Calculating correlation between the E-fields of two antennas
I am having a bit of a problem computing the cross correlation between two Electric-field patterns of antennas. I will try to state my problem clearly:
I have E-field values of an antenna for each value of phi and theta.
The E-field values are complex numbers and are given as dB V/m.
So in Matlab I have a Matrix of dimensions 181(0-180 degrees values of φ) x 360(for 360 values of Θ).
Now I have another complex E-field matrix of the same dimensions giving the E-field radiation pattern of another antenna.
Now, I want to compare the two E-field patterns to see how much similar are they to one another. For this purpose I need to calculate their cross-correlation coefficient so that I get a single value between -1 and +1.
I am not sure on how to obtain the cross-correlation, because you cannot use the complex values directly into the correlation formulas, because then you get really wrong results.
I am also attaching the E-field matrices of the two antennas for your reference. These can be uploaded in Matlab using 'load' command.
Kindly help me in this regard, I will be very grateful.
Comparing patterns and trying to collapse them into a single number has always been somewhat of a challenge. People routinely want to do that and I often find that it does not adequately describe an antenna or allow useful comparisons.
If I was trying to compare the two patterns you describe I would consider comparing normalized power patterns where I normalized to the highest E (converted to power) component. I would then plot nested 3D plots to see how they line up. Note that the power plots avoid the issue of comparing complex values.
I would also be inclined to use the conventional parameters of gain, beamwidth, sidelobe level, directivity and so on. The idea is to use parameters that people usually encounter.
I would be interested to see how your effort works out.
Good Luck.