Abstract：In massive multiple-input multiple-output (MIMO) systems, multi-cell pilot reuse is an important factor affecting the achievable system uplink rate. A generalized channel model with adaptable power control was used to derive the lower bound on the achievable uplink rate for both least square (LS) and minimum mean square error (MMSE) channel estimations. Then, the impact of pilot reuse as the number of base station (BS) antennas tends to infinity is analyzed based on these bounds. For uncorrelated channels, the ultimate achievable uplink rate of a user is mainly limited by pilot contamination and partially by the large-scale fading coefficients from a pilot interfering with users communicating to their base stations of their own cells due to power control. For correlated channels, pilot contamination is not the only factor that constrains the ultimate achievable system uplink rate, but always exists when LS channel estimation is used, but may vanish when MMSE is used.
何强, 张秀军, 肖立民, 周世东. 大规模MIMO系统中多小区导频重用对上行可达速率的影响[J]. 清华大学学报（自然科学版）, 2015, 55(5): 526-531.
HE Qiang, ZHANG Xiujun, XIAO Limin, ZHOU Shidong. Impact of multi-cell pilot reuse on the achievable uplink rate for massive MIMO systems. Journal of Tsinghua University(Science and Technology), 2015, 55(5): 526-531.
Marzetta T L. Noncooperative cellular wireless with unlimited numbers of base station antennas [J]. IEEE Trans Wireless Commun, 2010, 9(11): 3590-3600.
[2]
Rusek F, Persson D, Lau B K, et al. Scaling up MIMO: Opportunities and challenges with very large arrays [J]. IEEE Signal Process Mag, 2013, 30(1): 40-46.
[3]
Ngo H Q, Larsson E G, Marzetta T L. Energy and spectral efficiency of very large multiuser MIMO systems [J]. IEEE Trans Commun, 2013, 61(4): 1436-1449.
[4]
IMT-2020 (5G) Promotion Group. White paper on 5G concept [R/OL]. (2015-02-11).http://www.imt-2020.org.cn/zh/documents/listByQuery?currentPage=1&content=.
[5]
Jose J, Ashikhmin A, Marzetta T L, et al. Pilot contamination and precoding in multi-cell TDD systems [J]. IEEE Trans Wireless Commun, 2011, 10(8): 2640-2651.
[6]
Ngo H Q, Larsson E G, Marzetta T L. The multicell multiuser MIMO uplink with very large antenna arrays and a finite-dimensional channel [J]. IEEE Trans Commun, 2013, 61(6): 2350-2361.
[7]
Hoydis J, Brink S t, Debbah M. Massive MIMO in the UL/DL of cellular networks: How many antennas do we need [J]. IEEE J Sel Areas Commun, 2013, 31(2): 160-171.
[8]
Yin H, Gesbert D, Filippou M, et al. A coordinated approach to channel estimation in large-scale multiple antenna systems [J]. IEEE J Sel Areas Commun, 2013, 31(2): 264-273.
[9]
Kay S M. Fundamentals of Statistical Signal Processing: Estimation Theory [M]. Englewood Cliffs, NJ, USA: Prentice Hall, 1993.
[10]
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 [C]//Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Piscataway, NJ, USA: IEEE Press, 2011: 3464-3467.
[11]
Hassibi B, Hochwald B M. How much training is needed in multiple-antenna wireless links [J]. IEEE Trans Inf Theory, 2003, 49(4): 951-963.
[12]
Maiwald D, Kraus D. Calculation of moments of complex Wishart and complex inverse Wishart distributed matrices [J]. IEE Proc—Radar, Sonar and Navig, 2000, 147(4): 162-168.
[13]
You L, Gao X, Xia X, et al. Pilot reuse for massive MIMO transmission over spatially correlated Rayleigh fading channels [J/OL]. (2015-02-19).http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7045498.
2015, Vol. 55 
