• Title/Summary/Keyword: Lattice Reduction

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Lattice Reduction Aided Preceding Based on Seysen's Algorithm for Multiuser MIMO Systems (다중 사용자 MIMO 시스템을 위한 Seysen 알고리즘 기반 Lattice Reduction Aided 프리코팅)

  • An, Hong-Sun;Mohaisen, Manar;Chang, Kyung-Hi
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.34 no.9C
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    • pp.915-921
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    • 2009
  • Lenstra-Lenstra-Lovasz (LLL) algorithm, which is one of the lattice reduction (LR) techniques, has been extensively used to obtain better bases of the channel matrix. In this paper, we jointly apply Seysen's lattice reduction Algorithm (SA), instead of LLL, with the conventional linear precoding algorithms. Since SA obtains more orthogonal lattice bases compared to those obtained by LLL, lattice reduction aided (LRA) precoding based on SA algorithm outperforms the LRA precoding with LLL. Simulation results demonstrate that a gain of 0.5dB at target BER of $10^{-5}$ is achieved when SA is used instead of LLL or the LR stage.

EFFICIENT LATTICE REDUCTION UPDATING AND DOWNDATING METHODS AND ANALYSIS

  • PARK, JAEHYUN;PARK, YUNJU
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.2
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    • pp.171-188
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    • 2015
  • In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov${\acute{a}}$sz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.

Lattice-Reduction-Aided Preceding Using Seysen's Algorithm for Multi-User MIMO Systems (다중 사용자 다중 입출력 시스템에서 Seysen 기법을 이용한 격자 감소 기반 전부호화 기법)

  • Song, Hyung-Joon;Hong, Dae-Sik
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.46 no.6
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    • pp.86-93
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    • 2009
  • We investigate lattice-reduction-aided precoding techniques for multi-user multiple-input multiple-output (MIMO) channels. When assuming full knowledge of the channel state information only at the transmitter, a vector perturbation (VP) is a promising precoding scheme that approaches sum capacity and has simple receiver. However, its encoding is nondeterministic polynomial time (NP)-hard problem. Vector perturbation using lattice reduction algorithms can remarkably reduce its encoding complexity. In this paper, we propose a vector perturbation scheme using Seysen's lattice reduction (VP-SLR) with simultaneously reducing primal basis and dual one. Simulation results show that the proposed VP-SLR has better bit error rate (BER) and larger capacity than vector perturbation with Lenstra-Lenstra-Lovasz lattice reduction (VP-LLL) in addition to less encoding complexity.

Lattice Reduction-aided Detection with Out-of-Constellation Point Correction for MIMO Systems (MIMO 시스템을 위한 Out-of-Constellation Point 보정 Lattice Reduction-aided 검출기법)

  • Choi, Kwon-Hue
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.32 no.12A
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    • pp.1339-1345
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    • 2007
  • An important drawback in Lattice Reduction (LR) aided detectors has been investigated. For the solution, an improved LR aided detection with ignorable complexity overhead is proposed for MIMO system, where the additional correction operation is performed for the case of unreliable symbol decision. We found that LR aided detection errors mainly occur when the lattice points after the inverse lattice transform in the final step fall outside the constellation point set. In the proposed scheme, we check whether or not the lattice point obtained through LR detection is out of constellation. Only for the case of out of constellation, we additionally perform ML search with reduced search region restricted to the neighboring points near to the obtained lattice points. Using this approach, we can effectively and significantly improve the detection performance with just a slight complexity overhead which is negligible compared to full searched ML scheme. Simulation results show that the proposed scheme achieves the detection performance near to that of the ML detection with a lower computational complexity.

Complexity Reduction Scheme for Lattice Reduction-based MIMO Receiver under Time Varying Fading Environments (시변 페이딩 환경에서 Lattice Reduction 기반 MIMO 수신기를 위한 계산량 감소 기법)

  • Kim, Han-Nah;Choi, Kwon-Hue
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.34 no.11A
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    • pp.852-861
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    • 2009
  • We propose a complexity reduced Lattice Reduction(LR) scheme for MIMO detection under time varying fading environments. It is found that for successive MIMO transmission instances, the integer matrix P after LR decomposition remains the same or only a few elements of the matrix P are slightly changed. Based on this feature, we perform LR reduction by setting the initial values for P matrix for the decomposition to be the one obtained in the previous instance not starting from the identity matrix. Simulation results reveal that the proposed scheme drastically reduces overall complexity of LR reduction compared to the conventional scheme for various system parameters under time varying channels. We also show that the proposed scheme can be applied to Seysen LR as well as LLL(Lenstra, Lenstra, and Lavasaz)-LR.

A Vector-Perturbation Based Lattice-Reduction using look-Up Table (격자 감소 기반 전부호화 기법에서의 효율적인 Look-Up Table 생성 방법)

  • Han, Jae-Won;Park, Dae-Young
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.36 no.6A
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    • pp.551-557
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    • 2011
  • We investigate lattice-reduction-aided precoding techniques using Look-Up table (LUT) for multi-user multiple-input multiple-output(MIMO) systems. Lattice-reduction-aided vector perturbation (VP) gives large sum capacity with low encoding complexity. Nevertheless lattice-reduction process based on the LLL-Algorithm still requires high computational complexity since it involves several iterations of size reduction and column vector exchange. In this paper, we apply the LUT-aided lattice reduction on VP and propose a scheme to generate the LUT efficiently. Simulation results show that a proposed scheme has similar orthogonality defect and Bit-Error-Rate(BER) even with lower memory size.

Systolic Arrays for Lattice-Reduction-Aided MIMO Detection

  • Wang, Ni-Chun;Biglieri, Ezio;Yao, Kung
    • Journal of Communications and Networks
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    • v.13 no.5
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    • pp.481-493
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    • 2011
  • Multiple-input multiple-output (MIMO) technology provides high data rate and enhanced quality of service for wireless communications. Since the benefits from MIMO result in a heavy computational load in detectors, the design of low-complexity suboptimum receivers is currently an active area of research. Lattice-reduction-aided detection (LRAD) has been shown to be an effective low-complexity method with near-maximum-likelihood performance. In this paper, we advocate the use of systolic array architectures for MIMO receivers, and in particular we exhibit one of them based on LRAD. The "Lenstra-Lenstra-Lov$\acute{a}$sz (LLL) lattice reduction algorithm" and the ensuing linear detections or successive spatial-interference cancellations can be located in the same array, which is considerably hardware-efficient. Since the conventional form of the LLL algorithm is not immediately suitable for parallel processing, two modified LLL algorithms are considered here for the systolic array. LLL algorithm with full-size reduction-LLL is one of the versions more suitable for parallel processing. Another variant is the all-swap lattice-reduction (ASLR) algorithm for complex-valued lattices, which processes all lattice basis vectors simultaneously within one iteration. Our novel systolic array can operate both algorithms with different external logic controls. In order to simplify the systolic array design, we replace the Lov$\acute{a}$sz condition in the definition of LLL-reduced lattice with the looser Siegel condition. Simulation results show that for LR-aided linear detections, the bit-error-rate performance is still maintained with this relaxation. Comparisons between the two algorithms in terms of bit-error-rate performance, and average field-programmable gate array processing time in the systolic array are made, which shows that ASLR is a better choice for a systolic architecture, especially for systems with a large number of antennas.

Lattice-Reduction-Aided Detection based Extended Noise Variance Matrix using Semidefinite Relaxation in MIMO Systems (MIMO시스템에서 Semidefinite Relaxation을 이용한 잡음 분산 행렬 기반의 Lattice-Reduction-Aided 검출기)

  • Lee, Dong-Jin;Park, Su-Bin;Byun, Youn-Shik
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.33 no.11C
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    • pp.932-939
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    • 2008
  • Recently lattice-reduction (LR) has been used in signal detection for multiple-input multiple-output (MIMO) systems. The conventional LR aided detection schemes are combinations of LR and signal detection methods such as zero-forcing (ZF) and minimum mean square error (MMSE) detection. In this paper, we propose the Lattice-Reduction-aided scheme based on extended noise variance matrix to search good candidate symbol set in quantization step. Then this scheme estimates transmitted symbol with Semidefinite Relaxation by candidate symbol set. Simulation results in a random MIMO system show that the proposed scheme exhibits improved performance and a slight increase in complexity.

Block-Mode Lattice Reduction for Low-Complexity MIMO Detection

  • Choi, Kwon-Hue;Kim, Han-Nah;Kim, Soo-Young;Kim, Young-Il
    • ETRI Journal
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    • v.34 no.1
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    • pp.110-113
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    • 2012
  • We propose a very-low-complexity lattice-reduction (LR) algorithm for multi-input multi-output detection in time-varying channels. The proposed scheme reduces the complexity by performing LR in a block-wise manner. The proposed scheme takes advantage of the temporal correlation of the channel matrices in a block and its impact on the lattice transformation matrices during the LR process. From this, the proposed scheme can skip a number of redundant LR processes for consecutive channel matrices and performs a single LR in a block. As the Doppler frequency decreases, the complexity reduction efficiency becomes more significant.

Implementation of Lattice Reduction-aided Detector using GPU on SDR System (SDR 시스템에서 GPU를 사용한 Lattice Reduction-aided 검출기 구현)

  • Kim, Tae Hyun;Leem, Hyun Seok;Choi, Seung Won
    • Journal of Korea Society of Digital Industry and Information Management
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    • v.7 no.3
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    • pp.55-61
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    • 2011
  • This paper presents an implementation of Lattice Reduction (LR)-aided detector for Multiple-Input Multiple-Output (MIMO) system using Graphics Processing Unit (GPU). GPU is a parallel processor which has a number of Arithmetic Logic Units (ALUs), thus, it can minimize the operation time of LR algorithm through the parallelization using multiple threads in the GPU. Through the implemented LR-aided detector, we verify that the LR-aided detector operates a lot faster than Maximum Likelihood (ML) detector. The implemented LR-aided detector has been applied to WiMAX system to show the feasibility of its real-time processing. In addition, we demonstrate that the processing time can be reduced at the cost of 3dB SNR loss by limiting the repeating loop in Lenstra-Lenstra-Lovasz (LLL) algorithm which is frequently used in LR-aided detector.