ECC includes an applied field distribution in the integral, so there's essentially an RF environment parameter that is multiplied by the pattern to calculate the ECC.  If you use the S-parameters to determine coupling between the antennas and estimate correlation from that, you have no information about the real applied field (LOS plane wave, uniform omnidirectional, uniform spherical (isotropic), or whatever).  Presumably the estimate will correspond to the uniform spherical case where you could consider the integral multiplies each directional component by one.  

Using a 2D pattern to calculate ECC limits you to assuming the incoming fields are only two-dimensional in nature.  You have no idea what the majority of the pattern is actually doing to your correlation by only using a single cut.  Now, you might be able to apply a hybrid approach by comparing the S-parameter result to a uniform distribution on a single cut and see how far off the two are, but I'm not sure what that tells you about any other field distribution result.

ECC includes an applied field distribution in the integral, so there's essentially an RF environment parameter that is multiplied by the pattern to calculate the ECC.  If you use the S-parameters to determine coupling between the antennas and estimate correlation from that, you have no information about the real applied field (LOS plane wave, uniform omnidirectional, uniform spherical (isotropic), or whatever).  Presumably the estimate will correspond to the uniform spherical case where you could consider the integral multiplies each directional component by one.  

Using a 2D pattern to calculate ECC limits you to assuming the incoming fields are only two-dimensional in nature.  You have no idea what the majority of the pattern is actually doing to your correlation by only using a single cut.  Now, you might be able to apply a hybrid approach by comparing the S-parameter result to a uniform distribution on a single cut and see how far off the two are, but I'm not sure what that tells you about any other field distribution result.

Hello, I use the scattering parameters in CST or HFSS both are able to find the correlation form these parameters, the other approach is to evaluate it from far-field patterns, again available in CST and HFSS. I truest the latter.

Thank you Michael,

Your words mean that ECC is variable value and even if we are able to measure it in an anechoic chamber, this measured value will be nothing more than an ideal case in which the MIMO array won't live in when employed in any system. If I understood you correctly, how would we measure ECC in a worst case scenrio rather than ideal one??

Regarding comparing ECC from S-parameter to the ECC from farfield pattern, I've already done that and literature says that depending on the efficiency of the antenna the agreement would exist (high efficiency means good agreement). This was actually the case with me. But I'm still stuck on how to "measure" ECC from farfield ?

Thank you Hussien,

I'm familiar with extracting ECC from simulation, I'm actually facing problem measuring it from farfield not from S-parameter .. I'm trying to avoid such measurement of it is enough to measured it from S-parameters. The question is, when is it enough to do so?? :)

The E in ECC is for "effective", referring to "Effectively, what would the correlation between these two antennas be if you had this field distribution in your environment?"  It should also be noted that ECC uses a scalar field distribution, not vector, so it does not include the spatial correlation effects of the channel itself, or the correlation behavior of the antenna at the other end of the link.  From that standpoint is is just a property of the relative antenna patterns of the device, but you have the option to weight the contribution as a function of direction using the field distribution.

What you're actually MEASURING in the chamber are the two antenna patterns.  The ECC is a post-processed result of the two patterns.

I'm aware that I'm measuring pattern and that's exactly what I'm trying to avoid (because it is cumbersome if 3D measurements to be conducted at several different frequencies) ??.

Regarding your note that ECC is calculated via scalar field distribution, I think that is not accurate. Referring to the equation (which is available in literature) the numerator is a hermitian product between the complex vector field pattern. Also I can't get what interest do you have in the antenna on the other end of the link, I'm studying the effect of correlation between antennas forming a MIMO array??

 how to calculate ECC from radiation pattern in HFSS? can anyone tell me the steps for calulating ECC from rad pattern in hfss.

the very first paper

https://ieeexplore.ieee.org/document/1199929/ The modified one with exact formula from the electromagnetic fields instead of S-parameters

https://ieeexplore.ieee.org/abstract/document/7029004/

Please look at the second Paper, it is the most update paper which could answer your question.

I agree with Michael.

check out the following and note that the field equation requires a field distribution defined. Most people use isotropic environments for simplicity. I would not recommend the S-parameter formula at all! See reasons below:

Article Current Misuses and Future Prospects for Printed Multiple-In...

https://www.cambridge.org/core/journals/international-journal-of-microwave-and-wireless-technologies/article/correlation-coefficient-calculations-for-mimo-antenna-systems-a-comparative-study/9F18A2E80513827A71F724D44E09AE2A

As well as

http://us.artechhouse.com/Printed-MIMO-Antenna-Engineering-P1653.aspx

In HFSS: right click on Results -> click Output Variables -> give a Name -> add the following in the Expression box -> click on Add

mag((mag((conjg(S(1,1))*S(1,2))+(conjg(S(2,1))*S(2,2))))/(((1-mag(S(1,1))^2-mag(S(2,1))^2)*(1-mag(S(2,2))^2-mag(S(1,2))^2))^(1/2)))

After the simulation is complete... right click on Results -> go to Create Modal Solution Data Report -> Rectangular Plot -> click on Output Variables -> New Report.

Note: This formula using S-parameters is only valid for antennas with high efficiencies, i.e., very low loss resistance! For antennas with low radiation efficiencies one must always rely on the formula involving radiation patterns.