**1. Introduction**

The field of wireless communications has continued to expand. The authors in [1] noted that the expansion of wireless communication and GSM subscribers in recent times is astronomical. A key part of wireless communications technology is antenna. As the expansion of wireless communication technology continues globally, becoming a part of our day-to-day existence, problems brought about by such expansion require urgent and continuous attention. Experts and researchers have brought in a number of innovations, at least, to enable people freely enjoy the full benefit of ever-evolving wireless technology. Such innovations include the use of antenna arrays. By antenna arrays, I mean the connection of different antennas in such a way that the different antennas function as one lone antenna, enabling transmission only in the desired direction while suppressing it in any other direction.

The method of beamforming was also adopted in antenna arrays. Beamforming is a method in antenna arrays wherein a combination of antennas that forms an array is made to transmit signals towards a particular direction of interest instead of transmitting in all possible directions. In beamforming, the signal of each antenna that makes up the array will have its amplitude and phase adjusted so as to ensure that the transmitted signal is focused right onto the target beam. There are usually destructive and constructive effects associated with the combination of the different signals in beamforming arrays. Therefore, the radiation pattern does not have a single lobe but many of it, even different field strengths from different angles. So there exists the following: the main lobe which has the peak power, and it is the desired beam, the beam of interest; and the unwanted lobes that are smaller than the main lobes. The minor lobes do not radiate signals in the same direction as the main lobe but radiate in directions that are completely unnecessary. This is a very serious issue that requires attention so that the side lobe level could be reduced to the bearable minimum. The use of beamforming can be at both ends: at the receiving end and at the transmitting end. This is done primarily to obtain a spatial selectivity. When there is need for the detection and estimation of a particular signal of real interest, adaptive beamforming is used.

As mentioned, the arrangement of antennas to form arrays can be used for transmission or for reception. This means that instead of using a single antenna for transmission and a single antenna for reception, antenna arrays can be used for reception and transmission. Of course, the use of a single antenna for transmission or reception and an array antenna on the other side (either for reception or transmission) also exists. When multiple antennas are used at both the input (transmission) and output (reception), the technology is termed multiple input multiple out (MIMO) system. This arrangement is used to achieve better gain, more effective reliability in wireless communication [2], and for finding radio direction as pointed out in [3].

#### **1.1 Literature review**

The authors in [4] worked on optimizing planar and linear array antenna through the use of firefly algorithm. The authors described and reported three (3) case applications that show the effectiveness of firefly algorithm in achieving the anticipated optimization of array antenna, particularly planar array antenna. First, distribution of isoflux with linear array comprising of isotropic antennas that were not uniformly spaced had the radiation antenna synthesized. Then, radiators radiating equally in all directions and mounted on a nanosatellite that formed a planner array, though not uniformly spaced, was optimized. Lastly, the authors described an optimization process of a three by three planar array antenna used for the purpose of beam steering, having simultaneous level of side lobe. In [5] modeling of two annular ring array antennas, made up of elements radiating equally in all directions, was undertaken to generate isoflux radiation pattern to be used by satellites located in medium – earthorbit or geostationary-orbit. To minimize the level of the sidelobe and shape the beam, the authors made use of differential evolution (DE).

In [6] the study of circular antenna array design and the design of concentric circular array antennas made up of isotropic radiators for the reduction of the level of sidelobe optimally was undertaken. Firefly algorithm was relied upon in finding the optimum position and set of weights for the circular antenna arrays and for the concentric circular array antennas which can give a pattern of radiation with the level *The Issue of Sidelobe Level in Antenna Array: The Challenge and the Possible Solution DOI: http://dx.doi.org/10.5772/intechopen.106344*

of sidelobe really reduced. The authors noted that the firefly algorithm performed better than other optimization techniques like particle swamp optimization genetic algorithm (GA) etc.

A way of reducing poor convergence speed associated with firefly algorithm was investigated in [7]. The authors looked at minimization to a reasonable extent, of the sidelobe level without any serious consequence on the width of radiated beam. The results of the work were then compared to the result obtained using genetic algorithm. In [8] the authors carried out research to address the issue associated with synthesizing linear antenna array. Firefly algorithm was the optimization technique that the authors used in achieving their objective but with special emphasis on controlling the excitation of the amplitude of array element. A comparison of the firefly algorithm with Particle Swamp Optimization (PSO), Self Adaptive Differentials Evolution (SADE), and Tajuche Optimization method (TOM), with firefly algorithm showing better performance than others.

As can be seen in [9] a method which depended on evolutionary algorithm was used to synthesize rectangular antenna array pattern. Maximum excitation of antenna elements was noted by the authors. A total of thirty (30) isotropic antenna elements were considered, the spacing between successive elements was 0.5λ. Simulation results indicate that the peak sidelobe level was below 19 dB. In [10] a method of pattern synthesis that combined artificial bee colony and firefly algorithm was used to produce footprint patterns for a satellite based on rectangular planar array having antennas radiating equally in all directions. The authors carefully modified some key parameters like the phase, array elements state, and even the amplitude. The performance of generic algorithm, firefly algorithm, and artificial bee in getting the optimum solution to the wanted footprint patterns was also compared, with artificial bee colony and firefly algorithm seen to perform better than genetic algorithm.

Mandal et al. [11] presented a method or technique that uses differential algorithm (though of a single objective) to minimize a multi-objective fitness function. In the work, conflicting parameters were optimized. Such conflicting parameters were low maximum level of sideband radiation, low value associated with maximum level of sidelobe, and the main beams narrow beamwidth. The proposed method was then applied to a uniformly excited time-modulated linear antenna arrays and nonuniformly excited time-modulated linear antenna arrays in the synthesis of optimum pattern of low sidelobe at the frequency of operation. This was achieved by the suppression of the level of radiation in the side.

#### **1.2 Description of antenna array**

Antenna array is the arrangement of different antennas into a single one, designed to be used for a particular purpose. Antenna array comes in different shapes and sizes; hence, we have the linear antenna array, the rectangular, the planar and so forth. The size of antenna arrays is basically determined by the number of individual elements or antennas combined to form the array. Antenna array shape, distance between successive antenna elements, the amplitudes of excitation, and of course, element phase excitation are some of the factors on which array antenna factor depends. To have an optimized antenna array, [7] noted that the distance between the elements of the array has to be controlled. Controlling radiation pattern of antenna array is achieved by the amplitudes and phases of current excitation. Reduction of sidelobe and

suppressing interference can all be realized by a careful control of the key parameters as mentioned above.

Some experts classify antenna arrays into two, basing the classification on how the axis of the antenna relate to the radiation direction. Therefore, there are endfire array and broadside array. Endfire array is usually linear, having its radiation direction being the same as the line of the antennas. Normally, in endfire array, the phase difference by which the antennas are fed is equal to the distance between two adjacent antennas. However, the feeding of the antennas in broadside array is done in phase. This is to ensure that there is a perpendicular radiation of radio waves.

Of course, other types of antenna arrays exist, and they include, but not limited to:


Phased array is the category of antenna array that is designed with the capability of changing the shape and direction of radiated signal through electronic steering without having to move the antenna physically. The electronic steering is made possible by the difference (in phase) existing between the various signals coming from the antennas making up the array. Signals radiated by the antennas in phased array can either be in phase or out of phase. When they are in phase, the signals are added, resulting in additive signal amplitude. When the signals are however out of phase, the signals are seen to cancel out each other.

Phased array antenna has three basic types, namely, linear array which has the elements positioned on a straight line with only one phase shifter; Frequency scanning antenna array which does not have any phase shifter at all but the transmitters' frequency is used for beam steering; and the planar array which has the elements arranged in planar form, with each antenna having a phase shifter.

Despite great advantages and benefits of antenna array, there are obvious issues and challenges that need to be addressed to enable people enjoy the full benefit of wireless communications technology. In rectangular array, the issue lies with the level of side lobe which has to be reduced. There are also issues in array synthesis such as computational cost, especially as the size of the antenna increases. Experts have continued to search for possible solutions to the lingering problems associated with antenna arrays, using different methods and techniques.

The use of rectangular antenna array provides far better advantage than using single individual antenna elements in wireless communications. The advantage of using rectangular antenna array over the use of single antenna element in wireless *The Issue of Sidelobe Level in Antenna Array: The Challenge and the Possible Solution DOI: http://dx.doi.org/10.5772/intechopen.106344*

communications include the realization of low sidelobes, higher directivity of symmetrical patterns [12].

A rectangular antenna array can have M number of antenna elements in one direction and N number of antenna elements in the adjacent direction, giving rise to M by N rectangular array antenna elements (M x N).

The array factor computation for such M by N rectangular array takes into consideration the directions of the M elements and N elements, and it is given by [12].

$$AF = AF\_{M}AF\_{N} \tag{1}$$

Where AFM is the array factor in the M direction and AFN is the array factor in the N direction.

$$AF\_M = \sum\_{m=1}^{M} I\_{m1} \mathfrak{e}^{j(m-1)(kd\_M \text{Sin} \theta \text{Ca} \mathfrak{e} \mathfrak{z} + \text{ca}\_M)} \tag{2}$$

$$AF\_N = \sum\_{n=1}^{N} I\_{N1} \sigma^{j(N-1)(kd\_N \text{Sin}\theta \text{Ca}\otimes + \text{an}\_N)} \tag{3}$$

$$\text{K represents phase constant, and it is given by } k = \frac{2\pi}{\lambda} \tag{4}$$

*αM*= elements phase shift in the M direction. *αN*= element phase shift in the N direction.

*θ* = zenith angle.

∅ = azimutal angle.

*αN*= element progressive phase shift in N direction.

*αM*= element progressive phase shift in M direction.

If the rectangular array is symmetrical the computation of array factor is given by [3].

$$\mathbf{AF} = 4[\left| \sum\_{m=1}^{M} \sum\_{n=1}^{N/2} \text{Cost} \left( m - 0.5 \right) \left( k d\_m U + a\_m \right) \right| \text{Cost} \left( n - 0.5 \left( k d\_N \left( k d\_m V + a\_N \right) \right) a\_m \right) \tag{5}$$

In Eq. (6) above, v = sin ∅ sin *θ* while U = Cos ∅ Sin*θ:*

#### **1.3 Issues in antenna array**

Issues in antenna array include, but not limited to, the following:


**Figure 1.** *An antenna system model.*

One major issue in antenna array has to do with the synthesis of the array. When the specifications for antenna array design are provided, such as the structure of the required array, the number of required radiating elements, radiated pattern required and so forth, determining the exact excitation and the feeding network that gives such excitation and determining structure of the array that satisfy the requirements of the design, is a key problem. In [7] it was stated that algorithm for synthesizing array is more or less a minimization one.

Without considering beamforming network, antenna system can be conveniently represented as shown in **Figure 1** above. From **Figure 1**, p and a are the inputs which represent the required parameters with their electromagnetic and geometric properties respectively, b denotes output, which is the radiated field [7]. S denotes the operator, which is dependent on the frequency. It should be noted that while S is linear in a, it is non-linear in p. Based on **Figure 1**, b, p, and a denote the sharp constraint in the radiated field, in the parameter as well as excitation respectively; then the minimum of Eq. (6) needs to be found if the problem of antenna array has to be solved.

$$d^2 = \text{in} \mathfrak{f} \;/\left\langle \mathbf{y} \mathbf{-} \mathbf{y}\_c \right\rangle / 2 \tag{6}$$

$$\mathbf{Xn} = \beta\_0 e^{-rd^2i, i} \left(\mathbf{x}\_{\text{j}} \mathbf{x}\_i\right) + \mathbf{L} \left(\mathbf{rand}\right) \tag{7}$$

Note: L(rand) refers to the randomization based on levy flight, *xi* and *xj* represents the positions of i and j fireflies respectively.

$$L = 0.01 \left( \frac{d, \propto}{/d\_2 / /^{\bar{\theta}}} \right) \tag{8}$$

Where

$$\infty = \left(\frac{\Gamma(1+\beta)\sin\left(\frac{\beta\pi}{2}\right)}{\Gamma\left(\frac{\beta+1}{2}\right)\rho^2\left(\frac{\beta-1}{2}\right)}\right)^{\frac{1}{\beta}}\tag{9}$$

The coefficient of absorption, *Γ*, is used to determine speed of convergence.

### **1.4 The array**

To fully understand the challenge involved in antenna arrays, a quick look at Eq. (6) will prove helpful. Addressing problems of synthesis based on Eq. (6) has to do with finding a certain point where the set y is closest to yc. However, practically speaking, y and yc are non-convex, showing that there will be points of relative minimum and absolute minimum, and minimization algorithm is entangled in a local

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

minimum [13], thereby providing a wrong solution. The enlargement or trapping of the minimization algorithm is of key interest. Because as the size of antennas increase, number of secondary minima rises, and distinguishing between relative minimum and absolute minimum becomes rather difficult. Experts have therefore adopted algorithms for global minimization in order to solve the problem. In [13] it was emphasized that global optimization algorithms, practically stressing, do not provide any guarantee of realizing the optimum, especially with large problem size.

In any antenna array for improved performance, the challenge lies in getting an optimal set of spacing for the elements that satisfies the specification for the array, which of course must be based on how current is distributed with the elements of the antenna. When antenna array requires special radiation or when an off normal scanning is necessary, optimal thinning of antenna array gets highly difficult. Not to be forgotten is the fact that having array patterns optimized with respect to the location of the antenna element is non-linear as well as complex because the thinned array's array factor is not a linear function as far as element spacing is concerned.

There are also challenges like:


#### *1.4.1 Expansion of solution space*

The moment the size of the antenna is increased by increasing the number of antenna elements, solution space definitely expands to a large degree [14]. This implies, even from common sense, that searching exhaustively for solution is rather far more practical if the arrays are small.

#### *1.4.2 Complexity of landscape of solution space*

As mentioned, solution space increases as the antenna elements increase. And when this happens, there is every likelihood that the space for the landscape of solution will become more complex.

#### **1.5 Thinning of antenna array**

In array antenna, all the elements of the array are active. This makes the array performance to be degraded to some extent. However, some elements of the array can be made passive or be turned OFF. Hence, we have arrays that are fully populated, having all the elements active, and arrays that are partially populated, having some elements terminated to a well-matched load. The turning OFF of some elements of the array is termed thinning. Therefore, in thinned array, some elements are ON while some are OFF; in fully populated array all the elements are ON.

#### *1.5.1 Genetic algorithm-based thinned phase Array*

One major problem in phased array antenna is the level of side lobe which has to be reduced. Genetic algorithm is capable of optimizing the least level of the sidelobe. This is accomplished through the optimization of the OFF position and the ON position as regards the array antenna elements. As given in [15], the array factor for array antenna is:

$$AF = \sum\_{1}^{n} I\_n \, \mathcal{e}^{jn2\pi r(\cos\theta - \cos\mathcal{Q})} \tag{10}$$

Where n = number of elements and r = distance between elements. When using genetic algorithm for the optimization, Eq. (10) forms the cost function.
