Journal of the Institute of Electronics Engineers of Korea TC (대한전자공학회논문지TC)

The Institute of Electronics and Information Engineers (대한전자공학회)
권호 표지

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

  • 송형준 (연세대학교 전기전자공학부) ;
  • 홍대식 (연세대학교 전기전자공학부)
  • Published : 2009.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

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.

본 논문에서는 다중 사용자 다중 입출력 시스템을 위해 격자 감소 기법 기반 전부호화(preceding) 기법에 대해 연구하였다. 송신 단에서 완벽한 채널 상태 정보(CSI : Channel state information)를 이용할 수 있을 때, 벡터 분산 기법(VP : vector perturbation)은 큰 채널 전송 용량(sum capacity)을 얻을 수 있으면서 간단한 수신기로 구현될 수 있다. 그러나 VP 기법의 부호화는 비결정적 난해(NP-hard : nondeterministic polynomial time-hard) 문제이다. 이에 반해 격자 감소 기법 기반의 VP 기법은 부호화 복잡도를 크게 줄일 수 있다. 본 논문에서는 기본 및 이중 베이시스의 동시 감소를 통한 Seysen 격자 감소 기반 VP 기법(VP-SLR : vector perturbation with Seysen's lattice reduction)을 제안한다. 모의실험 결과는 LLL 기반 VP기법(VP-LLL : vector perturbation with Lenstra-Lenstra-Lovasz lattice reduction)에 비해 제안된 VP-SLR 기법이 더 낮은 비트 오류율(BER : bit error rate)과 더 큰 전송 용량을 가짐을 보여준다.

Keywords

References

  1. G. Caire and S. Shamai, 'On the Achievable Throughput of a Multi-Antenna Gaussian Broadcast Channel,' IEEE Trans. Inf. Theory, vol. 43, pp. 1691-1706, Jul. 2003
  2. B. M. Hochwald, C. B. Peel, and A. L. Swindlehurst, "A Vector-Perturbation Technique for Near-Capacity Multi-Antenna Multi-User Communication-Part II: Perturbation," IEEE Trans. Comm., vol. 53, no. 3, pp. 537-544, Jan. 2005 https://doi.org/10.1109/TCOMM.2004.841997
  3. C. Windpassinger, R. F. H. Fischer, and J. B. Huber, "Lattice-Reduction-Aided Broadcast Precoding," IEEE Trans. Comm., vol. 52, no. 12, pp. 2057-2060, Dec. 2004 https://doi.org/10.1109/TCOMM.2004.838732
  4. M. Taherzadeh, A. Mobasher, and A. K. Khandani, "Communication over MIMO Broadcast Channels Using Lattice-Basis Reduction," IEEE Trans. Inf. Theory, vol. 53, no. 12, pp. 4567-4582, Dec. 2007 https://doi.org/10.1109/TIT.2007.909095
  5. P. Viswanath and D. Tse, "Sum Capacity of the Vector Gaussian Broadcast Channel and Uplink-Downlink Duality," IEEE Trans. Inf. Theory, vol.49, pp. 1912-1921, Aug. 2003 https://doi.org/10.1109/TIT.2003.814483
  6. C. B. Peel, B. M. Hochwald, and A. L. Swindlehurst, "A Vector-Perturbation Technique for Near-Capacity Multi-Antenna Multi-User Communication-Part I: Channel Inversion and Regularization," IEEE Trans. Comm., vol. 53, no. 1, pp. 195-202, Jan. 2005 https://doi.org/10.1109/TCOMM.2004.840638
  7. M. O. Damen, A. Chkief, and J.-C. Belfiore, "Lattice Code Decoder for Space-Time Codes," IEEE Commu. Letter, vol. 4, pp. 161-163, May 2000 https://doi.org/10.1109/4234.846498
  8. A. K. Lenstra, H. W. Lenstra, and L. Lovasz, 'Factoring Polynomials with Rational Coefficients,' Math. Ann., vol. 261, pp. 515-534, Jul. 1982 https://doi.org/10.1007/BF01457454
  9. L. Babai, 'On Lovasz Lattice Reduction and the Nearest Lattice Point Problem,' Combinatorica, vol. 6, no. 1, pp. 1-13, May 1986 https://doi.org/10.1007/BF02579403
  10. M. Seysen, 'Simultaneous Reduction of a Lattice Basis and its Reciprocal Basis,' Combinatorica, vol. 13., pp. 363-376, 1993 https://doi.org/10.1007/BF01202355
  11. J. Hastad and J. C. Lagarias, 'Simultaneously Good Bases of a Lattice and its Reciprocal Lattice,' Math. Ann., vol. 287, pp. 163-174, 1990 https://doi.org/10.1007/BF01446883
  12. J. Shawe-Taylor, C. K. I. Williams, N. Cristianini, and J. Kanola, "On the Eigenvalue of the Gram Matrix and the Generalization Error of Kernel-PCA," IEEE Trans. Inf. Theory, vol. 51, no. 7, pp. 2510-2522, Jul. 2005 https://doi.org/10.1109/TIT.2005.850052