Topic
QR decomposition
About: QR decomposition is a research topic. Over the lifetime, 3504 publications have been published within this topic receiving 100599 citations. The topic is also known as: QR factorization.
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Patent•
08 Jan 2008
TL;DR: In this article, a correlation matrix creation section for removing a diagonal element from a predetermined row or column constituting an M×M array covariance matrix, and creating a correlated matrix by extracting a predetermined p number of correlations from (M−1) number of correlation after the diagonal element is removed while sequentially shifting one element at a time, and arraying the p number correlations in a matrix.
Abstract: An incoming wave number estimation device for receiving incoming radio waves by an array antenna in which a plurality (=M) of antenna elements are linearly arrayed with a same element spacing, and estimating the number of the incoming radio waves, including: a correlation matrix creation section for removing a diagonal element from a predetermined row or column constituting an M×M array covariance matrix, and creating a correlation matrix by extracting a predetermined p number of correlations from (M−1) number of correlations after the diagonal element is removed while sequentially shifting one element at a time, and arraying the p number correlations in a matrix; an estimation matrix creation section for creating an estimation matrix for estimating the incoming wave number using the correlation matrix; a QR decomposition section for performing QR decomposition on the estimation matrix; and an incoming wave number determination section for determining the number of incoming radio waves based on each row element of an upper triangular matrix factor obtained by the QR decomposition.
12 citations
Posted Content•
TL;DR: In this article, the authors proposed an algorithm using 12n^3+O(n^2) floating point operations for checking whether a lattice basis is LLL-reduced.
Abstract: Given a lattice basis of n vectors in Z^n, we propose an algorithm using 12n^3+O(n^2) floating point operations for checking whether the basis is LLL-reduced. If the basis is reduced then the algorithm will hopefully answer ''yes''. If the basis is not reduced, or if the precision used is not sufficient with respect to n, and to the numerical properties of the basis, the algorithm will answer ''failed''. Hence a positive answer is a rigorous certificate. For implementing the certificate itself, we propose a floating point algorithm for computing (certified) error bounds for the entries of the R factor of the QR matrix factorization. This algorithm takes into account all possible approximation and rounding errors. The cost 12n^3+O(n^2) of the certificate is only six times more than the cost of numerical algorithms for computing the QR factorization itself, and the certificate may be implemented using matrix library routines only. We report experiments that show that for a reduced basis of adequate dimension and quality the certificate succeeds, and establish the effectiveness of the certificate. This effectiveness is applied for certifying the output of fastest existing floating point heuristics of LLL reduction, without slowing down the whole process.
12 citations
TL;DR: Two particular implementations of the symmetric algorithm outperform both the modified Guam-Schmidt and the Hestenes-Sttefel algorithm and in most cases are superior in terms of accuracy to the QR algorithm.
Abstract: A large number of implementations of the symmetric algorithm in the ABS class for linear systems are compared on a set of ill-conditioned test problems, together with implementations of the modified Gbam-Schmidt, the Hestenes-Stiefei, and the QR algorithms. The results indicate the superiority of two particular implementations of the symmetric algorithm, which outperform both the modified Guam-Schmidt and the Hestenes-Sttefel algorithm and in most cases are superior in terms of accuracy to the QR algorithm.
12 citations
TL;DR: This paper proposes to estimate time-varying pieces of channel taps for pilot symbols based on basis expansion model (BEM), and subsequently to reconstruct time-domain (TD) channel response for data symbols by utilizing the Slepian sequences-based piece-wise interpolation, and designs an iterative least-squares QR decomposition algorithm to equalize the SC-FDM symbols.
Abstract: Similar to orthogonal frequency division multiplexing receiver, the frequency-domain (FD) channel estimation (CE) and equalization are indispensable parts in the coherent single carrier frequency division multiplexing (SC-FDM) receiver. When the channel varies slowly, the FD processing is cost effective. For the applications with high mobility, the traditional implementation of the SC-FDM receiver causes significant performance degradation. In this paper, we propose to estimate time-varying pieces of channel taps for pilot symbols based on basis expansion model (BEM), and subsequently to reconstruct time-domain (TD) channel response for data symbols by utilizing the Slepian sequences-based piece-wise interpolation. Furthermore, two simplified schemes, i.e., the Slepian sequences-based multiple-point interpolation and the segmented BEM, are developed to reduce the computational complexity of the TD-CE. The Cramer-Rao lower bound (CRLB) of channel impulse response (CIR) estimation is also analyzed. In the light of the sparsity of TD channel gain matrix, we design an iterative least-squares QR decomposition algorithm to equalize the SC-FDM symbols. In the simulated SC-FDM system, when considering the carrier frequency of 5.9 GHz and the velocity of about 510 km/h, we observe that the traditional FD methods cause the demodulation failure, while the proposed TD processing schemes achieve ideal error-probability performance and preserve a relatively low complexity.
12 citations
TL;DR: The proposed SQRD-based multi-user detection scheme is proposed by utilizing the a priori information from the channel decoder in the decomposition process through the use of a new extended channel matrix and significantly improves the BER performance.
Abstract: Compared with the well-known minimum mean-square error (mmse)-based turbo receivers, sorted QR decomposition (SQRD)-based data detection scheme has the advantages of lower complexity and better bit error rate (BER) due to the avoidance of matrix inversion and the use of successive interference cancelation. In this letter, we investigate SQRD-based data detection and soft interference cancelation in multi-user multiple-input multiple-output single-carrier frequency division multiple access system. We propose a new SQRD-based multi-user detection scheme by utilizing the a priori information from the channel decoder in the decomposition process through the use of a new extended channel matrix. The received signal vector for the current user’s data detection can be categorized into the expected signal, the interference, and the noise components, where the interference includes those from both the detected and the undetected users. Soft interference cancelation is then performed on the data. The residual interference from the detected users can be easily obtained due to the use of successive interference cancelation, whereas the interference from the undetected users can be obtained by using the a priori information from channel decoder. We further consider on how to extract the expected signal from the interference component, thus further improve the signal-to-interference-plus-noise ratio condition at the receiver. Simulation results show that the proposed scheme significantly improves the BER performance compared with the original SQRD-based multi-user detection scheme and the mmse-based turbo receivers.
12 citations