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General transformation for block diagonalization of multitime-scale singularly perturbed linear systems

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2008年第5期53卷 1303-1305页

作者： Prljaca, Naser Gajic, Zoran Univ Tuzla Fac Elect Engn Tuzla 75000 Bosnia & Herceg Rutgers State Univ Dept Elect & Comp Engn Piscataway NJ 08854 USA

In this technical note, a general transformation for block-diagonalization (decoupling) of multitime-scale singularly perturbed linear systems composed of N subsystems is presented. The resulting decoupling correspond... 详细信息

关键词： block diagonalization Chang transformation decoupling multitime-scale systems singular perturbations

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MIXED PRECISION RECURSIVE block diagonalization FOR BIVARIATE FUNCTIONS OF MATRICES

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2022年第2期43卷 638-660页

作者： Massei, Stefano Robol, Leonardo TUe Ctr Anal Sci Comp & Applicat NL-1015 Eindhoven North Brabant Netherlands Univ Pisa Dept Math I-56127 Pisa Italy

Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Frechet derivative along a direction, the evaluation of (univariate) functions of Kronecker-sum-structured matrices, and the solution of, Sylvester matrix equations. In this work, we propose a recursive block diagonalization algorithm for computing bivariate functions of matrices of small to medium size, for which dense linear algebra is appropriate. The algorithm combines a blocking strategy, as in the Schur-Parlett scheme, and an evaluation procedure for the diagonal blocks. We discuss two implementations of the latter. The first is a natural choice based on Taylor expansions, whereas the second is derivative-free and relies on a multiprecision perturb-and-diagonalize approach. In particular, the appropriate use of multiprecision guarantees backward stability without affecting the efficiency in the generic case. This makes the second approach more robust. The whole method has cubic complexity, and it is closely related to the well-known Bartels-Stewart algorithm for Sylvester matrix equations when applied to f(x, y) = 1/x+y. We validate the performances of the proposed numerical method on several problems with different conditioning properties.

关键词： bivariate matrix functions mixed precision block diagonalization perturb-and-diagonalize multiprecision function of matrices

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Partially Non-orthogonal block diagonalization-Based Precoding in Downlink Multiuser MIMO with Limited Channel State Information Feedback

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IEICE TRANSACTIONS ON COMMUNICATIONS 2011年第12期E94B卷 3280-3288页

作者： Tajika, Yuki Taoka, Hidekazu Higuchi, Kenichi Tokyo Univ Sci Dept Elect Engn Noda Chiba 2788510 Japan DoCoMo Commun Labs Europe GmbH D-80687 Munich Germany

This paper investigates a precoding method in downlink multiuser multiple-input multiple-output (MIMO) transmission with multiple base station (BS) cooperation, where each user device basically feeds back the instantaneous channel state information (CSI) to only the nearest BS, but the users near the cell edge additionally feedback the instantaneous CSI to the second nearest BS among the cooperating BSs. Our precoding method is categorized as a form of multi-cell processing (MCP) [5], in which the transmission information to a user is shared by the cooperating BSs in order to utilize fully the degrees of freedom of the spatial channel, and is based on block diagonalization of the channel matrix. However, since some elements of the channel matrix are unknown, we allow partially non-orthogonal transmission. More specifically, we allow inter-user interference to users with limited instantaneous CSI feedback from the channel where the instantaneous CSIs of those users are not obtained at the BSs. The other sources of inter-user interference are set to zero based on the block diagonalization of the channel matrix. The proposed method more efficiently utilizes the degrees of freedom of the spatial channel compared to the case with full orthogonal transmission at the cost of increased inter-user interference. Simulation results show the effectiveness of the proposed method compared to the conventional approaches, which can accommodate the partial CSI feedback scenario, from the viewpoints of the required transmission power and achievable throughput.

关键词： multiuser MIMO base station cooperation precoding block diagonalization channel state information

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The application of eigenpair stability to block diagonalization

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SIAM JOURNAL ON NUMERICAL ANALYSIS 1997年第3期34卷 1255-1268页

作者： Ghosh, N Hager, WW Sarmah, P UNIV FLORIDA DEPT MATH GAINESVILLE FL 32611 USA

An algorithm presented in Hager [Comput. Math. Appl., 14 (1987), pp. 561-572] for diagonalizing a matrix is generalized to a block matrix setting. It is shown that the resulting algorithm is locally quadratically convergent. A global convergence proof is given for matrices with separated eigenvalues and with relatively small off-diagonal elements. Numerical examples along with comparisons to the QR method are presented.

关键词： block diagonalization eigenpair stability eigenvalues eigenvectors

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Hybrid block diagonalization for Massive Multiuser MIMO Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2016年第1期64卷 201-211页

作者： Ni, Weiheng Dong, Xiaodai Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 3P6 Canada

For a massive multiple-input multiple-output (MIMO) system, restricting the number of RF chains to far less than the number of antenna elements can significantly reduce the implementation cost compared to the full complexity RF chain configuration. In this paper, we consider the downlink communication of a massive multiuser MIMO (MU-MIMO) system and propose a low-complexity hybrid block diagonalization (Hy-BD) scheme to approach the capacity performance of the traditional BD processing method. We aim to harvest the large array gain through the phase-only RF precoding and combining and then digital BD processing is performed on the equivalent baseband channel. The proposed Hy-BD scheme is examined in both the large Rayleigh fading channels and millimeter wave (mmWave) channels. A performance analysis is further conducted for single-path channels and large number of transmit and receive antennas. Finally, simulation results demonstrate that our Hy-BD scheme, with a lower implementation and computational complexity, achieves a capacity performance that is close to (sometimes even higher than) that of the traditional high-dimensional BD processing.

关键词： Massive MIMO large scale MU-MIMO hybrid processing block diagonalization limited RF chains mmWave

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User Selection Algorithms for block diagonalization Aided Multiuser Downlink mm-Wave Communication

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IEEE ACCESS 2017年 5卷 5760-5772页

作者： Rajashekar, Rakshith Hanzo, Lajos Univ Southampton Sch ECS Southampton SO17 1BJ Hants England

In order to meet the ever increasing data rate demands, the next generation of wireless communication systems is being designed for exploiting the large amounts of unused spectrum in the millimeter-wave (mm-wave) band. Since operating at mm-wave frequencies imposes several challenges, such as high-path loss, as well as both spatial and temporal channel sparsity, there is a significant research interest focused on designing feasible solutions for establishing reliable and high-throughput links at mm wave frequencies. In this paper, we consider a cellular system relying on hybrid beamforming aided base station (BS) as well as user equipment and study the user selection problem, which has not been hitherto studied in the literature. More specifically, we study the problem of selecting K'-users by the BS for communication out of K-users whilst ensuring that the sum rate is maximized. Specifically, we propose a user selection algorithm, which relies on the knowledge of both the channel gains and the angle of departure (AoD) of the channel paths spanning to the various users, which is termed the AoD aided user selection (AoD-US). Furthermore, we devise a pair of subspace metrics based on: 1) the angle between the subspaces spanned by the BS array response vectors;2) the ratio of interference and signal space dimensions of various users, in order to reduce the user search space in AoD-US. This modified user selection algorithm is termed the AoD aided user selection with user set pruning (AoD-US-P). Furthermore, we study the attainable sum-rate performance of the block-diagonalization aided downlink and show that the proposed selection algorithms guarantee both multiuser diversity and multiplexing gains. Additionally, the proposed algorithms are studied in the round-robin scheduling scenario, where all the K-users are scheduled for achieving fairness. Our simulation results revealed that the AoD-US-P achieves nearly the same performance as that achieved by the AoD-US despit

关键词： User selection scheduling block diagonalization mm-wave communication precoding and combining

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Multiuser MIMO User Selection Based on L ₂-Hausdorff Distance with block diagonalization

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WIRELESS PERSONAL COMMUNICATIONS 2016年第2期91卷 691-707页

作者： Yuan, Kun Cao, Yewen Wang, Deqiang Zhang, Huanjing China Elect Technol Grp Corp 14th Res Inst 8 Glarun Rd Nanjing 210039 Jiangsu Peoples R China Shandong Univ Sch Informat Sci & Engn 27 Shanda Nan Rd Jinan 250100 Peoples R China

block diagonalization (BD) is an important precoding method for multiuser multiple-input and multiple-output (MU-MIMO) broadcast channel (BC) systems. When the number of users is large, user selection (scheduling) should be performed so as to make full use of BD precoding. In this paper, based on -Hausdorff distance, we propose two novel user selection algorithms, namely GUS- and US-, for MU-MIMO BC systems with BD precoding to maximize the throughput. Both of the proposed algorithms select users iteratively and perform power allocation using the waterfilling method. In GUS-, -Hausdorff distance is used as a crucial factor for the user selection criterion. In US-, besides the criterion in GUS-, a similarity criterion based on -hausdorff distance is employed to reduce the cardinality of the candidate user set effectively. The complexities of the proposed algorithms are analyzed and compared with those of typical existing algorithms. Simulations have been carried out to verify the performance of the proposed algorithms. Numerical results suggest that the proposed algorithms outperform most of their rivals in terms of complexity and show competitive performance in throughput.

关键词： block diagonalization Downlink system L-2-Hausdorff distance MU-MIMO User selection Waterfilling

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FFT-Based block diagonalization at User Terminal for Implicit Beamforming in Multiuser MIMO System

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IEICE TRANSACTIONS ON COMMUNICATIONS 2016年第1期E99B卷 115-123页

作者： Kimoto, Hayate Nishimori, Kentaro Hiraguri, Takefumi Makino, Hideo Niigata Univ Grad Sch Sci & Technol Niigata 9502102 Japan Nippon Inst Technol Fac Engn Miyashiro Saitama 3458501 Japan

This paper proposes Fast Fourier Transform (FFT) based orthogonal beam selection method at the user terminals (UTs) to reduce the number of nulls for the other users except an intended user by the block diagonalization (BD) algorithm in multiuser MIMO (MU-MIMO) sytems. The BD algorithm has been proposed in order to realize MU-MIMO broadcast transmission with a realistic signal processing burden. The BD algorithm cancels inter-user interference by creating the weights so that the channel matrixes for the other users are set to be zero matrixes. However, when the number of transmit antennas is equals to the total number of received antennas, the transmission rate by the BD algorithm is decreased. The proposed method realizes the performance improvement compared to the conventional BD algorithm without the burden on the UTs. It is verified via bit error rate (BER) evaluation that the proposed method is effective compared to the conventional BD algorithm and antenna selection method. Moreover, the effectiveness of proposed method is verified by the performance evaluation considering medium access control (MAC) layer in a comparison with the conventional BD algorithm which needs the channel state information (CSI) feedback. Because the proposed method can be easily applied to beamforming without the CSI feedback (implicit beamforming), it is shown that the propose method is effective from a point of view on the transmission efficiency in MU-MIMO system.

关键词： multiuser MIMO block diagonalization FFT implicit beamforming IEEE802.11ac eigenvalue

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Modified block diagonalization Precoding in Multicell Cooperative Networks

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2012年第8期61卷 3819-3824页

作者： Zeng, Yong Gunawan, Erry Guan, Yong Liang Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639801 Singapore

In downlink multiuser multiple-input-multiple-output (MIMO) systems, block diagonalization (BD) is a practical linear precoding scheme that completely eliminates interuser interference. However, its sum rate performance is rather poor in practical signal-to-noise ratio (SNR) regions due to the transmit power boost problem. In this paper, we propose a modified BD precoding scheme to improve its low-to-medium SNR performance with the so-called "effective SNR enhancement" technique. The proposed transmit covariance matrices are obtained by first solving a power minimization problem subject to the minimum rate constraint achieved by BD and then properly scaling the solution until the power constraint is active. The power minimization problem is nonconvex in general. We therefore propose an efficient algorithm that approximately solves the problem. Simulation results demonstrate significant sum rate gains over BD and existing minimum mean square error (MMSE)-based precoding schemes.

关键词： block diagonalization convex optimization interference management precoding sum-rate maximization

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A Novel Adaptive Interference Admission Control Method for Layered Partially Non-orthogonal block diagonalization for Base Station Cooperative MIMO

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IEICE TRANSACTIONS ON COMMUNICATIONS 2014年第1期E97B卷 155-163页

作者： Oshima, Yusuke Benjebbour, Anass Higuchi, Kenichi Tokyo Univ Sci Grad Sch Sci & Technol Dept Elect Engn Noda Chiba 2788510 Japan NTT DOCOMO INC Yokosuka Kanagawa 2398536 Japan

This paper proposes a novel method for adaptively controlling the admission of interference to users in our previously proposed layered partially non-orthogonal block diagonalization (BD) precoding method for downlink multiuser multiple-input multiple-output (MIMO) transmission that employs cooperation among multiple base stations (BSs). The proposed method is applicable when some of the instantaneous channel state information (CSI) feedback between the user equipment and the respective BSs is missing if the path loss between the user equipment and BS is higher than a predetermined threshold. The proposed method suppresses the loss in the transmitter diversity (beam forming) gain caused by the perfect nulling of inter-user interference in BD. By allowing the inter-user interference from a link that has a high average path loss, the overall throughput performance of simple BD is enhanced. We show that the combination of layered transmission that restricts the set of BSs used for the signal transmission and adaptive control of interference admission significantly increases the throughput of BS cooperative multiuser MIMO with partial CSI feedback.

关键词： multiuser MIMO base station cooperation block diagonalization channel state information

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