Competitive optimization of cognitive radio MIMO systems via game theory

The concept of cognitive radio (CR) has recently received great attention from the researchers´ community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. In this paper, we propose a distributed approach based on game theory to design cognitive MIMO transceiver in hierarchical CR networks, where primary users establish null and/or soft shaping constraints on the transmit covariance matrix of secondary users, so that the interference generated by secondary users be confined within the interference-temperature limits. We formulate the resource allocation problem among secondary users as a strategic noncooperative game, where each transmit/receive pair competes against the others to maximize the information rate over his own MIMO channel, under transmit power and/or null/soft shaping constraints. We provide a unified set of conditions that guarantee the uniqueness and global asymptotic stability of the Nash equilibrium of all the proposed games through totally distributed and asynchronous algorithms. Interestingly, the proposed algorithms overcome the main drawback of classical waterfilling based algorithms-the violation of the interference-temperature limits-and they have many of the desired features required for cognitive radio applications, such as low-complexity, distributed nature, robustness against missing or outdated updates of the users, and fast convergence behavior.