Abstract
In this paper, we present a game-theoretic approach for the purpose of deriving the problem of joint beamforming and power control in cognitive radio (CR) multiple-input multiple-output (MIMO) broadcast channels (CR MIMO-BCs), where the primary users (PUs) coexist with the secondary users (SUs) and they share the same spectrum. The cognitive base station (CBS), which is equipped with multiple antennas, is capable of transmitting data to the SU’s multiple-antenna receiver by employing the technology of beamforming. The proposed approach is an application of separable games, which are formally stated by the subgames of beamforming and power control. Furthermore, based on the model of noncooperative separate games, separable cost functions for the parameters of beamforming and power control are also proposed, showing that these cost functions are convex. Therefore, the convex theory of a noncooperative game can be employed to investigate the best response strategies as well as existence of Nash equilibrium solutions. Finally, we propose an iterative algorithm to achieve the optimal Nash equilibrium of the proposed joint beamforming subgame and power control subgame. Numerical results verify both the convergence and the tracking properties of the proposed algorithm for variant scenarios.
Highlights
The radio spectrum available for wireless communication is extremely scarce due to the widely deployed wireless devices and services
In cognitive radio networks (CRNs), the licensed spectrum can be shared with secondary users (SUs), provided that they do not cause harmful interference to primary users (PUs)
We model the problem of joint power control and beamforming in CR multiple-input multiple-output (MIMO)-BCs as a noncooperative game
Summary
The radio spectrum available for wireless communication is extremely scarce due to the widely deployed wireless devices and services. In [17], the problem of joint transmit beamforming and power control was considered in CR MIMO-BCs, with the cognitive multiantenna base station (BS) being assumed to satisfy the QoS constraints of the served SUs while protecting one primary receiver from interference. SUs may access the primary spectrum without causing harmful interference to the PUs. For the case of non-zero-interference-power constraint in CR MIMO-BCs, both the SUs’ SNR constraints and the PUs’ interference power constraints usually result in quadratically constrained quadratic programming problems, which may not be directly solved by convex tools, especially when there is a rank constraint. Ρk = rank Hk denotes the rank of the SUk-transformed MIMO channel matrix, which is equivalent to the number of non-zero singular values and satisfies ρk ≤ min (Nt, Nr).
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