An Array with Crossed-Dipoles Elements for Controlling Side Lobes Pattern

— This paper introduces an array with a new element structure to achieve asymmetric sidelobe pattern nulling which is a much desired feature in many applications such as communication systems, tracking radars, and imaging. The proposed element structure consists of combining two simple wire dipoles in the horizontal and vertical positions to form a crossed dipole element. The array patterns of the horizontal and vertical dipoles alone share some common radiation feature such angular null positions which are exploited to provide sidelobe nulling. By properly scaling the array pattern of the horizontal dipoles and added or subtracted its array pattern from that of the vertical dipoles, a new array pattern corresponds to the crossed dipoles elements with controlled sidelobes pattern can be obtained. The scaling factor selects which sidelobes to be cancelled. The method is equally applied to the uniformly and nun-uniformly excited arrays. The proposed idea is verified by simulating an array with 10 half wavelength crossed dipoles using CST microwave studio.


INTRODUCTION
Currently antenna arrays play a very important role in enhancing the performances of many modern wireless communication systems through configuring their radiation patterns to be maximum at some desired directions and minimum at some other undesired directions. The sidelobe pattern nulling of antenna arrays can easily block the undesired signals at the antenna end. Thus, low sidelobes either on one side or both sides of the main beam and pattern nulling which they are depend on the excitation currents of the antennas are necessary for these applications. Many numerical algorithms have been proposed in the literature for optimizing the excitation currents to get the desired array patterns, for example see [1][2][3][4][5][6]. However, these optimization methods were generally difficult and complex. Thus, the authors in [7][8][9] investigated simpler methods for obtaining the required array patterns where they suggested formulating an appropriate auxiliary pattern from reusing two or more side elements whose sidelobes are similar to that of the complete array pattern. Then, a required pattern nulling was obtained by subtracting the auxiliary pattern form that of the complete array pattern. These methods were simple since only two or a few number of reused array elements was made re-adjustable. In [10], scanned sub-arrays were used to generate sum and difference patterns, while in [11][12] a genetic algorithm was used to find and optimize the most active elements that could effectively contribute to generate the required nulls. On the other hand, the authors in [13][14] suggested exploring common current excitations to simplify the array feeding network while generating the required array patterns.
In all of the aforementioned methods, the type of the array elements was not investigated. The aim of this paper is mainly to present an efficient structure of the radiation elements that can produce an array with required sidelobe pattern nulling. This can be achieved, by considering two dipole elements and putting them in a crossed form configuration such that their corresponding array patterns can be added or subtracted to produce a new pattern with required sidelobe nulling .

A. Conventional Array with Horizontal or Vertical Dipole Elements
Consider N dipole elements that are arranged linearly along the z-axis and positioned either horizontally toward the x-axis or vertically toward z-axis, as shown in Fig.1. The separation distance between any two adjacent dipoles is set to = 2 ⁄ . The element excitation amplitude of nth element is denoted by a n and its progressive phase is β. Thus, the array factor of such array in the far-field observations can be written as follows [15]: AF(θ) = ∑ a n N n=1 where a n is the amplitude element excitation coefficients, ψ = kd z cos θ + β, d z is the spacing between elements along the z-axis k = 2π λ ⁄ and λ is the wavelength in free space. Note that the array factors of these two configurations are same, only the element patters differ. Thus, the overall array pattern (AP) for these two configurations can be obtained by multiplying the element pattern by the array factor as follows The above two array patterns are plotted for N=20 dipoles as shown in Fig.2.
From figure 2, it can be seen that the resultant array pattern of the horizontal dipoles is in the form of sidelobes in which its nulls are exactly coincident with those of the resultant vertical array pattern. By combining these two antenna arrays with their resultant patterns of the vertical and horizontal array dipoles, one can get a new array with its elements as a two crossed dipoles.

B. An Array with Two Crossed Dipole Elements
In this section, the array elements are chosen such that the horizontal and vertical dipoles are combined to form a cross dipole for each array element. Then, the overall array pattern of the By applying the above equation for K=1 and N=20, an overall array pattern for the two crossed dipole elements can be obtained as shown in Fig.3.

III. SIMULATION RESULTS
To demonstrate the possibilities of the proposed method in generating the required pattern nulling, three various cases are presented where the first case is related to the uniformly excited arrays, while the other two cases are related to the non-uniformly excited arrays such as Dolph, and Taylor. In all cases, an array with 10 crossed-dipole elements along the z-axis is considered. Moreover, the interelement spacing between any two successive crossed-dipole elements is chosen to be 0.5 . For Dolph excited arrays, the desired SLL was set to −26 dB, while for Taylor excited arrays they are set to SLL = −20 dB, and nbar = 4. The scaling factor was variable for each case to get best match in the sidelobe regions of the horizontal and vertical array patterns. In the first case, the scaling factor was set to K=1 such that the third sidelobe can be cancelled. The array patterns according to (4) were obtained as shown in Fig. 4. Further, table I shows the performance measures in terms of directivity, both peak and average sidelobes, and the beamwidths of the tested arrays. It can be seen that the third sidelobes on the left side on the main beam in the uniform, Taylor, and Dolph array patterns with crossed-dipole elements are cancelled. Moreover, many of the other sidelobes on the left side were reduced down with compared to that of the vertical dipole array pattern.
In the second case, the scaling factor was set to K=1.767 and the resultants array patterns are as shown in Fig. 5 and their performance measures as shown in Table II. It can be seen that the second sidelobes are cancelled. Moreover, many of the other sidelobes on the left side were reduced down with compared to that of the vertical dipole array pattern. In the third case, the scaling factor was chosen, K=3.3, such that the first sidelobe in the proposed array can be cancelled. The resultants array patterns are as shown in Fig. 6 and their performance measures as shown in Table III. Finally, in order to consider the effects of element type, feeding position, mutual coupling, scattering and many other effects, full simulation using CST is done for 10 crossed-dipoles elements array with discrete ports as shown in Fig.7(left). The return loss curve has been shown in this figure (see Fig.7 right). Table IV shows the details of design parameters of the proposed crossed-dipoles elements.

IV. CONCLUSIONS
From the presented results, it can be found that the proposed array is capable to provide a required pattern with controlled nulls that depend on the selecting value of the scaling factor. The method is equally applicable to both uniformly and non-uniformly excited arrays. For all considered arrays, the differences between sidelobe levels on both sides of the main beam were more than -20 dB.
Moreover, the directivity of the proposed array was found to be slightly reduced with compared to that of the conventional array with single-dipole elements. Finally, an array with the proposed crossed-dipole elements was designed and simulated using CST microwave studio and its results were compared to the theoretical Matlab findings, which confidently validated the presented idea.
The proposed array can be further extended to include the circular polarization.