A novel dual band square patch antenna with better isolation and low correlation

The correct application of total active reflection coefficient to evaluate MIMO antenna systems and its generalization to N ports

“…It must be observed that the arguments of the cosine functions do not coincide with value 0 or with π/2 anywhere, disqualifying the use of Equations (6) and (8). Besides, the curves when θ = +45 does not take the same values as when θ = −45 ; this demonstrates that θ must be swept in the range from 0 to 360 [10,12], instead of the 0 to 180 interval reported in References 4,8,14. 6 | CONCLUSIONS Total active reflection coefficient is an enlightening tool for the evaluation of multi-antenna systems, and for assessing electromagnetic decoupling methods, since it is a metric that can be easily derived from the measurement of the S-parameters, and is the only MIMO parameter that describes the influence of the random phases of the involved signals over the system impedance bandwidth behavior. However, after performing an analysis of the state-of-the-art, a general misunderstanding of the physical meaning of TARC was found in several publications.…”

“…Then, by factoring | a 1 |, the TARC equation for two antennas described in Equation was derived. This expression can be found in References applied correctly, and in Reference mistakenly applied to a four‐element set of antennas. …”

“…This generalized equation controverts Equation of Reference which displays 2 ‐0.5 instead of the correct divider 4 ‐0.5 Also contradicts the authors of Reference , who reported Equation instead of Equation for N = 4, since their design has four patch antennas.…”

“…It must be observed that the arguments of the cosine functions do not coincide with value 0 or with π /2 anywhere, disqualifying the use of and . Besides, the curves when θ = +45° does not take the same values as when θ = −45°; this demonstrates that θ must be swept in the range from 0° to 360° [10, 12], instead of the 0° to 180° interval reported in References .…”

“…However, several authors have issued on leading journals on Antennas and Microwave Techniques imprecise equations to compute TARC on MIMO antennas, which disregard the information of random phases, and its impact on the performance of the antenna system vs frequency. After an examination of the state‐of‐the‐art on MIMO arrays performed by the authors of this work, it was found that many papers reported a correct evaluation of TARC expression by displaying a family of curves, given by the variations on the random phases θ i , along with the computation of other adequate antenna metrics. Whereas in several other papers a wrong version of the equation was used; or only one curve was displayed without a mathematical explanation of how it was derived; only one value at the resonance frequencies was reported in a table; and, finally, one curve obtained by averaging an unknown number of TARC curves was given .…”