A mathematical theory of antenna arrays with randomly spaced elements

Lo, Y.

doi:10.1109/tap.1964.1138220

Cited by 318 publications

(255 citation statements)

References 10 publications

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“…For TRAs the positions {X n }s are assumed independent and identically distributed (i.i.d. ), then the mean and the variance of the array factor read as [1] …”

Section: Totally Random Arraysmentioning

confidence: 99%

“…However, it is somehow simplified when the number of radiators is large. In this case, the Central Limit Theorem [11] allows to consider F and F to be jointly normal [1]. Moreover, if f (X) is even (as it is commonly assumed) [1] then the imaginary part of the mean pattern φ (u) = 0 and F (u) and F (u) become uncorrelated (and hence independent) for each value of u.…”

Section: Totally Random Arraysmentioning

confidence: 99%

“…Much of the work on random arrays dates back to the seminal paper by Lo [1] who was the first that systematically developed the theory for the case whereby radiators' positions are continuous i.i.d. random variables supported over the entire array aperture.…”

Section: Introductionmentioning

confidence: 99%

“…Accordingly, the design error measures how much the random radiation pattern deviates from its average. Such an error can be estimated under the L 2 norm by employing the Karhunen-Loeve expansion [1]. This however requires computing the eigenspectrum of the radiation pattern covariance function, which in general cannot be obtained in closed form.…”

Section: Introductionmentioning

confidence: 99%

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Generalised Random Binned Antenna Arrays

Buonanno¹,

Solimene²

2017

PIER C

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Abstract-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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“…For TRAs the positions {X n }s are assumed independent and identically distributed (i.i.d. ), then the mean and the variance of the array factor read as [1] …”

Section: Totally Random Arraysmentioning

confidence: 99%

Section: Totally Random Arraysmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalised Random Binned Antenna Arrays

Buonanno¹,

Solimene²

2017

PIER C

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“…The periodic nature of the arising layouts also enables an easier construction compared to other nonregular arrangements such as aperiodic structures [1]. Also for these reasons, array thinning has been deeply investigated and several methodologies have been proposed ranging from dynamic programming [3], random approaches [4,5], as well as stochastic tools based on genetic algorithms [1,6,7,8,9,10,11,12,13], simulated annealing [14], particle swarm optimizations [15,16,17], and pattern search [18]. Although very effective, these methodologies exhibit some drawbacks either in terms of PSL control (specifically, random layouts) or computational costs (namely, stochastic optimization-based techniques) especially when large layouts are at hand.…”

Section: Introductionmentioning

confidence: 99%

On the radiation properties of ADS-thinned dipole arrays

Moriyama

Oliveri

Salucci

et al. 2014

IEICE Electron. Express

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Abstract:The results of a full-wave analysis of the performances of ADS-based thinned arrays of wire dipoles are presented. The pattern features of the ADS layouts are numerically evaluated by considering different aperture sizes, lattice spacings, and dipole lengths. The outcomes are that, despite a slight and expected performance worsening, the a-priori PSL bounds deduced for the "ideal" case still provide useful guidelines for the design of ADS thinned layouts featuring real dipole elements.

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Synthesis Methods for Antennas

Stutzman

Licul²

2007

Modern Antenna Handbook

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A mathematical theory of antenna arrays with randomly spaced elements

Cited by 318 publications

References 10 publications

Generalised Random Binned Antenna Arrays

Generalised Random Binned Antenna Arrays

On the radiation properties of ADS-thinned dipole arrays

Synthesis Methods for Antennas

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