An In-Depth Statistical Analysis of the TARC Parameter to Evaluate the Real Impact of Random Phases in MIMO Antennas

A detailed statistical analysis of the total active reflection coefficient (TARC) is carried out in this paper for three 4-port MIMO antennas featuring different levels of isolation across its ports. This analysis is very useful to determine the most likely performance of a MIMO antenna in a real communications scenario. The TARC parameter is commonly evaluated for only several combinations of the random phase with which a signal reaches every input port of a MIMO antenna. By contrast, we have evaluated a million combinations to obtain the probability density function of the TARC, using frequency as its parameter. In this way, an expected value of the TARC is obtained for each frequency, as well as a confidence interval ($\Delta C{I}_{\mathrm{TARC}}$) where the TARC values occur with 90% probability. Additionally, we have introduced the term “TARC shadow”, a visual representation of the TARC as a function of the frequency where the probability function is projected into this 2D graphic with different colors to identify the most likely values of the TARC. To demonstrate these concepts, a full TARC evaluation was performed for three 4-port MIMO antennas with increasing isolation of 12.9 dB, 25.4 dB, and 37 dB between elements, and different values of the $S_{nn}$ and $S_{nm}$ parameters, with n and $m=$ 1 to 4. From this study, the importance of the isolation among ports and its comparison with the return losses becomes evident in achieving a MIMO antenna array insensitive to random phase variations occurring in the communication channel.