Removing channel interference in broadband multiple-input multiple-output ( MIMO) systems is a task which can be solved by applying a spatio-temporal vector coding (STVC) channel description and using singular value d...
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ISBN:
(纸本)9789897581373
Removing channel interference in broadband multiple-input multiple-output ( MIMO) systems is a task which can be solved by applying a spatio-temporal vector coding (STVC) channel description and using singular value decomposition (SVD) in combination with signal pre- and post-processing. In this contribution a polynomial matrix factorization channel description in combination with a specific SVD algorithm for polynomial matrices is analyzed and compared to the commonly used STVC SVD. This comparison points out the analogies and differences of both equalization methods. Furthermore, the bit error rate (BER) performance is evaluated for two different channel types and is optimized by applying bit-allocation schemes involving a power loading strategy. Our results, obtained by computer simulation, show that polynomial matrix factorization such as polynomialmatrix SVD could be an alternative signal processing approach compared to conventional SVD-based MIMO approaches in frequency-selective MIMO channels.
The method of moving surfaces is an effective tool to implicitize rational parametric surfaces,and it has been extensively studied in the past two *** essential step in surface implicitization using the method of movi...
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The method of moving surfaces is an effective tool to implicitize rational parametric surfaces,and it has been extensively studied in the past two *** essential step in surface implicitization using the method of moving surfaces is to compute aμ-basis of a parametric surface with respect to one ***μ-basis is a minimal basis of the syzygy module of a univariate polynomialmatrix with special structure defined by the parametric equation of the rational *** this paper,we present an efficient algorithm to compute theμ-basis of a parametric surface with respect to a variable based on the special structure of the corresponding univariate polynomial *** on the computational complexity of the algorithm is also *** demonstrate that our algorithm is much faster than the general method to compute theμ-bases of arbitrary polynomial matrices and outperforms the F_(5) algorithm based on Gröbner basis computation for relatively low degree rational surfaces.
Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, stati...
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Euclidean distance matrices (EDMs) are a major tool for localization from distances, with applications ranging from protein structure determination to global positioning and manifold learning. They are, however, static objects which serve to localize points from a snapshot of distances. If the objects move, one expects to do better by modeling the motion. In this paper, we introduce Kinetic Euclidean Distance Matrices (KEDMs)-a new kind of time-dependent distance matrices that incorporate motion. The entries of KEDMs become functions of time, the squared time-varying distances. We study two smooth trajectory models-polynomial and bandlimited trajectories-and show that these trajectories can be reconstructed from incomplete, noisy distance observations, scattered over multiple time instants. Our main contribution is a semidefinite relaxation, inspired by similar strategies for static EDMs. Similarly to the static case, the relaxation is followed by a spectral factorization step;however, because spectral factorization of polynomial matrices is more challenging than for constant matrices, we propose a new factorization method that uses anchor measurements. Extensive numerical experiments show that KEDMs and the new semidefinite relaxation accurately reconstruct trajectories from noisy, incomplete distance data and that, in fact, motion improves rather than degrades localization if properly modeled. This makes KEDMs a promising tool for problems in geometry of dynamic points sets.
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