An Efficient Approximation of Spatial Correlation Based on Gauss-Hermite Quadrature

An efficient spatial correlation approximation for clustered multiple-input multiple-output (MIMO) channels based on a hierarchical angle structure is presented. To avoid complicated numerical integrations, different approximations have been proposed in the literature. One approximation is expressed in a high order series expansion of Bessel functions, while the other suffers low accuracy for large angle spread. An approximation based on Gauss-Hermite quadrature (GHQ) is proposed, whose values are shown to match well with theoretical results when the antenna spacing is within a critical range. By exploring the properties of the abscissas and the weights of the GHQ, the proposed approximation can be effectively computed with only a few expansion terms, and its validity can be maintained over a large range of angle spread. The approximation errors of the proposed and existing methods are analyzed. Simulation results verify the accuracy of the analysis and the efficiency of the proposed approximation.