4. Conclusions

mentioned earlier, many elements have moved by more than a wavelength, and many of the new locations are overlapped with the formerly adjacent ones. The overlapping may be exploited in the array thinning, while the elements that are located closer than a half wavelength may result in a high mutual coupling. This mutual coupling could completely deteriorate the nulling capability of such arrays. Table 1 shows the optimized values of the element locations compared to those of

Figure 18(left) shows the variation of the cost function, i.e., output power at the

The Methods

nonuniform spaced array. It can be seen that it takes more than 140 iterations to reach the required depth of 40 dB. Figure 18(right) shows the instantaneous

Element # Original uniformly spaced array Fully nonuniform spaced array

desired nulls, with respect to the iteration number in the optimized fully

 0.25 0.2500 0.75 0.7087 1.25 1.0444 1.75 1.3522 2.25 1.9881 2.75 2.3441 3.25 2.8279 3.75 3.1272 4.25 3.5675 4.75 4.0763 5.25 4.5535 5.75 4.8767 6.25 5.7395 6.75 6.5707 7.25 7.2500

Convergence speed of the optimizer (left) and the Instantaneous element positions (right).

the uniformly spaced array.

Array Pattern Optimization

The bold values represent the optimized values.

Element locations (in wavelength).

Table 1.

Figure 18.

26

It is shown that the required sidelobe nulling can be accomplished either electronically by controlling the amplitude and/or phase of the excitations of the array elements or mechanically by controlling the positions of all or a small number of the array elements. Each approach has its own advantages and disadvantages. The electronic null steering methods are easy to implement, however, they are associated with some practical problems such as quantization errors which may cause a significant deviation in the desired null directions and finally leads to noticeable performance degradation. On the other hand, the mechanical null steering methods does not need digital attenuator and/or digital phase shifters, thus, they are free from any quantization errors. Instead, each array element in the mechanical null steering methods needs a servo-motor to make the element moveable. If all or most of the array elements are required to be movable, then a considerable extra time is needed for mechanical movement of the elements. This represents a real challenging issue in the practice.

To solve these aforementioned problems that were associated with both electronic and mechanical methods of sidelobe nulling, it is proposed to control only some selected elements rather than controlling all of the array elements that were required for array pattern reconfiguration. The number of the array elements, the operating frequency, and the accuracy at which the desired pattern is needed influence the final choice between the two approaches of electronic and mechanical sidelobe nulling.
