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Channel estimation in massive MIMO-based wireless network using spatially correlated channel-based three-dimensional array

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Abstract

To more benefit from the massive multiple-input multiple-output (M-MIMO) technology for improving the channel estimation (CE) process, each base station (BS) must have accurate channel state information as effectively as possible. In this work, we address the CE process for the M-MIMO network, considering a more practical scenario where the channels are spatially correlated, as the spatial correlation (SC) strongly affects the performance of M-MIMO systems. Additionally, the SC relies on several factors, such as the BS’s array arrangement. Thereby, we investigate the SC effect over CE using different array arrangements, wherein the SC is described using a gaussian local multi-scattering (GLMS) model. In addition, the performance of the Bayesian Minimum Mean Square Error estimator is investigated for correlated and uncorrelated channels. Besides, using the GLMS model for the uniform linear array (ULA) arrangement and based on the Kronecker product (KP), we propose the GLMS model for the uniform planar array arrangement. We also address the channel hardening and favorable propagation for both arrangements. Furthermore, we propose the GLMS model for the uniform circular array (UCA) arrangement, where we drive a theoretical demonstration of the GLMS model for the proposed UCA arrangement. Moreover, we propose a lower complexity GLMS model for uniform cylindrical array arrangement by relying on the KP of the proposed model for UCA arrangement and the GLMS model for vertical ULA (V-ULA) arrangement. The system performance is evaluated using the normalized mean square error metric, where the simulation results are in view to affirm our mathematical analysis.

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Abbreviations

\(\text {2D}\) :

Two-dimensional

\(\text {3D}\) :

Three-dimensional

\(\text {AACC}\) :

Average antenna correlation coefficient

\(\text {AD}\) :

Azimuth dimension

\(\text {ADn}\) :

Azimuth direction

\(\text {ASD}\) :

Angular standard deviation

\(\text {B-MMSE}\) :

Bayesian minimum mean square error

\(\text {BS}\) :

Base station

\(\text {CE}\) :

Channel estimation

\(\text {CH}\) :

Channel hardening

\(\text {CM}\) :

Co-variance matrix

\(\text {Co-P}\) :

Co-polarized

\(\text {ECM}\) :

Exponential correlation model

\(\text {ED}\) :

Elevation dimension

\(\text {EDn}\) :

Elevation direction

\(\text {Eff-SNR}\) :

Effective SNR

\(\text {FP}\) :

Favorable propagation

\(\text {GLMS}\) :

gaussian local multi-scattering

\(\text {HD}\) :

Horizontal dimension

\(\text {KP}\) :

Kronecker product

\(\text {LS}\) :

Least squares

\(\text {LSF}\) :

Large-scale fading

\(\text {M-MIMO}\) :

Massive multiple-input multiple-output

\(\text {N-AoA}\) :

Nominal angle of arrival

\(\text {NoA}\) :

Number of antennas

\(\text {NMSE}\) :

Normalized mean square error

\(\text {PC}\) :

Pilot contamination

\(\text {PS}\) :

Pilot sequence

\(\text {SC}\) :

Spatial correlation

\(\text {ScD}\) :

Spatially correlated

\(\text {SD}\) :

Spatial direction

\(\text {SSF}\) :

Small-scale fading

\(\text {TDD}\) :

Time division duplex

\(\text {UL}\) :

Uplink

\(\text {ULA}\) :

Uniform linear array

\(\text {UPA}\) :

Uniform planar array

\(\text {UCA}\) :

Uniform circular array

\(\text {UCLA}\) :

Uniform cylindrical array

\(\text {V-ULA}\) :

Vertical-uniform linear array

\(\text {VD}\) :

Vertical dimension

References

  1. Björnson, E., Hoydis, J., & Sanguinetti, L. (2017). Massive mimo networks: Spectral, energy, and hardware efficiency. Foundations and Trends in Signal Processing, 11(3–4), 154–655. https://doi.org/10.1561/2000000093.

    Article  Google Scholar 

  2. Albdran, S., Alshammari, A., Ahad, M. A. R., & Matin, M. (2016). Effect of exponential correlation model on channel estimation for massive mimo. In 2016 19th international conference on computer and information technology (ICCIT) (pp. 80–83). IEEE. https://doi.org/10.1109/ICCITECHN.2016.7860172

  3. Kim, H., & Choi, J. (2019). Channel estimation for spatially/temporally correlated massive mimo systems with one-bit adcs. EURASIP Journal on Wireless Communications and Networking, 2019(1), 1–15. https://doi.org/10.1186/s13638-019-1587.

    Article  Google Scholar 

  4. Temiz, M., Alsusa, E., & Danoon, L. (2019). Impact of imperfect channel estimation and antenna correlation on quantised massive multiple-input multiple-output systems. IET Communications, 13(9), 1262–1270. https://doi.org/10.1049/iet-com.2018.5860.

    Article  Google Scholar 

  5. Özdogan, Ö., Björnson, E., & Larsson, E. G. (2019). Massive mimo with spatially correlated rician fading channels. IEEE Transactions on Communications, 67(5), 3234–3250. https://doi.org/10.1109/TCOMM.2019.2893221.

    Article  Google Scholar 

  6. Adachi, F., Feeney, M. T., Parsons, J. D, & Williamson, A. G. (1986). Crosscorrelation between the envelopes of 900 mhz signals received at a mobile radio base station site. In IEE proceedings F-communications, radar and signal processing (Vol. 133, pp. 506–512). IET. https://doi.org/10.1049/ip-f-1.1986.0083.

  7. Trump, T., & Ottersten, B. (1996). Estimation of nominal direction of arrival and angular spread using an array of sensors. Signal Processing, 50(1–2), 57–69. https://doi.org/10.1016/0165-1684(96)00003-5.

    Article  Google Scholar 

  8. Yin, H., Gesbert, D., Filippou, M., & Liu, Y. (2013). A coordinated approach to channel estimation in large-scale multiple-antenna systems. IEEE Journal on Selected Areas in Communications, 31(2), 264–273. https://doi.org/10.1109/JSAC.2013.130214.

    Article  Google Scholar 

  9. Zetterberg, P., & Ottersten, B. (1995). The spectrum efficiency of a base station antenna array system for spatially selective transmission. IEEE Transactions on Vehicular Technology, 44(3), 651–660. https://doi.org/10.1109/VETEC.1994.345349.

    Article  Google Scholar 

  10. Mats, B. (2000). Antenna array signal processing for high rank data models. PhD thesis, Signaler, Sensorer OCH System.

  11. Adhikary, A., Nam, J., Ahn, J.-Y., & Caire, G. (2013). Joint spatial division and multiplexing-the large-scale array regime. IEEE Transactions on Information Theory, 59(10), 6441–6463. https://doi.org/10.1109/TIT.2013.2269476.

    Article  Google Scholar 

  12. Salz, J., & Winters, J. H. (1994). Effect of fading correlation on adaptive arrays in digital mobile radio. IEEE Transactions on Vehicular Technology, 43(4), 1049–1057. https://doi.org/10.1109/25.330168.

    Article  Google Scholar 

  13. Shiu, D.-S., Foschini, G. J., Gans, M. J., & Kahn, J. M. (2000). Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Transactions on communications, 48(3), 502–513. https://doi.org/10.1109/26.837052.

    Article  Google Scholar 

  14. Jiang, Z., Molisch, A. F., Caire, G., & Niu, Z. (2015). Achievable rates of fdd massive mimo systems with spatial channel correlation. IEEE Transactions on Wireless Communications, 14(5), 2868–2882. https://doi.org/10.1109/TWC.2015.2396058.

    Article  Google Scholar 

  15. Pedersen, K. I., Mogensen, P. E., & Fleury, B. H. (1997). Power azimuth spectrum in outdoor environments. Electronics Letters, 33(18), 1583–1584. https://doi.org/10.1049/el:19971029.

    Article  Google Scholar 

  16. Molisch, A. F. (2012). Wireless communications, Vol. 34. Wiley.

  17. Ying, D., Vook, F. W., Thomas, T. A., Love, D. J., & Amitava, G. (2014). Kronecker product correlation model and limited feedback codebook design in a 3d channel model. In 2014 IEEE international conference on communications (ICC) (pp. 5865–5870). IEEE. https://doi.org/10.1109/ICC.2014.6884258

  18. Gao, X., Edfors, O., Tufvesson, F., & Larsson, E. G. (2015). Massive mimo in real propagation environments: Do all antennas contribute equally? IEEE Transactions on Communications, 63(11), 3917–3928. https://doi.org/10.1109/TCOMM.2015.2462350.

    Article  Google Scholar 

  19. Gao, X., Edfors, O., Rusek, F., & Tufvesson, F. (2015). Massive mimo performance evaluation based on measured propagation data. IEEE Transactions on Wireless Communications, 14(7), 3899–3911. https://doi.org/10.1109/TWC.2015.2414413.

    Article  Google Scholar 

  20. Forenza, A., Love, D. J., & Heath, R. W. (2007). Simplified spatial correlation models for clustered mimo channels with different array configurations. IEEE Transactions on Vehicular Technology, 56(4), 1924–1934. https://doi.org/10.1109/TVT.2007.897212.

    Article  Google Scholar 

  21. Björnson, E., Hoydis, J., & Sanguinetti, L. (2017). Massive mimo has unlimited capacity. IEEE Transactions on Wireless Communications, 17(1), 574–590. https://doi.org/10.1109/TWC.2017.2768423.

    Article  Google Scholar 

  22. Pereira-de-Figueiredo, F. A., Mendes Lemes, D. A., Ferreira Dias, C., & Fraidenraich, G. (2020). Massive mimo channel estimation considering pilot contamination and spatially correlated channels. Electronics Letters, 56(8), 410–413. https://doi.org/10.1049/el.2019.3899.

    Article  Google Scholar 

  23. Wang, Z., Zhang, J., Björnson, E., & Ai, B. (2020). Uplink performance of cell-free massive mimo over spatially correlated rician fading channels. IEEE Communications Letters, 25(4), 1348–1352. https://doi.org/10.1109/LCOMM.2020.3041899.

    Article  Google Scholar 

  24. Björnson, E., & Sanguinetti, L. (2019). Making cell-free massive mimo competitive with mmse processing and centralized implementation. IEEE Transactions on Wireless Communications, 19(1), 77–90. https://doi.org/10.1109/TWC.2019.2941478.

    Article  Google Scholar 

  25. Zheng, J., Zhang, J., Björnson, E., & Ai, B. (2021). Impact of channel aging on cell-free massive mimo over spatially correlated channels. IEEE Transactions on Wireless Communications. https://doi.org/10.1109/TWC.2021.3074421.

    Article  Google Scholar 

  26. Femenias, G., Riera-Palou, F., Álvarez-Polegre, A., & García-Armada, A. (2020). Short-term power constrained cell-free massive-mimo over spatially correlated ricean fading. IEEE Transactions on Vehicular Technology, 69(12), 15200–15215. https://doi.org/10.1109/TVT.2020.3037009.

    Article  Google Scholar 

  27. Loyka, S. L. (2001). Channel capacity of mimo architecture using the exponential correlation matrix. IEEE Communications Letters, 5(9), 369–371. https://doi.org/10.1109/4234.951380.

    Article  Google Scholar 

  28. Shin, H., Win, M. Z., Lee, J. H., & Chiani, M. (2006). On the capacity of doubly correlated mimo channels. IEEE Transactions on Wireless Communications, 5(8), 2253–2265. https://doi.org/10.1109/TWC.2006.1687741.

    Article  Google Scholar 

  29. Byers, G. J., & Takawira, F. (2004). Spatially and temporally correlated mimo channels: Modeling and capacity analysis. IEEE Transactions on Vehicular Technology, 53(3), 634–643. https://doi.org/10.1109/TVT.2004.825766.

    Article  Google Scholar 

  30. Pätzold, M., & Hogstad, B. O. (2004). A space-time channel simulator for mimo channels based on the geometrical one-ring scattering model. Wireless Communications and Mobile Computing, 4(7), 727–737. https://doi.org/10.1109/VETECF.2004.1399949.

    Article  Google Scholar 

  31. Marzetta, T. L. (2016). Fundamentals of massive MIMO. Cambridge University Press.

  32. Kay, S. M. (1993). Fundamentals of statistical signal processing: Estimation theory. Prentice-Hall, Inc.

  33. Flam, J. T., Chatterjee, S., Kansanen, K., & Ekman, T. (2012). On mmse estimation: A linear model under gaussian mixture statistics. IEEE Transactions on Signal Processing, 60(7), 3840–3845. https://doi.org/10.1109/TSP.2012.2192112.

    Article  Google Scholar 

  34. Amadid, J., Boulouird, M., & Hassani, M. M. R. (2022). Channel estimation for massive mimo tdd systems and pilot contamination with uniformly distributed users. In S. Bennani, Y. Lakhrissi, G. Khaissidi, A. Mansouri, & Y. Khamlichi (Eds.), WITS 2020. Lecture Notes in Electrical Engineering (Vol. 745). Springer. https://doi.org/10.1007/978-981-33-6893-4_94

  35. Ngo, H. Q., & Larsson, E. G. (2017). No downlink pilots are needed in tdd massive mimo. IEEE Transactions on Wireless Communications, 16(5), 2921–2935. https://doi.org/10.1109/TWC.2017.2672540.

    Article  Google Scholar 

  36. Huang, K.-W., Wang, H.-M., Hou, J., & Jin, S. (2018). Joint spatial division and diversity for massive mimo systems. IEEE Transactions on Communications, 67(1), 258–272. https://doi.org/10.1109/TCOMM.2018.2870415.

    Article  Google Scholar 

  37. Yanping, L., Tao, C., & Liu, L. (2019). Correlation investigation for uniform circular array based on measured massive mimo. International Journal of Pattern Recognition and Artificial Intelligence, 33(09), 1958010. https://doi.org/10.1142/S0218001419580102.

    Article  Google Scholar 

  38. Zhou, J., Sasaki, S., Muramatsu, S., Kikuchi, H., & Onozato, Y. (2003). Spatial correlation functions for a circular antenna array and their applications in wireless communication systems. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 86(7), 1716–1723. https://doi.org/10.1109/GLOCOM.2003.1258410.

    Article  Google Scholar 

  39. Chang, A.-C., & Jen, C.-W. (2006). Subspace-based techniques for 2-d doa estimation with uniform circular array under local scattering. Journal of the Chinese Institute of Engineers, 29(4), 663–673. https://doi.org/10.1080/02533839.2006.9671162.

    Article  Google Scholar 

  40. Moose, P. H. (1994). A technique for orthogonal frequency division multiplexing frequency offset correction. IEEE Transactions on Communications, 42(10), 2908–2914. https://doi.org/10.1109/26.328961.

    Article  Google Scholar 

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Authors and Affiliations

  1. Instrumentation, Signals and Physical Systems (I2SP) Group, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco

    Jamal Amadid & Abdelhamid Riadi

  2. Smart Systems and Applications (SSA) Group, National School of Applied Sciences of Marrakesh (ENSA-M), Cadi Ayyad University, Marrakesh, Morocco

    Mohamed Boulouird

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Amadid, J., Boulouird, M. & Riadi, A. Channel estimation in massive MIMO-based wireless network using spatially correlated channel-based three-dimensional array. Telecommun Syst 79, 323–340 (2022). https://doi.org/10.1007/s11235-021-00873-z

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