MIMO Channel Model with Propagation Mechanism and the Properties of Correlation and Eigenvalue in Mobile Environments

Abstract

This paper described a spatial correlation and eigenvalue in a multiple-input multiple-output (MIMO) channel. A MIMO channel model with a multipath propagation mechanism was proposed and showed the channel matrix. The spatial correlation coefficient formula 𝜌𝑖−𝑗,𝑖′−𝑗′(𝑏𝑚) between MIMO channel matrix elements was derived for the model and was expressed as a directive wave term added to the product of mobile site correlation 𝜌𝑖−𝑖′(𝑚) and base site correlation 𝜌𝑗−𝑗′(𝑏) without LOS path, which are calculated independently of each other. By using 𝜌𝑖−𝑗,𝑖′−𝑗′(𝑏𝑚), it is possible to create the channel matrix element with a fixed correlation value estimated by 𝜌𝑖−𝑗,𝑖′−𝑗′(𝑏𝑚) for a given multipath condition and a given antenna configuration. Furthermore, the correlation and the channel matrix eigenvalue were simulated, and the simulated and theoretical correlation values agreed well. The simulated eigenvalue showed that the average of the first eigenvalue λ1 hardly depends on the correlation 𝜌𝑖−𝑗,𝑖′−𝑗′(𝑏𝑚), but the others do depend on 𝜌𝑖−𝑗,𝑖′−𝑗′(𝑏𝑚) and approach 𝜆1 as 𝜌𝑖−𝑗,𝑖′−𝑗′(𝑏𝑚) decreases. Moreover, as the path moves into LOS, the 𝜆1 state with mobile movement becomes more stable than the 𝜆1 of NLOS path.