• Title/Summary/Keyword: Gram-Schmidt procedure

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A Novel Subspace Tracking Algorithm and Its Application to Blind Multiuser Detection in Cellular CDMA Systems

  • Ali, Imran;Kim, Doug-Nyun;Song, Yun-Jeong;Azeemi, Naeem Zafar
    • Journal of Communications and Networks
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    • v.12 no.3
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    • pp.216-221
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    • 2010
  • In this paper, we propose and develop a new algorithm for the principle subspace tracking by orthonormalizing the eigenvectors using an approximation of Gram-Schmidt procedure. We carry out a novel mathematical derivation to show that when this approximated version of Gram-Schmidt procedure is added to a modified form of projection approximation subspace tracking deflation (PASTd) algorithm, the eigenvectors can be orthonormalized within a linear computational complexity. While the PASTd algorithm tries to extracts orthonormalized eigenvectors, the new scheme orthonormalizes the eigenvectors after their extraction, yielding much more tacking efficiency. We apply the new tracking scheme for blind adaptive multiuser detection for non-stationary cellular CDMA environment and use extensive simulation results to demonstrate the performance improvement of the proposed scheme.

Blind Adaptive Multiuser Detection for the MC-CDMA Systems Using Orthogonalized Subspace Tracking

  • Ali, Imran;Kim, Doug-Nyun;Lim, Jong-Soo
    • ETRI Journal
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    • v.31 no.2
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    • pp.193-200
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    • 2009
  • In this paper, we study the performance of subspace-based multiuser detection techniques for multicarrier code-division multiple access (MC-CDMA) systems. We propose an improvement in the PASTd algorithm by cascading it with the classical Gram-Schmidt procedure to orthonormalize the eigenvectors after their sequential extraction. The tracking of signal subspace using this algorithm, which we call OPASTd, has a faster convergence as the eigenvectors are orthonormalized at each discrete time sample. This improved PASTd algorithm is then used to implement the subspace blind adaptive multiuser detection for MC-CDMA. We also show that, for multiuser detection, the complexity of the proposed scheme is lower than that of many other orthogonalization schemes found in the literature. Extensive simulation results are presented and discussed to demonstrate the performance of the proposed scheme.

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THE EXISTENCE THEOREM OF ORTHOGONAL MATRICES WITH p NONZERO ENTRIES

  • CHEON, GI-SANG;LEE, SANG-GU;SONG, SEOK-ZUN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.4 no.1
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    • pp.109-119
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    • 2000
  • It was shown that if Q is a fully indecomposable $n{\times}n$ orthogonal matrix then Q has at least 4n-4 nonzero entries in 1993. In this paper, we show that for each integer p with $4n-4{\leq}p{\leq}n^2$, there exist a fully indecomposable $n{\times}n$ orthogonal matrix with exactly p nonzero entries. Furthermore, we obtain a method of construction of a fully indecomposable $n{\times}n$ orthogonal matrix which has exactly 4n-4 nonzero entries. This is a part of the study in sparse matrices.

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