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53
A unified framework for optimizing linear nonregenerative multicarrier MIMO relay communication systems
 IEEE TRANS. SIGNAL PROCESS
, 2009
"... In this paper, we develop a unified framework for linear nonregenerative multicarrier multipleinput multipleoutput (MIMO) relay communications in the absence of the direct source–destination link. This unified framework classifies most commonly used design objectives such as the minimal meansqu ..."
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Cited by 93 (50 self)
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In this paper, we develop a unified framework for linear nonregenerative multicarrier multipleinput multipleoutput (MIMO) relay communications in the absence of the direct source–destination link. This unified framework classifies most commonly used design objectives such as the minimal meansquare error and the maximal mutual information into two categories: Schurconcave and Schurconvex functions. We prove that for Schurconcave objective functions, the optimal source precoding matrix and relay amplifying matrix jointly diagonalize the source–relay–destination channel matrix and convert the multicarrier MIMO relay channel into parallel singleinput singleoutput (SISO) relay channels. While for Schurconvex objectives, such joint diagonalization occurs after a specific rotation of the source precoding matrix. After the optimal structure of the source and relay matrices is determined, the linear nonregenerative relay design problem boils down to the issue of power loading among the resulting SISO relay channels. We show that this power loading problem can be efficiently solved by an alternating technique. Numerical examples demonstrate the effectiveness of the proposed framework.
New bounds on the LiebThirring constants
 Invent. Math
"... ABSTRACT. Improved estimates on the constants Lγ,d, for 1/2 < γ < 3/2, d ∈ N in the inequalities for the eigenvalue moments of Schrödinger operators are established. 1. ..."
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Cited by 25 (9 self)
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ABSTRACT. Improved estimates on the constants Lγ,d, for 1/2 < γ < 3/2, d ∈ N in the inequalities for the eigenvalue moments of Schrödinger operators are established. 1.
MIMO diversity in the presence of double scattering
 IEEE Trans. Inform. Theory
"... Abstract—The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MI ..."
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Cited by 16 (4 self)
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Abstract—The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MIMO) systems, with an emphasis on orthogonal space–time block codes (OSTBC), in terms of the symbol error probability (SEP), the effective fading figure (EFF), and the capacity at low signaltonoise ratio (SNR). In particular, we consider a general family of MIMO channels known as doublescattering channels—i.e., Rayleigh product MIMO channels—which encompasses a variety of propagation environments from independent and identically distributed (i.i.d.) Rayleigh to degenerate keyhole or pinhole cases by embracing both rankdeficient and spatial correlation effects. It is shown that a MIMO system with transmit and receive antennas achieves the diversity of order
Minimization of convex functionals over frame operators
 Adv. Comput. Math
"... Abstract. We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the BenedettoFickus frame potential. Our approach depends on majorization techniques. We also consider some perturb ..."
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Cited by 15 (9 self)
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Abstract. We present results about minimization of convex functionals defined over a finite set of vectors in a finite dimensional Hilbert space, that extend several known results for the BenedettoFickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator of a set of vectors is realized as the frame operator of a set of vectors which is close to the original one. 1.
A SCHURHORN THEOREM IN II1 FACTORS
, 2007
"... Abstract. Given a II1 factor M and a diffuse abelian von Neumann subalgebra A ⊂ M, we prove a version of the SchurHorn theorem, namely EA(UM(b)) σsot = {a ∈ A sa: a ≺ b}, b ∈ M sa, where ≺ denotes spectral majorization, EA the unique tracepreserving conditional expectation onto A, and UM(b) the u ..."
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Cited by 14 (3 self)
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Abstract. Given a II1 factor M and a diffuse abelian von Neumann subalgebra A ⊂ M, we prove a version of the SchurHorn theorem, namely EA(UM(b)) σsot = {a ∈ A sa: a ≺ b}, b ∈ M sa, where ≺ denotes spectral majorization, EA the unique tracepreserving conditional expectation onto A, and UM(b) the unitary orbit of b in M. This result is inspired by a recent problem posed by Arveson and Kadison. 1.
A general approach to sparse basis selection: Majorization, concavity, and affine scaling
 IN PROCEEDINGS OF THE TWELFTH ANNUAL CONFERENCE ON COMPUTATIONAL LEARNING THEORY
, 1997
"... Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures use ..."
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Cited by 10 (5 self)
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Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schurconcave functions, which are the class of functions consistent with the socalled Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schurconcave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.
Optimal reconstruction systems for erasures and the qpotential, preprint
"... Abstract. We introduce the qpotential as an extension of the BenedettoFickus frame potential, defined on general reconstruction systems and we show that protocols are the minimizers of this potential under certain restrictions. We extend recent results of B.G. Bodmann on the structure of optimal p ..."
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Cited by 10 (4 self)
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Abstract. We introduce the qpotential as an extension of the BenedettoFickus frame potential, defined on general reconstruction systems and we show that protocols are the minimizers of this potential under certain restrictions. We extend recent results of B.G. Bodmann on the structure of optimal protocols with respect to 1 and 2 lost packets where the worst (normalized) reconstruction error is computed with respect to a compatible unitarily invariant norm. We finally describe necessary and sufficient (spectral) conditions, that we call qfundamental inequalities, for the existence of protocols with prescribed properties by relating this problem to Klyachko’s and Fulton’s theory on sums of hermitian operators.
Radjabalipuor,The structure of linear operators strongly preserving majorizations of matrices
 Electronic Journal of Linear Algebra
"... Abstract. A matrix majorization relation A ≺r B (resp., A ≺ℓ B) on the collection Mn of all n × n real matrices is a relation A = BR (resp., A = RB) forsomen × n row stochastic matrix R (depending on A and B). These right and left matrix majorizations have been considered by some authors under the n ..."
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Cited by 9 (3 self)
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Abstract. A matrix majorization relation A ≺r B (resp., A ≺ℓ B) on the collection Mn of all n × n real matrices is a relation A = BR (resp., A = RB) forsomen × n row stochastic matrix R (depending on A and B). These right and left matrix majorizations have been considered by some authors under the names “matrix majorization ” and “weak matrix majorization, ” respectively. Also, a multivariate majorization A ≺rmul B (resp., A ≺ℓmul B) isarelationA = BD (resp., A = DB) forsomen × n doubly stochastic matrix D (depending on A and B). The linear operators T: Mn → Mn which strongly preserve each of the above mentioned majorizations are characterized. Recall that an operator T: Mn → Mn strongly preserves a relation R on Mn when R(T (X),T(Y)) if and only if R(X, Y). The results are the sharpening of wellknown representations TX = CXD or TX = CXtD for linear operators preserving invertible matrices.
SPECTRAL ORDER AND ISOTONIC DIFFERENTIAL OPERATORS OF LAGUERREPÓLYA TYPE
, 2004
"... Abstract. The spectral order on R n induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We show that all differential operators of LaguerrePólya type preserve the spectral order. We also establish a global monotony property for infinite families of def ..."
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Cited by 8 (6 self)
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Abstract. The spectral order on R n induces a natural partial ordering on the manifold Hn of monic hyperbolic polynomials of degree n. We show that all differential operators of LaguerrePólya type preserve the spectral order. We also establish a global monotony property for infinite families of deformations of these operators parametrized by the space l ∞ of real bounded sequences. As a consequence, we deduce that the monoid A ′ of linear operators that preserve averages of zero sets and hyperbolicity consists only of differential operators of LaguerrePólya type which are both extensive and isotonic. In particular, these results imply that any hyperbolic polynomial is the global minimum of its A ′orbit and that Appell polynomials are characterized by a global minimum property with respect to the spectral order.
Measures and dynamics of entangled states
, 2005
"... We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of ..."
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Cited by 6 (1 self)
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We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for