What is the AF of a semi circular antenna array? In what ways is it different from a circular array? Can we theoretically create a semi circular array using the windowing method (like in DSP) on a circular array?
If all the elements are in phase or the phase varies linearly across the antenna then the array factor of a semicircular array is the same as for any shape array. If the elements all have the same amplitude then the array factor is just the number of antenna elements. This only describes the increase in gain at the peak. The shape of the array changes the size and shape of the sidelobe pattern. A semicircular array will usually have higher sidelobes in the direction perpendicular to the straight edge, than a circular array will have.