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

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 full-wave EM 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.