1. A method for setting a radiation pattern for an array antenna including a plurality of radiating elements, the method comprising: receiving an identification of a target shape of an array factor amplitude; accessing geometric parameters of the array antenna, the geometric parameters being capable of describing the number and spacing of the plurality of radiating elements; accessing the target shape of the array factor amplitude based on the received identification of the target shape of the array factor amplitude and the accessed geometric parameters describing the array antenna; calculating an array factor phase based on the accessed target shape of the array factor amplitude by applying the formula: 
 φ(θ)=Hilb{ln( M (θ))} wherein M(θ) denotes the accessed target shape of the array factor amplitude as a function of an angle θ measured with respect to a reference direction, Hilb{ln( M (θ))} denotes the Hilbert transform of a natural logarithm of the accessed target shape of the array factor amplitude, and φ(θ)denotes the calculated array factor phase; calculating array antenna weight coefficients using the least mean square method, where a target function used in the least mean square method is a complex function derived from the accessed target shape of the array factor amplitude and the calculated array factor phase, wherein the calculated weight coefficients determine the array factor; and, applying the determined array factor to the antenna array.