In binned arrays, radiators are classically located according to a uniform probability distribution. By doing so, it has been shown that they have the same mean radiation pattern as totally random arrays (i.e., the ones for which the radiators' positions are continuous independent and identically distributed random variables defined over the whole array aperture) but a lower variance. In this paper, we introduce a new class of generalised binned arrays by generalising the rule for assigning the radiators' positions. These new binned arrays, while maintaining the aforesaid advantage (in terms of the variance behaviour), allow to set the mean radiation pattern according to some design requirements. The achievable performance is estimated by measuring how much the radiation pattern deviates from the desired mean radiation pattern by resorting to the up-crossing theory. In particular, the study is developed for the case of symmetric arrays, which allows for easier maths. The paper includes an extensive numerical analysis which allows to check the developed theory. In particular, it focuses on the comparison between the generalised binned array and the totally random ones. A comparison with the nonuniform arrays coming from the density tapering approach is also presented. The latter appears natural in view of the new bins selection rule, which, as will be shown, is a sort of density-tapering in which the role of the reference current is played by the radiators' position density distribution.
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