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 triagular-rectangular-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 element-to-element separation of 0.76 wavelength.

This letter investigates sidelobe levels of a two-bit digital phased array composed of a small number of elements. Among several phase shifter designs applicable to phased arrays, a two-bit design needs the least number of circuit elements so that the development and manufacturing need the lowest cost. Now the following questions arise. Is a two-bit phased array practical? How low can its sidelobe level be reduced? To answer the questions, three methods are tried to reduce the sidelobe level of a uniformly-excited linear array of isotropic elements. The methods are the quadratic-phase feed method, the partially randomizing method of periodic phase errors, and the genetic algorithm (GA) approach. Among the methods, the quadratic-phase feed method provides the lowest sidelobe level around -12.5 dB - -13.2 dB in the steering angles from 0 to 48 degrees for a 21-element, half-wavelength spacing array, and -11.2 dB - -13.0 dB in the steering angles from 0 to 30 degrees for an 11-element, 0.6-wavelength spacing array. Although it depends on the system requirement, these values would be acceptable in some applications, hence a two-bit phased array designed properly may be practical in an actual system.

A trinary-phased array, in which a phase quantization unit of phase shifters is 120 degrees is examined. The phase quantization unit of 120 degrees is the roughest value in practical phased array applications. Despite its rough phase quantization, the sidelobe level of less than -9 dB is attained by a genetic algorithm approach.