Abstract
In this paper we consider the characterisation of linear statistically thinned arrays. Their side-lobe level is often given in terms of the angle independent array factor variance, which does not capture the actual statistical fluctuations of the power pattern around its average, or by some analytical formulas which overcome this limitation by estimating the probability distribution of the peak side-lobe level. Here, the aim is to refine existing theory in order to obtain a more precise estimation of the statistical features of thinned arrays. For the general asymmetric case, we exploit an analytical expression of the variance of the power pattern. This measures the dispersion of the power pattern around its average and in conjunction with the Chebyshev’s inequality allows to find a lower bound, for each fixed angle, of the power pattern probability distribution. For symmetric thinned arrays, the power pattern probability distribution is precisely obtained without resorting to some strong assumptions which are usually employed to get tractable expressions. Also, this result, along with the up-crossing method, allows to obtain a theoretical and new expression for the peak side-lobe level probability distribution as well as for the deviation between the thinned array factor and the reference one. The theoretical findings are checked through a Monte Carlo numerical analysis. The numerical results show that the theoretical predictions work very well and are more accurate than previous literature estimations. Finally, since the symmetric thinned arrays actually exploit half the available degrees of freedom, a numerical comparison is run with the asymmetric ones. The comparison shows that asymmetric and symmetric statistically thinned arrays exhibit similar performances.
Highlights
N ONUNIFORMLY-SPACED ARRAYS consist of elements arranged at a non-constant separation spacing [1]
The paper by Willey [5] and the contribution by Doyle [1] can be considered the pioneering and seminal results towards the development of the deterministic density-tapering. These approaches are founded in some procedures by which the spatial density of a nonuniformly-spaced array is determined according to the amplitude tapering of a reference array
We have shown that symmetric linear statistically thinned arrays and the asymmetric ones exhibit similar behaviours but the former have the advantage of being easier to characterise
Summary
Consider a linear array of N isotropic radiators deployed along the x axis within the segment [−L/2, L/2] (see Fig. 1). An analogous of (8) can be obtained as well In this case it is possible to determine the distribution of the power-pattern (or of the array factor magnitude) in a very simple way, without resorting to any approximation [20]. Previous formulas can only allow to estimate (statistically) the deviation of the array factor from the reference one for each given u, whereas information relating to the entire observation range cannot be determined To this end, we adapt to the present case the methodologies introduced in [20] [28]- [33], in which random arrays were considered
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