Directivity-Aware Degrees of Freedom Analysis for Extremely Large-Scale MIMO

TL;DR

This work addresses how antenna directivity and element spacing affect the effective degrees of freedom (EDoF) and ergodic capacity in extremely large-scale MIMO (XL-MIMO) systems under isotropic Rayleigh scattering. It uses a wavenumber-domain channel representation to express the channel via direction-specific coupling coefficients and introduces a directivity-aware analysis of these coefficients, deriving analytic forms for $\sigma_T^2(m_x,m_y)$ with a general pattern $G(\theta,\phi)=\cos^m\theta$ and defining an effective DoF $\eta_e$ based on large coefficients. An EM-simulation-based coupling-coefficients (EMCC) method is proposed to estimate the wavenumber-domain couplings from full-wave simulations, enabling evaluation of EDoF and capacity for RIS, patch, and dipole arrays; results show RIS can achieve higher EDoF with near-even coefficient distributions and reveal optimal element spacings around $0.43\lambda$ for maximizing capacity. Overall, the framework links antenna directivity and spacing to the availability of orthogonal communication modes, providing design guidance for XL-MIMO implementations and surfaces.

Abstract

Extremely large-scale multiple-input multiple-output (XL-MIMO) communications, enabled by numerous antenna elements integrated into large antenna surfaces, can provide increased effective degree of freedom (EDoF) to achieve high diversity gain. However, it remains an open problem that how the EDoF is influenced by the directional radiation pattern of antenna elements. In this work, empowered by the wavenumber-domain channel representation, we analyze the EDoF in a general case where the directivity of antennas, determined by the antenna structure and element spacing, is considered. Specifically, we first reveal the uneven distribution of directivity-aware wavenumber-domain coupling coefficients, i.e., channel gain towards different directions, in the isotropic Rayleigh fading channel. EDoF is then calculated based on such distribution of coupling coefficients. A numerical method is also provided to obtain coupling coefficients via electromagnetic full-wave simulations. Due to the influence of antenna directivity, how EDoF and ergodic channel capacity vary with the element spacing are explored via simulations for different antenna types.

Figures (6)

• Figure 1: An XL-MIMO communication system in isotropic scattering Rayleigh channel.
• Figure 2: Distribution of coupling coefficients for different cases of $m$.
• Figure 3: Coupling Coefficients of different sizes of antenna array.
• Figure 4: The distributions of coupling coefficients of different antenna types and element spacing.
• Figure 5: EDoF vs. element spacing of different antenna types.