On the Use of the $Z$ Transform of LTI Systems for the Synthesis of Steered Beams and Nulls in the Radiation Pattern of Leaky-Wave Antenna Arrays

Abstract

This paper addresses the use of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> transform to synthesize radiation patterns with prescribed nulls from a phased array of electronically reconfigurable leaky-wave antennas (LWAs). This approach provides the relationship between such antennas and linear and time invariant (LTI) systems. Using this signal processing perspective, the proper locations of the poles and zeros of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Z$</tex-math></inline-formula> transform of the associated LTI system provide a radiation pattern with prescribed specifications (mainly main lobes’ directions and surrounding radiation nulls). Then, these poles and zeros’ positions can be transformed into particular values of the LWA array control coefficients. The effectiveness of the proposed technique is demonstrated with the synthesis of various radiation patterns, with application to reconfigurable smart antennas. A comparison with more conventional uniform linear array architecture is also performed to evaluate the synthesis flexibility and system complexity of the proposed approach.