Abstract
Demands of wireless data traffic, throughput, the number of wireless mobile connections and devices will always increase. In addition, the concern about energy consumption is also growing for wireless communication systems. Massive MIMO system is a new emerging research area to resolve these issues. In this paper, the performance of Massive MIMO downlink including linear precoding is evaluated. Spectral efficiency through achievable rate and energy efficiency through transmit power of ZF and MRT linear precoding is investigated under practical limitations, such as imperfect CSI, less complexity processing and inter user interference. Since ZF and MRT precoding can balance the system performance and complexity. Different channel estimation values are considered in order to compare the performance of these precoding techniques in the given system. The achievable rate and the downlink transmit power of ZF and MRT precoding techniques are derived, analyzed and compared under the same conditions and assumptions. Several scenarios are considered to investigate these performance parameters. It is found that when the ratio of BS antennas and number of users is large, ZF is better than MRT while when the ratio is quite small it makes MRT better than ZF for the same conditions.
Similar content being viewed by others
References
Index, C. V .N. (2014). Global mobile data traffic forecast update, 2013–2018. UR l:http://www.cisco.com/c/en/us/solutions/collateral/service-provider/visual-networking-index-vni/white_paper_c11-520862.html. Visited on 14 May 2014.
Marzetta, T. L. (2015). Massive mimo: An introduction. Bell Labs Technical Journal, 20, 11–22.
Andrews, J. G., Buzzi, S., Choi, W., Hanly, S. V., Lozano, A., Soong, A. C., et al. (2014). What will 5g be? IEEE Journal on Selected Areas in Communications, 32(6), 1065–1082.
Gesbert, D., Kountouris, M., Heath, R. W, Jr., Chae, C.-B., & Sälzer, T. (2007). Shifting the mimo paradigm. IEEE Signal Processing Magazine, 24(5), 36–46.
Marzetta, T. L. (2010). Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Transactions on Wireless Communications, 9(11), 3590–3600.
Qiao, D., Wu, Y., & Chen, Y. (2014). Massive mimo architecture for 5g networks: Co-located, or distributed?. In: 2014 11th international symposium on wireless communications systems (ISWCS). IEEE, pp. 192–197.
Boccardi, F., Heath, R. W., Lozano, A., Marzetta, T. L., & Popovski, P. (2014). Five disruptive technology directions for 5g. IEEE Communications Magazine, 52(2), 74–80.
Rusek, F., Persson, D., Lau, B. K., Larsson, E. G., Marzetta, T. L., Edfors, O., et al. (2013). Scaling up mimo: Opportunities and challenges with very large arrays. IEEE Signal Processing Magazine, 30(1), 40–60.
Larsson, E., Edfors, O., Tufvesson, F., & Marzetta, T. (2014). Massive mimo for next generation wireless systems. IEEE Communications Magazine, 52(2), 186–195.
Hoydis, J., Ten Brink, S., & Debbah, M. (2013). Massive mimo in the ul/dl of cellular networks: How many antennas do we need? IEEE Journal on Selected Areas in Communications, 31(2), 160–171.
Shepard, C., Yu, H., Anand, N., Li, E., Marzetta, T., Yang, R., & Zhong, L. (2012). Argos: Practical many-antenna base stations. In Proceedings of the 18th annual international conference on Mobile computing and networking. ACM, pp. 53–64.
Mohammed, S. K., & Larsson, E. G. (2013). Per-antenna constant envelope precoding for large multi-user mimo systems. IEEE Transactions on Communications, 61(3), 1059–1071.
Hoydis, J., Ten Brink, S., & Debbah, M. (2011). Massive mimo: How many antennas do we need?. In 2011 49th Annual Allerton conference on communication, control, and computing (Allerton). IEEE, pp. 545–550.
Jose, J., Ashikhmin, A., Marzetta, T. L., & Vishwanath, S. (2011). Pilot contamination and precoding in multi-cell TDD systems. IEEE Transactions on Wireless Communications, 10(8), 2640–2651.
Mohan, K.J., Gogoi, O., & Gogoi, P. (2014). Interference cancellation in massive mimo base stations with certain precoding techniques in faded environment. In 2014 international conference on signal processing and integrated networks (SPIN). IEEE, pp. 795–800.
Huh, H., Caire, G., Papadopoulos, H. C., Ramprashad, S., et al. (2012). “Achieving” massive mimo” spectral efficiency with a not-so-large number of antennas. IEEE Transactions on Wireless Communications, 11(9), 3226–3239.
Prabhu, H., Edfors, O., Rodrigues, J., Liu, L., & Rusek, F. (2014). A low-complex peak-to-average power reduction scheme for OFDM based massive mimo systems. In: 2014 6th international symposium on communications, control and signal processing (ISCCSP). IEEE, pp. 114–117.
Björnson, E., Bengtsson, M., & Ottersten, B. (2014). Optimal multiuser transmit beamforming: A difficult problem with a simple solution structure. arXiv preprint arXiv:1404.0408.
Lee, J., Han, J.-K., & Zhang, J. (2009). Mimo technologies in 3GPP ITE and ITE-advanced. EURASIP Journal on Wireless Communications and Networking, 2009, 3.
Selvan, V., Iqbal, M. S., & Al-Raweshidy, H. (2014). Performance analysis of linear precoding schemes for very large multi-user mimo downlink system. In 2014 fourth international conference on innovative computing technology (INTECH). IEEE, pp. 219–224.
Lim, Y.-G., Chae, C.-B., & Caire, G. (2013). Performance analysis of massive mimo for cell-boundary users. arXiv preprint arXiv:1309.7817.
Zhao, L., Zheng, K., Long, H., & Zhao, H. (2014). Performance analysis for downlink massive mimo system with ZF precoding. Transactions on Emerging Telecommunications Technologies, 25(12), 1219–1230.
Parfait, T., Kuang, Y., & Jerry, K. (2014). Performance analysis and comparison of ZF and MRT based downlink massive mimo systems. In 2014 sixth international conference on ubiquitous and future networks (ICUFN). IEEE, pp. 383–388.
Ngo, H. Q., Larsson, E. G., & Marzetta, T. L. (2013). Energy and spectral efficiency of very large multiuser mimo systems. IEEE Transactions on Communications, 61(4), 1436–1449.
Hoydis, J., Ten Brink, S., & Debbah, M. (2012). Comparison of linear precoding schemes for downlink massive mimo. In 2012 IEEE international conference on communications (ICC). IEEE, pp. 2135–2139.
Zhang, Q., Jin, S., Wong, K.-K., Zhu, H., & Matthaiou, M. (2014). Power scaling of uplink massive mimo systems with arbitrary-rank channel means. IEEE Journal of Selected Topics in Signal Processing, 8(5), 966–981.
Bjornson, E., Sanguinetti, L., Hoydis, J., & Debbah, M. (2014). Designing multi-user mimo for energy efficiency: When is massive mimo the answer?. In 2014 IEEE wireless communications and networking conference (WCNC). IEEE, pp. 242–247.
Yin, X., Yu, X., Liu, Y., Tan, W., & Chen, X. (2013). Performance analysis of multiuser mimo system with adaptive modulation and imperfect CSI. In IET international conference on information and communications technologies (IETICT 2013). IET, pp. 571–576.
Ngo, H. Q. (2015). Massive MIMO: Fundamentals and system designs (Vol. 1642). Linköping: Linköping University Electronic Press.
Larsson, E. G., Edfors, O., Tufvesson, F., & Marzetta, T. L. (2014). Massive MIMO for Next Generation Wireless Systems. IEEE Communications Magazine, 52(2), 186–195.
Nishimori, K., Cho, K., Takatori, Y., & Hori, T. (2001). Automatic calibration method using transmitting signals of an adaptive array for TDD systems. IEEE Transactions on Vehicular Technology, 50(6), 1636–1640.
Rogalin, R., Bursalioglu, O. Y., Papadopoulos, H. C., Caire, G., & Molisch, A. F. (2013). Hardware-impairment compensation for enabling distributed large-scale mimo. In Information theory and applications workshop (ITA). IEEE, pp. 1–10.
Frigyes, I., Bitó, J., & Bakki, P. (2008). Advances in mobile and wireless communications: Views of the 16th IST mobile and wireless communication summit. Berlin: Springer.
Madhow, U. (2008). Fundamentals of digital communication. Cambridge: Cambridge University Press.
Marzetta, T. L., & Hochwald, B. M. (2006). Fast transfer of channel state information in wireless systems. IEEE Transactions on Signal Processing, 54(4), 1268–1278.
Ngo, H. Q., Larsson, E. G., & Marzetta, T. L. (2013). Massive mu-mimo downlink tdd systems with linear precoding and downlink pilots. In 2013 51st Annual Allerton conference on communication, control, and computing (Allerton). IEEE, pp. 293–298.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix 1
The desired signal power \(S_k\), interference \(I_k\) and Noise \(n_k\) is
and
By substituting the valuse of \(S_k, I_k\) and \(n_k\) in (13), the SINR of the kth user is given as
When the value of M and K is large [23], then
The diversity order measures the number of independent paths over which the data is received [23]
where \(\alpha = \frac{M}{K}\)
Putting the values of (27) in (26) and after some manipulations, we obtain the result of (9).
Appendix 2
Received Signal at the k th user is given as
Therefore, SINR of MRT precoding under imperfect CSI is
where \('\beta '\) for imperfct CSI is given as
But from [36]
and
Substituting (30), (31) and (32) in (29) and after some manipulations, we obtain the result of (11)
Rights and permissions
About this article
Cite this article
Israr, A., Rauf, Z., Muhammad, J. et al. Performance Analysis of Downlink Linear Precoding in Massive MIMO Systems Under Imperfect CSI. Wireless Pers Commun 96, 2603–2619 (2017). https://doi.org/10.1007/s11277-017-4314-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11277-017-4314-0