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Maximizing Sum Rates in Cognitive Radio Networks: Convex Relaxation and Global Optimization Algorithms
"... Abstract—A key challenge in wireless cognitive radio networks is to maximize the total throughput also known as the sum rates of all the users while avoiding the interference of unlicensed band secondary users from overwhelming the licensed band primary users. We study the weighted sum rate maximiza ..."
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Abstract—A key challenge in wireless cognitive radio networks is to maximize the total throughput also known as the sum rates of all the users while avoiding the interference of unlicensed band secondary users from overwhelming the licensed band primary users. We study the weighted sum rate maximization problem with both power budget and interference temperature constraints in a cognitive radio network. This problem is nonconvex and generally hard to solve. We propose a reformulationrelaxation technique that leverages nonnegative matrix theory to first obtain a relaxed problem with nonnegative matrix spectral radius constraints. A useful upper bound on the sum rates is then obtained by solving a convex optimization problem over a closed bounded convex set. It also enables the sumrate optimality to be quantified analytically through the spectrum of speciallycrafted nonnegative matrices. Furthermore, we obtain polynomialtime verifiable sufficient conditions that can identify polynomialtime solvable problem instances, which can be solved by a fixedpoint algorithm. As a byproduct, an interesting optimality equivalence between the nonconvex sum rate problem and the convex maxmin rate problem is established. In the general case, we propose a global optimization algorithm by utilizing our convex relaxation and branchandbound to compute an optimal solution. Our technique exploits the nonnegativity of the physical quantities, e.g., channel parameters, powers and rates, that enables key tools in nonnegative matrix theory such as the (linear and nonlinear) PerronFrobenius theorem, quasiinvertibility, FriedlandKarlin inequalities to be employed naturally. Numerical results are presented to show that our proposed algorithms are theoretically sound and have relatively fast convergence time even for largescale problems. Index Terms—Optimization, convex relaxation, cognitive radio networks, nonnegative matrix theory. I.
IEEE JOURNAL OF SELECTED AREAS IN COMMUNICATIONS 1 Beamforming Duality and Algorithms for Weighted Sum Rate Maximization in Cognitive Radio Networks
"... In this paper, we investigate the joint design of transmit beamforming and power control to maximize the weighted sum rate in the multipleinput singleoutput (MISO) cognitive radio network constrained by arbitrary power budgets and interference temperatures. The nonnegativity of the physical quanti ..."
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In this paper, we investigate the joint design of transmit beamforming and power control to maximize the weighted sum rate in the multipleinput singleoutput (MISO) cognitive radio network constrained by arbitrary power budgets and interference temperatures. The nonnegativity of the physical quantities, e.g., channel parameters, powers, and rates, is exploited to enable key tools in nonnegative matrix theory, such as the (linear and nonlinear) PerronFrobenius theory, quasiinvertibility, and FriedlandKarlin inequalities, to tackle this nonconvex problem. Under certain (quasiinvertibility) sufficient condition, we propose a tight convex relaxation technique that relaxes multiple constraints to bound the global optimal value in a systematic way. Then, a singleinput multipleoutput (SIMO)MISO duality is established through a virtual dual SIMO network and Lagrange duality. This SIMOMISO duality is equivalent to the zero Lagrange duality gap condition that connects the optimality conditions of the primal MISO network and the virtual dual SIMO network. Moreover, by exploiting the SIMOMISO duality, an algorithm is developed to solve the sum rate maximization problem optimally. Numerical examples demonstrate the computational efficiency of our algorithm when the number of transmit antennas is large. Index Terms Optimization, convex relaxation, cognitive radio network, nonnegative matrix theory, quasiinvertibility, KarushKuhnTucker conditions, PerronFrobenius theorem. I.
RESEARCH Open Access
"... Sum rate maximization via joint scheduling and link adaptation for interferencecoupled wireless systems Eduardo D Castañeda1,2*, Ramiro SamanoRobles2 and Atílio Gameiro1,2 The work presented in this paper addresses the sum rate maximization problem for the downlink of a wireless network where mult ..."
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Sum rate maximization via joint scheduling and link adaptation for interferencecoupled wireless systems Eduardo D Castañeda1,2*, Ramiro SamanoRobles2 and Atílio Gameiro1,2 The work presented in this paper addresses the sum rate maximization problem for the downlink of a wireless network where multiple transmitterreceiver links share the same medium and thus potentially interfere with each other. The solution of this problem requires the optimization of two aspects: the first one is the set of links that can be jointly scheduled, and the second is the set modulation and coding schemes (MCSs) that maximize the sum rate. A feasible link achieves a certain MCS if its signaltointerferenceplusnoise ratio (SINR) is above a threshold or target SINR associated with the MCS and the SINR of each link is coupled with the other links ’ powers that are required to achieve their respective MCSs. Since the available MCSs form a finite set, the rate maximization problem has a combinatorial nature. We present iterative algorithms that find a suboptimal solution to the combinatorial problem by operating in two phases. Phase one verifies the feasibility of the MCS assignment by performing either eigenvalue analysis or power consumption analysis, and phase two uses the feasibility information delivered by phase one to modify either the set of links (user removal) or the MCS assignment if feasibility conditions are not fulfilled. Our approach extends the concept of user removal to the case of adaptive modulation, and this generalization allows us to schedule users more efficiently, improving outage probability figures. Numerical results show that the proposed algorithms achieved a good tradeoff between sum rate performance and complexity. Moreover, our algorithms are a low complex alternative to the stateoftheart userremoval algorithms with minimum gap in outage performance.