The Experts below are selected from a list of 96 Experts worldwide ranked by ideXlab platform
Thomas L Marzetta - One of the best experts on this subject based on the ideXlab platform.
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Multiple-antennas and isotropically random unitary inputs: the received signal density in closed form
2002Co-Authors: Babak Hassibi, Thomas L Marzetta, Senior MemberAbstract:Abstract—An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix—having orthonormal columns, and a probability density that is invariant to Premultiplication by an independent unitary matrix—plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. In this paper, we take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for = min ( 2) transmit antennas, where is the number of receive antennas and is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna. Index Terms—Isotropically random (i.r.) unitary matrix, mul-tiple antennas, unitary space–time modulation (USTM), wireless communications. I
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multiple antennas and isotropically random unitary inputs the received signal density in closed form
International Symposium on Information Theory, 2001Co-Authors: Babak Hassibi, Thomas L MarzettaAbstract:An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix-having orthonormal columns, and a probability density that is invariant to Premultiplication by an independent unitary matrix-plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. We take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for M=min(N, T/2) transmit antennas, where N is the number of receive antennas and T is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna.
Babak Hassibi - One of the best experts on this subject based on the ideXlab platform.
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Multiple-antennas and isotropically random unitary inputs: the received signal density in closed form
2002Co-Authors: Babak Hassibi, Thomas L Marzetta, Senior MemberAbstract:Abstract—An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix—having orthonormal columns, and a probability density that is invariant to Premultiplication by an independent unitary matrix—plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. In this paper, we take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for = min ( 2) transmit antennas, where is the number of receive antennas and is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna. Index Terms—Isotropically random (i.r.) unitary matrix, mul-tiple antennas, unitary space–time modulation (USTM), wireless communications. I
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multiple antennas and isotropically random unitary inputs the received signal density in closed form
International Symposium on Information Theory, 2001Co-Authors: Babak Hassibi, Thomas L MarzettaAbstract:An important open problem in multiple-antenna communications theory is to compute the capacity of a wireless link subject to flat Rayleigh block-fading, with no channel-state information (CSI) available either to the transmitter or to the receiver. The isotropically random (i.r.) unitary matrix-having orthonormal columns, and a probability density that is invariant to Premultiplication by an independent unitary matrix-plays a central role in the calculation of capacity and in some special cases happens to be capacity-achieving. We take an important step toward computing this capacity by obtaining, in closed form, the probability density of the received signal when transmitting i.r. unitary matrices. The technique is based on analytically computing the expectation of an exponential quadratic function of an i.r. unitary matrix and makes use of a Fourier integral representation of the constituent Dirac delta functions in the underlying density. Our formula for the received signal density enables us to evaluate the mutual information for any case of interest, something that could previously only be done for single transmit and receive antennas. Numerical results show that at high signal-to-noise ratio (SNR), the mutual information is maximized for M=min(N, T/2) transmit antennas, where N is the number of receive antennas and T is the length of the coherence interval, whereas at low SNR, the mutual information is maximized by allocating all transmit power to a single antenna.
M.j. Kim - One of the best experts on this subject based on the ideXlab platform.
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ICASSP - Fast multiscale statistical signal processing algorithms
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics Speech and Signal Processing, 1992Co-Authors: A.h. Tewfik, M.j. KimAbstract:It is shown that a large set of (not necessarily stationary) correlation matrices may be transformed into a matrix that consists of essentially banded subblocks. The transformation is accomplished by Premultiplication and postmultiplication with an orthogonal matrix whose elements are derived from the impulse response of a suitably designed cascade of alias-free multirate analysis filter banks. It is further proved that the Cholesky factor of the transformed matrix also consists of essentially banded subblocks. These two observations are combined to show that the linear positive definite systems of equations that arise in statistical signal processing can be solved in O(max(N log/sup 2/ (N), N/sup 2/)) operations while matrix-vector multiplication steps may be implemented in O(N log (N)) operations. An error analysis of the proposed linear positive definite system solver is also provided. >
Sofia Lambropoulou - One of the best experts on this subject based on the ideXlab platform.
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Algebraic Markov equivalence for links in three-manifolds
Compositio Mathematica, 2006Co-Authors: Sofia Lambropoulou, Colin RourkeAbstract:Let B-n denote the classical braid group on n strands and let the mixed braid group B-m,B-n be the subgroup of Bm+n comprising braids for which the first m strands form the identity braid. Let B-m,B-infinity = boolean OR(n) B-m,B-n. We describe explicit algebraic moves on B-m,B-infinity such that equivalence classes under these moves classify oriented links up to isotopy in a link complement or in a closed, connected, oriented three-manifold. The moves depend on a fixed link representing the manifold in S-3. More precisely, for link complements the moves are the two familiar moves of the classical Markov equivalence together with 'twisted' conjugation by certain loops a(i). This means Premultiplication by a(i)(-1) and postmultiplication by a 'combed' version of a(i). For closed three-manifolds there is an additional set of 'combed' band moves that correspond to sliding moves over the surgery link. The main tool in the proofs is the one-move Markov theorem using L-moves (adding in-box crossings). The resulting algebraic classification is a direct extension of the classical Markov theorem that classifies links in S-3 up to isotopy, and potentially leads to powerful new link invariants, which have been explored in special cases by the first author. It also provides a controlled range of isotopy moves, useful for studying skein modules of three-manifolds.
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Algebraic Markov equivalence for links in 3-manifolds
arXiv: Geometric Topology, 2004Co-Authors: Sofia Lambropoulou, Colin RourkeAbstract:Let $B_n$ denote the classical braid group on $n$ strands and let the {\em mixed braid group} $B_{m,n}$ be the subgroup of $B_{m+n}$ comprising braids for which the first $m$ strands form the identity braid. Let $B_{m,\infty}=\cup_nB_{m,n}$. We will describe explicit algebraic moves on $B_{m,\infty}$ such that equivalence classes under these moves classify oriented links up to isotopy in a link complement or in a closed, connected, oriented 3--manifold. The moves depend on a fixed link representing the manifold in $S^3$. More precisely, for link complements the moves are: the two familiar moves of the classical Markov equivalence together with {\em `twisted' conjugation} by certain loops $a_i$. This means Premultiplication by ${a_i}^{-1}$ and postmultiplication by a `combed' version of $a_i$. For closed 3--manifolds there is an additional set of {\it `combed' band moves} which correspond to sliding moves over the surgery link. The main tool in the proofs is the one-move Markov Theorem using {\it $L$--moves} \cite{LR} (adding in-box crossings). The resulting algebraic classification is a direct extension of the classical Markov Theorem that classifies links in $S^3$ up to isotopy, and potentially leads to powerful new link invariants, which have been explored in special cases by the first author. It also provides a controlled range of isotopy moves, useful for studying skein modules of 3--manifolds.
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Algebraic Markov equivalence for links in 3manifolds (submitted for publication). See arXiv:math.GT/0405493 v1
2004Co-Authors: Sofia Lambropoulou, Colin RourkeAbstract:Let Bn denote the classical braid group on n strands and let the mixed braid group Bm,n be the subgroup of Bm+n comprising braids for which the first m strands form the identity braid. Let Bm, ∞ = ∪nBm,n. We will describe explicit algebraic moves on Bm, ∞ such that equivalence classes under these moves classify links in a link complement or in a closed connected 3-manifold. The moves depend on a fixed link representing the manifold in S 3. More precisely for link complements the moves are: the two familiar moves of the Markov equivalence, adding a crossing at the right hand side of the braid and conjugation by crossing, together with ‘twisted ’ conjugation by certain simple loops ai. This means Premultiplication by ai and postmultiplication by a ‘combed’ version of ai. For 3–manifolds there is an additional set of ‘combed’ band moves which correspond to band moves over the surgery link. The main tool in the proofs is the one-move Markov Theorem using L– moves (adding in-box crossings). The resulting classification is a direct extension of the classical Markov Theorem that classifies links in S 3, and potentially leads to powerful new link invariants, which have been explored in special cases by the first author. It also provides a controlled range of isotopy moves, useful for studying skein modules of 3–manifolds
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Algebraic Markov equivalence for links in 3manifolds (submitted for publication). See arXiv:math.GT/0405493 v1
2004Co-Authors: Sofia Lambropoulou, C. P. RourkeAbstract:Abstract. Let Bn denote the classical braid group on n strands and let the mixed braid group Bm,n be the subgroup of Bm+n comprising braids for which the first m strands form the identity braid. Let Bm, ∞ = ∪nBm,n. We will describe explicit algebraic moves on Bm, ∞ such that equivalence classes under these moves classify oriented links up to isotopy in a link complement or in a closed, connected, oriented 3–manifold. The moves depend on a fixed link representing the manifold in S 3. More precisely, for link complements the moves are: the two familiar moves of the classical Markov equivalence together with ‘twisted’ conjugation by certain loops ai. This means Premultiplication by ai −1 and postmultiplication by a ‘combed ’ version of ai. For closed 3–manifolds there is an additional set of ‘combed ’ band moves which correspond to sliding moves over the surgery link. The main tool in the proofs is the one-move Markov Theorem using L–moves [12] (adding in-box crossings). The resulting algebraic classification is a direct extension of the classical Markov Theorem that classifies links in S 3 up to isotopy, and potentially leads to powerful new link invariants, which have been explored in special cases by the first author. It also provides a controlled range of isotopy moves, useful for studying skein modules of 3–manifolds
Colin Rourke - One of the best experts on this subject based on the ideXlab platform.
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Algebraic Markov equivalence for links in three-manifolds
Compositio Mathematica, 2006Co-Authors: Sofia Lambropoulou, Colin RourkeAbstract:Let B-n denote the classical braid group on n strands and let the mixed braid group B-m,B-n be the subgroup of Bm+n comprising braids for which the first m strands form the identity braid. Let B-m,B-infinity = boolean OR(n) B-m,B-n. We describe explicit algebraic moves on B-m,B-infinity such that equivalence classes under these moves classify oriented links up to isotopy in a link complement or in a closed, connected, oriented three-manifold. The moves depend on a fixed link representing the manifold in S-3. More precisely, for link complements the moves are the two familiar moves of the classical Markov equivalence together with 'twisted' conjugation by certain loops a(i). This means Premultiplication by a(i)(-1) and postmultiplication by a 'combed' version of a(i). For closed three-manifolds there is an additional set of 'combed' band moves that correspond to sliding moves over the surgery link. The main tool in the proofs is the one-move Markov theorem using L-moves (adding in-box crossings). The resulting algebraic classification is a direct extension of the classical Markov theorem that classifies links in S-3 up to isotopy, and potentially leads to powerful new link invariants, which have been explored in special cases by the first author. It also provides a controlled range of isotopy moves, useful for studying skein modules of three-manifolds.
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Algebraic Markov equivalence for links in 3-manifolds
arXiv: Geometric Topology, 2004Co-Authors: Sofia Lambropoulou, Colin RourkeAbstract:Let $B_n$ denote the classical braid group on $n$ strands and let the {\em mixed braid group} $B_{m,n}$ be the subgroup of $B_{m+n}$ comprising braids for which the first $m$ strands form the identity braid. Let $B_{m,\infty}=\cup_nB_{m,n}$. We will describe explicit algebraic moves on $B_{m,\infty}$ such that equivalence classes under these moves classify oriented links up to isotopy in a link complement or in a closed, connected, oriented 3--manifold. The moves depend on a fixed link representing the manifold in $S^3$. More precisely, for link complements the moves are: the two familiar moves of the classical Markov equivalence together with {\em `twisted' conjugation} by certain loops $a_i$. This means Premultiplication by ${a_i}^{-1}$ and postmultiplication by a `combed' version of $a_i$. For closed 3--manifolds there is an additional set of {\it `combed' band moves} which correspond to sliding moves over the surgery link. The main tool in the proofs is the one-move Markov Theorem using {\it $L$--moves} \cite{LR} (adding in-box crossings). The resulting algebraic classification is a direct extension of the classical Markov Theorem that classifies links in $S^3$ up to isotopy, and potentially leads to powerful new link invariants, which have been explored in special cases by the first author. It also provides a controlled range of isotopy moves, useful for studying skein modules of 3--manifolds.
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Algebraic Markov equivalence for links in 3manifolds (submitted for publication). See arXiv:math.GT/0405493 v1
2004Co-Authors: Sofia Lambropoulou, Colin RourkeAbstract:Let Bn denote the classical braid group on n strands and let the mixed braid group Bm,n be the subgroup of Bm+n comprising braids for which the first m strands form the identity braid. Let Bm, ∞ = ∪nBm,n. We will describe explicit algebraic moves on Bm, ∞ such that equivalence classes under these moves classify links in a link complement or in a closed connected 3-manifold. The moves depend on a fixed link representing the manifold in S 3. More precisely for link complements the moves are: the two familiar moves of the Markov equivalence, adding a crossing at the right hand side of the braid and conjugation by crossing, together with ‘twisted ’ conjugation by certain simple loops ai. This means Premultiplication by ai and postmultiplication by a ‘combed’ version of ai. For 3–manifolds there is an additional set of ‘combed’ band moves which correspond to band moves over the surgery link. The main tool in the proofs is the one-move Markov Theorem using L– moves (adding in-box crossings). The resulting classification is a direct extension of the classical Markov Theorem that classifies links in S 3, and potentially leads to powerful new link invariants, which have been explored in special cases by the first author. It also provides a controlled range of isotopy moves, useful for studying skein modules of 3–manifolds