In this paper, we consider the problem of optimizing the transmit covariance matrix for a multiple-input multiple-output (MIMO) Gaussian wiretap channel. The scenario of interest consists of a transmitter, a legitimat...
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ISBN:
(纸本)9781479928934
In this paper, we consider the problem of optimizing the transmit covariance matrix for a multiple-input multiple-output (MIMO) Gaussian wiretap channel. The scenario of interest consists of a transmitter, a legitimate receiver, and multiple non-cooperating eavesdroppers that are all equipped with multiple antennas. Specifically, we design the transmit covariance matrix by maximizing the secrecy rate under a total power constraint, which is a non-convexdifference of convex functions (DC) programming problem. We develop an algorithm, termed alternating matrix POTDC algorithm, based on alternating optimization of the eigenvalues and the eigenvectors of the transmit covariance matrix. The proposed alternating matrix POTDC method provides insights into the non-convex nature of the problem and is very general, i.e., additional constraints on the covariance matrix can easily be incorporated. The secrecy rate performance of the proposed algorithm is demonstrated by simulations.
In this paper, we consider a multiple-input multiple-output (MIMO) broadcast relay channel (BRC), in which the communication of a multi-antenna base station (BS) with several multi-antenna mobile stations (MS) is assi...
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ISBN:
(纸本)9781479914814
In this paper, we consider a multiple-input multiple-output (MIMO) broadcast relay channel (BRC), in which the communication of a multi-antenna base station (BS) with several multi-antenna mobile stations (MS) is assisted by a fixed half-duplex multi-antenna relay station (RS). Applying dirty paper coding (DPC) at the BS and beamforming at the RS, we jointly optimize the transmit covariance matrices at the BS and the beamforming matrix at the RS by maximizing the system sum rate, which is a nonconvex problem. To solve this problem, we resort to the more tractable sum rate maximization in the dual multiple access relay channel (MARC), which is still a nonconvexdifference of convex functions (DC) programming problem. We develop an iterative algorithm, termed alternating matrix polynomial time DC (POTDC) algorithm, based on an alternating optimization of the beamforming matrix and the transmit covariance matrices. The resulting covariance matrices for the MARC are then mapped to the desired BRC covariance matrices. The sum rate performance of the proposed algorithm is demonstrated by simulations.
The problem of finding a global minimizer of the difference of polyhedral functions is considered. By means of conjugate functions, necessary and sufficient conditions for the unboundedness and the boundedness of such...
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The problem of finding a global minimizer of the difference of polyhedral functions is considered. By means of conjugate functions, necessary and sufficient conditions for the unboundedness and the boundedness of such functions in R (n) are derived. Using hypodifferentials of polyhedral functions, necessary and sufficient conditions for a global unconstrained minimum on R (n) are proved.
In this paper we establish necessary as well as sufficient conditions for a given feasible point to be a global minimizer of smooth minimization problems with mixed variables. These problems, for instance, cover box c...
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In this paper we establish necessary as well as sufficient conditions for a given feasible point to be a global minimizer of smooth minimization problems with mixed variables. These problems, for instance, cover box constrained smooth minimization problems and bivalent optimization problems. In particular, our results provide necessary global optimality conditions for differenceconvex minimization problems, whereas our sufficient conditions give easily veri. able conditions for global optimality of various classes of nonconvex minimization problems, including the class of difference of convex and quadratic minimization problems. We discuss numerical examples to illustrate the optimality conditions.
Let C(n,p) be the set of p-compositions of an integer n, i.e., the set of p-tuples alpha = (alpha (1),...,alpha (p)) of nonnegative integers such that alpha (1) +...+ alpha (p) = n. The main result of this paper is an...
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Let C(n,p) be the set of p-compositions of an integer n, i.e., the set of p-tuples alpha = (alpha (1),...,alpha (p)) of nonnegative integers such that alpha (1) +...+ alpha (p) = n. The main result of this paper is an explicit formula for the determinant of the matrix whose entries are alpha (beta) = alpha (beta1)(1) ... alpha (betap)(p) where alpha, beta is an element of C (n, p). The formula shows that the determinant is positive and has a nice factorization. As an application, it is shown that the polynomials p(alpha)(x) = (alpha (1)x(1) + ... +alpha (p)x(p))(n) with alpha is an element of C(n, p) form a basis of the vector space H-n[x(1),..., x(p)] of homogeneous polynomials of degree n in p variables. The result is of interest in the context of global optimization because it allows an explicit representation of polynomials as a difference of convex functions.
In this paper, we show that a DC representation can be obtained explicitly for the composition of a gauge with a DC mapping, so that the optimization of certain functions involving terms of this kind can be made by us...
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In this paper, we show that a DC representation can be obtained explicitly for the composition of a gauge with a DC mapping, so that the optimization of certain functions involving terms of this kind can be made by using standard DC optimization techniques. Applications to facility location theory and multiple-criteria decision making are presented.
Simple necessary optimality conditions are formulated for a function f of the form f = g - h, where g and h are nonsmooth functions. Related sufficient conditions are given for local minimization and global minimization.
Simple necessary optimality conditions are formulated for a function f of the form f = g - h, where g and h are nonsmooth functions. Related sufficient conditions are given for local minimization and global minimization.
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