Abstract
In this paper, we design a low-complexity multiuser millimeter-wave massive-multiple-input-multiple-output system with the help of a hybrid analog/digital precoding architecture. Hybrid precoding is used to reduce the hardware cost and power consumption of millimeter-wave large-scale antenna systems. In this manner, we proposed a novel approach to solve the well-known zero-forcing algorithm by using an iterative optimization method called the conjugate gradient method. The problem is transformed into an optimization problem, and the complex matrix inverse operation required in the zero-forcing algorithm is eliminated. Hence, the complexity of the zero-forcing algorithm is reduced while the spectral efficiency is maintained at the same level as that of the reference zero-forcing detector. The simulation results demonstrate that the proposed conjugate gradient-based algorithm achieves better performance than competing methods in terms of complexity and spectral efficiency.
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The data that support the findings of this study are available from the corresponding author, upon reasonable request.
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Code is available from the corresponding author, upon reasonable request.
References
Alsharif MH, Nordin R (2017) Evolution towards fifth generation (5G) wireless networks: current trends and challenges in the deployment of millimetre wave, massive MIMO, and small cells. Telecommun Syst 64(4):617–637. https://doi.org/10.1007/s11235-016-0195-x
Pi Z, Khan F (2011) An introduction to millimeter-wave mobile broadband systems. IEEE Commun Mag 49(6):101–107. https://doi.org/10.1109/MCOM.2011.5783993
Rappaport TS et al (2013) Millimeter wave mobile communications for 5G cellular: it will work! IEEE Access 1:335–349. https://doi.org/10.1109/ACCESS.2013.2260813
F. Salahdine, T Han, and N Zhang (2023) 5G, 6G, and beyond: recent advances and future challenges, Annales des Telecommunications/Annals of Telecommunicationshttps://doi.org/10.1007/s12243-022-00938-3
Vu M, Paulraj A (2007) MIMO wireless linear precoding. IEEE Signal Process Mag 24(5):86–105. https://doi.org/10.1109/MSP.2007.904811
Alkhateeb A, Mo J, Gonzalez-Prelcic N, Heath RW (2014) MIMO precoding and combining solutions for millimeter-wave systems. IEEE Commun Mag 52(12):122–131. https://doi.org/10.1109/MCOM.2014.6979963
Ding Y, Kim KJ, Koike-Akino T, Pajovic M, Wang P, Orlik P (2017) Spatial scattering modulation for uplink millimeter-wave systems. IEEE Commun Lett 21(7):1493–1496. https://doi.org/10.1109/LCOMM.2017.2684126
Mesleh R, Younis A (2018) Capacity analysis for LOS millimeter-wave quadrature spatial modulation. Wireless Netw 24(6):1905–1914. https://doi.org/10.1007/s11276-017-1444-y
Kafizov A, Elzanaty A, Alouini M-S (2022) Probabilistic shaping based spatial modulation for spectral-efficient VLC. IEEE Trans Wirel Commun 1276(10):8259–8275. https://doi.org/10.1109/TWC.2022.3164991
El Ayach O, Rajagopal S, Abu-Surra S, Pi Z, Heath RW (2014) Spatially sparse precoding in millimeter wave MIMO systems. IEEE Trans Wirel Commun 13(3):1499–1513. https://doi.org/10.1109/TWC.2014.011714.130846
Salh A et al (2022) Low computational complexity for optimizing energy efficiency in mm-wave hybrid precoding system for 5G. IEEE Access 10:4714–4727. https://doi.org/10.1109/ACCESS.2021.3139338
Kebede T, Wondie Y, Steinbrunn J, Kassa HB, Kornegay KT (2022) Precoding and beamforming techniques in mmwave-massive MIMO: performance assessment. IEEE Access 10:16365–16387. https://doi.org/10.1109/ACCESS.2022.3149301
Alkhateeb A, Leus G, Heath RW (2015) Limited feedback hybrid precoding for multi-user millimeter wave systems. IEEE Trans Wirel Commun 14(11):6481–6494. https://doi.org/10.1109/TWC.2015.2455980
Alkhateeb A, El Ayach O, Leus G, Heath RW (2014) Channel estimation and hybrid precoding for millimeter wave cellular systems. IEEE J Sel Top Signal Process 8(5):831–846. https://doi.org/10.1109/JSTSP.2014.2334278
Noh J, Kim T, Seol J, Lee C (2016) Zero-forcing based hybrid beamforming for multi-user millimeter wave systems. IET Commun 10(18):2670–2677. https://doi.org/10.1049/iet-com.2016.0769
Yu X, Shen J-C, Zhang J, Letaief KB (2016) Alternating minimization algorithms for hybrid precoding in millimeter wave MIMO systems. IEEE J Sel Top Signal Process 10(3):485–500. https://doi.org/10.1109/JSTSP.2016.2523903
Rusu C, Mendez-Rial R, Gonzalez-Prelcic N, Heath RW (2016) Low complexity hybrid precoding strategies for millimeter wave communication systems. IEEE Trans Wirel Commun 15(12):8380–8393. https://doi.org/10.1109/TWC.2016.2614495
Chen JC (2019) Gradient projection-based alternating minimization algorithm for designing hybrid beamforming in millimeter-wave MIMO systems. IEEE Commun Lett 23(1):112–115. https://doi.org/10.1109/LCOMM.2018.2878712
Mulla M, Ulusoy AH, Rizaner A, Amca H (2020) Barzilai-Borwein gradient algorithm based alternating minimization for single user millimeter wave systems. IEEE Wireless Commun Lett 9(4):508–512. https://doi.org/10.1109/LWC.2019.2960691
Ni W, Dong X (2016) Hybrid block diagonalization for massive multiuser MIMO systems. IEEE Trans Commun 64(1):201–211. https://doi.org/10.1109/TCOMM.2015.2502954
A. Li, and C Masouros (2017) Hybrid precoding and combining design for millimeter-wave multi-user MIMO based on SVD, in 2017 IEEE International Conference on Communications (ICC), IEEE, 1–6. https://doi.org/10.1109/ICC.2017.7996970.
Elbir AM, Papazafeiropoulos AK (2020) Hybrid precoding for multiuser millimeter wave massive MIMO systems: a deep learning approach. IEEE Trans Veh Technol 69(1):552–563. https://doi.org/10.1109/TVT.2019.2951501
Zhang Y, Dong X, Yin F, Qu M (2022) Tree-coding-aided adaptive-cross-entropy algorithm for hybrid precoding with low-resolution analog phase shifters. IEEE Trans Veh Technol 71(6):6807–6812. https://doi.org/10.1109/TVT.2022.3165689
W. Wu, and D Liu (2019) Hybrid processing for multi-user millimeter-wave massive MIMO systems via matrix decomposition, in 2019 IEEE Wireless Communications and Networking Conference Workshop (WCNCW), IEEE,. 1–6. https://doi.org/10.1109/WCNCW.2019.8902608.
I. Khaled, C. Langlais, A. El Falou, M. Jezequel, and B. ElHasssan (2020) Joint SDMA and power-domain NOMA system for multi-user mm-wave communications, in 2020 International Wireless Communications and Mobile Computing (IWCMC), IEEE, 1112–1117. https://doi.org/10.1109/IWCMC48107.2020.9148204.
G. H. Golub and C. F. Van Loan, Matrix computations (4th Ed.). John Hopkins University Press, 2013.
S. Boyd, and L Vandenberghe (2004) Convex optimization. Cambridge University Press, https://doi.org/10.1017/CBO9780511804441
Saleh AAM, Valenzuela R (1987) A statistical model for indoor multipath propagation. IEEE J Sel Areas Commun 5(2):128–137. https://doi.org/10.1109/JSAC.1987.1146527
Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 1934 49(6):409. https://doi.org/10.6028/jres.049.044
J Richard, and S August (1994) An introduction to the conjugate gradient method without the agonizing pain, Science (1979).
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All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Mustafa Mulla, Ali Hakan Ulusoy, Ahmet Rizaner, and Hasan Amca. The first draft of the manuscript was written by Mustafa Mulla and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Mulla, M., Ulusoy, A.H., Rizaner, A. et al. A low-complexity iterative algorithm for multiuser millimeter-wave systems. Ann. Telecommun. 79, 101–110 (2024). https://doi.org/10.1007/s12243-023-00979-2
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DOI: https://doi.org/10.1007/s12243-023-00979-2