Application of the Spiral Optimization Technique to Antenna Array Design

Motivation

Antenna array systems communicate directionally by forming patterns with the main beam in the direction of the desired user (Recioui and Azrar, 2007). When the antenna array directs its main lobe with enhanced gain in the direction of the user, it naturally forms side lobes and nulls or areas of medium and minimal gain respectively in directions away from the main lobe. Hence the level of the sidelobes needs to be as minimum as possible for the sake of interference reduction (Recioui and Azrar, 2007; Recioui et al., 2008).

Pattern synthesis techniques are, in general, based on the variations of the array parameters such as the element excitations (amplitude and/or phase) and positions of array elements. The characteristics of the desired pattern can vary depending on the required application. Some synthesis methods are concerned with reducing the Sidelobe Level (SLL) while preserving the gain of the main beam (Elliot, 2003). Others deal with null control to eliminate the effects of interference and jamming. Other methods of controlling the array pattern use non-uniform excitation and phased arrays (Steyskal et al, 1986).

The method of controlling both amplitude and phase is the most effective since it has larger solution alternatives (Steyskal et al., 1986). However, it is also the most expensive considering the cost of the controllers used for phase shifters and variable attenuators. Moreover, when the number of elements in the array increases, the computational time to find the values of element amplitudes and phases will also increase. The amplitude-only control (Bevelacqua and Balanis, 2007; Monorchio et al., 2007) uses a set of variable attenuators to adjust the element amplitudes.

The problem of the phase-only and position-only nulling is generally nonlinear, and it cannot be solved by analytical methods without any approximation. In order to steer the nulls symmetrically with respect to the main beam, the methods based on nonlinear optimization techniques have been proposed (Shore, 1984; Haupt, 1997). However, the resultant patterns of these methods have considerable pattern distortion because the phase perturbations used are large. Phase-only null synthesizing (Shore, 1984; Haupt, 1997; Liao and Chu, 1997; Akdagli and Guney, 2004) is less complicated and attractive for the phased arrays since the required controls are available at no extra cost, but it still has common problems.

The element position control with the use of a mechanical driving system, such as servomotors, is an alternative way to create nulls in the radiation pattern (Haupt, 1997; Abu-Al-Nadi et al., 2006; Akdagli et al., 2002). In this case, the amplitudes and phases can be solely used for the pattern synthesis with the desired sidelobe level and main beam characteristics.

The Schelkunoff array polynomial method (Schelkunoff, 1943) has been used to synthesize the equispaced linear array pattern. In this method, the pattern synthesis problem is reduced to the determination of proper roots of the array polynomial for a desired pattern. From this the element excitations are determined. The works reported in literature considered large arrays based on various optimization techniques together with the Schelkunoff unit circle representation of the array polynomial for uniform linear array. A genetic algorithm has been used for the pattern synthesis by (Monorchio et. al., 2007). Optimized low sidelobe levels have been presented by (Yu et. al., 2004). The optimization has been performed for different beamwidth values and the tradeoff between the sidelobe level and the main beam examined. Another genetic algorithm based optimizer has been proposed by (Recioui et al., 2008) and the results have been compared with other techniques.