3.3.1 Same element number array with array orientation diversity

In this section, we analyzed the influence of the array orientation diversity on the beampattern synthesis by simulation results. We initialize four virtual ULAs (named Array 1, Array 2, Array 3, Array 4, with orientation �10<sup>∘</sup> , 0<sup>∘</sup> , 10<sup>∘</sup> , 20<sup>∘</sup> , respectively) with each subarray aperture of 25λ owning a uniform interspacing λ=8. Besides, we initialize <sup>Q</sup> as a unit matrix and choose <sup>δ</sup> <sup>¼</sup> <sup>10</sup>�<sup>4</sup> and <sup>p</sup> <sup>¼</sup> 2 in our simulations. Figure 4 shows a 19-element beampattern synthesis performance in four cases with one-, two-, three-, and four-array orientations. From Figure 4, we can see that our proposed method and BCS algorithm can improve performance with increasing array orientation diversity (from 1 to 4); the optimal antenna positions and the corresponding excitation amplitudes of the four cases are displayed in Figures 5–8, respectively. Note that for the four cases of Figures 5–8, the required normalized radiated energies of BCS approach [17] are correspondingly bigger than that of our proposed method.

Figure 6.

Figure 4.

Figure 5.

44

4 array orientation.

Advances in Array Optimization

A 19-element array performance obtained by BCS inversion algorithm [17] and our method with increasing array orientation diversity. (a) 1 array orientation, (b) 2 array orientations, (c) 3 array orientations, and (d)

Element positions and excitation amplitudes in a 19-element one-array orientation.

Element positions and excitation amplitudes in a 19-element two-array orientation.

Figure 7. Element positions and excitation amplitudes in a 19-element three-array orientation.

3.3.2 Approximate beampattern performance with array orientation diversity

DOI: http://dx.doi.org/10.5772/intechopen.88881

that our proposed method needs less radiation energy for all four cases.

Element positions and excitation amplitudes in an 18-element one-array orientation antenna.

Element positions and excitation amplitudes in an 11-element two-array orientation antenna.

Figure 10.

Figure 11.

47

To demonstrate another advantage of array orientation diversity, we examine the beampattern synthesis of an 18-element array, 11-element array, 10-element array, and 10-element array correspondingly with one orientation, two orientations, three orientations, and four orientations using BCS algorithm and our method, respectively. The optimal beampatterns exhibit maximal sidelobes of 7.72, 8.01, 7.59, and 7.88 dB, respectively, which are shown in Figure 9. Figures 10–13 provide all the corresponding antenna positions and excitation amplitudes for all the four cases mentioned above. Obviously, given the array size, using orientation diversity can economize seven (or eight) elements without reducing the array performance. But more diversity is not always better enough, as shown in Figures 11–13. Besides, the excitation amplitudes in Figures 10–13 show

Convex Optimization and Array Orientation Diversity-Based Sparse Array Beampattern Synthesis

Figure 8. Element positions and excitation amplitudes in a 19-element four-array orientation antenna.

#### Figure 9.

Optimal beampattern of different element number array by using "BCS inversion algorithm [17]" vs. "our method." (a) 1 array orientation, (b) 2 array orientations, (c) 3 array orientations, and (d) 4 array orientations.

Convex Optimization and Array Orientation Diversity-Based Sparse Array Beampattern Synthesis DOI: http://dx.doi.org/10.5772/intechopen.88881
