Cognitive MIMO Research Articles

Spectrum Sharing in MIMO Cognitive Radio Networks Based on Cooperative Game Theory

In a MIMO cognitive radio network, multiple secondary users sense the spatial channels and share the spectrum use with incumbent primary users. Each secondary transmitter competes with others to increase its own information rate while generating limited total interference to the primary receivers. In order to maximize the sum-rate of the cognitive radio network, the problem of secondary user transmission is modeled as a cooperative game. The strategy of each secondary user is the transmit covariance matrix, and the utility is an approximation of the information rate. The secondary users negotiate over the allocation of the interference budget and reach at a bargaining solution that maximizes the network utility. With well-designed individual utility and network utility functions, the bargaining solution is unique and Pareto optimal. An efficient distributed algorithm is developed that converges quickly to the optimal solution with moderate signaling within the network. Numerical results show the performance improvement in sum-rate of the MIMO cognitive radio network at the bargaining solution of the cooperative game compared with the Nash-equilibrium solution of the non-cooperative game.

Joint Transmit Antenna Selection and User Selection in Cognitive Radio MIMO Systems

Using multiple antennas in coexisting radio systems can cancel or control the co-channel interference and hence improves the overall spectrum efficiency. However, the hardware complexity and costs limit the usage of multiple-antenna technology. Antenna selection may reduce such costs while partly remaining the advantage of the multiple-antenna technology. In this paper, a fixed power cognitive radio system model jointly combined with antenna selection and users selection is set up. And the mathematical closed-form expressions of the channel capacity and bit error rate (BER) are obtained through mathematical derivation. Simulation verifies the correctness of theoretical results and shows that the system exists an optimal transmit power which optimizes the system performance. Furthermore, the influences of users number and antennas number on the system performance have been studied.

Game-Theoretic Joint Power Allocation and Beamforming for Cognitive MIMO Systems with Finite Feedback

In the paper, we consider the imperfect channel state information (CSI) in practical cognitive MIMO systems. We first analyze the feedback of quantified CSI from the primary user (PU) and propose a joint power allocation and beamforming algorithm via game theory. Compared with the game under the condition of perfect CSI, new utility function and cost function are constructed under imperfect CSI. We analyze the error introduced from the uniformly quantified CSI and obtain new constraints. Besides, existence of the Nash equilibrium in case of both perfect CSI and imperfect CSI are proven. We propose a new iterative algorithm to reach the Nash equilibrium (NE). Simulation results show that the proposed algorithm can converge quickly.

Spectrum Sharing in MIMO Cognitive Radio Systems with Imperfect Channel State Information

Spectrum Sharing in MIMO Cognitive Radio Systems with Imperfect Channel State Information

Erratum to: Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

Erratum to: Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

On the Throughput and Energy Efficiency of Cognitive MIMO Transmissions

In this paper, throughput and energy efficiency of cognitive multiple-input-multiple-output (MIMO) systems operating under quality-of-service (QoS) constraints, interference limitations, and imperfect channel sensing are studied. It is assumed that transmission power and covariance of the input signal vectors are varied, depending on the sensed activities of primary users (PUs) in the system. Interference constraints are applied on the transmission power levels of cognitive radios (CRs) to provide protection for the PUs, whose activities are modeled as a Markov chain. Considering the reliability of the transmissions and channel sensing results, a state transition model is provided. Throughput is determined by formulating the effective capacity. The first derivative of the effective capacity is derived in the low-power regime, and the minimum bit energy requirements in the presence of QoS limitations and imperfect sensing results are identified. Minimum energy per bit is shown to be achieved by beamforming in the maximal-eigenvalue eigenspace of certain matrices related to the channel matrix. In a special case, wideband slope is determined for a more refined analysis of energy efficiency. Numerical results are provided for the throughput for various levels of buffer constraints and different number of transmit and receive antennas. The impact of interference constraints and benefits of multiple-antenna transmissions are determined. It is shown that increasing the number of antennas when the interference power constraint is stringent is generally beneficial. On the other hand, it is shown that, under relatively loose interference constraints, increasing the number of antennas beyond a certain level does not lead to much increase in throughput.

Joint Beamforming and Power Allocation for Cognitive MIMO Systems Under Imperfect CSI Based on Game Theory

The problem of joint beamforming and power allocation for cognitive multi-input multi-output systems is studied via game theory. The objective is to maximize the sum utility of secondary users (SUs...

Energy Efficient Spectrum Sharing Strategy Selection for Cognitive MIMO Interference Channels

In this paper, we propose a promising discrete game-theoretic framework for distributed energy efficient discrete spectrum sharing strategy selection (i.e., joint discrete power control and multimode precoding strategy selection) with limited feedback for cognitive MIMO interference channels. Given the competitive nature, the secondary users are assumed to be selfish and noncooperative, each of whom attempts to maximize its individual energy efficiency under a minimum data rate constraint and an interference power constraint. A mechanism for shutting down links is proposed to reduce interference and save energy. A payoff function is designed to guarantee the feasibility of the pure strategy Nash equilibrium with no need to know the infeasible strategy profiles (a spectrum sharing strategy profile is said to be feasible if the stated constraints are satisfied; otherwise, the spectrum sharing strategy profile is said to be infeasible, i.e., they may not satisfy the interference power constraint and minimum data rate constraint) in advance. We then investigate the existence and the feasibility of the pure strategy Nash equilibrium, and further devise a pricing-based distributed algorithm for spectrum strategy selection. The proposed algorithm is proved to converge to a feasible pure strategy Nash equilibrium under specific conditions. Moreover, by studying the relationship between our proposed game and the social optimum, we find that the pricing mechanism can result in Pareto improvement and lead to better convergence for the proposed distributed algorithm. Numerical results show that our designed algorithm significantly outperforms the random selection algorithm and the pricing mechanism has a dramatic effect in improving the system performance.

Joint Beamforming and Power Allocation for Multiple Primary Users and Secondary Users in Cognitive MIMO Systems via Game Theory

We consider a system where a licensed radio spectrum is shared by multiple primary users(PUs) and secondary users(SUs). As the spectrum of interest is licensed to primary network, power and channel allocation must be carried out within the cognitive radio network so that no excessive interference is caused to PUs. For this system, we study the joint beamforming and power allocation problem via game theory in this paper. The problem is formulated as a non-cooperative beamforming and power allocation game, subject to the interference constraints of PUs as well as the peak transmission power constraints of SUs. We design a joint beamforming and power allocation algorithm for maximizing the total throughput of SUs, which is implemented by alternating iteration of minimum mean square error based decision feedback beamforming and a best response based iterative power allocation algorithm. Simulation results show that the algorithm has better performance than an existing algorithm and can converge to a locally optimal sum utility.

On Degrees of Freedom of the Cognitive MIMO Two-Interfering Multiple-Access Channels

This paper characterizes the exact spatial Degrees of Freedom (DoF) region of the two-user multiple-input–multiple-output two-interfering multiple-access channels (2-IMACs), which models the uplink transmission in cellular networks, for three scenarios. The first scenario is the 2-IMAC without cognition, for which the achievability is generalized for more than two transmitters in each multiple-access channel. The two-user 2-IMACs' DoF regions are also derived for two different genie-aided cognition scenarios. Here, zero forcing by transmitters and interference alignment are studied in a network with more than two transmitters, whereas previous works dealt with two-transmitter networks. We also perform a comparative analysis on the DoF of the three scenarios.

Power Minimization in MIMO Cognitive Networks using Beamforming Games

We consider a multi-channel multi-user cognitive radio MIMO network in which each node controls its antenna radiation directions and allocates power for each data stream by adjusting its precoding matrices. Under a noncooperative game, we optimize the set of precoding matrices (one per channel) at each node so as to minimize the total transmit power in the network. Using recession analysis and the theory of variational inequalities, we obtain sufficient conditions that guarantee the existence and uniqueness of the game's Nash Equilibrium (NE). Low-complexity distributed algorithms are also developed by exploiting the strong duality of the convex per-user optimization problem. To improve the efficiency of the NE, we introduce pricing policies that employ a novel network interference function. Existence and uniqueness of the new NE under pricing are studied. Simulations confirm the effectiveness of our joint optimization approach.

Prescient Precoding in Heterogeneous DSA Networks with Both Underlay and Interweave MIMO Cognitive Radios

This work examines a novel heterogeneous dynamic spectrum access network where the primary users (PUs) coexist with both underlay and interweave cognitive transmitters (UCTs and ICTs); all terminals being potentially equipped with multiple antennas. UCTs are allowed to transmit concurrently with PUs subject to interference constraints, while the ICTs employ spectrum sensing and are permitted to access the shared spectrum only when both PUs and UCTs are absent. We investigate the design of MIMO precoding algorithms for the UCT that increase the detection probability at the ICTs, while simultaneously meeting a desired Quality-of-Service target to the underlay cognitive receivers (UCRs) and constraining interference leaked to PUs. The objective of such a proactive approach, referred to as prescient precoding, is to minimize the probability of interference from ICTs to the UCRs and primary receivers due to imperfect spectrum sensing. We begin with downlink prescient precoding algorithms for multiple single-antenna UCRs and multi-antenna PUs/ICTs. We then present prescient block-diagonalization algorithms for the MIMO underlay downlink where spatial multiplexing is performed for a plurality of multi-antenna UCRs. Numerical experiments demonstrate that prescient precoding by UCTs provides a pronounced performance gain compared to conventional underlay precoding strategies.

Dynamic Resource Allocation for MIMO Cognitive Networks With Low Control Traffic and Low Computational Complexity

Radio spectrum scarcity hampers the development of new wireless technologies and services. Cognitive radios have been proposed to enable unlicensed (or secondary) users to borrow locally idle bands of the spectrum provided that no significant interference is created for the licensed (or primary) users. Fast adaptation to the changing spectrum availability is naturally a major requirement in such systems. This adaptation consists of detecting the spectrum occupied by the primary users, computing a new resource allocation for the secondary network, and communicating this allocation through the network. In that context, we develop a resource allocation scheme for multi-input–multi-output wireless mesh networks. The proposed algorithm combines low computational complexity and light control traffic thanks to a combination of relevant approximations in the general nonpolynomial-hard allocation problem. The allocation consists of two steps. First, a centralized carrier allocation is performed at a coordinator node based on partial knowledge of the network parameters. Then, each node locally computes its power allocation through simple water-filling algorithms. Numerical results show that compared to state-of-the-art techniques, 10% of the total throughput of the network is sacrificed to reduce the computation time and the control traffic by two orders of magnitude.

Robust Utility Maximization and Admission Control for a MIMO Cognitive Radio Network

This paper considers a multiple-input-multiple-output (MIMO) cognitive radio network, in which a single primary user (PU) coexists with multiple secondary users (SUs). Standard cognitive radio techniques require perfect channel state information (CSI) and are sensitive to the errors in channel estimation. In practice, such errors are inevitable due to finite feedback resources, quantization errors, and other physical constraints. As a result, robustness has become a crucial issue. Under the assumption of norm-bounded channel imperfections, we develop a robust energy-aware design that strives to admit the maximum number of served SUs and enhance the transmit rate of the secondary links while using the least transmit power while imposing the upper limit of the interference temperature to the PU. A utility function is introduced to achieve the multi-objective function by dealing with the tradeoff between maximizing the transmit rate and minimizing the transmit power. Instead of using the deterministic target, the signal-to-interference-and-noise ratio (SINR) target becomes one of the ongoing optimization variables, which is dynamically adapted with the channel condition under the pre-specified bit-error-rate (BER) requirement, and acts as admission control implicitly, i.e., the cognitive link is not allowed to transmit as long as its SINR falls to zero. Due to its nonconvexity and NP-hardness, the underlying problem is reformulated in a semidefinite programming (SDP) form and solved via an iterative bisection search approach. Simulation results are provided to validate the robustness and efficiency of the proposed scheme.

Linear precoding design for cognitive multiuser MIMO systems using a leakage-based approach

In this paper, we develop linear precoding schemes for cognitive radio (CR) multiuser multiple-input multiple-output (MU-MIMO) downlink systems. A secondary user base station (SBS) with multiple secondary users (SUs) sharing the primary user (PU) spectrum is considered. In the proposed scheme, the block diagonalisation (BD) algorithm is adopted to remove the co-channel interference from the SBS to the PU completely, and the matching weighted signal-to-leakage-and-noise ratio (SLNR) maximisation algorithm is proposed to mitigate interference between SUs. We also discuss the cases where the SBS has only partial channel information and the channel estimation with errors, respectively. The proposed scheme does not require a strict restriction on the number of transmit and receive antennas. Simulation results show that the proposed scheme can achieve high sum rate throughput with affordable complexity.

Sum-rate maximising in cognitive MIMO ad-hoc networks using weighted MMSE approach

This reported work focuses on weighted sum-rate maximisation (WSRM) of cognitive radio ad-hoc networks, where a K user multiple-input multiple-output interference network (K-MIMO-IFN) uses the same spectrum with a licenced primary user. Because the WSRM problem in K-MIMO-IFN is non-convex and it is difficult to get an optimal solution directly, the weighted minimum mean square error (MMSE) approach is used to make the problem easier to handle. This report then proposes a dual-MMSE-algorithm, which iteratively finds a local optimal solution and only needs the local channel knowledge. Simulation results show that the proposed algorithm outperforms other conventional algorithms.

Interference mitigation for cognitive radio MIMO systems based on practical precoding

In this paper, we propose two subspace-projection-based precoding schemes, namely, full-projection (FP)- and partial-projection (PP)-based precoding, for a cognitive radio multiple-input multiple-output (CR-MIMO) network to mitigate its interference to a primary time-division-duplexing (TDD) system. The proposed precoding schemes are capable of estimating interference channels between CR and primary networks, and incorporating the interference from the primary to the CR system into CR precoding via a novel sensing approach. Then, the CR performance and resulting interference of the proposed precoding schemes are analyzed and evaluated. By fully projecting the CR transmission onto a null space of the interference channels, the FP-based precoding scheme can effectively avoid interfering the primary system with boosted CR throughput. While, the PP-based scheme is able to further improve the CR throughput by partially projecting its transmission onto the null space.

Power Allocation Over Fading Cognitive MIMO Channels: An Ergodic Capacity Perspective

This paper studies the power allocation problem for a cognitive radio (CR) multiple-input-multiple-output (MIMO) system under spectrum sharing with an existing primary radio network. In particular, the ergodic capacity maximization problem is studied in the Rayleigh fading cognitive MIMO channel under both the total transmit power constraint and a set of interference power constraints where each is applied at one of the primary receivers (PRs). This paper considers that the channel from primary transmitter (PT) to secondary receiver (SR), and the channel from secondary transmitter (ST) to SR are both in short-term fading due to the mobility of SR, whereas the channels from ST to PRs are in long-term fading. By using the Lagrangian dual method, the optimal transmit precoding matrix is derived, and some nearly optimal power allocation algorithms are proposed to maximize the bounds of secondary user ergodic capacity. Performance analysis and simulation results show that the proposed schemes can approach the comparative capacity of the optimal power allocation algorithm, which has perfect instant channel state information (CSI), particularly when the antenna number of the ST exceeds the total antenna number of PRs.

Space Correlation Based Joint Admission Control in Cognitive MIMO Systems

A joint transmit-receive admission control strategy based on spatial information in cognitive MIMO systems is proposed. By exploiting space correlation features between cognitive transmission and interference from cognitive base station (CBS) to primary user (PU) as well as from primary base station (PBS) to cognitive user (CU), appropriate primary system and its channel are selected. Then spectrum sharing is carried out employing signal subspace orthogonal projection. Simulation results show that the proposed scheme could achieve near-optimal system throughput performance with reduced complexity.

Cognitive Radio MIMO Gaussian Broadcast Channels with the Power Constraint

The cognitive radio multiple-input multiple-output Gaussian broadcast channels are studied where multiple antennas are available for both primary users and secondary users in a spectrum sharing environment, and the sum-rate capacity is also obtained under both the SUs’ transmit power constraint and interference power constraint at the primary receivers. The paper principally consists of two steps. First, a duality technique and dirty paper coding are adopted to simplify the channels. Second, we propose an iterative power allocation algorithm to obtain the maximum sum-rate capacity and examine the effects of the constraint parameters on the concerned quantities. Finally, numerical simulation results are presented to validate the proposed theoretical analysis.