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Furthermore, in MIFT, based on the idea of gradual thinning which is inspired by perturbation theory, an adaptively changed fill factor f is introduced into above procedures so that in each iteration cycle of one arbitrary trial, the element excitations are gradually truncated, which makes the most useful element excitations that contribute to the sidelobe level retained, and thereby we expect to find the optimum solution through only a small number of trials.
Comparing the two methods, it could be seen that MIFT has the same steps as IFT from step 2) to step 6) [33,34].
The first aspect is that unlike the equal 0/1 probability for all the initial element distributions in IFT, the initial element distributions are set equal to one with probability of 0.9 and to zero with probability of 0.1 in MIFT. It means that the array is approaching full.
The advantage of MIFT could be explained by perturbation theory.
Accordingly, in the first step of MIFT, a near-filled initial array would be enjoyed because it has higher directivity than the sparse-filled array (If the array is filled, the obtained results in all trials would be identical).
Therefore, both IFT and MIFT need several independent trials among which the optimum solution is selected.
We first considered demonstrating the difference between IFT and MIFT. Suppose a 200-element thinned array with the object fill factor [f.sub.0] = 50%.
Figures 1(a) and (b) respectively depict the normalized far field patterns produced by IFT and MIFT. The maximum sidelobe level (MSLL) obtained by MIFT is -19.01 dB, 1.96dB lower than that obtained by IFT.
Then, to further demonstrate the effectiveness of MIFT, we consider applying MIFT to various linear arrays for the purpose of getting lower SLL as well as an appropriate beamwidth.
It can be seen that the result yielded by MIFT has obviously high percentage of element distributions with low MSLL than the result produced by IFT.
Therefore, in MIFT, the bad solutions are massively excluded so that only a small number of trials, corresponding to a small number of iterations, is needed to reach the optimum solution.
In the second test case, MIFT is applied to the same antenna array but with the object fill factor [f.sub.0] of 66%, RPSL -24.55 dB.