# Is an antenna array with a tilted (rotated) antenna element always less optimal than a perfectly aligned antenna array?

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?

• " is it still possible to achieve maximum total array gain by setting the tilted antenna element at a magical phase value?" - Why would it? Feb 7, 2022 at 19:06
• Less optimal is not a thing. Something is either optimal with respect to some criteria it is not. Feb 8, 2022 at 1:08

When discussing a linear array of elements, assuming the elements are identical (uniform linear array), the pattern can be written as: $$G(\theta) = G_A(\theta)G_E(\theta)$$ where $$\G\$$ is the total pattern, $$\G_A\$$ is the array factor and $$\G_E\$$ is the element factor. This is know as the pattern multiplication principle.