Multiple-input multiple-output (MIMO) antennas are commonly evaluated by using the correlation coefficient. However, the correlation has several different definitions and calculation methods, and this misleads the real performance of the MIMO antennas. This paper describes five definitions and their differences of the correlation, i.e., signal correlation, channel correlation, fading correlation, complex pattern correlation, and S-parameter-based correlation. The difference of these characteristics is theoretically and numerically discussed, and their relations are schematically presented. Furthermore, the relationship between the correlation coefficient and the antenna element spacing is numerically evaluated, and it is shown that correlation coefficient calculated only from the S-parameter yields the error greater than 10% when the efficiency of the antenna is lower than 97%.
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