Two-Dimensional Arrays Optimized for Wide-Scanning Phased Array Based on Potential Function Method

For phased and adaptive arrays of antennas, an optimal arrangement of antenna elements is essential to avoid grating lobes in the visible angular region of the array. Large sidelobes cause degradation in signal-to-noise ratio; grating lobes, in the worst case, cause malfunctions. One method of evaluating sidelobe level is square integration. For a given set element positions, evaluation by square integration of the sidelobes involves Fourier transform and numerical integration. For faster evaluation, we developed an equivalent transform algorithm that requires no numerical Fourier transform or integration. Using this new algorithm, we introduced a fast trial-and-error algorithm that iteratively applies random perturbation to the array, evaluates the function, and minimizes it. A number of separate runs of this algorithm have been conducted under the constraint of 3-fold rotational symmetry for stability. The optimal output, for which the function is minimized, is a uniformly spaced equilateral-triangular-type arrays that, unfortunately, has unwanted grating lobes. However the algorithm also yields variations trapped at local minima, some of which do not have grating lobes and whose sidelobe peaks are sufficiently low within a wide angular region. For the case N = 12, a characteristic triagularrectangular-type array often arises, which has not only better sidelobe properties as evaluated by square-integration and peak sidelobe, but also sufficient element-to-element clearance. For the case N = 36, one of the results achieves a peak-sidelobe level of −8 dB, with a minimum elementto-element separation of 0.76 wavelength. key words: two-dimensional array optimization, adaptive array, sidelobe reduction