Suppose I have a traditional linear antenna array. My element factor follows a cosine shape between 0-180 degrees. The relationship between my theoretical total antenna array pattern and the element factor is illustrated by this graph (screen shot from analog.com, article written by Peter Delos, Bob Broughton and Jon Kraft).
My understanding is that the theoretical array factor does not consider element pattern, and the total pattern is closest to the array factor at the angle where the element factor is at maximum.
If one of the antennas in my antenna array is tilted, is it still possible to achieve maximum total array gain by setting the tilted antenna element at a magical phase value? If one of the antennas is tilted,is the performance of the beam-forming always worse than the ideal condition?