Global Characterization of Linear Statistically Thinned Antenna Arrays

Abstract

In this paper we consider the characterisation of linear statistically thinned arrays. Their sidelobe 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 derive an analytical expression of the variance of the power pattern. This measures the dispersion of the power pattern around the 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.

Statistically Thinned Array Antennas for Simultaneous Multibeam Applications

“…Herein, we address the case of symmetric thinned arrays, which are obtained by thinning only half the array, and then, for each remaining element, by locating further elements in the position −x n . The corresponding thinned array factor is given by [20]…”

“…Since the {F n } N/2 n=1 are random variables, F (u) is a stochastic process whose mean and variance are respectively given as [20]…”

“…If the number N is sufficiently large, by virtue of the Lyapunov Central Limit Theorem [22], F (u) is Gaussian (for each u), that is F (u) ∼ N F ref (u), σ 2 (u) . Furthermore, since F (u) is periodic, µ(u) and σ(u) are periodic as well [20]. Under these conditions, the cumulative distribution function (cdf ) of the array factor magnitude (and consequently of the power-pattern) is easily found to be expressed as [20] [23] [24] P {F (u)…”

“…To satisfy this need, several results have been produced over the years in literature, starting from the papers [1] and [3]. Recently, in [20], more accurate results have been presented for the case of symmetric thinned arrays. In particular, the up-crossing method has been used, but avoiding simplified assumptions which degrade the accuracy.…”

“…The second scheme relies on a single feeding network, so the beams are no longer independent. In both cases, the approach developed in [20] is adopted to estimate the achievable performance in terms of two parameters, namely the array factor variance and the "distance" error between the statistical array factor and the reference one. The former is a local measure of the array factor dispersion around the reference array; the latter provides a "global" metric.…”