An Improved Upper Bound on the Maximum Eigenvalue of Exponential Model Based Spatial Correlation Matrices in Massive MIMO Systems

Massive Multiple-Input, Multiple-Output (MIMO) communications are considered as one of the most promising directions for the next generation communications and have attracted extensive research interests. The using of exponential model is recognized as an effective manner to describe the spatial correlation matrix in a spatially correlated MIMO channel for its simple form and accurate fitting on the experimental measurements. Based on this useful exponential model, an improved upper bound on the maximum eigenvalue of the spatial correlation matrix is given in this paper. Complying with the existing results, the proposed upper bound is also a function of the number of antennas and the absolute value of correlation coefficient. However, the proposed upper bound is obtained using a trace-based derivation, which is tighter than existing results in high spatial correlation massive MIMO systems. Simulations show that the proposed upper bound is closer to the true maximum eigenvalues for both uniform linear array and uniform planar array scenarios, which is expected to be widely used in massive MIMO systems