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.

翻译：超大规模多输入多输出（XL-MIMO）通信通过将大量天线单元集成于大型天线表面实现，能够提供更高的有效自由度（EDoF）以获得显著的分集增益。然而，天线单元的定向辐射模式如何影响EDoF仍是一个待解决的问题。本研究借助波数域信道表征方法，在考虑天线方向性（由天线结构及单元间距决定）的一般性场景下分析了EDoF。具体而言，我们首先揭示了各向同性瑞利衰落信道中方向性感知的波数域耦合系数（即指向不同方向的信道增益）的非均匀分布特性，进而基于该耦合系数分布计算EDoF。本文还提供了通过电磁全波仿真获取耦合系数的数值计算方法。针对不同天线类型，通过仿真探究了在天线方向性影响下，EDoF与遍历信道容量随单元间距的变化规律。