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Cognitive radio (CR) systems improve the spectral efficiency by allowing the coexistence in harmony of primary users (PUs), the legacy users, with secondary users (SUs). This coexistence is built on the premises that no SU can generate interference higher than some prescribed limits against PUs. The system design based on perfect channel state information (CSI) can easily end up violating the interference limits in a realistic situation where CSI may be imperfect. In this paper, we propose a robust design of CR systems, composed of multiple PUs and multiple noncooperative SUs, in either single-input single-output (SISO) frequency-selective channels or more general multiple-input multiple-output (MIMO) channels. We formulate the design of the SU network as a noncooperative game, where the SUs compete with each other over the resources made available by the PUs, by maximizing their own information rates subject to the transmit power and robust interference constraints. Following the philosophy of the worst-case robustness, we take explicitly into account the imperfectness of SU-to-PU CSI by adopting proper interference constraints that are robust with respect to the worst channel errors. Relying on the variational inequality theory, we study the existence and uniqueness properties of the Nash equilibria of the resulting robust games, and devise totally asynchronous and distributed algorithms along with their convergency properties. We also propose efficient numerical methods, based on decomposition techniques, to compute the robust transmit strategy for each SU.
Date of Publication: March 2011