Optimal Spectrum Sharing in MIMO Cognitive Radio Networks via Semidefinite Programming

Abstract

Abstract-In cognitive radio (CR) networks with multipleinput multiple-output (MIMO) links, secondary users (SUs) can exploit "spectrum holes" in the space domain to access the spectrum allocated to a primary system. However, they need to suppress the interference caused to primary users (PUs), as the secondary system should be transparent to the primary system. In this paper, we study the optimal secondarylink beamforming pattern that balances between the SU's throughput and the interference it causes to PUs. In particular, we aim to maximize the throughput of the SU, while keeping the interference temperature at the primary receivers below a certain threshold.Unlike traditional MIMO systems, SUs may not have the luxury of knowing the channel state information (CSI) on the links to PUs. This presents a key challenge for a secondary transmitter to steer interference away from primary receivers. In this paper, we consider three scenarios, namely when the secondary transmitter has complete, partial, or no knowledge about the channels to the primary receivers. In particular, when complete CSI is not available, the interference-temperature constraints are to be satisfied with high probability, thus resulting in chance constraints that are typically hard to deal with. Our contribution is fourfold. First, by analyzing the distributional characteristics of MIMO channels, we propose a unified homogeneous quadratically constrained quadratic program (QCQP) formulation that can be applied to all three scenarios, in which different levels of CSI knowledge give rise to either deterministic or probabilistic interference-temperature constraints. The homogeneous QCQP formulation, though non-convex, is amenable to semidefinite programming (SDP) relaxation methods. Secondly, we show that the SDP relaxation admits no gap when the number of primary links is no larger than two. A polynomial-time algorithm is presented to compute the optimal solution to the QCQP problem efficiently. Thirdly, we propose a randomized polynomial-time algorithm for constructing a near-optimal solution to the QCQP problem when there are more than two primary links. Finally, we show that when the secondary transmitter has no CSI on the links to primary receivers, the optimal solution to the QCQP problem can be found by a simple matrix eigenvalue-eigenvector computation, which can be done much more efficiently than solving the QCQP directly.

Ten years of research in spectrum sensing and sharing in cognitive radio

“…For multi-antenna systems, most study jointly optimizes power allocation and beamforming [92][93][94][95]. Under IPCs and peak TPCs, the power allocation and beamforming design for sum-rate maximization and signal-to-interference-plus-noise ratios (SINRs) balancing problems have been studied for SIMO systems in [92].…”

“…The study of SINR-balancing has been extended into MIMO systems in [93], where a robust beamforming design is developed to limit the interference leakage to PU below a specific threshold with a certain probability. Beamforming for MIMO systems has been proposed to maximize the SINR of SUs under IPCs in [94]. A unified homogeneous quadratically constrained quadratic program is used to solve the optimization problems.…”

Uncertainty area-based interference mitigation for cognitive radio

“…However, it is still not applicable in our scheme because of our assumed PAs' location information inaccuracy for the MANET. The authors in [19] have aimed to maximize the throughput of SNs while keeping the interference temperature at PAs below a certain threshold, even without channel knowledge to the PAs. In fact, they study the optimal secondary-link beamforming pattern to steer interference away from PAs, which is unfortunatly too dependent on an accurate PAs' location information.…”

Joint beamforming and power control algorithm for cognitive MIMO broadcast channels via game theory

“…Semidefinite programming (SDP) relaxation can be used to convert the aforementioned problem into a convex optimization problem by dropping the rank constraint, consequently generating a local optimum [18]. It is shown in [19] that under certain conditions, a new solution can be generated from the one obtained by SDP relaxation without ruining the constraints or changing the objection function. Actually, most of the resulting problems of joint beamforming and power control are inherently non-convex, and consequently, no global optimality of an efficient solution can be guaranteed theoretically [20].…”