“…For antennas arrayed in transversal direction ( y ), the far‐field radiation amplitude F ( θ , ϕ ) is defined as the product of the far field of a single antenna R ( θ , ϕ ) and the array factor A ( θ , ϕ ), i.e., F ( θ , ϕ ) = R ( θ , ϕ ) × A ( θ , ϕ ). [
29 ] The array factor depends on the amplitude and phase of each antenna and can be calculated as [ 43 ]
where C n is the complex amplitude of the n th antenna, k is the wavenumber in the medium where the far field is being calculated, and d n is the distance from the origin of each antenna in transversal direction ( y ). A specific input excitation of the antenna array will determine the value of the complex amplitudes C n and thus the array factor A ( θ , ϕ ).…”