A Fourier Phase Mode Approach for Chebyshev Pattern Synthesis in Circular Antenna Array

Abstract

Abstract-In this article, a novel phase mode analysis for a circular antenna array is discussed. This proposition experiments on the synthesis of Dolph-Chebyshev pattern for circular geometry employing directional element 1 + cos(φ). Here, for pattern synthesis a modified uniform sampling method is proposed, and for investigation of continuous current excitation in a circular array, a Fourier phasemode approach is proposed. The synthesis process permits generation of complex weights for each element to produce the Chebyshev pattern with a desired beamwidth or Side Lobe Level (SLL). The radius is a key factor for a circular geometry and also decides the pattern synthesis, which is determined by using the phase mode concept. Also, this article contributes to the formulation of a mathematical relationship between the number of phase modes (P ) and the number of antenna elements in the array (N ) such as N = 2(P − 1).

Synthesis of circular arrays with sidelobes of individually arbitrary levels

“…Many kinds of optimization techniques such as invasive weed, genetic algorithm, particle swarm have been presented to find the optimum positions of the antennas. Both amplitude and/or phase of the antennas may also be considered as the unknown parameters to synthesize the radiation pattern of circular arrays …”

“…For amplitude‐phase synthesis, some kinds of optimization methods such as genetic algorithm, particle swarm, and differential evolution have been used . In some works, a particular radiation pattern such as Chebyshev's pattern, that is, equal‐ripple, has been designed, for amplitude‐phase synthesis. Phase‐only synthesis is also possible for design of circular arrays .…”

“…Both amplitude and/or phase of the antennas may also be considered as the unknown parameters to synthesize the radiation pattern of circular arrays. [8][9][10][11] For amplitude-phase synthesis, some kinds of optimization methods such as genetic algorithm, particle swarm, and differential evolution have been used. 8 In some works, a particular radiation pattern such as Chebyshev's pattern, that is, equal-ripple, has been designed, [9][10][11] for amplitude-phase synthesis.…”