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Munemasa Akihiro - One of the best experts on this subject based on the ideXlab platform.

  • Complex Hadamard matrices attached to even orthogonal schemes of class 4
    2016
    Co-Authors: Ikuta Takuya, Munemasa Akihiro
    Abstract:

    A complex Hadamard matrix is a square matrix W with complex entries of absolute value 1 satisfying WW*=nI, where * stands for the Hermitian Transpose and I is the identity matrix of order n. In this paper, we give constructions of complex Hadamard matrices in the Bose-Mesner algebra of a certain 4-class symmetric association scheme. Moreover, we determine the Nomura algebras to show that the resulting matrices are not decomposable into nontrivial generalized tensor products.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1411.005

  • Complex Hadamard Matrices contained in a Bose–Mesner algebra
    De Gruyter, 2015
    Co-Authors: Ikuta Takuya, Munemasa Akihiro
    Abstract:

    Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian Transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products

  • Complex Hadamard matrices contained in a Bose-Mesner algebra
    'Walter de Gruyter GmbH', 2015
    Co-Authors: Ikuta Takuya, Munemasa Akihiro
    Abstract:

    A complex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying $HH^*= nI$, where $*$ stands for the Hermitian Transpose and I is the identity matrix of order $n$. In this paper, we first determine the image of a certain rational map from the $d$-dimensional complex projective space to $\mathbb{C}^{d(d+1)/2}$. Applying this result with $d=3$, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose-Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products.Comment: 28 pages + Appendix A + Appendix

Ikuta Takuya - One of the best experts on this subject based on the ideXlab platform.

  • Complex Hadamard matrices attached to even orthogonal schemes of class 4
    2016
    Co-Authors: Ikuta Takuya, Munemasa Akihiro
    Abstract:

    A complex Hadamard matrix is a square matrix W with complex entries of absolute value 1 satisfying WW*=nI, where * stands for the Hermitian Transpose and I is the identity matrix of order n. In this paper, we give constructions of complex Hadamard matrices in the Bose-Mesner algebra of a certain 4-class symmetric association scheme. Moreover, we determine the Nomura algebras to show that the resulting matrices are not decomposable into nontrivial generalized tensor products.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1411.005

  • Complex Hadamard Matrices contained in a Bose–Mesner algebra
    De Gruyter, 2015
    Co-Authors: Ikuta Takuya, Munemasa Akihiro
    Abstract:

    Acomplex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying HH* = nI, where * stands for the Hermitian Transpose and I is the identity matrix of order n. In this paper, we first determine the image of a certain rational map from the d-dimensional complex projective space to Cd(d+1)/2. Applying this result with d = 3, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose–Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products

  • Complex Hadamard matrices contained in a Bose-Mesner algebra
    'Walter de Gruyter GmbH', 2015
    Co-Authors: Ikuta Takuya, Munemasa Akihiro
    Abstract:

    A complex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying $HH^*= nI$, where $*$ stands for the Hermitian Transpose and I is the identity matrix of order $n$. In this paper, we first determine the image of a certain rational map from the $d$-dimensional complex projective space to $\mathbb{C}^{d(d+1)/2}$. Applying this result with $d=3$, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose-Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products.Comment: 28 pages + Appendix A + Appendix

Athanassios Manikas - One of the best experts on this subject based on the ideXlab platform.

  • Interference cancellation beamforming robust to pointing errors
    2016
    Co-Authors: Jie Zhuang, Athanassios Manikas
    Abstract:

    Abstract: The conventional Wiener–Hopf beamformer is subject to substantial performance degradation in the presence of steering vector pointing errors. By removing the effects of the desired signal, the modified Wiener–Hopf beamformer avoids this problem but allows cochannel interferences to pass through in order to maximise the signal-to-noise ratio. In this study, a novel array beamformer is proposed, which not only reduces the effect of pointing errors, but also asymptotically provides complete interference rejection. In particular, the proposed beamformer utilises a vector space projection method and employs a one-step computation for the desired signal power. Using this, the effects of the desired signal can be extracted to form the desired-signal-absent covariance matrix. Thus, a weight vector orthogonal with the interference subspace can be constructed. Numerical results demonstrate the superior performance of the proposed beamformer in the presence of pointing errors relative to other existing approaches such as ‘diagonal loading’, ‘robust Capon ’ and ‘signal subspace projection ’ beamformers. Notation a scalar A, a column vector A matrix (·)T (·)H Transpose, Hermitian Transpose (·) * complex conjugate P projection operator matrix P ⊥ complement projection operator matrix IN N × N identity matrix· ‖ ‖ Euclidean norm E { · } expectation operator P{A} principal eigenvector of the matrix A eigmax(A) maximum eigenvalue of the matrix A eigi(A) ith largest eigenvalue of the matrix AL[A] linear subspace spanned by the columns of the matrix A

  • (·)H Hermitian Transpose
    2015
    Co-Authors: Zhijie Chen, Athanassios Manikas
    Abstract:

    Abstract—In this paper a novel approach is proposed for estimating the direction-of-departure (DOD) in a frequency-selective multipath channel, where both the transmitter (Tx) and receiver (Rx) employ an antenna array. In particular, the proposed approach exploits the cooperation between the Tx and Rx beamformers, such that the Tx beamformer rotates its mainlobe in a synchronized manner that is known to the Rx. This operation allows the DODs of the multiple paths to be estimated at the Rx by making a set of power measurements. The performance of the proposed approach is investigated using computer simulation studies. NOTATION

Akihiro Munemasa - One of the best experts on this subject based on the ideXlab platform.

  • complex hadamard matrices contained in a bose mesner algebra
    arXiv: Combinatorics, 2014
    Co-Authors: Takuya Ikuta, Akihiro Munemasa
    Abstract:

    A complex Hadamard matrix is a square matrix H with complex entries of absolute value 1 satisfying $HH^*= nI$, where $*$ stands for the Hermitian Transpose and I is the identity matrix of order $n$. In this paper, we first determine the image of a certain rational map from the $d$-dimensional complex projective space to $\mathbb{C}^{d(d+1)/2}$. Applying this result with $d=3$, we give constructions of complex Hadamard matrices, and more generally, type-II matrices, in the Bose-Mesner algebra of a certain 3-class symmetric association scheme. In particular, we recover the complex Hadamard matrices of order 15 found by Ada Chan. We compute the Haagerup sets to show inequivalence of resulting type-II matrices, and determine the Nomura algebras to show that the resulting matrices are not decomposable into generalized tensor products.

Weaver Nik - One of the best experts on this subject based on the ideXlab platform.

  • The "quantum" Turan problem for operator systems
    2018
    Co-Authors: Weaver Nik
    Abstract:

    Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under Hermitian Transpose. A "quantum k-clique" for V is a rank k orthogonal projection P in M_n(C) for which dim(PVP) = k^2, and a "quantum k-anticlique" is a rank k orthogonal projection for which dim(PVP) = 1. We give upper and lower bounds both for the largest dimension of V which would ensure the existence of a quantum k-anticlique, and for the smallest dimension of V which would ensure the existence of a quantum k-clique.Comment: 13 page