Abstract: In this paper we study the effective degree of freedom (EDoF) for extremely large-scale multiple-input multiple-output (XL-MIMO) systems. We consider two XL-MIMO hardware designs, uniform planar array (UPA) based and continuous aperture (CAP) based XL-MIMO, as well as two representative near-field channel models: scalar Green function based and dyadic Green function with triple polarization based models. First, for UPA-based XL-MIMO with a discrete array aperture, we evaluate the EDoF performance by applying discrete channel matrices generated by the scalar or dyadic Green channel model. Then, for CAP-based XL-MIMO, a tailored EDoF performance evaluation framework for a two-dimensional (2D) CAP plane based system is constructed by leveraging asymptotic analysis and extending the analysis approaches for a one-dimensional (1D) CAP line segment based system. This framework incorporates the triple-polarized auto-correlation kernel function, which can efficiently capture the impact of multiple polarization on the EDoF performance. Numerical results show that, with an increase in the number of antennas, the UPA-based XL-MIMO system can achieve an EDoF performance close to the EDoF performance for the CAP plane based XL-MIMO system. Moreover, the EDoF performance can be enhanced by the multiple polarization in channels and increased physical size of the transceiver.

基于三极化的近场平面XL-MIMO有效自由度分析

[1]Arnoldus HF, 2001. Representation of the near-field, middle-field, and far-field electromagnetic Green’s functions in reciprocal space. J Opt Soc Am B, 18(4):547-555.

[2]Björnson E, Sanguinetti L, Wymeersch H, et al., 2019. Massive MIMO is a reality—what is next?: five promising research directions for antenna arrays. Dig Signal Process, 94:3-20.

[3]Björnson E, Chae CB, Heath RWJr, et al., 2024. Towards 6G MIMO: massive spatial multiplexing, dense arrays, and interplay between electromagnetics and processing.

[4]Chen SF, Zhang JY, Björnson E, et al., 2021. Structured massive access for scalable cell-free massive MIMO systems. IEEE J Sel Areas Commun, 39(4):1086-1100.

[5]Chen SF, Zhang JY, Björnson E, et al., 2023. Energy-efficient cell-free massive MIMO through sparse large-scale fading processing. IEEE Trans Wirel Commun, 22(12):9374-9389.

[6]Cui MY, Dai LL, 2022. Channel estimation for extremely large-scale MIMO: far-field or near-field? IEEE Trans Commun, 70(4):2663-2677.

[7]Cui MY, Wu ZD, Lu Y, et al., 2023. Near-field MIMO communications for 6G: fundamentals, challenges, potentials, and future directions. IEEE Commun Mag, 61(1):40-46.

[8]Du HY, Wang JC, Niyato D, et al., 2023. Semantic communications for wireless sensing: RIS-aided encoding and self-supervised decoding. IEEE J Sel Areas Commun, 41(8):2547-2562.

[9]Du HY, Zhang RC, Liu YQ, et al., 2024. Enhancing deep reinforcement learning: a tutorial on generative diffusion models in network optimization. IEEE Commun Surv Tut, 26(4):2611-2646.

[10]Gan X, Zhong CJ, Huang CW, et al., 2021. RIS-assisted multi-user MISO communications exploiting statistical CSI. IEEE Trans Commun, 69(10):6781-6792.

[11]Gong TR, Gavriilidis P, Ji R, et al., 2024. Holographic MIMO communications: theoretical foundations, enabling technologies, and future directions. IEEE Commun Surv Tut, 26(1):196-257.

[12]Huang CW, Yang ZH, Alexandropoulos GC, et al., 2021. Multi-hop RIS-empowered terahertz communications: a DRL-based hybrid beamforming design. IEEE J Sel Areas Commun, 39(6):1663-1677.

[13]Jiang YH, Gao FF, 2023. Electromagnetic channel model for near field MIMO systems in the half space. IEEE Commun Lett, 27(2):706-710.

[14]Lei H, Zhang JY, Xiao HH, et al., 2024a. Channel estimation for XL-MIMO systems with polar-domain multi-scale residual dense network. IEEE Trans Veh Technol, 73(1):1479-1484.

[15]Lei H, Zhang JY, Wang Z, et al., 2024b. Hybrid-field channel estimation for XL-MIMO systems with stochastic gradient pursuit algorithm. IEEE Trans Signal Process, 72:2998-3012.

[16]Letaief KB, Chen W, Shi YM, et al., 2019. The roadmap to 6G: AI empowered wireless networks. IEEE Commun Mag, 57(8):84-90.

[17]Liu YW, Ouyang CJ, Wang ZL, et al., 2024. Near-field communications: a comprehensive survey.

[18]Liu ZH, Zhang JY, Liu ZL, et al., 2024. Double-layer power control for mobile cell-free XL-MIMO with multi-agent reinforcement learning. IEEE Trans Wirel Commun, 23(5):4658-4674.

[19]Liu ZL, Zhang JY, Liu ZH, et al., 2024. Cell-free XL-MIMO meets multi-agent reinforcement learning: architectures, challenges, and future directions. IEEE Wirel Commun, 31(4):155-162.

[20]Lu HQ, Zeng Y, 2022. Communicating with extremely large-scale array/surface: unified modeling and performance analysis. IEEE Trans Wirel Commun, 21(6):4039-4053.

[21]Lu HQ, Zeng Y, You CS, et al., 2023. A tutorial on near-field XL-MIMO communications towards 6G.

[22]Marzetta TL, 2010. Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans Wirel Commun, 9(11):3590-3600.

[23]Ouyang CJ, Liu YW, Yang HW, 2022. Performance of downlink and uplink integrated sensing and communications (ISAC) systems. IEEE Wirel Commun Lett, 11(9):1850-1854.

[24]Ouyang CJ, Liu YW, Zhang XQ, et al., 2023. Near-field communications: a degree-of-freedom perspective.

[25]Shi EY, Zhang JY, Du HY, et al., 2024. RIS-aided cell-free massive MIMO systems for 6G: fundamentals, system design, and applications. Proc IEEE, 112(4):331-364.

[26]Sun G, He L, Sun ZM, et al., 2024. Joint task offloading and resource allocation in aerial-terrestrial UAV networks with edge and fog computing for post-disaster rescue. IEEE Trans Mob Comput, 23(9):8582-8600.

[27]Tang P, Zhang JH, Miao HY, et al., 2024. XL-MIMO channel measurement, characterization, and modeling for 6G: a survey. Front Inform Technol Electron Eng, early access.

[28]Tataria H, Shafi M, Molisch AF, et al., 2021. 6G wireless systems: vision, requirements, challenges, insights, and opportunities. Proc IEEE, 109(7):1166-1199.

[29]Wang Z, Zhang JY, Du HY, et al., 2024a. Extremely large-scale MIMO: fundamentals, challenges, solutions, and future directions. IEEE Wirel Commun, 31(3):117-124.

[30]Wang Z, Zhang JY, Du HY, et al., 2024b. A tutorial on extremely large-scale MIMO for 6G: fundamentals, signal processing, and applications. IEEE Commun Surv Tut, 26(3):1560-1605.

[31]Wei L, Huang CW, Alexandropoulos GC, et al., 2023. Tripolarized holographic MIMO surfaces for near-field communications: channel modeling and precoding design. IEEE Trans Wirel Commun, 22(12):8828-8842.

[32]Xie ZY, Liu YW, Xu JQ, et al., 2023. Performance analysis for near-field MIMO: discrete and continuous aperture antennas. IEEE Wirel Commun Lett, 12(12):2258-2262.

[33]Xu BK, Zhang JY, Li JX, et al., 2023. Jac-PCG based low-complexity precoding for extremely large-scale MIMO systems. IEEE Trans Veh Technol, 72(12):16811-16816.

[34]Xu BK, Zhang JY, Du HY, et al., 2024. Resource allocation for near-field communications: fundamentals, tools, and outlooks. IEEE Wirel Commun, 31(5):42-50.

[35]You CS, Zhang YP, Wu CY, et al., 2023. Near-field beam management for extremely large-scale array communications.

[36]You XH, Wang CX, Huang J, et al., 2021. Towards 6G wireless communication networks: vision, enabling technologies, and new paradigm shifts. Sci China Inform Sci, 64(1):110301.

[37]Yuan SSA, He Z, Chen XM, et al., 2022. Electromagnetic effective degree of freedom of an MIMO system in free space. IEEE Antenn Wirel Propag Lett, 21(3):446-450.

[38]Yuan SSA, Wu J, Xu HJ, et al., 2024. Breaking the degrees-of-freedom limit of holographic MIMO communications: a 3-D antenna array topology. IEEE Trans Veh Technol, 73(8):11276-11288.

[39]Zhang JY, Björnson E, Matthaiou M, et al., 2020. Prospective multiple antenna technologies for beyond 5G. IEEE J Sel Areas Commun, 38(8):1637-1660.

[40]Zhang JY, Zhang J, Björnson E, et al., 2021. Local partial zero-forcing combining for cell-free massive MIMO systems. IEEE Trans Commun, 69(12):8459-8473.

[41]Zhang ZJ, Dai LL, 2023. Pattern-division multiplexing for multi-user continuous-aperture MIMO. IEEE J Sel Areas Commun, 41(8):2350-2366.

[42]Zheng JK, Zhang JY, Cheng JL, et al., 2023. Asynchronous cell-free massive MIMO with rate-splitting. IEEE J Sel Areas Commun, 41(5):1366-1382.