SCIENCE CHINA Information Sciences, Volume 60, Issue 4: 042302(2017) https://doi.org/10.1007/s11432-016-0069-0

Resource allocation for pilot-assisted massive MIMO transmission

More info
  • ReceivedJan 28, 2016
  • AcceptedMar 30, 2016
  • PublishedNov 17, 2016


This paper is on the resource allocation problem for pilot-assisted multi-user massive multiple-input-multiple-output (MIMO) uplink with linear minimum mean-squared error (MMSE) channel estimation and detection. {We utilize the angular domain channel representation for uniform linear antenna arrays, and adopt its equivalent independent and nonidentical distributed channel model.} For a given coherence interval and total energy budget, we study the joint optimization of the training length and the training power to maximize the achievable sum-rate. For tractable analysis and low-complexity solution, a tight approximation on the achievable sum-rate is derived first. Then the training length optimization for fixed training power and the training power optimization for fixed training length with respect to the approximate sum-rate maximization are both shown to be concave. An alternative optimization that solves the training length and power iteratively is proposed for the joint resource allocation. In addition, for the special case that the training and data transmission powers are equal, we derive the optimal training lengths for both high and low signal-to-noise-ratio (SNR) regions. Numerical results show the tightness of the derived sum-rate approximation and also the significant performance advantage of the proposed resource allocation.

Funded by

National High-tech R&D Program of China(863)

"source" : null , "contract" : "2015AA011305"

National Natural Science Foundation of China(61320106003)

National Natural Science Foundation of China(61521061)

National Science and Technology Major Project of China(2015ZX03001035-002)

Natural Science Foundation Program through Jiangsu Province of China(BK20150852)

Program for Jiangsu Innovation Team Natural Science Foundation through the Jiangsu Higher Education Institutions of China(15KJB510025)

"source" : null , "contract" : "2014AA01A704"



This work was supported by National High-tech R&D Program of China (863) (Grant Nos. 2015AA011305, 2014AA01A704), National Natural Science Foundation of China (Grant Nos. 61320106003, 61521061), National Science and Technology Major Project of China (Grant No. 2015ZX03001035-002), Program for Jiangsu Innovation Team, Natural Science Foundation through the Jiangsu Higher Education Institutions of China (Grant No. 15KJB510025), and Natural Science Foundation Program through Jiangsu Province of China (Grant No. BK20150852). We would like to sincerely thank Dr. JING Yindi at the Department of Electrical and Computer Engineering of the University of Alberta for helpful discussion and suggestion.


[1] {You X H, Pan Z W, Gao X Q, et al. } {The 5G mobile communication: the development trends and its emerging key techniques (in Chinese). Sci Sin Inform, } 2014, 44: 551-563 Google Scholar

[2] {Marzetta T L. } {Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans Wirel Commun, 2010, 9: 3590-3600 CrossRef Google Scholar

[3] {Ngo H Q, Marzetta T L, Larsson E G. } {Energy and spectral efficiency of very large multiuser MIMO systems}. IEEE Trans Commun, 2013, 61: 1436-1449 CrossRef Google Scholar

[4] {Ashikhmin A, Marzetta T L.} {Pilot contamination precoding in multi-cell large scale antenna systems}. In: {Proceedings of IEEE International Symposium on Information Theory}, Cambridge, 2012. 1137--1141. Google Scholar

[5] {Gopalakrishnan B, Jindal N.} {An analysis of pilot contamination on multi-user MIMO cellular systems with many antennas}. In: {Proceedings of IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications}, San Francisco, 2011. 381--385. Google Scholar

[6] {Hoydis J, Brink S, Debbah M.} {Massive MIMO in the UL/DL of cellular networks: how many antennas do we need?} {IEEE J Sel Areas Commun}, 2013, 31: 160--171. Google Scholar

[7] Tse D, Viswanath P. {Fundamentals of Wireless Communication}. London: Cambridge University Press, 2009. Google Scholar

[8] {Yin H F, Gesbert D, Filippou M, et al. } {A coordinated approach to channel estimation in large-scale multiple-antenna systems}. IEEE J Sel Areas Commun, 2013, 31: 264-273 CrossRef Google Scholar

[9] {Adhikary A, Nam J, Ahn J Y, et al. } {Joint spatial division and multiplexing-the large-scale array regime}. IEEE Trans Inf Theory, 2013, 59: 6441-6463 CrossRef Google Scholar

[10] {Sun C, Gao X Q, Jin S, et al. } {Beam division multiple access transmission for massive MIMO communications}. IEEE Trans Commun, 2015, 63: 2170-2184 CrossRef Google Scholar

[11] {Hassibi B, Hochwald B M.} {How much training is needed in multiple-antenna wireless links?} {IEEE Trans Inf Theory}, 2003, 49: 951--963. Google Scholar

[12] {Ngo H Q, Marzetta T L, Larsson E G. } {Massive MIMO with optimal power and training duration allocation}. IEEE Wirel Commun Lett, 2014, 3: 605-608 CrossRef Google Scholar

[13] {Guo K F, Guo Y, Fodor G, et al.} {Uplink power control with MMSE receiver in multi-cell MU-Massive-MIMO systems}. In: {Proceedings of IEEE International Conference on Communications}, Sydney, 2014. 5184--5190. Google Scholar

[14] {You L, Gao X Q, Xia X G, et al. } {Pilot reuse for massive MIMO transmission over spatially correlated Rayleigh fading channels}. IEEE Trans Wirel Commun, 2015, 14: 3352-3366 CrossRef Google Scholar

[15] {Pedersen K I, Mogensen P E, Fleury B H. } {A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments}. IEEE Trans Wirel Commun, 2000, 49: 437-447 Google Scholar

[16] {Biguesh M, Gershman A B. } {Training-based MIMO channel estimation: a study of estimator tradeoffs and optimal training signals}. IEEE Trans Signal Process, 2006, 54: 884-893 CrossRef Google Scholar

[17] {Zhang X L, Matthaiou M, Coldrey M, et al. } {Impact of residual transmit RF impairments on training-based MIMO systems}. IEEE Trans Commun, 2015, 63: 2899-2911 CrossRef Google Scholar

[18] Moon T K, Stirling W C. {Mathematical Methods and Algorithms for Signal Processing}. Upper Saddle River: Prentice Hall, 2000. Google Scholar

[19] {Li P, Paul D, Narasimhan R, et al. } {On the distribution of SINR for the MMSE MIMO receiver and performance analysis}. IEEE Trans Inf Theory, 2006, 52: 271-286 CrossRef Google Scholar

[20] Boyd S, Vandenberghe L. {Convex Optimization}. London: Cambridge University Press, 2004. Google Scholar

[21] Gao F F, Zhang R, Liang Y C, et al. Design of learning based MIMO cognitive radio systems. IEEE Trans Veh Technol, 2010, 59: 1707-1720 CrossRef Google Scholar

[22] {Ngo H Q, Marzetta T L, Larsson E G.} {Analysis of the pilot contamination effect in very large multicell multiuser MIMO systems for physical channel models}. In: {Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, Prague, 2011. 3464--3467. Google Scholar

[23] Chong E K P, Zak S H. {An Introduction to Optimization}. 3rd ed. Hoboken: Wiley-Interscience, 2008. Google Scholar

[24] {Cho Y S, Kim J, Yang W Y, et al.} {MIMO-OFDM Wireless Communications with MATLAB}. Singapore: John Wiley & Sons (Asia) Pte Ltd., 2010. Google Scholar

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有