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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第4期57卷 1634-1637页

作者： Vetter, Henning Ponnampalam, Vishakan Sandell, Magnus Hoeher, Peter Adam Toshiba Res Europe Ltd Telecommun Res Lab Bristol BS1 4ND Avon England Univ Kiel Informat & Coding Theory Lab Fac Engn D-24143 Kiel Germany

A common technique to perform lattice basis reduction is the Lenstra, Lenstra, Lovasz (lll) algorithm. An implementation of this algorithm in real-time systems suffers from the problem of variable run-time and complexity. This correspondence proposes a modification of the lll algorithm. The signal flow is altered to follow a deterministic structure, which promises to obtain an easier implementation as well as a fixed execution time known in advance. In the case of a maximum number of iterations as it is likely in real-time systems, our modification clearly outperforms the original lll algorithm as far as the quality of the reduced lattice basis is concerned.

关键词： Lattice reduction lll algorithm MIMO systems

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An Improved Quantization Scheme for Lattice-Reduction Aided MIMO Detection Based on Gram-Schmidt Orthogonalization

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2013年第12期E96A卷 2405-2414页

作者： Hou, Wei Fujino, Tadashi Kojima, Toshiharu Univ Electrocommun Dept Informat & Commun Chofu Tokyo 1828585 Japan

Lattice-reduction (LR) technique has been adopted to improve the performance and reduce the complexity in MIMO data detection. This paper presents an improved quantization scheme for LR aided MIMO detection based on Gram-Schmidt orthogonalization. For the LR aided detection, the quantization step applies the simple rounding operation, which often leads to the quantization errors. Meanwhile, these errors may result in the detection errors. Hence the purpose of the proposed detection is to further solve the problem of degrading the performance due to the quantization errors in the signal estimation. In this paper, the proposed quantization scheme decreases the quantization errors using a simple tree search with a threshold function. Through the analysis and the simulation results, we observe that the proposed detection can achieve the nearly optimal performance with very low complexity, and require a little additional complexity compared to the conventional LR-MMSE detection in the high E-b/N-0 region. Furthermore, this quantization error reduction scheme is also efficient even for the high modulation order.

关键词： Gram-Schmidt orthogonalization lll algorithm lattice-reduction MIMO quantization error

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Experimental quality evaluation of lattice basis reduction methods for decorrelating low-dimensional integer least squares problems

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EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING 2013年第1期2013卷 1页

作者： Xu, Peiliang Kyoto Univ Disaster Prevent Res Inst Kyoto 6110011 Japan

Reduction can be important to aid quickly attaining the integer least squares (ILS) estimate from noisy data. We present an improved lll algorithm with fixed complexity by extending a parallel reduction method for positive definite quadratic forms to lattice vectors. We propose the minimum angle of a reduced basis as an alternative quality measure of orthogonality, which is intuitively more appealing to measure the extent of orthogonality of a reduced basis. Although the lll algorithm and its variants have been widely used in practice, experimental simulations were only carried out recently and limited to the quality measures of the Hermite factor, practical running behaviors and reduced Gram-Schmidt coefficients. We conduct a large scale of experiments to comprehensively evaluate and compare five reduction methods for decorrelating ILS problems, including the lll algorithm, its variant with deep insertions and our improved lll algorithm with fixed complexity, based on six quality measures of reduction. We use the results of the experiments to investigate the mean running behaviors of the lll algorithm and its variants with deep insertions and the sorted QR ordering, respectively. The improved lll algorithm with fixed complexity is shown to perform as well as the lll algorithm with deep insertions with respect to the quality measures on length reduction but significantly better than this lll variant with respect to the other quality measures. In particular, our algorithm is of fixed complexity, but the lll algorithm with deep insertions could seemingly not be terminated in polynomial time of the dimension of an ILS problem. It is shown to perform much better than the other three reduction methods with respect to all the six quality measures. More than six millions of the reduced Gram-Schmidt coefficients from each of the five reduction methods clearly show that they are not uniformly distributed but depend on the reduction algorithms used. The simulation results of

关键词： Integer linear model Integer least squares Closest point problem Lattice reduction lll algorithm

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The measure of totally positive algebraic integers

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JOURNAL OF NUMBER THEORY 2013年第1期133卷 12-19页

作者： Mu, Quanwu Wu, Qiang SW Univ China Dept Math Chongqing 400715 Peoples R China

For a totally positive algebraic integer alpha not equal 0, 1 of degree d, we consider the set R of values of L(alpha)(1/d) = R(alpha) and the set L of values of M(alpha)(1/d) = Omega(alpha). where L(alpha) is the length of cc and M(alpha) is the Mahler measure of alpha. In this paper, we prove that all except finitely many totally positive algebraic integers alpha have R(alpha) >= 2.364950 and Omega(alpha) >= 1.721916. The computation uses a family of explicit auxiliary functions. We notice that several polynomials with complex roots are used to construct the functions. We also find eight totally positive irreducible polynomials with absolute length greater than 2.364950 and less than 2.37. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Totally positive algebraic integer Absolute length Absolute Mahler measure Explicit auxiliary function Semi-infinite linear programming lll algorithm

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Efficient Quantization Scheme for Lattice-Reduction Aided MIMO Detection

Efficient Quantization Scheme for Lattice-Reduction Aided MI...

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International Conference on Advanced Technologies for Communications (ATC)

作者： Hou, Wei Fujino, Tadashi Kojima, Toshiharu Univ Electrocommun Grad Sch Informat & Commun Engn & Informat Tokyo 1828585 Japan

ISBN: (纸本)9781479910861;9781479910885

In this paper, we present an efficient quantization scheme for lattice-reduction (LR) aided (LRA) MIMO detection using Gram-Schmidt orthogonalization. For the LRA detection, the quantization step applies the simple rounding operation, which often leads to the quantization errors. Meanwhile, these errors may result in the detection errors. Hence, the motivation of the proposed detection is to further solve the problem of degrading the performance due to the quantization errors in the signal estimation. In this paper, the proposed quantization scheme decreases the quantization errors using a simple tree search with a threshold function. Through the analysis and the simulation results, the proposed detection can achieve the near-ML performance with only a little additional complexity.

关键词： Gram-Schmidt Orthogonalization lll algorithm Lattice-reduction MIMO Quantization error

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An Improved Integer Ambiguity Decorrelation algorithm

An Improved Integer Ambiguity Decorrelation Algorithm

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32nd Chinese Control Conference (CCC)

作者： Xu Dingjie Chen Xiao Shen Feng Harbin Engn Univ Harbin 150001 Peoples R China

ISBN: (纸本)9781479900305

The solution of integer ambiguity was regarded as a key technology of precise attitude measuring algorithm, which rapidity and accuracy is influenced by the relevance of ambiguity vector. Since the deficiency of present decorrelation way in LAMBDA algorithm, it was hard to solve. This paper used a sort way to optimization the method of decorrelation, and improved the iterative process of lll and white filter algorithms iterative process improvement. The simulation results shown that the optimized of decorrelation algorithm was suit for the lll and white filter algorithms. And the settlement effects were better to relevance with a higher success rate.

关键词： Integer Ambiguity LAMBDA lll algorithm white filter algorithm

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Improved Lattice Reduction-Aided MIMO Successive Interference Cancellation Under Imperfect Channel Estimation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2012年第6期60卷 3346-3351页

作者： Park, Jaehyun Chun, Joohwan ETRI Broadcasting & Telecommun Convergence Res Lab Taejon 305701 South Korea Korea Adv Inst Sci & Technol Div Elect Engn Sch Elect Engn & Comp Sci Taejon 305701 South Korea

Lattice reduction (LR) and successive interference cancellation (SIC) are two well-known techniques that can be used to improve detection performance over linear detectors for multiple-input multiple-output (MIMO) systems. However, the LR technique and the SIC technique usually need perfect knowledge on the channel at the receiver, and the use of these techniques with an erroneous channel matrix even worsens the detection performance compared to linear detectors. In this correspondence, we shall show how to modify these techniques to make them robust under imperfect channel estimation. Information needed for the proposed algorithm is moderate;the variance of channel estimation error is the only requirement. Furthermore, our algorithm is not sensitive to the error in the variance of channel estimation error.

关键词： Channel estimation error lattice reduction lll algorithm SIC

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A Diagonal Lattice Reduction algorithm for MIMO Detection

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IEEE SIGNAL PROCESSING LETTERS 2012年第5期19卷 311-314页

作者： Zhang, Wen Qiao, Sanzheng Wei, Yimin Fudan Univ Sch Math Sci Shanghai 200433 Peoples R China McMaster Univ Dept Comp & Software Hamilton ON L8S 4K1 Canada Fudan Univ Shanghai Key Lab Contemporary Appl Math Shanghai 200433 Peoples R China

Recently, an efficient lattice reduction method, called the effective lll (Elll) algorithm, was presented for the detection of multiinput multioutput (MIMO) systems. In this letter, a novel lattice reduction criterion, called diagonal reduction, is proposed. The diagonal reduction is weaker than the Elll reduction, however, like the Elll reduction, it has identical performance with the lll reduction when applied for the sphere decoding and successive interference cancelation (SIC) decoding. It improves the efficiency of the Elll algorithm by significantly reducing the size-reduction operations. Furthermore, we present a greedy column traverse strategy, which reduces the column swap operations in addition to the size-reduction operations.

关键词： Effective lll algorithm lattice reduction lll algorithm MIMO systems

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Integer estimation methods for GPS ambiguity resolution: an applications oriented review and improvement

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SURVEY REVIEW 2012年第324期43卷 59-71页

作者： Xu, Peiliang Shi, Chuang Liu, Jingnan Kyoto Univ Disaster Prevent Res Inst Kyoto 6110011 Japan Wuhan Univ GNSS Res Ctr Wuhan 430071 Peoples R China

The integer least squares (ILS) problem, also known as the weighted closest point problem, is highly interdisciplinary, but no algorithm can find its global optimal integer solution in polynomial time. We first outline two suboptimal integer solutions, which can be important either in real time communication systems or to solve high dimensional GPS integer ambiguity unknowns. We then focus on the most efficient algorithm to search for the exact integer solution, which is shown to be faster than LAMBDA in the sense that the ratio of integer candidates to be checked by the efficient algorithm to those by LAMBDA can be theoretically expressed by r(m) where r <= 1 and m is the number of integer unknowns. Finally, we further improve the searching efficiency of the most powerful combined algorithm by implementing two sorting strategies, which can either be used for finding the exact integer solution or for constructing a suboptimal integer solution. Test examples clearly demonstrate that the improved methods can perform significantly better than the most powerful combined algorithm to simultaneously find the optimal and second optimal integer solutions, if the ILS problem cannot be well reduced.

关键词： Global positioning system Integer linear model Integer least squares Closest point problem Lattice reduction lll algorithm

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An efficient algorithm for clustered integer least squares problems

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2012年第1期19卷 19-30页

作者： Chun, Joohwan Park, Jaehyun Korea Adv Inst Sci & Technol Dept Elect Engn Taejon 305701 South Korea

The integer least squares problem is known to be NP-hard, and the algorithms such as the sphere decoding algorithm, which give the optimal solution, are usually too slow. To obtain a solution efficiently one may use one of the suboptimal algorithms such as the ordered successive interference cancellation (OSIC) algorithm or the lll-aided OSIC algorithm that first modifies the system of equations using the lll algorithm due to Lenstra, Lenstra, and Lovasz. However, these suboptimal algorithms still may not be fast enough depending on the applications. In this paper we present two decoupling techniques to speed-up the lll-aided OSIC algorithm. Our lll-aided decoupled OSIC algorithm, which is applicable to clustered integer least squares problems, has the accuracy comparable to the ordinary lll-aided OSIC algorithm (without decoupling), but is much faster than the OSIC algorithm or the lll-aided OSIC algorithm. Copyright (C) 2011 John Wiley & Sons, Ltd.

关键词： integer least squares lll algorithm lattice reduction

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