Browse > Article
http://dx.doi.org/10.1109/JCN.2016.000099

Performance of ZF Precoder in Downlink Massive MIMO with Non-Uniform User Distribution  

Kong, Chuili (Institute of Information and Communication Engineering, Zhejiang University)
Zhong, Caijun (Institute of Information and Communication Engineering, Zhejiang University)
Zhang, Zhaoyang (Institute of Information and Communication Engineering, Zhejiang University)
Publication Information
Journal of Communications and Networks / v.18, no.5, 2016 , pp. 688-698 More about this Journal
Abstract
In this paper, we investigate the achievable sum rate and energy efficiency of downlink massive multiple-input multiple-output antenna systems with zero-forcing precoding, by taking into account the randomness of user locations. Specifically, we propose two types of non-uniform user distributions, namely, center-intensive user distribution and edge-intensive user distribution. Based on these user distributions, we derive novel tight lower and upper bounds on the average sum rate. In addition, the impact of user distributions on the optimal number of users maximizing the sum rate is characterized. Moreover, by adopting a realistic power consumption model which accounts for the transmit power, circuit power and signal processing power, the energy efficiency of the system is studied. In particular, closed-form solutions for the key system parameters, such as the number of antennas and the optimal transmit signal-to-noise ratio maximizing the energy efficiency, are obtained. The findings of the paper suggest that user distribution has a significant impact on the system performance: for instance, the highest average sum rate is achieved with the center-intensive user distribution, while the lowest average sum rate is obtained with the edge-intensive user distribution. Also, more users can be served with the center-intensive user distribution.
Keywords
Energy efficiency; massive MIMO systems; non-uniform user distribution; sum rate;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
연도 인용수 순위
1 M. Matthaiou, C. Zhong, and T. Ratnarajah, "Novel generic bounds on the sum rate of MIMO ZF receivers," IEEE Trans. Signal Process., vol. 59, no. 9, pp. 4341-4353, Sept. 2011.   DOI
2 R. M. Gorless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, "On the Lambert W function," Adv. Comput. Math., vol. 5, no. 4, pp. 329-359, Feb. 1996.   DOI
3 A. Adhikary, H. S. Dhillon, and G. Caire, "Massive-MIMO meets HetNet: Interference coordination through spatial blanking," IEEE J. Sel. Areas Commun., vol. 33, no. 6, pp. 1171-1186, June 2015.   DOI
4 Z. Gong and M. Haenggi, "Interference and outage in mobile random networks: Expectation, distribution, and correlation," IEEE Trans. Mobile Comput., vol. 13, no. 2, pp. 337-349, Feb. 2014.   DOI
5 L. Liang, W. Xu, and X. Dong, "Low-complexity hybrid precoding in massive multiuser MIMO systems," IEEE Wireless Commun. Lett., vol. 3, no. 6, pp. 653-656, Dec. 2014.   DOI
6 I. S. Gradshteyn and I. M. Ryzhik, Tables of Intergrals, Serious and Products, 7th ed. San Diago: Acadamic Press, 2007.
7 M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, New York: Dover Publication Inc., 1974.
8 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 Mathematics, vol. 5, no. 1, pp. 329-359, Nov. 1996.   DOI
9 T. D. Novlan, H. S. Dhillon, and J. G. Andrews, "Analytical modeling of uplink cellular networks," IEEE Trans. Wireless Commun., vol. 12, no. 6, pp. 2669-2679, June 2013.   DOI
10 E. Bjornson, L. Sanguinetti, J. Hoydis, and M. Debbah, "Designing multiuser MIMO for energy efficiency: When is massive MIMO the answer?," in Proc. IEEE WCNC, Apr. 2014, pp. 242-247.
11 C. Martin and B. Ottersten, "Asymptotic eigenvalue distributions and capacity for MIMO channels under correlated fading," IEEE Trans. Wireless Commun., vol. 3, no. 4, pp. 1350-1359, July 2004.   DOI
12 G. Miao, "Energy efficient uplink massive multi-user MIMO," IEEE Trans. Wireless Commun., vol. 12, no. 5, pp. 2302-2313, May 2013.   DOI
13 T. L. Marzetta, "Noncooperative cellular wireless with unlimited numbers of base station antennas," IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3590-3600, Nov. 2010.   DOI
14 H. Q. Ngo, E. G. Larsson, and T. L. Marzetta, "Energy and spectral efficiency of very large multiuser MIMO systems," IEEE Trans. Commun., vol. 61, no. 4, pp. 1436-1449, Apr. 2013.   DOI
15 J. Hoydis, S. ten Brink, and M. Debbah, "Massive MIMO in the UL/DL of cellular networks: How many antennas do we need?," IEEE J. Sel. Areas Commun., vol. 31, no. 2, pp. 160-171, Feb. 2013.   DOI
16 H. Yang and T. L. Marzetta, "Performance of conjugate and zero-forcing beamforming in large-scale antenna systems," IEEE J. Sel. Areas Com-mun., vol. 31, no. 2, pp. 172-179, Feb. 2013.   DOI
17 Q. Zhang, S. Jin, K.-K. Wong, H. Zhu, and M. Matthaiou, "Power scaling of uplink massive MIMO systems with arbitrary-rank channel means," IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp. 966-981, Oct. 2014.   DOI
18 K. T. Truong and R. W. Heath Jr., "Effect of channel aging in massive MIMO systems,"IEEE J. Commun. Netw., vol. 15, no. 4, pp. 338-351, Aug. 2013.   DOI
19 C. Kong, C. Zhong, A. Papazafeiropoulos, M. Matthaiou, and Z. Zhang, "Sum-rate and power scaling of massive MIMO systems with channel aging," IEEE Trans. Commun., vol. 63, no. 12, pp. 4879-4893, Dec. 2015.   DOI
20 C. Kong, C. Zhong, A. Papazafeiropoulos, M. Matthaiou, and Z. Zhang, "Effect of channel aging on the sum rate of uplink massive MIMO systems," in Proc. IEEE ISIT, June 2015, pp. 1222-1226.
21 C. Kong, C. Zhong, M.Matthaiou, E. Bjornson, and Z. Zhang, "Multi-pair two-way AF relaying systems with massive arrays and imperfect CSI," in Proc. IEEE ICASSP, Mar. 2016, pp. 3651-3655.
22 S. Park, C.-B. Chae, and S. Bahk, "Before/after precoding massive MIMO systems for cloud radio access networks," IEEE J. Commun. Netw., vol. 15, no. 4, pp. 398-406, Aug. 2013.   DOI
23 M. S. Sim, J. Park, C.-B. Chae, and R. W. Heath Jr. "Compressed channel feedback for correlated massiveMIMO systems," IEEE J. Commun. Netw., vol. 18, no. 1, pp. 95-104, Feb. 2016.   DOI
24 R. Kudo, S.M. D. Armour, J. P.McGeehan, andM.Mizoguchi, "A channel state information feedback method for massive MIMO-OFDM," IEEE J. Commun. Netw., vol. 15, no. 4, pp. 352-361, Aug. 2013.   DOI
25 C. Kong, C. Zhong, M. Matthaiou, and Z. Zhang, "Performance of downlink massive MIMO in Ricean fading channels with ZF precoder," in Proc. IEEE ICC, pp. 1776-1782, June 2015.
26 C. Li, J. Zhang, and K. B. Letaief, "Throughput and energy efficiency analysis of small cell networks with multi-antenna base stations," IEEE Trans. Wireless Commun., vol. 13, no. 5, pp. 2505-2517, May 2014.   DOI
27 L. Zhao, K. Zheng, H. Long, and H. Zhao, "Performance analysis for downlink massive MIMO system with ZF precoding," Trans. Emerging Telecom. Technol., 2013.
28 M. Newton and J. Thompson, "Classification and generation of nonuniform user distributions for cellular multi-hop networks," in Proc. IEEE ICC, June 2006, pp. 4549-4553.
29 H. S. Dhillon, R. K. Ganti, and J. G. Andrews, "Modeling non-uniform UE distributions in downlink cellular networks," IEEE Wireless Commun. Lett., vol. 2, no. 3, pp. 339-342, June 2013.   DOI