorithm is presented. 
Tian Zhang, Wei Chen, Zhu Han, and Zhigang Cao
cs.GT cs.NI