The core aim of this work is the maximization of the achievable data rate of the secondary user pairs (SU pairs), while ensuring the QoS of primary users (PUs). All users are assumed to be equipped with multiple antennas. It is assumed that when PUs are present, the direct communication between SU pairs introduces intolerable interference to PUs and thereby SUs transmit signal using the cooperation of one of the SUs and avoid transmission in the direct channel. In brief, an adaptive cooperative strategy for MIMO cognitive radio networks is proposed. At the presence of PUs, the issue of joint relay selection and power allocation in underlay MIMO cooperative cognitive radio networks (U-MIMO-CCRN) is addressed. The optimal approach for determining the power allocation and the cooperating SU is proposed. Besides, the outage probability of the proposed system is further derived. Due to high complexity of the optimal approach, a low complexity approach is further proposed and its performance is evaluated using simulations. The simulation results reveal that the performance loss due to the low complexity approach is only about 14%, while the complexity is greatly reduced. 1. Introduction Since the issuance of the report of Federal Communications Commission (FCC) in 2002, which revealed the spectrum inefficiency in the incumbent wireless communication systems, cognitive radio (CR) has been regarded as one potential technology to activate the utilization of spectrum resources in the recent evolution of wireless communication systems [1]. As a consequence, the overlay and underlay modes can be developed, based on the definitions of spectrum holes in [1] and the operation modes in [2], to use the white and gray spectrum holes, respectively. Cognitive radio (CR), MIMO communications, and cooperative communications are among the most promising solutions to improve spectrum utilization and efficiency. Dynamic and opportunistic spectrum access allows CR nodes to communicate on temporarily idle or underutilized frequencies. MIMO systems boost spectral efficiency by having a multiantenna node that simultaneously transmit multiple data streams. To further enhance the performance of cognitive radio networks, a cooperative relay network can be incorporated. Thus, in the underlay CR system with an interference temperature (IT) limit, the cooperative relay networks can also be applied to have a better capacity and error rate performance, trade-off between achievable rate and network lifetime, maximum signal-to-interference-plus-noise ratio (SINR) at the destination node,
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