On Massive MIMO System Convergence: Analysis Using Geometry-Based Stochastic Model

Patrick Danuor^1, , Reynah Akwafo², Stephen Nuagah³ and Emmanuel Nyaho-Tamakloe⁴

¹Department of Electrical and Electronic Engineering, Ho Technical University, Ho, Ghana

²Department of Electrical and Electronic Engineering, Bolgatanga Technical University, Bolgatanga, Ghana

³Department of Electrical and Electronic Engineering, Tamale Technical University, Tamale, Ghana

⁴Department of Telecommunications Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

Cite this paper:
Patrick Danuor, Reynah Akwafo, Stephen Nuagah and Emmanuel Nyaho-Tamakloe. On Massive MIMO System Convergence: Analysis Using Geometry-Based Stochastic Model. Wireless and Mobile Technologies. 2020; 4(1):1-5. doi: 10.12691/wmt-4-1-1

Abstract

In this paper, three-dimensional massive multi-input multi-output (MIMO) system convergence is analyzed using a geometry-based stochastic channel model. The concept of Maximum Distributive Power is introduced to examine the performance of massive MIMO regarding the Gaussian and the Arbitrary Q-power Cosine distributions of arrival. Verification is accomplished with the help of computer simulation where excellent agreement is found between theoretical and simulation results. We present results to show that higher Q-power values of the Arbitrary Q-power Cosine distribution creates mismatch between the simulated and theoretical correlation coefficients unlike the Gaussian distribution. The practical relevance is that, careful selection of higher Q-power values for 3D massive MIMO channel planning is vital to enhance massive MIMO Convergence. This is demonstrated in the convergence outcomes where higher Q-power values deteriorates the convergence to massive MIMO favorable propagation as the transmit antenna increases. Finally, experimental outcomes illustrate that it requires antenna separation of more than half wavelength to enhance convergence rates at higher Q-power values.

Keywords:
channel model convergence favorable propagation massive MIMO spatial correlation

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References:

[1]	T. L. Marzetta, “Noncooperative cellular wireless with unlimited numbers of base station antennas,” IEEE Transactions on Wireless Communications, vol. 9, no. 11, pp. 3590-3600, November 2010.
[2]	P. J. Smith, C. Neil, M. Shafi, and P. A. Dmochowski, “On the Convergence of massive MIMO systems,” in Proc. IEEE Int. Conf. Communication, Jun. 2014, pp.5191-5196.
[3]	C. T. Neil, M. Shafi, P. J. Smith, and P. A. Dmochowski, “On the impact of antenna topologies for massive MIMO systems,” in Proc. IEEE Int. Conf. Communication Jun. 2015 pp. 2030-2035.
[4]	K. Zheng, S. Ou, and X. Yin, “Massive MIMO channel models: A survey,” Int. J. Antennas Propagation, vol. 2014, Jun. 2014, Art. no. 848071.
[5]	C. T. Neil, A. Garcia-Rodriguez, P. J. Smith, P. A. Dmochowski,C. Masouros, & M. Shafi, “On the performance of spatially correlated large antenna arrays for millimeter-wave frequencies,” IEEE Transactions on Antennas and Propagation, vol.66 no. 1, pp. 132-148, 2018.
[6]	Q.-U.-A. Nadeem, A. Kammoun, M. Debbah, and M.-S. Alouini, “A generalized spatial correlation model for 3d MIMO channels based on the Fourier coefficients of power spectrums”, IEEE Transactions on Signal Processing, vol. 63, no. 14, pp. 3971-3686, July, 2015.
[7]	J. S. K. Raj, A. S. Prabu, N. Vikram, and J. Schoebel, “Spatial correlation and MIMO capacity of uniform rectangular dipole arrays”, IEEE Antennas Wireless Propagation Lett., vol. 7, pp. 97-100,2008.
[8]	Q. -U. -A. Nadeem, A. Kammoun, M. Debbah, and M. -S. Alounini, “Spatial Correlation of a Uniform Circular Array in 3D MIMO Systems”, in Proc. 17th Int. Workshop Signal Process. Adv. Wireless Communication (SPAWC), Edinburgh, U.K., 2016, pp. 1-6.
[9]	A. Kammoun, M. Debbah, & M. S. Alouini, “3D massive MIMO systems: Modeling and performance analysis,” IEEE Transactions on wireless communications, vol. 14 no. 12, pp. 6926-6939, 2017.
[10]	S. K. Young and J. S. Thompson, “A 3-dimensional spatial fading correlation model for electromagnetic vector sensors,” in Proc. 6th Int. Symposium Antennas, Propagation EM Theory, Beijing, China, 2003, pp. 843-846.
[11]	J. B. Andersen and K. I. Pedersen, “Angle-of-Arrival statistics for low resolution antennas,” IEEE Trans. Antennas Propagation, vol. 50, no. 3, pp.391-395, Mar. 2002.
[12]	W. J. L. Queiroz, F. Madeiro, W. T. A. Lopes and M. S. Alencar. “Spatial Correlation for DOA Characterization Using Von Misses, Cosine, and Gaussian Distributions” Journal of Antennas and Propagation vol. 2011, pp. 1-12.
[13]	S. K. Yong & J. S. Thompson, “Three-dimensional spatial fading correlation models for compact MIMO receivers”, IEEE Transactions on Wireless Communications, vol.4, no. 6, pp. 2857-2858, November 2005.
[14]	A. Milton and S. A. Irene, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. NY, USA: Dover, 1964.
[15]	E. Bjornson, J. Hoydis, M. Kountouris, and M. Debbah, “Massive MIMO systems with non-ideal hardware: Energy efficiency, estimation and capacity limits, “IEEE Transaction Inf. Theory, vol. 60, no. 11, pp.7112-7139, Nov. 2014.