**2. Solution to antenna array problems**

Side lobe level, which is one of the key parameters to be minimized for effective performance of the antenna arrays, can actually be optimized or reduced in such a way that the system performance will not be adversely affected. Here, the use of enhanced firefly algorithm is considered.

#### **2.1 Side lobe level (SLL) optimization using enhanced firefly algorithm**

Though the use of enhanced firefly algorithm for effective reduction of side lobe level in antenna array will be presented here, it is however necessary to briefly describe firefly algorithm and state the reason for the choice of enhanced firefly algorithm instead of firefly algorithm itself.

#### *2.1.1 Firefly algorithm*

Humans have learnt so much from the natural world and they have applied such lessons in addressing some problems that face us. The behavior of some living things have been studied extensively and key aspect of their life mimicked by humans. One of such living things is the firefly, an insect that emits light, especially at twilight, to get the attention of other fireflies for matting. It uses that method to prey on other fireflies.

Experts mimic the way firefly flashes light to attract other fireflies to solve problems that are not linear, among others. Hence, there is firefly algorithm (FA) which rely on certain assumptions like: attraction between fireflies is independent of their sex: brightness of firefly is determined by objective function (OF) for such firefly algorithm, the most important things being the light intensity denoted by I and the attractiveness denoted by *β:* The extent of a firefly's brightness will determine how attractive it will be. The following equation gives the light intensity.

$$\mathbf{I}\_{\ } = l\_{\boldsymbol{\theta}} \mathbf{e}^{-\operatorname{yd}^2} \tag{11}$$

Where *lo* is the initial light intensity, y is coefficient of absorption of light while d is the distance between two given fireflies. Similarly, the attraction is given by:

$$
\beta = \beta\_o e^{-\gamma d^2} \tag{12}
$$

## *The Issue of Sidelobe Level in Antenna Array: The Challenge and the Possible Solution DOI: http://dx.doi.org/10.5772/intechopen.106344*

Where *β<sup>o</sup>* is the attractiveness when d = 0. One major drawback of firefly algorithm is that it takes longer to attain global optimization if the array is bulky. To address this drawback, the firefly algorithm is improved, giving rise to improved or enhanced firefly algorithm (EFA).

### *2.1.2 Enhanced firefly algorithm*

Enhanced firefly algorithm is adopted to address the problem of slow convergence, thereby overcoming the challenge of optimizing sidelobe level without serious consequence on the beam width.

A careful implementation of the flowchart for firefly algorithm can bring about real result in terms of reduction of sidelobe levels. Equations (11 and 12) are very important in the application of enhanced firefly algorithm (**Figure 2**).

#### **2.2 Solution to thinning problem in antenna array**

Addressing thinning issues also solves the problem of cost and power consumption, as these issues come about because of the bulky nature of some antenna arrays. One method that can be used to address the thinning problem associated with antenna array is the genetic algorithm. Compared to some frequently used techniques or methods, genetic algorithm offers great advantages owing to its robustness nature. Key advantages of genetic algorithm include the following:


One version of genetic algorithm that can be applied to solving antenna array thinning problems is the simple genetic algorithm (SGA) version. As the name implies, application of this version of genetic algorithm is actually simple. The steps, in the proper order, are as listed below:


*Antenna Arrays - Applications to Modern Wireless and Space-Born Systems*

#### **Figure 2.**

*Flowchart of enhanced firefly algorithm.*


*The Issue of Sidelobe Level in Antenna Array: The Challenge and the Possible Solution DOI: http://dx.doi.org/10.5772/intechopen.106344*


#### **2.3 Presentation of results and discusion**

This part of the research deals with the results of the work carried out, and the discussion is based on the result. Figures are presented and discussed accordingly.

As can be verified from **Figure 3**, side lobe level is smaller for the optimized thinned array when compared with the level of the sidelobe for a fully populated array. This shows that when optimizing sidelobe level for antenna array using the method of thinning, genetic algorithm can be used for such optimization. The plot shows that for a fully populated array at an angle of 90°, the sidelobe level was 12.967 dB while for the thinned array optimized with genetic algorithm for the same angle of 90°, the level of sidelobe reduced to 16.857 dB.

As **Figure 4** shows, in thinned array optimized with genetic algorithm, the halfpower beamwidth is higher compared to the level for fully populated array. While the half power beamwidth for thinned array optimized with genetic algorithm was 60° from **Figure 4**, for fully populated array the half power beamwidth was about 54.5°. This is an indication that when all the elements of an antenna array are ON, the gain is not the same as when some elements of the array are OFF. Thinning, therefore, is a key way of overcoming some challenges in antenna array, especially if thinning is optimized with genetic algorithm.

In **Figure 5**, the radiation pattern for antenna array of ten elements separated 0.5λ apart, having sidelobe level optimized using genetic algorithm is compared with the radiation pattern for antenna array of ten elements separated 0.5λ apart, having sidelobe level optimized using enhanced firefly algorithm. The plot shows that using enhanced firefly for sidelobe level optimization in antenna array is better than using the popular genetic algorithm. This is because optimizing using enhanced firefly has lower sidelobe level compared to optimizing using genetic algorithm.

#### **Figure 3.**

*A plot of SLL(dB) variation against tilt angle (deg.) for fully populated Array and optimized thinned Array using genetic algorithm.*

#### **Figure 4.**

*A plot of half-power beam width (deg.) variation against tilt angle (deg.) for fully populated Array and optimized thinned Array using genetic algorithm.*

**Figure 5.**

*An Array radiation pattern of ten elements spaced 0.5λ optimized with EFA.*

Presented in **Figure 6** is the radiation pattern for antenna array of ten elements separated 0.5λ apart, with normalized power plotted against radiation angle in degree. On one hand, the sidelobe level is optimized using genetic algorithm and on the other hand, the sidelobe level is optimized using enhanced firefly. The result of the optimizations using genetic algorithm and enhanced firefly algorithm are compared. Again, the plot reveals that using enhanced firefly for sidelobe level optimization in antenna array is better than using genetic algorithm. The reason for this inference is because

*The Issue of Sidelobe Level in Antenna Array: The Challenge and the Possible Solution DOI: http://dx.doi.org/10.5772/intechopen.106344*

**Figure 6.** *A plot of normalized power (dB) against angle (deg) for 10 elements optimized with EFA.*

optimization of sidelobe level using enhanced firefly has lower side lobe level compared to optimization using genetic algorithm.
