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 point antennas, 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.

翻译：本文针对近场XL-MIMO系统，专门构建了一个有效自由度（EDoF）性能分析框架。我们探索了五种具有代表性的不同XL-MIMO硬件设计，包括基于点天线的均匀平面阵列（UPA）、二维（2D）连续孔径（CAP）平面、基于贴片天线的UPA、均匀线性阵列（ULA）以及一维（1D）CAP线段XL-MIMO系统。我们的分析涵盖两种近场信道模型：基于标量格林函数和基于并矢格林函数的信道模型。更重要的是，在应用基于标量格林函数的信道时，我们推导出了闭式EDoF表达式，刻画了收发机物理尺寸、传输距离和载波频率的影响。数值结果中，我们评估并比较了所有考察的XL-MIMO设计的EDoF性能，验证了所提出闭式表达式的准确性。此外，我们观察到，随着天线数量的增加，基于UPA和基于ULA的系统的EDoF性能分别趋近于2D CAP平面和1D CAP线段的系统。进一步地，我们揭示近场XL-MIMO系统的EDoF性能主要由阵列孔径尺寸决定，而非单纯的天线数量。