Linear random antenna arrays are usually studied in conjunction with uniform excitations with, at most, a linear phase shift in order to steer the main beam. This offers some advantages in terms of the feeding network but puts limitations on the array factor that can be obtained. The authors introduce unequally excited random arrays whose excitation currents are obtained by suitable transformations of the random variables related to the element positions. Besides, the first- and secondorder statistic characterisation, the uniform norm (i.e. the supremum) of difference between the mean (the desired one) and the actual array factors is estimated. In particular, while in the general case, this is achieved only via a Monte Carlo study, for the case of symmetric arrays (where the elements are randomly deployed symmetrically with respect to the array aperture centre) that norm is analytically estimated using the up-crossing theory for random processes. It is shown that the proposed unequally excited random arrays, unlike some other previous approaches, allow shaping the mean radiation pattern. However, the procedure in general yields reduced achievable performance. Therefore, the theoretical findings are checked through some numerical examples only for the important class of multi-beam array factors.
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