Correlation Error Metrics of Simulated MIMO Channels

In the simulation of multiple-input multiple-output (MIMO) radio systems, accurate channel models are needed. Channel models have to be approximated to reach reasonable complexity of practical radio channel simulators, but the approximation should not cause too high error in the simulation. The error of the MIMO correlation matrix can be measured via different metrics such as correlation matrix distance (CMD) and mean square error (MSE). This paper compares the different metrics of correlation error, and investigates the impact of different approximations on the MIMO correlation matrix. From the results it was found that a modified MSE (Mod-MSE) presented in this paper and CMD have quite similar behavior, but Mod-MSE is independent of the correlation matrix size and the level of the original correlation. Thus, Mod-MSE shows only the error on correlation. Channel model approximations are, e.g., limited number of impulse responses, phase error between the channels, and synchronization error in simulator start-up. The impact of the approximations is investigated via the CMD and Mod-MSE analysis. The results show that the number of impulse responses should be in the order of 100 000 or more, phase error of less than 5 degrees is acceptable, and the synchronization error is critical when highly correlated channels are simulated. Another result of this paper is that the Mod-MSE is more recommendable metric than CMD.