A new approach to mitigate pilot contamination in massive MIMO systems is proposed in this paper. We consider two cells from the first tier of copilot cells of a cellular network where the base stations (BSs) are equipped with uniform linear arrays with hybrid beamforming adopted. We consider one cell as the cell of interest containing a typical desired user, and the other cell contains an interfering user sending data and contaminating pilot signals to the BS of the cell of interest. We derive a closed-form expression for the desired user's achievable rate as a function of the interfering user's angle of arrival (AoA). We model the ray propagation from the interfering user to the BS of the cell of interest and its related AoA as Gaussian distribution. Based on the model, we derive closed-form expressions for the pilot contamination level in the cell of interest, and for the desired user's data path gain estimation error due to pilot contamination. A perfect agreement is found between theoretical and Monte Carlo simulation results which show that when the interfering user's AoA is increased the pilot contamination level is significantly minimized, the desired user's data path gain estimation error also minimized, and hence its data rate is significantly increased. Moreover, we show in our analysis that the interfering user's AoA can be effectively controlled and increased by reducing the copilot cells' radius.
2. Rusek, F., D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, and F. Tufvesson, "Scaling up MIMO: Opportunities and challenges with very large arrays," IEEE Sig. Proc. Mag., Vol. 30, No. 1, 40-60, Jan. 2013.
doi:10.1109/MSP.2011.2178495
3. Ngo, H. Q., E. G. Larsson, and T. L. Marzetta, "Energy and spectral efficiency of very large multiuser MIMO systems," IEEE Trans Commun., Vol. 61, No. 4, 1436-1449, Apr. 2013.
doi:10.1109/TCOMM.2013.020413.110848
4. Yao, R., T. Li, Y. Liu, X. Zuo, and H. Liu, "Analytical approximation of the channel rate for massive MIMO system with large but finite number of antennas," IEEE Access, Vol. 6, 6496-6504, Mar. 2018.
doi:10.1109/ACCESS.2017.2787668
5. Prasad, K. N. R. S. V., E. Hossain, and V. K. Bhargava, "Energy efficiency in massive MIMO-based 5G networks: opportunities and challenges," IEEE Wirel. Commun., Vol. 24, No. 3, 86-94, 2017.
doi:10.1109/MWC.2016.1500374WC
6. Chen, Z., F. Sohrabi, and W. Yu, "Multi-cell sparse activity detection for massive random access: massive MIMO versus cooperative MIMO," IEEE Trans. Commun., Vol. 18, No. 8, 4060-4074, Aug. 2019.
7. Wahhamy, A. A., N. E. Buris, H. Zhu, H. A. Rizzo, and S. Yahya, "An efficient paradigm for evaluating the channel capacity of closed-loop massive MIMO systems," Progress In Electromagnetics Research C, Vol. 98, 1-16, 2020.
doi:10.2528/PIERC19082806
8. Ge, X., K. Huang, C. X. Wang, X. Hong, and X. Yang, "Capacity analysis of a multi-cell multi-antenna cooperative cellular network with co-channel interference," IEEE Trans. Wireless Commun., Vol. 10, No. 10, 3298-3308, Oct. 2011.
doi:10.1109/TWC.2011.11.101551
9. Lakshminarayara, S., M. Assaad, and M. Debbah, "Coordinated multicell beamforming for massive MIMO: A random matrix approach," IEEE Trans. Info. Theory, Vol. 61, No. 6, 3387-3412, Jun. 2015.
doi:10.1109/TIT.2015.2421446
10. Khansefid, A. and H. Minn, "Achievable downlink rates of MRC and ZF precoders in massive MIMO with uplink and downlink pilot contamination," IEEE Trans. Commun., Vol. 63, No. 12, 4849-4864, Dec. 2015.
doi:10.1109/TCOMM.2015.2482965
11. Parida, P. and H. S. Dhillon, "Stochastic geometry-based uplink analysis of massive MIMO systems with fractional pilot reuse," IEEE Trans. Wireless Commun., Vol. 18, No. 3, 1651-1668, Mar. 2019.
doi:10.1109/TWC.2019.2895061
12. Liu, G., H. Deng, X. Qian, W. Wang, and G. Peng, "Joint pilot allocation and power control to enhance max-min spectral efficiency in TDD massive MIMO systems," IEEE Access, Vol. 7, 149191-149201, Oct. 2019.
13. Figueiredo, F. A. P. D., C. F. Dias, F. A. C. M. Cardoso, and G. Fraidenraich, "On the distribution of an effective channel estimator for multi-cell massive MIMO," IEEE Access, Vol. 7, 114508-114519, Aug. 2019.
doi:10.1109/ACCESS.2019.2935686
14. Akbar, N., S. Yan, A. M. Khattak, and N. Yang, "On the pilot contamination attack in multi-cell multiuser massive MIMO networks," IEEE Trans. Commun., Vol. 68, No. 4, 2264-2276, Apr. 2020.
doi:10.1109/TCOMM.2020.2967760
15. Elijah, O., C. H. Leow, T. A. Rahman, S. Nunoo, and S. Z. Iliya, "A comprehensive survey of pilot contamination in massive MIMO-5G system," IEEE Commun Surveys & Tutorials, Vol. 18, No. 2, 905-923, 2016 (Second Quarter).
doi:10.1109/COMST.2015.2504379
16. Yin, H., D. Gesbert, M. Filippou, and Y. Liu, "A coordinated approach to channel estimation in large-scale multiple-antenna systems," IEEE Journal on Selected Areas in Communications, Vol. 31, No. 2, 264-273, Feb. 2013.
doi:10.1109/JSAC.2013.130214
17. Yin, H., D. Gesbert, M. C. Filippou, and Y. Liu, "Decontaminating pilots in massive MIMO systems," Proc. of IEEE Int. Conf. Commun. (ICC), 3170-3175, Jun. 2013.
18. Muller, R., L. Cottatellucci, and M. Vehkapera, "Blind pilot decontamination," IEEE Journal on Selected Topics in Signal Processing, Vol. 8, No. 5, 773-786, Oct. 2014.
doi:10.1109/JSTSP.2014.2310053
19. Mazlan, M. H., M. Behjati, R. Nordin, and M. Ismail, "Wiener-based smoother and predictor for massive MIMO downlink system under pilot contamination," Telecommunication Systems, Vol. 67, No. 3, 387-399, Mar. 2018.
doi:10.1007/s11235-017-0341-0
20. Amiri, E., R. Mueller, W. Gerstacker, and , "Blind pilot decontamination in massive MIMO by independent component analysis," Proc. of IEEEE Global Communications Conference (GLOBECOM), 1-5, Dec. 2017.
21. Mazlan, M. H., E. Ali, A. M. Ramly, and R. Nordin, "Pilot decontamination using coordinated wiener predictor in massive-MIMO system," IEEE Access, Vol. 6, 73180-73190, Dec. 2018.
doi:10.1109/ACCESS.2018.2881743
22. Smaili, N., M. Djeddou, and A. Azrar, "Pilot contamination mitigation based on antenna subset transmission for mmWave massive MIMO," International Journal of Communication Systems, Vol. 31, No. 14, 1-12, Jul. 2018.
23. Ali, E., M. smail, R. Nordin, F. Abdulah, and M. H. Mazlan, "Performance analysis of inter-cell interference reduction using AOA-based beamforming in Mm wave massive MIMO systems," Proc. of IEEE 13th Malaysia International Conference on Communication (MICC), 235-240, Nov. 2017.
24. Tebe, P. I., Y. Kuang, A. E. Ampoma, and K. A. Opare, "Mitigating pilot contamination in massive MIMO using cell size reduction," IEICE Transactions on Communications, Vol. E101-B, No. 5, 1280-1290, May 2018.
doi:10.1587/transcom.2017EBP3189
25. Rappaport, T. S., "Wireless communications: principles and practice," Publishing House of Electronics Industry, 68-71, 2nd Edition, Prentice Hall, Beijing, China, 2004.
26. Zhu, G., K. Huang, V. K. N. Lau, B. Xia, X. Li, and S. Zhang, "Hybrid beamforming via the Kronecker decomposition for the millimeter-wave massive MIMO systems," IEEE Journal on Selected Areas in Communications, Vol. 35, No. 9, 2097-2114, Sep. 2017.
doi:10.1109/JSAC.2017.2720099
27. Maschietti, F., D. Gesbert, P. de Kerret, and H. Wymeersch, "Robust location-aided beam alignment in millimeter wave massive MIMO," Proc. of IEEE Global Communications Conference (GLOBECOM), 1-6, Dec. 2017.
28. Hashemi, M., A. Sabharwal, C. E. Koksal, and N. B. Shroff, "Efficient beam alignment in millimeter wave systems using contextual bandits," Proc. of IEEE Conference on Computer Communications (INFOCOM), 2393-2401, Apr. 2018.
29. Shafin, R., L. Liu, J. Zhang, and Y. C. Wu, "DoA estimation and capacity analysis for 3-D milimeter wave massive MIMO/FD-MIMO OFDM systems," IEEE Trans. Wireless Commun., Vol. 15, No. 10, 6963-6978, Oct. 2016.
doi:10.1109/TWC.2016.2594173
30. Cacciola, M., S. Calcagno, G. Megali, F. C. Morabito, D. Pellicano, and M. Versaci, "FEA design and misfit minimization for in-depth flaw characterization in metallic plates with Eddy current nondestructive testing," IEEE Trans. Magn., Vol. 45, No. 3, 1506-1509, Mar. 2009.
doi:10.1109/TMAG.2009.2012691
31. Versaci, M., "Fuzzy approach and Eddy current NDT/NDE devices in industrial applications," IEEE Electronics Letters, Vol. 52, No. 11, 943-945, May 2016.
doi:10.1049/el.2015.3409
32. Kazerouni, A., F. J. Lopez-Martinez, and A. Goldsmith, "Increasing capacity in massive MIMO networks via small cells," Proc. of IEEE Global Communications Conference (GLOBECOM) Workshop, 358-363, Dec. 2014.
33. Tan, W., X. Feng, G. Liu, W. Tan, M. Zhou, and C. Li, "Spectral efficiency of massive MIMO Systems with multiple sub-arrays antenna," IEEE Access, Vol. 6, 31213-31223, Jun. 2018.
doi:10.1109/ACCESS.2018.2845666
34. Marzetta, T. L., "Noncooperative cellular wireless with unlimited numbers of base station antennas," IEEE Trans. Wireless Commun., Vol. 9, No. 11, 3590-3600, Nov. 2010.
doi:10.1109/TWC.2010.092810.091092
35. Zetterberg, P., Mobile cellular communications with base station antenna arrays: Spectrum efficiency, algorithms and propagation Models, Ph.D. thesis, Royal Institute of Technology, Sweden, available online on December, 2008.
36. Calcagno, S., F. L. Foresta, and M. Versaci, "Independent component analysis and discrete wavelet transform for artifact removal in biomedical signal processing," American Journal of Applied Sciences, Vol. 11, No. 1, 57-68, 2014.
doi:10.3844/ajassp.2014.57.68
37. Yang, X. and A. O. Fapojuwo, "Performance analysis of hexagonal cellular networks in fading channels," Wireless Commun. Mob. Computing, Vol. 2016, No. 16, 850-867, Jan. 2015.
38. Chen, Y., X. Wen, and Z. Lu, "Achievable spectral efficiency of Hybrid beamforming massive MIMO systems with quantized phase shifters, channel non-reciprocity and estimation errors," IEEE Access, Vol. 8, 71304-71317, Apr. 2020.
doi:10.1109/ACCESS.2020.2987613
Submit
