Modeling and Analysis of Spatial Correlation for Near-Field Communications

The near-field spatial correlation for multiple-input multiple-output (MIMO) communications in multi-path fading channels is analyzed. Based on the general non-uniform spherical wave (NUSW) model, an analytical integral-form expression for near-field spatial correlation is derived, which generalizes the conventional uniform plane wave (UPW)-based far-field spatial correlation. Furthermore, by considering the specific von Mises-Fisher distribution of scatterer locations, a simplified closed-form near-field spatial correlation expression is derived. It is rigorously proved that 1) in contrast to the far-field spatial correlation, the near-field spatial correlation no longer exhibits spatial stationary property, and 2) the NUSW-based near-field spatial correlation model depends on the power location spectrum, which encompasses both the angles and distances of the scatterers. Next, the developed near-field spatial correlation can be utilized to derive a closed-form expression for the effective degrees of freedom (EDoF). Additionally, a correlation-based stochastic channel model is constructed for MIMO communications, from which an optimal transmission strategy is devised. Subsequently, the power allocation is optimized to achieve the maximum ergodic spectral efficiency. Numerical results validate 1) the significance of near-field spatial correlation modeling for MIMO communications, 2) near-field MIMO exhibits a higher EDoF than the conventional far-field counterpart, and 3) the constructed correlation-based stochastic channel model facilitates the derivation of an optimal transmission strategy, thereby maximizing ergodic spectral efficiency.