On asymptotic favorable propagation condition for massive MIMO with co-located user terminals

In this paper, the asymptotic favorable propagation (FP) condition is thoroughly analyzed under the assumption that user terminals (UTs) are gathered in a size-limited circular area. Uniform distribution is assumed for UTs. Assumptions that are accordant with realistic propagation environment are used, which mathematically bring in close-form approximations for mean and variance of FP. Based on these approximations, we can quantify the speed of convergence to FP when the array size goes large. It is written as a function of environmental characteristics, such as line-of-sight (LOS) direction, straight-line distance, etc. Furthermore, the needed array size to achieve channel orthogonality for data transmission can be calculated for co-located UTs based on proposed approximations, which provides suggestions in massive MIMO systems design.