Spatial Multiplexing Characterization With Effective Degrees of Freedom Metrics for Near-Field MIMO Systems

This paper presents a comparative analysis of Effective Degrees of Freedom (EDoF) metrics for near-field Multiple-Input Multiple-Output (MIMO) systems. The study investigates three prominent EDoF metrics: $\Psi _{\mathrm{{e}}}$ (EDoF based on the eigenvalue spread of the channel gramian matrix), $N_{\mathrm{{H}}}$ (EDoF based on Geometry of transmit and receive antenna arrays), and $K_{\mathrm{{e}}}$ (EDoF based on Effective Multiplexing Gain). The behavior and applicability of these metrics are examined across various near-field MIMO configurations and channel conditions. The analysis includes a detailed examination of how these metrics respond to changes in array geometry, signal-to-noise ratio (SNR), antenna spacing, and user antenna configurations in the near-field regime. Novel analytical frameworks and simulation methodologies specifically tailored for near-field scenarios are introduced, where spherical wave propagation and solid angle ($\Omega$) are used to characterize the spatial relationships between transmit (Tx) and receive (Rx) arrays. The results demonstrate the unique strengths and limitations of each EDoF metric in near-field conditions, providing important insights for the design and optimization of near-field, high-capacity MIMO systems.