Random arrays have been typically studied by considering real uniform excitations. This is suited for single-beam radiation patterns but does not allow for more sophisticated patterns. Indeed, only even patterns, with respect to the steering angle, can be achieved. To overcome this limitation, we recently proposed a new model whereby the excitation coefficients are not uniform and are determined by means of two random variable transformations. In this paper, we deal more extensively with the properties of this model, highlighting things that have not been pointed out previously. In order to get analytical results, we just consider symmetric random arrays. For such a case, we determine the design error, that is the cumulative distribution function of the supremum of the the difference between the actual and desired array factors. It is shown that general shaped beams can be actually achieved but at the cost of an increase of the design error as compared to the single-beam case. Numerical analysis validates the presented theory.
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