Probabilistic Density-Tapered Antenna Arrays

In this paper we perform an accurate performance analysis of the generalised random binned antenna arrays, emphasising their tie with another type of aperiodic arrays that are obtained through the density-tapering methods (density-tapered arrays). In fact, since the former share with the latter the same procedure of the array aperture subdivision, we call such random arrays also probabilistic density-tapered arrays. In essence, one of our aims is to emphasise the fact that the generalised binned arrays can play a double role: in the first one they can be used as a tool for an a priori analysis of “deterministic” density-tapered arrays, on the other hand, they can be exploited in order to synthesise aperiodic arrays by generating different sample arrays, then choosing the best one. However, the second role is feasible when the number of antenna elements is very high because in this way the variance of the array factor has sufficiently low values. Our analysis focuses mostly on symmetric generalised binned arrays, since they can be manipulated more easily from the mathematical point of view than the asymmetric ones and also because, from the point of view of density-tapering, different reference currents are even real and positive continuous functions, giving symmetric density-tapered arrays.