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A probabilistic approach to the problem of large antenna arrays

1964; The National Institute of Standards and Technology; Volume: 68D; Issue: 9 Linguagem: Inglês

10.6028/jres.068d.101

2376-5771

Y. Lo,

Antenna Design and Optimization

Antenna arrays of very high resolution can be d esigned withou t using a large nu mber of clements if t h ey are spaced properly.However, ther e exi sts no gener al theory whi ch would y ield a solution to t his problem because of its analytical diffi culty.In this paper a probabilistic a pproach is mad e d espi te t he problem itself bei ng not proba bilistic ori ginally.This approach is tantamoun t to the stud y of all ou tcomes for man y possible element positions (under a certa in rul e) by in volong t he well-known powerful law of large numbers in probability.From t his in vestigation it is found t h at the sidelobe level is closely rel ated to the number of clement~, and to a mu ch lesser degree to the aperture dim ension.As a result extre mely hi gh resolution could be achi eved with ver y fe w "Ie ments.On the other hand , for a given number of elements hi gher aml hi gher resolu tion could be obtained by spreadin g these elem cnts over a larger and larger apert.urewhereas the sidelobe level wou ld r cm a in substanti ally th e same an d t he directive gai n constant.. Four sample arrays with 100 to 1000 elcm e nts llaye b ee n designed b y the Mon te Carlo meth od.Stat istical proper t ies of the computed p at tern s agrce almost cxact.lywith those predicted from the t h eory.Their sidelobe levels also agrce with the thcoretical valu es r cmar kably closel y.For practica l intcres t it is shown that an array can be actuall y design cd t o produce a bcamwidth of about 1 minu te of arc by using only 100 isotropic eleme nts ovcr an apertnre of 4X 103 wavelengths, the sidelobe level bein g -8.4 dB and the directi ve gain 20 dB o ver that of a single elcment, For thc sample array of 1000 elemen ts, the beamwirlt h is 0.5 minutes of arc wi th sidelobe level of -18 dB.It is also possiblc to r edu ce t his beamwidt h appreciably.