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Sum Ergodic Capacity Analysis Using Asymptotic Design of Massive MU-MIMO Systems

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Abstract

This communication attempts to characterize the performance metrics of downlink Massive MU-MIMO systems impaired by cochannel interference and additive noise over a Rayleigh fading environment. We obtain close-form solutions for the probability density function of signal-to-interference-plus-noise ratio (SINR) and the sum ergodic capacity. The proposed work structures SINR in a quadratic form and thereby imposes a condition on its signal and interference power for a large transmit antenna diversity order; the conditional form is then analyzed using a distance correlation metric. Eventually, the sum ergodic capacity is expressed in a close-form by means of a residue theory approach and validated using the Monte Carlo simulation means.

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Notes

  1. A special case of residue theory is generalized from [9] as

    $$\begin{aligned} \frac{1}{2\pi } \int _{-\infty }^{\infty }\frac{e^{j \omega p}}{a+ j \omega }~d\omega = e^{-a p} u(a p),\quad a > 0 . \end{aligned}$$

References

  1. Marzetta, T. L. (2010). Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Transactions on Wireless Communications, 9(11), 3590–3600.

    Article  Google Scholar 

  2. 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.

    Article  Google Scholar 

  3. Zheng, K., Zhao, L., Mei, J., Shao, B., Xiang, W., & Hanzo, L. (2015). Survey of large-scale MIMO systems. IEEE Communications Surveys & Tutorials, 17(3), 1738–1760.

    Article  Google Scholar 

  4. Li, X., Zhou, L., Jin, S., & Gao, X. (2012). Multi-user multiple-input single-output downlink transmission systems exploiting statistical channel state information. IET Communications, 6(18), 3114–3121.

    Article  MathSciNet  Google Scholar 

  5. Kim, H., Lee, S. R., Lee, K. J., & Lee, I. (2012). Transmission schemes based on sum rate analysis in distributed antenna systems. IEEE Transactions on Wireless Communications, 11(3), 1201–1209.

    Article  Google Scholar 

  6. Li, J. H., & Su, H. J. (2014). Opportunistic feedback reduction for multiuser MIMO broadcast channel with orthogonal beamforming. IEEE Transactions on Wireless Communications, 13(3), 1321–1333.

    Article  Google Scholar 

  7. Choi, W., & Andrews, J. G. (2007). Downlink performance and capacity of distributed antenna systems in a multicell environment. IEEE Transactions on Wireless Communications, 6(1), 69–73.

    Article  Google Scholar 

  8. Székely, G. J., Rizzo, M. L., Bakirov, N. K., et al. (2007). Measuring and testing dependence by correlation of distances. The Annals of Statistics, 35(6), 2769–2794.

    Article  MathSciNet  MATH  Google Scholar 

  9. Al-Naffouri, T. Y., Moinuddin, M., Ajeeb, N., Hassibi, B., & Moustakas, A. L. (2016). On the distribution of indefinite quadratic forms in Gaussian random variables. IEEE Transactions on Communications, 64(1), 153–165.

    Article  Google Scholar 

  10. Al-Naffouri, T., Sharif, M., & Hassibi, B. (2009). How much does transmit correlation affect the sum-rate scaling of MIMO Gaussian broadcast channels? IEEE Transactions on Communications, 57(2), 562–572.

    Article  Google Scholar 

  11. Hassan, A. K., Moinuddin, M., Al-Saggaf, U. M., & Al-Naffouri, T. Y. (2017). Performance analysis of beamforming in MU-MIMO systems for Rayleigh fading channels. IEEE Access, 5, 3709–3720.

    Article  Google Scholar 

  12. Dai, M., & Clerckx, B. (2015). Transmit beamforming for MISO broadcast channels with statistical and delayed CSIT. IEEE Transactions on Communications, 63(4), 1202–1215.

    Article  Google Scholar 

  13. 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 array. IEEE Signal Processing Magazine, 30(1), 40–60.

    Article  Google Scholar 

  14. Gradštejn, I. S., Ryžik, I. M., Jeffrey, A., & Zwillinger, D. (2007). Table of integrals, series, and products. New York: Elsevier/Academic.

    Google Scholar 

  15. Bjornson, E., Hammarwall, D., & Ottersten, B. (2009). Exploiting quantized channel norm feedback through conditional statistics in arbitrarily correlated MIMO systems. IEEE Transactions on Signal Processing, 57(10), 4027–4041.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This project was funded by the Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, under Grant No. (CEIES-16-12-02). The authors, therefore, acknowledge the technical and financial support of CEIES.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Ghulam Ishaq Khan Institute of Engineering Sciences and Technology, Topi, 23640, Pakistan

    Ahmad Kamal Hassan

  2. Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, Saudi Arabia

    Ahmad Kamal Hassan, Muhammad Moinuddin & Ubaid M. Al-Saggaf

  3. Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

    Muhammad Moinuddin & Ubaid M. Al-Saggaf

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  1. Ahmad Kamal Hassan
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  2. Muhammad Moinuddin
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  3. Ubaid M. Al-Saggaf
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Correspondence to Ahmad Kamal Hassan.

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Hassan, A.K., Moinuddin, M. & Al-Saggaf, U.M. Sum Ergodic Capacity Analysis Using Asymptotic Design of Massive MU-MIMO Systems. Wireless Pers Commun 100, 1743–1752 (2018). https://doi.org/10.1007/s11277-018-5669-6

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