# NON UNIFORM ARRAY ANTENNA WITH THREE LUNEBURG LENSES

### Abstract

A fundamental part of the work of any communication device, such as radio, television, mobile phone, etc., is the signal filtration. Filtration is the process of separation of the signals that carry the needed information, from other signals, noise, etc. This is necessary for the proper operation of the communication device. The filters synthesis is a mathematical problem for an approximation of the ideal filter response. This is an ideal function, comprising rectangular shape. The ideal function cannot be realized because it contradicts the basic physical principles. For this reason, it is replaced by another, which can be realized by the existing technical devices. In many filter syntheses problems, the approximating function is polynomial. The goal is to define a low degree polynomial that approximates the ideal function with high precision (minimal error). A new mathematical method in the approximation theory is named „compressed cosines “. The method is applicable in the communication technologies. The method uses Remez’ exchange algorithm, which has fast convergence and low computational complexity. As a result, an optimal third degree trigonometric polynomial is defined. The proposed polynomial meets the requirements of the approximation theory: approximation of the ideal filter function with high precision (minimal error). The described properties are proved by comparison with Chebyshev polynomials. In the approximation theory such polynomial of 4-th degree (practically 3-th degree) with better approximating properties is not known. The proposed polynomial is successfully applied for digital FIR filters and antenna arrays design. This article is an extension of research on the method of compressed cosines in array antennas synthesis. Theory and technical solution for the synthesis of non-uniformly spaced linear array with three Luneburg lenses are proposed. The applied theory allows synthesis of broadband array with high selectivity and without side-lobe array factor. Such an antenna system has no analogues. The array antenna is suitable for radio astronomy and radio location.

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*Knowledge International Journal*,

*19*(4), 1665 - 1671. Retrieved from https://ikm.mk/ojs/index.php/KIJ/article/view/3667