Analytical Framework for Effective Degrees of Freedom in Near-Field XL-MIMO

Abstract

Extremely large-scale multiple-input-multiple-output (XL-MIMO) is an emerging transceiver technology for enabling next-generation communication systems, due to its potential for substantial enhancement in both the spectral efficiency and spatial resolution. However, the achievable performance limits of various promising XL-MIMO configurations have yet to be fully evaluated, compared, and discussed. In this paper, we develop an effective degrees of freedom (EDoF) performance analysis framework specifically tailored for near-field XL-MIMO systems. We explore five representative distinct XL-MIMO hardware designs, including uniform planar array (UPA)-based with infinitely thin dipoles, two-dimensional (2D) continuous aperture (CAP) plane-based, UPA-based with patch antennas, uniform linear array (ULA)-based, and one-dimensional (1D) CAP line segment-based XL-MIMO systems. Our analysis encompasses two near-field channel models: the scalar and dyadic Green's function-based channel models. More importantly, when applying the scalar Green's function-based channel, we derive EDoF expressions in the closed-form, characterizing the impacts of the physical size of the transceiver, the transmitting distance, and the carrier frequency. In our numerical results, we evaluate and compare the EDoF performance across all examined XL-MIMO designs, confirming the accuracy of our proposed closed-form expressions. Furthermore, we observe that with an increasing number of antennas, the EDoF performance for both UPA-based and ULA-based systems approaches that of 2D CAP plane and 1D CAP line segment-based systems, respectively. Moreover, we unveil that the EDoF performance for near-field XL-MIMO systems is predominantly determined by the array aperture size rather than the sheer number of antennas.

Figures (12)

• Figure 1: A UPA-based XL-MIMO system with each antenna element being a sizeless infinitely thin dipoles.
• Figure 2: EDoF performance for UPA-based with infinitely thin dipoles and 2D CAP plane-based XL-MIMO system with $L_{t,V}=L_{r,V}=10\lambda$ over the dyadic and scalar Green's function-based channels.
• Figure 3: EDoF performance for the square UPA-based XL-MIMO system with $L_{t,V}=L_{r,V}=\sqrt{2}/2\, \mathrm{m}$ and $M_{H,V}=N_{H,V}$, and the ULA-based XL-MIMO system with $L_{t}=L_{r}=1\, \mathrm{m}$ and $M=N$ against the total number of antennas $M=N$ over the scalar Green's function-based channel. Each antenna element is an infinitely thin dipole.
• Figure 4: EDoF performance for the UPA-based XL-MIMO system with $M_{H,V}=N_{H,V}=\sqrt{M}$ and ULA-based XL-MIMO system with $M=N$ against $\sqrt{M}$ over different antenna spacing. Each antenna element is an infinitely thin dipole.
• Figure 5: EDoF performance for the UPA-based XL-MIMO system with infinitely thin dipoles or patch antenna elements against the number of antennas per side $M_V=N_V$ with $L_{t,V}=L_{r,V}=10\lambda$, $D=10\lambda$, and $A_{r,\left\{ H,V \right\}}=A_{t,\left\{ H,V \right\}}=\lambda /2$ over both the dyadic and scalar Green's function-based channels.

Theorems & Definitions (18)

• Remark 1
• Remark 2
• Theorem 1
• Remark 3
• Remark 4
• Corollary 1
• Remark 5
• Theorem 2
• Remark 6
• Corollary 2