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Optimal Numbers of Base Station Antennas and Users in Multiuser Massive MIMO Systems with Pilot Overhead

다중 사용자 Massive MIMO 시스템의 파일럿 오버헤드를 고려한 최적 기지국 안테나 수 및 사용자 수 분석

  • Jung, Minchae (School of Electrical and Electronic Engineering, Yonsei University) ;
  • Choi, Sooyong (School of Electrical and Electronic Engineering, Yonsei University)
  • Received : 2016.09.26
  • Accepted : 2016.11.23
  • Published : 2016.11.30

Abstract

In this paper, we consider multiuser massive multiple-input and multiple-output (MIMO) system where multiusers simultaneously utilize massive antennas of base station (BS). With a downlink frame structure considering pilot signals, we derive the ergodic cell capacity based on zero-forcing beamforming (ZFBF) technique. This paper proves that the ergodic cell capacity is concave function with respect to the numbers of BS antennas and users, and derives the optimum numbers of BS antennas and users maximizing ergodic cell capacity. From the simulation results, it is shown that the derived numbers of BS antennas and users has the optimum value for the maximum ergodic cell capacity, and the ergodic cell capacity with the derived optimum values increases with respect to the transmit SNR(Signal to Noise Ratio).

본 논문에서는 다중 사용자(multiuser)가 다수의 기지국 안테나(MIMO, Multiple-Input and Multiple-Output)를 동시에 사용하는 다중 사용자 massive MIMO 시스템 환경을 고려한다. 다중 사용자를 동시에 지원하기 위해 기지국에서는 ZFBF(Zero-Forcing Beamforming) 기법을 고려하고 수신 신호 검출을 위해 파일럿 신호를 고려한 하향 링크 프레임 구조를 적용하여 평균 셀 용량을 도출한다. 평균 셀 용량은 기지국 안테나 수 및 사용자 수에 대해 오목 함수 (concave function)임을 수식적으로 증명하고, 오목 함수 특징을 통해 최적의 기지국 안테나 수 및 사용자 수를 도출한다. 실험 결과를 통해 수식적으로 도출한 최적 값을 검증하고, 최적값 기반의 평균 셀 용량은 송신 SNR(Signal to Noise Ratio)에 비례하여 증가함을 확인할 수 있다.

Keywords

References

  1. G. Lee, Y. Sung, J. So, and J. Seo, "Research trend for 5G massive MIMO realization (5G Massive MIMO 실현을 위한 연구 동향)," Mag. IEIE, vol. 42, no. 10, pp. 858-876, Oct. 2015.
  2. A. J. Paulraj and T. Kailath, Increasing capacity in wireless broadcast systems using distributed transmission/directional reception, U.S. Patent, no. 5,345,599, 1994.
  3. I. E. Telatar, "Capacity of multi-antenna Gaussian channels," Eur. Trans. Telecommun., vol. 10, no. 6, pp. 585-595, Nov./Dec. 1999. https://doi.org/10.1002/ett.4460100604
  4. H. Ngo, E. Larsson, and T. Marzetta, "Energy and spectral efficiency of very large multiuser MIMO systems," IEEE Trans. Commun., vol. 61, no. 4, pp. 1436-1449, Feb. 2013. https://doi.org/10.1109/TCOMM.2013.020413.110848
  5. C. Peel, B. Hochwald, and A. Swindelhurst, "A vector-perturbation technique for nearcapacity multiantenna multiuser communicationpart I: channel inversion and regularization," IEEE Trans. Commun., vol. 53, no. 1, pp. 195-202, Jan. 2005. https://doi.org/10.1109/TCOMM.2004.840638
  6. T. Yoo and A. Goldsmith, "On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming," IEEE J. Sel. Areas in Commun., vol. 24, no. 3, pp. 528-541, Mar. 2006. https://doi.org/10.1109/JSAC.2005.862421
  7. C. Chae, S. Shim, and R. Heath, "Block diagonalized vector perturbation for multiuser MIMO systems," IEEE Trans. Wireless Commun., vol. 7, no. 11, pp. 4051-4057, Nov. 2008. https://doi.org/10.1109/T-WC.2008.070262
  8. H. Sung, S. Lee, and I. Lee, "Generalized channel inversion methods for multiuser MIMO systems," IEEE Trans. Commun., vol. 57, no. 11, pp. 3489-3499, Nov. 2009. https://doi.org/10.1109/TCOMM.2009.11.070404
  9. F. Rusek, D. Persson, B. Lau, E. Larsson, T. Marzetta, O. Edfors, and F. Tufvesson, "Scaling up MIMO: opportunities and challenges with very large arrays," IEEE Sign. Process. Mag., vol. 30, no. 1, pp. 40-60, Jan. 2013. https://doi.org/10.1109/MSP.2011.2178495
  10. T. Marzetta, "Noncooperative cellular wireless with unlimited numbers of base station antennas," IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590-3600, Nov. 2010. https://doi.org/10.1109/TWC.2010.092810.091092
  11. Y. Lim, C. Chae, and G. Caire, "Performance analysis of massive MIMO for cell-boundary users," IEEE Trans. Wireless Commun., vol. 14, no. 12, pp. 6827-6842, Dec. 2015. https://doi.org/10.1109/TWC.2015.2460751
  12. M. Jung, T. Kim, K. Min, Y. Kim, J. Lee, and S. Choi, "Asymptotic distribution of system capacity in multiuser MIMO systems with large number of antennas," in Proc. IEEE VTC Spring, pp. 1-5, Dresden, Germany, Jun. 2013.
  13. B. Hochwald and S. Vishwanath, "Space-time multiple access: Linear growth in the sum rate," in Proc. 40th Annu. Allerton Conf. Commun., Contr. Comput., Monticello, IL, Oct. 2002.
  14. S. Wagner, R. Couillet, M. Debbah, and D. Slock, "Large system analysis of linear precoding in correlated MISO broadcast channels under limited feedback," IEEE Trans. Inf. Theory, vol. 58, no. 7, Jul. 2012.
  15. M. Jung, Y. Kim, J. Lee, and S. Choi, "Optimal number of users in zero-forcing based multiuser MIMO systems with large number of antennas," J. Commun. and Networks (JCN), vol. 49, no. 4, pp. 362-369, Aug. 2013.
  16. M. Jung and S. Choi, "Optimal number of base station antennas and users in MF based multiuser massive MIMO systems," J. KICS, vol. 38A, no. 08, pp. 724-732, Aug. 2013. https://doi.org/10.7840/kics.2013.38A.8.724
  17. K. Min, M. Jung, T. Kim, Y. Kim, J. Lee, and S. Choi, "Pilot power ratio for uplink sum-rate maximization in zero-forcing based MUMIMO systems with large number of antennas," in Proc. IEEE VTC Fall, Las Vegas, USA, Sept. 2013.
  18. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, "On the lambert w-function," Advances in Computational Math., vol. 5, no. 1, pp. 329-359, Dec. 1996. https://doi.org/10.1007/BF02124750
  19. 3GPP TS 36.211 v8.6.0, Physical channels and modulation (Release 8), Mar. 2009.