use of truncated perturbation values are almost the same. The results show that the designed perturbed pattern that makes use of both techniques is insensitive to the small variations of the designed perturbations. The corresponding X X Ž . truncated perturbation values ␦ and ⌬ for Figure 4 b are n n
listed in Table .
The triple nulls imposed case with the same conditions as in Figure is shown in Figure , with corresponding perturbation values with and without truncation, as given in Table and 2, respectively. Comparisons between phase and position perturbations give results similar to those of Figure . Note that the maximum perturbation values become generally larger for both techniques as the number of imposed nulls increases. This is because as the number of imposed nulls increases, a larger degree of freedom for the design is required because the perturbation values are increased accordingly. The quality of the designs demonstrated above is verified by executing the search algorithm several times. Results with performances very similar to those presented herein are always obtained.
CONCLUSION
Both phase and position perturbations that make use of the genetic algorithm have been successfully applied to the problem of pattern nulling for linear antenna arrays. It has been demonstrated that both techniques can steer the array nulls to the prescribed interference directions and minimize the perturbations simultaneously. In addition, the perturbed patterns designed are found to be less sensitive to small variations in the perturbations. Numerical results for a 20-element linear antenna array with single and triple imposed nulls demonstrated, respectively, show the effectiveness of the nulling techniques.