In this paper, joint optimization of throughput and error rate via cooperative spectrum sensing in cognitive radio networks is investigated. An optimization problem is formulated, which aims to maximize the average ac...
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In this paper, joint optimization of throughput and error rate via cooperative spectrum sensing in cognitive radio networks is investigated. An optimization problem is formulated, which aims to maximize the average achievable throughput of cooperating cognitive users while keeping the error rate at a lower level. This is a multi-variable nonconvex optimization problem. Instead of solving it directly, we propose an iterative algorithm which jointly optimizes the threshold and sensing time together to decrease the effect of the error and to increase the achievable throughput. We first prove that the local error rate of the cognitive user is a convex function of energy threshold and determine a closed-form for the optimal threshold which minimizes the error rate. Then we show that the AND rule is the optimal fusion rule to maximize the achievable throughput. Furthermore we determine the least number of cooperating cognitive users that can guarantee a minimum target error rate. This initial nonconvex problem is converted into a single variable convex optimization problem which can be successfully solved by common methods e.g. Newton's method. Simulation results illustrate the fast convergence and effectiveness of the joint iterative algorithm. (c) 2012 Elsevier B.V. All rights reserved.
Traveling salesman problem (TSP) is one of the extensively studied NP-hard problems. The recent research showed that the TSP on sparse graphs could be resolved in the relatively shorter computation time than that on t...
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Traveling salesman problem (TSP) is one of the extensively studied NP-hard problems. The recent research showed that the TSP on sparse graphs could be resolved in the relatively shorter computation time than that on the complete graph K-n. This paper updates a previous probability model for the optimal Hamiltonian cycle edges according to the frequency quadrilaterals in Kn. A new binomial distribution for TSP is rebuilt to show the probability that an edge e has the frequency 5 in a frequency quadrilateral. Based on the binomial distribution, an iterative algorithm is designed to compute the sparse graphs for TSP. There are two steps at each computation cycle. Firstly, N frequency quadrilaterals containing an edge e in the input graph is chosen to compute the average frequency (f) over bar (e) with the frequency quadrilaterals where e has the frequency 5. Secondly, half edges with the small values (f) over bar (e) are eliminated. The two steps are repeated until a sparse graph is computed. The computation time of the algorithm is O(Nn(2)). For the TSP instances in the TSPLIB, the experimental results illustrated that the sparse graphs with the O(n log(2)n) edges are computed and the original optimal solution is preserved. The experiments means the optimal Hamiltonian cycle edges have the bigger average frequency (f) over bar (e) in K-n and the subgraphs of K-n so they are preserved in the computation process.
Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AXB = E that is appropriate when there is error in the matrix E. In this paper, by means of real rep...
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Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AXB = E that is appropriate when there is error in the matrix E. In this paper, by means of real representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, which is different from that in [T. Jiang, L. Chen, Algebraic algorithms for least squares problem in quaternionic quantum theory, Comput. Phys. Comm. 176 (2007) 481-485: T. Jiang, M. Wei, Equality constrained least squares problem over quaternion field, Appl. Math. Lett. 16 (2003) 883-888), and derive an iterative method for finding the minimum-norm solution of the QLS problem in quaternionic quantum theory. (C) 2008 Elsevier B.V. All rights reserved.
In this paper, a novel iterative algorithm is developed for solving the coupled algebraic Riccati equation arising from the quadratic optimal control problem for continuous-time Markovian jump linear systems. First, t...
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In this paper, a novel iterative algorithm is developed for solving the coupled algebraic Riccati equation arising from the quadratic optimal control problem for continuous-time Markovian jump linear systems. First, two existing iterative algorithms to solve the coupled Riccati matrix equation are reviewed. Next, based on analysis for these two algorithms, a new iterative algorithm that combines both the information in the current iterative step and the information in the last iterative step is proposed. It is shown that the proposed algorithm with proper initial conditions can monotonically converge to the unique positive definite solution of the coupled Riccati matrix equation if the associated Markovian jump system is stochastically stabilizable. Also, numerical examples show that the presented algorithm is faster than some previous algorithms when the weighted parameter is appropriately selected. (C) 2019 Elsevier Inc. All rights reserved.
The paper is indicated to constructing a modified conjugate gradient iterative (MCG) algorithm to solve the generalized periodic multiple coupled Sylvester matrix equations. It can be proved that the proposed approach...
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The paper is indicated to constructing a modified conjugate gradient iterative (MCG) algorithm to solve the generalized periodic multiple coupled Sylvester matrix equations. It can be proved that the proposed approach can find the solution within finite iteration steps in the absence of round-off errors. Furthermore, we provide a method for choosing the initial matrices to obtain the least Frobenius norm solution of the system. Some numerical examples are illustrated to show the performance of the proposed approach and its superiority over the existing method CG. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Let C be a nonempty closed convex subset of a real strictly convex and reflexive Banach space E which has a uniformly Gateaux differentiable norm. Let f : C -> C be a given contractive mapping and {T-n}(n-1)(infini...
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Let C be a nonempty closed convex subset of a real strictly convex and reflexive Banach space E which has a uniformly Gateaux differentiable norm. Let f : C -> C be a given contractive mapping and {T-n}(n-1)(infinity) : C -> C be an infinite family of nonexpansive mappings such that the common. fixed point sets F := boolean AND(infinity)(n-1) F(T-n) not equal empty set. Let {alpha(n)} and {beta(n)} be two real sequences in [0, 1]. For given x(0) is an element of C arbitrarily, let the sequence {x(n)} be generated iteratively by x(n+1) = alpha(n)f(x(n)) + beta(n)x(n) + (1 - alpha(n) - beta(n))W(n)x(n), where W-n is the W-mapping generated by the mappings T-n;Tn-1,..., T-1 and xi(n), xi(n-1),..., xi(1). Suppose the iterative parameters {alpha(n)} and {beta(b)} satisfy the following control conditions: (C1) lim(n ->infinity) alpha(n) = 0;(C2) Sigma(infinity)(n-0) alpha(n) = infinity;(B5) lim sup(n ->infinity) beta(n) < 1. Then the sequence {x(n)} converges strongly to p is an element of F where p is the unique solution in F to the following variational inequality: <(I - f)p,j(p - x*)> <= 0 for all x* is an element of F. (C) 2008 Elsevier Inc. All rights reserved.
In this paper, we study a new system of generalized mixed equilibrium problems involving skew-symmetric bifunctions (SGMEP) in reflexive Banach spaces. A system of auxiliary mixed equilibrium problems (SAMEP) for solv...
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In this paper, we study a new system of generalized mixed equilibrium problems involving skew-symmetric bifunctions (SGMEP) in reflexive Banach spaces. A system of auxiliary mixed equilibrium problems (SAMEP) for solving the SGMEP is introduced and the existence and uniqueness of the solutions of the SAMEP is first proved. Next, by using the auxiliary principle technique, a new iterative algorithm to compute the approximate solutions of the SGMEP is suggested and analyzed. Finally, the strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild conditions. These results improve, unify and generalize some known results in recent literature. (C) 2011 Elsevier Inc. All rights reserved.
A fast iterative algorithm for frequency estimation is developed in this paper to improve the frequency tracking performance. If the signal is transformed by a mathematical tool, the signal to noise ratio (SNR) should...
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A fast iterative algorithm for frequency estimation is developed in this paper to improve the frequency tracking performance. If the signal is transformed by a mathematical tool, the signal to noise ratio (SNR) should not be greatly reduced after the transformation. The analysis presented in this paper showed that the traditional method for frequency estimation causes large noise at high frequency range, therefore, the suitable estimation range of traditional method is only from 0 to fs/6 Hz (fs is the sample frequency). In order to overcome this limitation, a new structure of iterative algorithm is established to extend the upper bound frequency from fs/6 to fs/2 Hz. The experimental noisy sinusoid signal frequency estimation and chirp signal frequency tracking confirmed that the novel algorithm showed improved performance. Furthermore, the average estimation error was decreased over 30% (under SNR = 15 dB) when applying the novel iterative algorithm. The novel iterative algorithm will have broad applications in fields of signal processing and communication systems. (C) 2016 Elsevier Ltd. All rights reserved.
In this paper, we proposed an algorithm for solving the linear systems of matrix equations {Sigma(N)(i=1) A(i)((1))X(i)B(i)((1)) = C-(1), over the generalized (P, Q)-reflexive matrix X-l is an element of R-nxm (A(l)((...
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In this paper, we proposed an algorithm for solving the linear systems of matrix equations {Sigma(N)(i=1) A(i)((1))X(i)B(i)((1)) = C-(1), over the generalized (P, Q)-reflexive matrix X-l is an element of R-nxm (A(l)((i)) is an element of Sigma(N)(i=1) A(i)((1))X(i)B(i)((1)) = C-(M). R-pxn, B-l((i)) is an element of R-mxq, C-(i) is an element of R-pxq, l = 1, 2,..., N, i = 1, 2,..., M). According to the algorithm, the solvability of the problem can be determined automatically. When the problem is consistent over the generalized (P, Q)-reflexive matrix X-l (l = 1,..., N), for any generalized (P, Q)-reflexive initial iterative matrices X-l(0) (l = 1,..., N), the generalized (P, Q)-reflexive solution can be obtained within finite iterative steps in the absence of roundoff errors. The unique least-norm generalized (P, Q)-reflexive solution can also be derived when the appropriate initial iterative matrices are chosen. A sufficient and necessary condition for which the linear systems of matrix equations is inconsistent is given. Furthermore, the optimal approximate solution for a group of given matrices Y-l (l = 1,..., N) can be derived by finding the least-norm generalized (P, Q)-reflexive solution of a new corresponding linear system of matrix equations. Finally, we present a numerical example to verify the theoretical results of this paper. (C) 2011 Elsevier Ltd. All rights reserved.
In the "first-order reliability method" (FORM), the HL-RF iterative algorithm is a recommended and widely used one to locate the design point and calculate the reliability index. However it may fail to conve...
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In the "first-order reliability method" (FORM), the HL-RF iterative algorithm is a recommended and widely used one to locate the design point and calculate the reliability index. However it may fail to converge if the limit state surface at the design point is highly nonlinear. In this paper, an easy iterative algorithm, which introduces a "new" step length to control the convergence of the sequence and can be named as finite-step-length iterative algorithm, is present. It is proved that the HL-RF method is a special case of this proposed algorithm when the step length tends to infinity and the reason why the HL-RF diverges is illustrated. This proposed algorithm is much easier than other optimization schemes, especially than the modified HL-RF algorithm, because the process of line search for obtaining the step length is not needed. Numerical results indicate that the proposed algorithm is effective and as simple as the HL-RF but more robust.
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