Gene, forgive me if I am incorrect but I am going to assume you have
an engineering degree and are fully conversant with the work of the
masters. I f I am not correct then we can stop at this point Otherwise
I fully recommend that you check out the web foe a book on fields and
waves or something like that by a professor at Rutgers University. In
chapter 21 he delves very deeply into an array consisting of four
elements all of which are resonant.

You really need to learn how to communicate your ideas. You don't know or
won't say the author or the title of the book, or you would just have us
guess.


Ofcourse he doesn't mention anything of mine but you will notice that
the array he chose is actually what I refer to as a Gaussian array
since it meets all the requirements that I have

Could this be the book?

http://www.ece.rutgers.edu/~orfanidi/ewa/