Hierarchic Power Allocation for Spectrum Sharing in OFDM-Based Cognitive Radio Networks

In this paper, a Stackelberg game is built to model the joint power allocation of the primary user (PU) network and the secondary user (SU) network hierarchically in orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) networks. We formulate the PU and 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 a certain threshold. First, we focus on the single-PU-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' reactions. The analytical algorithm has two steps. First, the PU optimizes its power allocation by considering the SUs' reactions to its action. In the power optimization of the PU, there is a subgame for power allocation of SUs given the fixed transmit power of the PU. The existence and uniqueness for the Nash equilibrium (NE) of the subgame are investigated. We also propose an iterative algorithm to obtain the NE and derive the closed-form solutions of the NE for the perfectly symmetric channel. Second, the SUs allocate the power according to the NE of the subgame given the 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-multi-SU scenario, and a distributed iterative algorithm is presented.