2. Electronic null steering methods

This technique involves the modification of amplitude and/or phase excitations of an N-element array. The amplitude and/or phase excitations of these array

Sidelobe Nulling by Optimizing Selected Elements in the Linear and Planar Arrays DOI: http://dx.doi.org/10.5772/intechopen.84507

elements should be specifically selected through an appropriate control system that is connected to each of the array elements. Clearly, for such electronic null steering strategy and for N elements linear array, we need N variable attenuators and N variable phase shifters for the feeding network. This results in a very complex feeding network especially for a large number of elements which, of course, becomes expensive and may be impractical. Therefore, a less costly and simpler system for reducing the effect of interfering signals is needed. In this section, a simple technique for sidelobe nulling over a wide angular region in the linear arrays is introduced, where only the electronic excitations of the two side elements of the array were needed to be controllable while maintaining the same performance of interference suppression. Thus, the feeding network of the proposed linear array contains, in most designs, only two phase shifters and one attenuator.

#### 2.1 Linear array

pattern of such antenna arrays can be reconfigured to have maximum directive gain in the direction of its main beam and low sidelobes or deep nulls toward other

In the literature, several strategies have been described to reshape the array radiation pattern. Among them, electronic phased arrays or more specifically beam forming has received considerable attention [1–3]. However, most of the adaptive algorithms that were used in such type of antennas are time-consuming because they involve a large number of iterations and they are not able to provide global optimum solutions. Reconfiguration of the array pattern with prescribed sidelobe

approaches. The proposed approaches were genetic algorithm [4, 5], particle swarm optimization [6, 7], simulated annealing [8, 9], ant colony optimization [10], differential evolution algorithm [11], firefly algorithm [12], and some other methods [13], where the amplitude and/or phase of the elements excitations are the optimi-

Apart from the aforementioned approaches, new directions in antenna array pattern reconfiguration have been proposed based on either adding a small number of extra elements on each side of the linear array [14–16], or by reusing the side (or end) elements of the linear arrays [17] or planar arrays [18, 19]. In these papers, the calculations that were required to find the values of the amplitude and phase excitations of the side elements basically relied on simple mathematical formulations and none of the optimization algorithms were used. Thus, the solutions were not optimum and there was a necessary need to search for an optimum solution for such an important scenario. Therefore, instead of a simple analytical method that was presented in [17], a more powerful method based on the genetic algorithm was proposed to find the optimal values of the amplitude and phase excitations for those electronically controllable edge elements with less computational time [20]. The method presented in [20] is further extended to obtain multiple wide nulls by properly selecting and optimizing the most effective elements in the array [21]. Wide nulls were also obtained by turning off some selected elements in the uniformly spaced linear arrays by means of binary genetic algorithm [22]. In all of those pervious works, the null steering was performed electronically by controlling

On the other hand, the mechanical null steering methods that are based on the controlling of the separation distance between the array elements were considered as an alternative and competitive solution to the electronic counterpart [23–25]. In [26], the author proved that the mechanical null steering made better patterns when compared with the electronic counterpart [20], by mechanically controlling the positions of the extreme elements while leaving all the electronic excitations

The chapter is organized as follows: Section 2 provides a theoretical overview about electronic null steering including fully and partially controlled array elements. It also contains the sensitivity analysis of the generated nulls as well as how much the nulling is robust with respect to variations in the reconfigured amplitude and phase excitations. Section 3 provides a theoretical overview of a mechanical null steering including fully nonuniform spaced arrays and the proposed solution. It also

This technique involves the modification of amplitude and/or phase excitations

explains the implementation strategies of the aforementioned technologies.

of an N-element array. The amplitude and/or phase excitations of these array

structure mask can be also achieved by means of the global optimization

the amplitude and phase excitations of the array elements.

including the edge elements constant.

2. Electronic null steering methods

8

unwanted directions.

Array Pattern Optimization

zation parameters.

Consider a linear array of N isotropic elements which are mechanically fixed by selecting the separation distance between the array elements to be uniform at a constant value d. These elements are symmetrically disposed with respect to the origin along the x-axis and suppose that a harmonic plane wave with wavelength λ is incident from direction θ and propagates across the array. The I signal outputs from the array elements are weighted by the amplitude excitation coefficients An and phase excitation coefficients Pn then summed to give the linear array output. The sidelobe nulling was achieved by properly adjusting the values of the attenuators and phase shifters that are connected to each element.

#### 2.1.1 Single null

This subsection presents an efficient method for controlling the amplitude and phase excitations of the end elements by means of global optimization algorithms such as genetic algorithm or particle swarm optimization to generate a sector sidelobe nulling in the linear arrays without any reduction in the array gain [20]. To maintain the gain of the designed array and also to increase the convergence rate of the used optimization algorithms, some constraints on the searching spaces are included.

### 2.1.2 The electronic single null steering method

The structure of the electronically null steering array, with controlled amplitudes A1 and AN as well as controlled phases P1 and PN for the first and the last elements in a linear array is shown in Figure 1 [20]. The amplitudes and phases of the edge-element excitations can be considered as either symmetric or asymmetric excitation. Note that the proposed array under the asymmetric excitation will have 4 degrees of freedom, while for the symmetric case it will have only 2 degrees of freedom. These numbers are also true when considering the optimization parameters. The far-field pattern of the electronically null steering array with controlled amplitude and phase excitations, assuming even number of elements, can be written as [20]:

$$\mathbf{AF(u)} = \underbrace{\sum\_{n=2}^{N/2} \cos\left(n - \frac{1}{2}\right)}\_{\text{N-2 uniform array}} + \underbrace{A\_1 \mathbf{e}^{j\left(\frac{N-1}{2}\right)\Psi + P\_1} + A\_N \mathbf{e}^{-j\left(\frac{N-1}{2}\right)\Psi + P\_N}}\_{\text{Edge elements alone}} \tag{1}$$

where ψ ¼ ð Þ 2πd=λ u þ β. Here, u ¼ sin ð Þθ , and θ is the observation angle from the array normal, d is the element spacing which is selected to be fixed at d ¼ λ=2 for all array elements, and β is the phase shift required to steer the angle of the main beam. Knowing the direction of the interfering signals, ui, i ¼ 1, 2, …I (where I is the total number of interfering signals), and substituting for AF uð Þ¼<sup>i</sup> 0 according to the interference suppression condition, the nulls directions ui can be computed from (1). elements are controlled including the two edge elements) is considered. In this example, the total number of array elements are chosen to be N = 30 elements, the amplitude excitation of the original array elements is chosen to be uniform and the phase excitation is set to zero. In this scenario, the genetic algorithm is used to optimize the amplitude excitations of all array elements while the phase excitations are left unchanged. The required sidelobe level was set at 40 dB. Figure 2 shows the optimized array pattern along with the original uniform array pattern. It can be seen that the required sidelobe level is accurately achieved while the HPBW and FNBW have increased. The amplitude excitations of all array elements are greatly changed except a small number of the central elements. Moreover, the optimizer

Sidelobe Nulling by Optimizing Selected Elements in the Linear and Planar Arrays

For a fully controlled array, the number of degrees of freedom is quite enough to reduce the sidelobe level and at the same time to place the desired nulls, as shown in Figure 3. Here, as in the previous case, the required sidelobe level is chosen to be

needs at least 250 iterations to converge.

DOI: http://dx.doi.org/10.5772/intechopen.84507

Results for fully electronic null steering method for N = 30 and SLL = 40 dB.

Results for fully electronic null steering method with amplitude only control for N = 30, SLL = 40 dB, and a

Figure 2.

Figure 3.

11

single wide null.

For asymmetric array, note that the above equation cannot be solved analytically using the method introduced in [17] since it is a function of four unknown parameters, i.e., A1, AN, P1, and PN. On the other hand, the optimal values of these four parameters, subject to some constraints, can be easily found using any global optimization algorithm such as genetic algorithm or particle swarm optimization (PSO), as can be seen in the following subsection [20]. As mentioned earlier, the main constraints that are applied during the optimization process are the depth of the generated nulls and the main beam shape preservation. Moreover, some constraints on the optimization parameters are also considered, where the minimum and maximum values of the optimized amplitudes A1 and AN are set to 0 and 1, respectively, and for optimized phases P1 and PN are set to �π=2andπ=2, respectively [20]. To show the effectiveness of the proposed method, it is applied to uniformly excited linear arrays as well as some nonuniformly excited linear arrays such as Dolph and Tayler arrays as can be seen in the following subsection [20].

## 2.1.3 The results

In order to show the advantages of the proposed array with controlled two edge elements, first the fully controlled array (i.e., the amplitude excitation of all array

Figure 1. Block diagram of the single wide null method [20].
