The Issue of Sidelobe Level in Antenna Array: The Challenge and the Possible Solution

Abstract

This work looked at the issue of sidelobe level associated with antenna array and the challenge, providing a way that the issue and challenge can be overcome. Different authors have used different techniques in trying to find solutions to the problems in antenna array. This research work considered enhanced firefly algorithm and genetic algorithm as techniques or methods in addressing the issues in antenna array, such as side lobe level reduction. The work has shown that enhanced firefly algorithm (EFA) performs better than genetic algorithm (GA) in optimizing side lobe level of antenna array without any serious effect on the beam width. The best side lobe level obtained while using enhanced firefly was (−32.5 dB) compared to the value of (−20.0 dB) obtained with genetic algorithm. It was also found that tilting beam towards the direction of end fire, genetic algorithm optimization technique can be used to reasonably reduce the level of side lobe in array antennas. It was also found from this research work that reducing the number of active elements in an antenna array by way of turning OFF some elements can be used to improve performance of the array.

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 – earth-orbit 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 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 non-uniformly 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:

• Parasitic arrays

• Turnstile array

• Yagi-Uda array

• Parasitic array

• Collinear array

• Rectangular array

• Phased array

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 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].

$$\mathit{AF}={\mathit{AF}}_M{\mathit{AF}}_N$$E1

Where AF_M is the array factor in the M direction and AF_N is the array factor in the N direction.

$${\mathit{AF}}_M=\sum _{m=1}^M{I}_{m1}{e}^{j\left(m-1\right)\left(k{d}_M\mathit{\text{SinθCos}}\varnothing +{\alpha }_M\right)}$$E2

$${\mathit{AF}}_N=\sum _{n=1}^N{I}_{N1}{e}^{j\left(N-1\right)\left(k{d}_N\mathit{\text{SinθCos}}\varnothing +{\alpha }_N\right)}$$E3

$$\text{K represents phase constant, and it is given by}k=\frac{2\pi }{\lambda }$$E4

${\alpha }_M$= elements phase shift in the M direction.

${\alpha }_N$= element phase shift in the N direction.

$\theta$ = zenith angle.

$\varnothing$ = azimutal angle.

${\alpha }_N$= element progressive phase shift in N direction.

${\alpha }_M$= element progressive phase shift in M direction.

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

$$\text{AF=4}\left[\left[\sum _{m=1}^M\sum _{n=1}^{N/2}\mathit{Cos}\left(m-0.5\right)\left(k{d}_{m}U+{\alpha }_m\right)\right)\mathit{Cos}\left(n-0.5\left(k{d}_N\left(k{d}_{m}V+{\alpha }_N\right)\right){\alpha }_m\right)\right)$$E5

In Eq. (6) above, v = sin $\varnothing sin\theta$ while U = Cos $\varnothing$ Sin$\theta .$

1.3 Issues in antenna array

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

• High level of side lobe

• Array synthesis problems

• Thinning issues

• Cost, power consumption etc.

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.

Figure 1.

An antenna system model.

$$d^2=\mathit{inf}//\mathrm{y}–y_c//2$$E6

$$\mathrm{Xn}={\beta }_0{e}^{-r{d}^{2}i,i}\left(x_j–x_i\right)+\mathrm{L}\left(rand\right)$$E7

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

$$L=0.01\left(\frac{d,\propto }{/d_2/{/}^{\frac{1}{\beta }}}\right)$$E8

Where

$$\propto ={\left(\frac{\mathrm{\Gamma }\left(1+\beta \right)\mathit{sin}\left(\frac{\mathit{\beta \pi }}{2}\right)}{\mathrm{\Gamma }\left(\frac{\beta +1}{2}\right){\beta }^2\left(\frac{\beta -1}{2}\right)}\right)}^{\frac{1}{\beta }}$$E9

The coefficient of absorption, $\Gamma ,$ 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 y_c. However, practically speaking, y and y_c are non-convex, showing that there will be points of relative minimum and absolute minimum, and minimization algorithm is entangled in a local 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:

• Expansion of solution space

• Complexity of landscape of solution space

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:

$$\mathit{AF}=\sum _1^n{I}_n.e^{\mathit{jn}2\mathit{\pi r}\left(\mathit{\text{cosθ}}-\mathit{cos}\varnothing \right)}$$E10

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

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 $\beta .$ The extent of a firefly’s brightness will determine how attractive it will be. The following equation gives the light intensity.

$$\text{I =}{l}_o{e}^{-y{d}^2}$$E11

Where $l_o$ 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:

$$\beta ={\beta }_o{e}^{-y{d}^2}$$E12

Where ${\beta }_o$ 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).

Figure 2.

Flowchart of enhanced firefly algorithm.

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:

• It performs well even with large variable numbers

• It does not need information of any kind on derivative

• The search from a spacious sampling involving the cost surface is done simultaneously

• It is very capable of working with experimental or generated data

• It does not provide a single solution but a group of optimum parameters

• Its optimization can be done with discreet or continuous parameters

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:

• Coding of the parameters right onto the genes. This coding simply means a move from one space to another space such as from the parameter space to the one of the chromosomes. This coding also provides the transformation of the coded parameters to a string length of coded genes.

• Creation of initial population. This initial population is taken randomly, and it forms the chromosomes’ starting matrix with its matrix elements which can either be in floating point, binary or floating point and mixed binary.

• Evaluation of fitness. Here, the evaluation of the original matrix to ascertain its suitability is carried out. Depending on the problem, the choice of the cost function is then made. It should be mentioned at this point that where the optimization is multi-objective, then normalization of each cost and separately weighing before a combination is undertaken to give one scalar quantity.

• Natural selection. Under this stage, the theory of survival of the fittest is applied. Two key methods exist for using natural selection: reject every other chromosome while retaining healthy ones; all chromosomes above certain value already predetermined are retained while others are discarded.

• Selection of a mate. Mating is carried out among the best members of the actual population. This mating is usually on probability. Tournament selection approach and that of Roullete Wheel are some of the very key approaches that are applied under selection of a mate.

• Off-spring selection. Crossover and mutation are main operators upon which the off-spring are produced. Mutation has to do with inducing variations in the population while crossover uses the parents to produce off-spring.

• Criteria for termination. The process of termination repeats until a criterion for termination is met. This happens when either the required iterations or the cost is satisfied.

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.

Figure 3.

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

As Figure 4 shows, in thinned array optimized with genetic algorithm, the half-power 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.

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.

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

Figure 6.

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

3. Conclusion

This work looked at the issue of sidelobe level in antenna array and the challenge in reducing the sidelobe level, providing a way the issue and challenge can be overcome. Related literatures were reviewed, different antenna arrays listed, issues and challenges presented, and solution to the issue of sidelobe level outlined, with graphs. This work has shown that enhanced firefly algorithm (EFA) performs better than genetic algorithm (GA) in optimizing sidelobe level of antenna array without any serious effect on the beamwidth. Since sidelobe level can be optimized through phase or amplitude excitations, it is found that randomly-amplitude excited elements of rectangular antenna array have good sidelobe level than randomly-phase excited elements of rectangular antenna array. The best sidelobe level obtained while using enhanced firefly was (−32.5 dB) compared to the value of (−20.0 dB) obtained with genetic algorithm. As a way of improving this or similar work, the author suggests that a comparison of enhanced firefly algorithm with all other key optimization methods or techniques should be undertaken.

It was also found that tilting beam towards the direction of end fire, genetic algorithm optimization technique can be used to reasonably reduce the level of sidelobe in array antennas. Equally worthy of note, as found from this work, is the fact that reducing the number of active elements in an antenna array by way of turning OFF some elements can be used to improve performance of the array.

Acknowledgments

I wish to thank my wife and children, Onu Faith, Onu Kingdom, and Onu Treasure for the encouragement I received from them to continue this important work. The Almighty God is highly appreciated for the wisdom to carry out this work.

Nomenclature

AF

Array factor

EFA

Enhanced firefly

FA

Firefly algorithm

GA

Genetic algorithm

MIMO

Multiple input multiple output

PSO

Particle swamp optimization

SADE

Self-adaptive differential evolution

SGA

Simple genetic algorithm

SLL

Side lobe level

TOM

Tajuche optimization method

α_M

elements phase shift in the M direction

α_N

element phase shift in the N direction

θ

zenith angle

∅

azimuthal angle

α_N

element progressive phase shift in N direction

α_M

element progressive phase shift in M direction