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Optimal resource allocation for MIMO ad hoc cognitive radio networks
 in Proc. 46th Annu. Allerton Conf. Commun., Control, Comput
, 2008
"... Abstract—Maximization of the weighted sumrate of secondary users (SUs) possibly equipped with multiantenna transmitters and receivers is considered in the context of cognitive radio (CR) networks with coexisting primary users (PUs). The total interference power received at the primary receiver is ..."
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Abstract—Maximization of the weighted sumrate of secondary users (SUs) possibly equipped with multiantenna transmitters and receivers is considered in the context of cognitive radio (CR) networks with coexisting primary users (PUs). The total interference power received at the primary receiver is constrained to maintain reliable communication for the PU. An interference channel configuration is considered for ad hoc networking, where the receivers treat the interference from undesired transmitters as noise. Without the CR constraint, a convergent distributed algorithm is developed to obtain (at least) a locally optimal solution. With the CR constraint, a semidistributed algorithm is introduced. An alternative centralized algorithm based on geometric programming and network duality is also developed. Numerical results show the efficacy of the proposed algorithms. The novel approach is flexible to accommodate modifications aiming at interference alignment. However, the standalone weighted sumrate optimal schemes proposed here have merits over interferencealignment alternatives especially for practical SNR values. Index Terms—Ad hoc network, cognitive radio, interference network, MIMO, optimization. I.
Decomposition by partial linearization: Parallel optimization of multiuser systems
 IEEE Trans. on Signal Processing
, 2014
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A Block Successive Upper Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization
, 2014
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Giannakis, “Distributed optimal beamformers for cognitive radios robust to channel uncertainties
 IEEE Trans. Sig. Proc
, 2012
"... Abstract—Through spatial multiplexing and diversity, multiinput multioutput (MIMO) cognitive radio (CR) networks can markedly increase transmission rates and reliability, while controlling the interference inflicted to peer nodes and primary users (PUs) via beamforming. The present paper optimiz ..."
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Abstract—Through spatial multiplexing and diversity, multiinput multioutput (MIMO) cognitive radio (CR) networks can markedly increase transmission rates and reliability, while controlling the interference inflicted to peer nodes and primary users (PUs) via beamforming. The present paper optimizes the design of transmit and receivebeamformers for ad hoc CR networks when CRtoCR channels are known, but CRtoPU channels cannot be estimated accurately. Capitalizing on a normbounded channel uncertainty model, the optimal beamforming design is formulated to minimize the overall meansquare error (MSE) from all data streams, while enforcing protection of the PU system when the CRtoPU channels are uncertain. Even though the resultant optimization problem is nonconvex, algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations, along with suitable convex approximation techniques. Enticingly, the novel schemes also lend themselves naturally to distributed implementations. Numerical tests are reported to corroborate the analytical findings. Index Terms—Beamforming, channel uncertainty, cognitive radios, distributed algorithms, MIMO wireless networks, robust optimization. I.
Robust MIMO Cognitive Radio Systems Under Interference Temperature Constraints
 IEEE Journal on Selected Areas in Communications
, 2013
"... Abstract—Cognitive Radio (CR) systems are built on the coexistence of primary users (PUs) and secondary users (SUs), the latter being allowed to share spectral resources with the PUs but under strict interference limitations. However, such limitations may easily be violated by SUs if perfect SUtoP ..."
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Abstract—Cognitive Radio (CR) systems are built on the coexistence of primary users (PUs) and secondary users (SUs), the latter being allowed to share spectral resources with the PUs but under strict interference limitations. However, such limitations may easily be violated by SUs if perfect SUtoPU channel state information (CSI) is not available at the secondary transmitters, which always happens in practice. In this paper, we propose a distributed design of MIMO CR networks under global interference temperature constraints that is robust (in the worstcase sense) against SUtoPU channel uncertainties. More specifically, we consider two alternative formulations that are complementary to each other in terms of signaling and system performance, namely: a gametheoretical design and a socialoriented optimization. To study and solve the proposed formulations we hinge on the new theory of finitedimensional variational inequalities (VI) in the complex domain and a novel parallel decomposition technique for nonconvex sumutility problems with coupling constraints, respectively. A major contribution of this paper is to devise a new class of distributed bestresponse algorithms with provable convergence. The algorithms differ in computational complexity, convergence speed, communication overhead, and achievable performance; they are thus applicable to a variety of CR scenarios, either cooperative or noncooperative, which allow the SUs to explore the tradeoff between signaling and performance.
PriceBased Joint Beamforming and Spectrum Management in MultiAntenna Cognitive Radio Networks
"... Abstract—We consider the problem of maximizing the throughput of a multiantenna cognitive radio (CR) network. With spatial multiplexing over each frequency band, a multiantenna CR node controls its antenna radiation directions and allocates power for each data stream by appropriately adjusting its ..."
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Abstract—We consider the problem of maximizing the throughput of a multiantenna cognitive radio (CR) network. With spatial multiplexing over each frequency band, a multiantenna CR node controls its antenna radiation directions and allocates power for each data stream by appropriately adjusting its precoding matrix. Our objective is to design a set of precoding matrices (one per band) at each CR node so that power and spectrum are optimally allocated for the node and its interference is steered away from unintended receivers. The problem is nonconvex, with the number of variables growing quadratically with the number of antenna elements. To tackle it, we translate it into a noncooperative game. We derive an optimal pricing policy for each node, which adapts to the node’s neighboring conditions and drives the game to a NashEquilibrium (NE). The network throughput under this NE equals to that of a locally optimal solution of the nonconvex centralized problem. To find the set of precoding matrices at each node (best response), we develop a lowcomplexity distributed algorithm by exploiting the strong duality of the convex peruser optimization problem. The number of variables in the distributed algorithm is independent of the number of antenna elements. A centralized (cooperative) algorithm is also developed. Simulations show that the network throughput under the distributed algorithm rapidly converges to that of the centralized one. Finally, we develop a MAC protocol that implements our resource allocation and beamforming scheme. Extensive simulations show that the proposed protocol dramatically improves the network throughput and reduces power consumption. Index Terms—Noncooperative game, pricing, cognitive radio, MIMO, power allocation, frequency management, beamforming. I.
A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities
 Proceedings of the 2011 Winter Simulation Conference
, 2011
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Network Formation Games in Cooperative MIMO Interference Systems
"... Abstract—This paper considers the cooperative optimization of mutual information in the MIMO Gaussian interference channel in a fully distributed manner via game theory. Null shaping constraints are enforced in the design of transmit covariance matrices to enable interference mitigation among links. ..."
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Abstract—This paper considers the cooperative optimization of mutual information in the MIMO Gaussian interference channel in a fully distributed manner via game theory. Null shaping constraints are enforced in the design of transmit covariance matrices to enable interference mitigation among links. The transmit covariance matrices leading to the Nash Equilibrium (NE) are derived, and the existence and uniqueness of the NE is analyzed. The formation of the cooperative sets, that represent the cooperation relationship among links, is considered as coalition games and network formation games. We prove that the proposed coalition formation (CF) and coalition graph formation (CGF) algorithms are Nashstable, and the proposed network formation (NF) algorithm converges to a Nash Equilibrium. Simulation results show that the proposed CF and CGF algorithms have significant advantages when the antennas at the transmitters is large, and the proposed NF algorithm enhances the sum rate of the system apparently even at low signaltonoise ratio region and/or with small number of transmit antennas. Index Terms—Game theory, MIMO Interference channel, cooperative network, rate maximization. I.
LEARNING DISTRIBUTED POWER ALLOCATION POLICIES IN MIMO CHANNELS
"... In this paper 1, we study the discrete power allocation game for the fast fading multipleinput multipleoutput multiple access channel. Each player or transmitter chooses its own transmit power policy from a certain finite set to optimize its individual transmission rate. First, we prove the existe ..."
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In this paper 1, we study the discrete power allocation game for the fast fading multipleinput multipleoutput multiple access channel. Each player or transmitter chooses its own transmit power policy from a certain finite set to optimize its individual transmission rate. First, we prove the existence of at least one pure strategy Nash equilibrium. Then, we investigate two learning algorithms that allow the players to converge to either one of the NE states or to the set of correlated equilibria. At last, we compare the performance of the considered discrete game with the continuous game in [7]. 1.
Robust Downlink Beamforming With Partial Channel State Information for Conventional and Cognitive Radio Networks
"... Abstract—We address the problemofrobustmultiuserdownlink beamforming under the assumption that the transmitter has partial covariancebased channel state information (CSI). In our approach, the uncertainty on the channel covariance matrices is assumed to be confined in an ellipsoid of given size and ..."
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Abstract—We address the problemofrobustmultiuserdownlink beamforming under the assumption that the transmitter has partial covariancebased channel state information (CSI). In our approach, the uncertainty on the channel covariance matrices is assumed to be confined in an ellipsoid of given size and shape, where prior knowledge about the statistical distribution of the CSI mismatch is taken into account. The goal is to minimize the transmitted power under the worstcase qualityofservice (QoS) constraints. We extend the developed robust problem to downlink beamforming in cognitive radio (CR) networks where QoS constraints apply to the users of the secondary network (SN) and interference leaked to the primary users (PUs) is required to be below a given interference threshold. We avoid the coarse approximations used by previous solutions and obtain exact reformulations for both worstcase problems based on Lagrange duality. The resulting problems can then be approximated using semidefinite relaxation (SDR). Further, we consider a popular alternative robust approach that is based on probabilistic QoS and interference constraints and show that both approaches are generally equivalent. Computer simulations show that the proposed techniques provide substantial performance improvements over earlier robust downlink beamforming techniques for both the conventional and the CR scenarios. Index Terms—Downlink beamforming, cognitive radio, convex optimization, user qualityofservice. I.