Spatial fading correlation (SFC) mainly depends on power azimuth spectrum (PAS) of arrival signals and the transceiver mode of multi-antenna arrays. This paper investigates in depth the approximate algorithm and its complexity in SFC of multi-antenna arrays in a mobile communication system. First, we derive the closed-form formulas for SFCs under three typical PAS: i. e. a uniform distribution, a Gaussian distribution and a Laplace distribution. Based on these theoretical formulas, we study the approximate algorithm when the angle spread in PAS for arrival signals is small. From this, we develop a multi-antenna reception channel model and analyze in detail the impact of the antenna array and electric wave propagation parameters we choose on the capacity of multiple-input multiple-output (MIMO) channel. By using theoretical calculations and simulation experiments, we find that in a particular situation the approximate algorithm provides a good approximation for SFC. Furthermore, a method is used to quantify the applicability and calculation efficiency while analyzing the MIMO multi-antenna array. Finally, it can be concluded that the approximate method has a good approximation in particular situations, and it will greatly reduce the theoretical computational complexity. The method we suggest will improve the efficiency of analyzing and simulating a complex MIMO multi-antenna system.