interference suppression of linear antenna arrays by phase-only control using a clonal selection...

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Journal of the Franklin Institute 345 (2008) 254–266

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Interference suppression of linear antenna arrays byphase-only control using a clonal selection algorithm

K. Guneya,�, B. Babayigitb, A. Akdaglia

aDepartment of Electrical and Electronics Engineering, Erciyes University, 38039 Kayseri, TurkeybDepartment of Computer Engineering, Erciyes University, 38039 Kayseri, Turkey

Received 15 December 2006; received in revised form 3 July 2007; accepted 11 September 2007

Abstract

In this paper, an efficient technique based on clonal selection algorithm (CLONALG) for linear

antenna array pattern synthesis with null steering by controlling only the element excitation phases is

presented. The CLONALG is an evolutionary computation method inspired by the clonal selection

principle of human immune system. To show the versatility and flexibility of the proposed

CLONALG, some examples of Chebyshev array pattern with the imposed single, multiple and broad

nulls are given. The sensitivity of the nulling patterns due to small variations of the element phases is

also investigated.

r 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Keywords: Linear antenna arrays; Pattern nulling; Phase-only control; Clonal selection algorithm

1. Introduction

Pattern nulling methods that achieve suppression of interfering signals from prescribeddirections while receiving the desired signal from a chosen look direction are important inradar, sonar and many communication systems. Pattern nulling methods, includingcontrolling the complex weights (both the amplitude and phase), amplitude-only, phase-only, and position-only, have been extensively studied in the literature [1–19]. Interferencesuppression with complex weights is the most efficient because it has greater degrees of

2.00 r 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

.jfranklin.2007.09.002

nding author.

dresses: [email protected] (K. Guney), [email protected] (B. Babayigit),

yes.edu.tr (A. Akdagli).

www.elsevier.com/locate/jfranklin

dx.doi.org/10.1016/j.jfranklin.2007.09.002

mailto:[email protected]



ARTICLE IN PRESSK. Guney et al. / Journal of the Franklin Institute 345 (2008) 254–266 255

freedom for the solution space [1]. On the other hand, it is also the most expensiveconsidering the cost of both phase shifter and variable attenuator for each array element.Furthermore, when the number of elements in the antenna array increases, thecomputational time to find the values of element amplitudes and phases will also increase.The amplitude-only control uses a set of variable attenuators to adjust the elementamplitudes [3,4,13,14,19]. If the array elements possess even symmetry about the center ofthe array, the number of attenuators and the computational time are halved. The problem ofphase-only and position-only nulling is inherently nonlinear and cannot be solved directly byan analytical method. By assuming that the phase or position perturbations are small, thenulling equations can be linearized. The phase-only control [5,6,9,17] utilizes the phaseshifters while the position-only control [7–11,15] needs a mechanical driving system such asservomotors to move the array elements. The array pattern nulling with phase-only controlhas been attractive for the phased antenna arrays because it is less complicated and therequired controls are available at no extra cost. Moreover, it is also easier to control mainbeam direction by controlling the phase weights instead of controlling the amplitude weights.

In order to obtain the multiple or broad nulls in the radiation pattern with the use ofphase-only control, the large phase perturbations are needed. However, the large phaseperturbations require nonlinear optimization techniques. It is well known that the classicaloptimization techniques used for array pattern synthesis need a starting point that isreasonably close to the final solution, or they are likely to be stuck in local minima. As thenumber of parameters and, hence, the size of solution space increases, the quality ofsolution firmly depends on the estimation of initial values. If the initial values fall in aregion of the solution space where all the local solutions are poor, a local search is limitedto finding the best of these poor solutions. Because of these disadvantages of the classicaloptimization techniques, the evolutionary optimization methods [4,6,8,9,12,14–16,18–22]have been presented for the pattern synthesis of linear antenna arrays with the prescribednulls. These optimization methods are capable of performing better solutions than theclassical optimization techniques and conventional analytical approaches.

In this paper, the technique for antenna array pattern synthesis with null steering usingthe clonal selection algorithm (CLONALG) [23] by controlling only the element excitationphases is presented. The patterns with the single, multiple and broad nulls imposed at theinterference directions are achieved with a good performance. The CLONALG is arelatively novel evolutionary optimization algorithm that is developed on the basis of theclonal selection principle [24,25] of the human immune system (IS). It has the ability ofgetting out local minima, operates on a population of points in search spacesimultaneously, not on just one point, does not use the derivative or any otherinformation, and employs probabilistic transition rules instead of deterministic ones. Ithas also the advantage of being simple to implement and easy to understand. Because ofthese good features, CLONALG has been used in the literature [23,26–33] for solvingvarious kinds of challenging engineering problems. In our previous work [32], theCLONALG has been firstly applied to solve the pattern nulling problem of the linearantenna array by amplitude-only control. However, in this article, CLONALG is used forthe pattern nulling of linear arrays by phase-only control. We also used the CLONALG todesign a reconfigurable dual-beam linear antenna array [33].

In this paper, the next section briefly explains the formulation of the problem. The basicprinciples of the human IS and the CLONALG are presented in the following section. Thenumerical examples are then presented and conclusion is made.

ARTICLE IN PRESSK. Guney et al. / Journal of the Franklin Institute 345 (2008) 254–266256

2. Formulation

If the elements are symmetrically placed and conjugate-symmetrically excited about thecenter of a linear array, the far field array factor of this array with an even number (2N) ofisotropic elements can be written as

F ðyÞ ¼ 2XN

k¼1

ak cos2pl

dk sin yþ dk

� �, (1)

where dk is the distance between position of the kth element and the array center, y isscanning angle from broadside, and ak and dk are amplitude and phase weights of the kthelement, respectively. In this particular problem of null synthesising, we restrictedourselves to find an appropriate set of dk to place array nulls at any prescribed directions.Therefore, the following cost function to be minimized by using the CLONALG isconstructed.

C ¼X90�

y¼�90�W ðyÞjFoðyÞ � FdðyÞj, (2)

where Fo(y) and Fd(y) are, respectively, the pattern obtained by using CLONALG and thedesired pattern. To control the null depth level, W(y) is included in the cost function.

3. Clonal selection algorithm

3.1. Immune system

The IS [24] is one of the most complex bodily systems and its complexity can becompared to that of the human brain. The IS consists of cells, molecules, tissues, andorgans spread throughout the human body. The main aim of the IS is to defend the humanbody against harmful molecules or substances called antigen. The IS first recognizes theantigen and then mounts a response to eliminate it.The fundamental components of the IS are the lymphocytes which are white blood cells

specialized mainly in the recognition of antigens. Within the human body, lymphocytes arefound in two forms, B lymphocytes (B-cells) and T lymphocytes (T-cells). B-cells areproduced and developed within the bone marrow, and T-cells are produced in the bonemarrow and then migrated to the thymus for further development. These two types of cellsdiffer in their modes of antigen recognition. B-cells are capable of recognizing antigens freein solution while T-cells require antigens to be presented by other accessory cells. BothB-cells and T-cells present receptor molecules on their surfaces responsible for recognizingantigenic patterns. The T-cell receptor is called TCR and the B-cell receptor is called BCRor antibody.Each antibody will respond optimally to a specific antigen rather like a key which fits

into a keyhole. When antigens and antibodies have complementary shapes, they can bindtogether. The degree of the binding is called affinity. The higher the affinity, the strongerthe binding. After the recognition process, the IS initiates an adaptive response mechanismto cull out the invading antigens. An adequate response to the antigen is generated byclonal selection.


3.2. Clonal selection principle

The clonal selection principle [24,25] explains how an immune response is mounted whenan antigenic pattern is recognized by a B-cell. As it is shown in Fig. 1, when an antigen isdetected, the B-cells that best recognize the antigen will start to proliferate by cloning.Cloning is a mitotic process which produces exact copies of the parent cells. The higher theaffinity of a B-cell to available antigens, the more likely it will clone. The cloned cells canundergo somatic hypermutation, creating offspring B-cells with mutated receptors. Thishypermutation process enables the new cells to match the antigen more closely. Some ofnew cloned cells will be differentiated into antibody secreting plasma cells. The B-cells withhigh antigenic affinities are selected to become memory cells. The B-cells that are notstimulated to proliferate as they do not match any antigens will eventually die. The processcontinues reproducing B-cells more and more specific to present antigens. The cloning andmaturation processes are called the clonal selection principle.

When the antigens have been successfully eliminated, memory cells remain and circulatein the blood, lymph, and tissues for very long periods of time. The first exposition to theantigen triggers the primary response. In this phase, the antigen is recognized and thememory is developed. During the secondary response, which occurs when the same antigenis encountered again, as a result of the stimulation of the cells already specialized andpresent as memory cells, a rapid and more abundant production of antibodies is observed.

selection

B-cells

memory cells

antibodies

antigen

plasma cells

proliferation/maturation

Fig. 1. The clonal selection principle.


3.3. Clonal selection algorithm

The CLONALG [23], inspired by the clonal selection principle of the human IS, is a newlydiscovered population-based algorithm capable of solving different types of engineeringoptimization problems [23,26–33]. A flowchart of the CLONALG is shown in Fig. 2.The CLONALG starts by randomly generating an initial population (Npop) of antibodies

in a given bounds for the problem (antigen) considered. Each antibody which means acandidate solution is represented by a binary string of bits. The length of bit string is suitablyselected by the user to obtain a reasonable precision for the problem. The antibodies areevaluated over an affinity (fitness) function and sorted in decreasing order of affinity. Theantibodies with n highest affinity are selected and then cloned proportionally to theiraffinities. The number of clones generated for each of the selected antibodies is given by

Nc ¼Xn

i¼1

roundbNpop

i

� �, (3)

Initialize

Evaluate and Select (1)

Clone

Evaluate and Select (2)

Hypermutate

Population Update

TerminationCondition

Final Solution

Yes

No

Fig. 2. Flowchart of the CLONALG.


where b is the multiplying factor and round (.) is the operator that rounds its argumenttoward the closest integer. A subpopulation is constructed with an antibody and its clones.The clones are subjected to a hypermutation process inversely proportional to their affinity:the higher the affinity, the lower the mutation rate. The maturated clones are then evaluatedover the affinity function, and the best antibody of each subpopulation is selected forsurviving. The antibody population is updated by replacing the antibodies having m lowestaffinities with the new ones generated randomly. With this replacement, the diversity ofantibody population is maintained so that the new areas of the search space can bepotentially explored. These processes are repeated until a termination criterion is attained.An overview of the clonal selection principle and the CLONALG, from immunology andengineering points of view, can be found in [23].

4. Numerical results

In this section, six examples of a linear array with 20 isotropic elements have beensimulated to illustrate the versatility and flexibility of the proposed CLONALG. A 30 dBChebyshev pattern given in Fig. 3 for 20 equispaced elements with l/2 interelement spacingis utilized as the initial pattern. The element excitation phases are determined by using theCLONALG to yield the Chebyshev pattern with the single, multiple and broad-band nullsin the prescribed directions of interference. The affinity value of the antibodies inCLONALG is calculated by

AFF ¼1

1þ C. (4)

The number of iteration and the population size of the antibodies (Npop) are,respectively, selected as 200 and 50, and each antibody is represented by a string of16 bits. The CLONALG parameter values of n, b, and m are set to 30, 2, and 20,

θ (degree)

-20-40-60-80 0 20 40 60 80

IF(θ

)I (

dB

)

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Fig. 3. The initial Chebyshev pattern.


respectively. The results for the all examples herein are obtained within 3min on a personalcomputer with a Pentium IV processor running at 2400MHz. This is sufficient to obtainsatisfactory patterns with the desired performance on the average.As the first application of CLONALG, the interference direction yi is selected at the

peak of the first sidelobe, which occurs about �101. The values of the cost functionparameters given in Eq. (2) are chosen as follows:

FdðyÞ ¼0; for y ¼ yi

Initial pattern else where

((5)

and

W ðyÞ ¼100; for y ¼ yi

1; else where

(. (6)

In Fig. 4, the resultant nulling pattern is shown. As it can be seen from this figure, thepattern preserves overall characteristics of the initial Chebyshev pattern with a littledisturbance except for the nulling location (yi ¼ �101), and there is an unavoidablesidelobe level increase in the direction symmetric to nulling direction with respect to themain beam.To inspect the flexibility of the CLONALG, in the second example, it is intended to

obtain a null depth level deeper than that of the first example. Thus, W(y) is modified asgiven below while Fd(y) is the same as that of the first example.

W ðyÞ ¼200; for y ¼ yi

1 else where

�(7)

The pattern obtained by the CLONALG for the values of W(y) given in Eq. (7) is shownin Fig. 5. The null depth level of the pattern given in Fig. 5 is �175 dB while the null depth

-150

-140

-130

-120

-110

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

θ (degree)

-20-40-60-80 0 20 40 60 80

IF(θ

)I (

dB

)

Fig. 4. Radiation pattern with one imposed null at �101.

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-180

-160

-140

-120

-100

-80

-60

-40

-20

0

θ (degree)

-20-40-60-80 0 20 40 60 80

IF(θ

)I (

dB

)

Fig. 5. Radiation pattern having one imposed null at �101 with a null depth level deeper than that of the first

example.

K. Guney et al. / Journal of the Franklin Institute 345 (2008) 254–266 261

level of the pattern in Fig. 4 is �130 dB. But in response to such an improvement of thenull depth level, the maximum sidelobe level of the pattern in Fig. 5 is �24 dB while that ofthe pattern in Fig. 4 is �25.5 dB.

The broad-band nulls are needed when the direction of arrival of the unwantedinterference may vary slightly with time or may not be known exactly, and where acomparatively sharp null would require continuous steering for obtaining a reasonablevalue for the signal-to-noise ratio. To illustrate the broad-band interference suppressioncapability of the proposed nulling method, in the third example, the pattern having abroad null located at 141 (the peak of the second sidelobe) with Dyi ¼ 51 is achieved and isshown in Fig. 6. From the figure, a null depth level deeper than �55 dB is obtained over thespatial region of interest.

In the fourth and fifth examples, the pattern with two nulls imposed at the peaks of thefirst and the third sidelobes (yi1 ¼ �101 and yi2 ¼ 201), and the pattern having triple nullsimposed at the peaks of the first, the third and the fifth sidelobes (yi1 ¼ �331, yi2 ¼ �101and yi3 ¼ 201) are obtained, separately. The patterns with multiple nulls are given in Figs. 7and 8. Referring to Figs. 7 and 8, it can be seen that all the nulls in the imposed directionsare deeper than �130 dB.

In this paper, the sensitivity of the phase-only nulling by using the CLONALG has alsobeen investigated by truncating the phase values of the nulling pattern given in Fig. 8 to thesecond decimal position. The pattern obtained by using the truncated element phases isillustrated in Fig. 9. It is clear that the pattern of Fig. 9 is almost the same as the pattern ofFig. 8, except for the shallower null depth levels, which are still deeper than �100 dB.These results apparently confirm that the nulling pattern obtained by using the phase-onlycontrol is insensitive to the small variations of the element phases.

The element phase weights obtained by CLONALG for Figs. 4–9 have odd symmetryabout the center of the array and are listed in Table 1. It is apparent from Figs. 4–9 that the

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-70

-60

-50

-40

-30

-20

-10

0

θ (degree)

-20-40-60-80 0 20 40 60 80

IF(θ

)I (

dB

)

Fig. 6. Radiation pattern with a broad null sector centered 141 with Dyi ¼ 51.

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

θ (degree)

-20-40-60-80 0 20 40 60 80

IF(θ

)I (

dB

)

Fig. 7. Radiation pattern with double imposed null at �101 and 201.

K. Guney et al. / Journal of the Franklin Institute 345 (2008) 254–266262

patterns are not symmetric with respect to the main beam. This is a consequence of theodd-symmetry of the element phases around the array center which, coupled with the evensymmetry of the element amplitudes, results in a pattern that is not symmetric about themaim beam peak at 01. It should also be noted that since the element phases have odd-symmetry about the center of the array, the number of phase shifters to be used is 2N,but the number of controllers for the phase shifters is N for an array with 2N elements.

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-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

θ (degree)

-20-40-60-80 0 20 40 60 80

IF(θ

)I (

dB

)

Fig. 8. Radiation pattern with triple imposed null at �331, �101 and 201.

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

θ (degree)

-20-40-60-80 0 20 40 60 80

IF(θ

)I (

dB

)

Fig. 9. Radiation pattern with triple imposed null at �331, �101 and 201 obtained by using the truncated element

phases.

K. Guney et al. / Journal of the Franklin Institute 345 (2008) 254–266 263

The design approach proposed here can be used in practice for null steering of linearantenna arrays by employing phase shifters.

The results shown in Figs. 4–9 illustrate that the CLONALG proposed in this work canaccurately produce the nulling patterns by controlling only the element phases of the lineararray. The proposed nulling technique preserves the characteristics of the initial Chebyshevpattern with little pattern disturbance except for the nulling directions. The half power

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Table 1

The element amplitudes (ak) of the initial Chebyshev array and the element phases (dk) of nulling patterns given in

Figs. 4–9

k Initial Chebyshev pattern Element phases (in degree) computed with the CLONALG

Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9

71 1.00000 70.67884 70.94721 84.60521 70.00000 72.12166 72.12

72 0.97010 72.52537 72.54983 89.60208 80.94532 71.77571 71.78

73 0.91243 74.90905 73.33467 84.45331 80.26287 81.97550 81.98

74 0.83102 77.55388 73.18570 73.21905 72.97233 71.67132 71.67

75 0.73147 710.22076 71.86710 71.96376 74.81794 78.19679 78.20

76 0.62034 711.78024 80.16982 87.54631 73.12245 73.49120 73.49

77 0.50461 711.44099 82.36465 814.58716 82.86467 88.29494 88.29

78 0.39104 79.31635 84.05179 812.22153 89.85367 89.90317 89.90

79 0.28558 77.46226 84.40960 722.31928 810.81676 82.75661 82.76

710 0.32561 72.67571 81.62646 725.13342 82.76487 80.20157 80.20

K. Guney et al. / Journal of the Franklin Institute 345 (2008) 254–266264

beam width of the nulling patterns obtained by using the CLONALG is almost equal tothat of initial Chebyshev pattern. The validity of the proposed null steering technique isalso verified by executing the CLONALG several times, and results with very similarperformances to those presented herein are always obtained.

5. Conclusions

In this paper, the CLONALG has been used for interference suppression of a linearantenna array by phase-only control. The computer simulation results show that thephase-only control using the CLONALG is efficient for forming nulls for any prescribeddirections while the main beam and the sidelobes are quite close to the initial pattern. Byusing the CLONALG, the null depth level of the nulling pattern can easily be controlled.Practical considerations regarding the sensitivity of the achieved patterns due to smallvariations of the element phases are also investigated to verify the validity of the presentednulling technique. Although only linear antenna arrays have been considered here, theCLONALG can be applied to arrays with complex geometry as well as nonisotropicelements.

Statement of contribution

In this paper, the technique for antenna array pattern synthesis with null steering usingthe clonal selection algorithm (CLONALG) [23] by controlling only the element excitationphases is presented. The patterns with the single, multiple and broad nulls imposed at theinterference directions are achieved with a good performance. The CLONALG is arelatively novel evolutionary optimization algorithm that is developed on the basis of theclonal selection principle [24,25] of the human immune system (IS). It has the ability ofgetting out local minima, operates on a population of points in search spacesimultaneously, not on just one point, does not use the derivative or any otherinformation, and employs probabilistic transition rules instead of deterministic ones. Ithas also the advantage of being simple to implement and easy to understand.


The computer simulation results show that the phase-only control using the CLONALGis efficient for forming nulls for any prescribed directions while the main beam and thesidelobes are quite close to the initial pattern. By using the CLONALG, the null depthlevel of the nulling pattern can easily be controlled. Practical considerations regarding thesensitivity of the achieved patterns due to small variations of the element phases are alsoinvestigated to verify the validity of the presented nulling technique. Although only linearantenna arrays have been considered here, the CLONALG can be applied to arrays withcomplex geometry as well as nonisotropic elements.

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