Impact of Array Structure Geometries on the Performance of Circular Array Pattern

Husain YOUSIF

Dept. of Radio Electronics, Brno University of Technology, Purkyňova 118, 612 00 Brno, Czech Republic

xyousi00@feec.vutbr.cz

Abstract. Space division multiple access (SDMA) is still a good topic for increasing channel capacity in future wireless communication systems. Improving performance of the user in the spatial domain depends on the array geometries and as a result of the optimum element geometries for SDMA should be defined, beamforming play a very important role providing fundamental theory of design procedure. However the pattern of antenna array is determined by array geometry. This paper focuses on various geometries of eight antenna arrays using patch elements placed on ring shapes.

Keywords Array factor, circular array, main lobe, pattern beamforming, side lobes.

1. Introduction The smart antenna system design is subdivided into

three major areas: antenna design, adaptive beamforming algorithm and adaptive estimation of direction of arrival (DoA). Narrower main-beam and more nulls in the pattern can resolve the Signals-Of-Interest (SOI) more accurately and allow the smart antenna system to reject more Signals-Not-Of-Interest (SNOI). Studies on array geometries have shown that its pattern is influenced by the position and structure of antenna array. Linear array has excellent directivity and it can form the least main-lobe in a given direction, but it is difficult to be kept consistent in large range and do not treat equally all azimuths [1].

This paper mainly deals with circular arrays as the multi-ring arrays and analyzes the performance of array pattern based on the eight elements circular arrays with one main-lobe and investigates impact of array structure and radius on the pattern of the antenna array. The results calculated without presence of mutual coupling effects, which will be investigated in the next paper using LMS as adaptive beamforming algorithm.

2. Array Geometries The analysis of the radiation in the plane that contains

the array is referred to as the azimuth (or horizontal) plane. Local coordinates on the circle are (R,φ), by (r,Ө,φ) (see fig. 1b). The mutual coupling effect will be neglected.

Let us make some elementary observations of the differences between linear and circular array. For the linear array in fig. 2a, the radiating elements are identical, with equal spacing d, and they all point in the same direction. The far-field radiation function in the azimuth plane is:

∑=n

jkndneVELE φφφ sin)()( (1)

where Vn is the excitation amplitude of element n and k is the propagation constant k=2π/λ. The element factor EL(φ) is common to all elements and was therefore brought outside the summation sign in this equation. The radiation function is the product of the element factor and the array factor [2].

The corresponding far-field expression for the circular array (see fig. 2b), in the azimuth plane is:

)cos()()( ϕφϕφφ Δ−Δ−=∑ njkR

nn enELVE (2)

where R is the radius of ring and the phase has been referenced to the center of the circle. The identical elements are spaced R∆φ along the circle, each element pointing in the radial direction. The element function can, therefore, in general not be brought outside the summation, since it is a function of the element position; there is no common element factor [3], [4].

Fig. 1. Local and far-field (a), coordinates for the circular

array (b).

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Fig. 2. Linear array (a), part of a circular array (b).

With the linear array, the beam can be focused in direction φ0 by applying a linear phase shift ψ(n) to the elements along the array [1], [3] is:

0sin)( φψ kndn = . (3)

With the circular array, similarly the phase values to each element can be imposed so that they add up coherently in the direction φ0 . The proper phase excitation (beam cophasal excitation) can be obtained for each element n by choosing

)cos()( 0 ϕφψ Δ−= nkRn . (4)

Thus, the radiation function for the focused, circular case becomes

)]cos()[cos( 0)()( ϕφϕφϕφφ Δ−−Δ−Δ−=∑ nnjkR

nn enELVE .(5)

Circular arrays are particularly suitable to generate a beam with equal radiation in all directions in the azimuthally plane (an omindirectional beam) by virtue of their circular symmetry [5], [6].

3. The Eight Elements Circular Arrays Fig. 3 shows the eight elements circular array with

radius aψas the array elements uniformly distributed in the circumference of circular antenna array and the elements are excited with equal phase and amplitude. Figures in this paper presents patterns for the array factors.

Fig. 3. Eight elements circular array geometry.

The pattern of the eight elements circular array, with main-lobe corresponds to the angle α = 45°, MML as maximum main lobe width and MMS as minimum side-lobe width is shown in fig. 4.

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Fig. 4. Eight elements array pattern with radius a = 0.5λ.

When a = 0.5λ, MML = 65° and the maximum side-lobe corresponds to the angle α = 75°, and the power of maximum side lobe is just less than half power.

Fig. 5 shows, when a = 0.7λ, MML= 40°, with increasing of the circle radius, the value of MML decreases simultaneously and the number of side-lobe increases. The signal out of main-lobe cannot be efficiently restrained. Therefore the width of minimum main-lobe is 40° in the eight elements circular array. But the performance is not ideal. In order to improve the performance characteristic of the antenna array, the multi-layer circular array is used.

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Fig. 5. Eight elements array pattern with radius a = 0.7 λ

The pattern function of concentric circular array [7], [8] is:

( ) ( )[ ]

( ) ( )[ ]

2

1

0

coscos2

1

0

coscos2

0

1011

...

11

)(

⎟⎟⎠

⎞++

⎜⎜⎝

⎛+

×=

∑

∑−

=

Δ−−Δ−

−

=

Δ−−Δ−

N

n

nnRj

N

n

nnRj

mmm

e

eNM

Fϕφϕφ

λπ

ϕφϕφλπ

θ (6)

where M is the number of rings and N is the number of elements in the ring.

4. 4+4 Circular Array

The structure of 4+4 two-ring array is shown in fig. 6. This multi-ring array consists of two circular arrays uniformly distributed in the circumference of antenna array. The included angle of the first element of two rings connected with the center of circle is β. During the searching, the outer ring is fixed and the location and direction of the inner ring with respect to outer ring is adjusted. It assumed that the radius of outside circle is a1 and the radius of inside circle is a2.. Fig.7 shows the pattern when, a1 = 0.9λ, a2 = 0.45λ, β = 0° and the side-lobes have high power level. Fig. 8 shows the radiation pattern when, a1 = 0. 9λ, a2 = 0.45λ, β = 45° main-lobe is large and the side-lobes decreases simultaneously. Fig. 9 shows the best performance when, a1 = λ, a2 = 0.7λ, β = 45° the side-lobes are considerably weak.

Fig. 6. Structure of 4+4 two-ring array

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Fig. 7. Pattern for 4+4 two-ring array with a1 = 0.9λ, a2 = 0.45λ

and β = 0°

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Fig. 8. Pattern for 4+4 two-ring array, a1 = 0. 9λ, a2 = 0.45λ and

β = 45°

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Fig. 9. Pattern for 4+4 two-ring array, a1 = λ, a2 = 0.7λ, β = 45°

5. 5+3 Circular Array

Fig. 10. Structure of 5+3 two-ring array

Fig. 10 shows the structure of 5+3 circular array. The outer ring has five antenna elements with the radius a1 = 1.3λ and the number of array elements on the inner ring is three with radius a2 = λ. Fig. 11 indicates the radiation pattern of array when β = 45° and side-lobes are also much stronger.

From comparing Fig. 11 with other array patterns that were illustrated before, it is shown the later design has the narrowest main-lobe about 20° and some side-lobes. They

are excessive for a good design. By comprising some arrays, it is obvious when the numbers of elements of outer ring are odd the performance is better than the case of even elements, and the conclusion can be generalized through simulation by computer.

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Fig. 11. Pattern for 5+3 two ring array with a1 = 1.3λ, a2 = λ and

β = 45°.

6. Conclusion In this paper some structures of eight elements

antenna arrays are investigated. The radius of circle array mainly influences main lobe of pattern, larger radius makes narrower main-lobe and more side-lobes.

In 4+4 circular array structure the main lobe looks narrower than eight elements antenna arrays. The best performance pattern is obtained, when the included angle of the first element of two rings connected with the center of circle is 45° and for the radius a1 = λ, a2 = 0.7λ.

The two-ring 5+3 circular array structure with a1 = 1.3λ, a2 = λ and β = 45° shows that the main lobe is the narrowest about 20° with some side-lobes look good for design. The odd number of elements of outer ring gives better performance than the case of even elements.

The power of side-lobe can be reduced by using two concentric circle arrays. From computer simulation, the geometry of antenna array can improve the pattern performance of antenna array, as the total elements of antenna array are fixed.

The conclusion of this paper is general. For multi-ring array, increasing the number of rings might improve performance of pattern. However the numbers of rings are restricted on a given antenna. Most of the time increasing ring number needs more elements and thus is more expensive. In fact, the optimum performance of pattern can be obtained by adjusting the number of rings.

An effective design for eliminating the effect of mutual coupling can be proposed and examined by using beam forming algorithm as LMS, which will be investigated in the next paper.

References [1] ALLEN, B., GHAVAMI, M. Adaptive Array Systems Fundamentals

and Applications. West Sussex: John Wiley & Sons Ltd, 2005.

[2] DAVIES, D. The Handbook of Antenna Design. vol II, A. W. Rudge, et al., London, England: Peter Perigrinus, 1983.

[3] MAILLOUX, J. Phased Array Antenna Handbook. 2 nd ed. Norwood: Artech House, 2005.

[4] YASHCHYSHYN, E. Principle of smart antennas and selected applications. In Proceedings of the 19th International Traveling Summer School on Microwaves and Lightwaves. Roma (Italy), 2009, p. 202 – 241.

[5] ROSTAN, R., GOTTWALD G., WIESBECK, W. Design and performance of conformal microstrip patch arrays on cylindrical surfaces. In Proceedings of the 24th European Microwave conference EuMC 94. Cannes, France, 1994, p. 1756 – 1761.

[6] LO, Y. T., RICHRDS, F. Theory and experiment on microstrip antennas. IEEE Transactions on Antennas and Propagation, 1979, vol. 27, p. 137 – 145.

[7] SUREAU, C., KEEPING, K. Sidelobe control in cylindrical arrays. IEEE Transactions on Antennas and Propagation, 1982, vol. 30, no. 5, p. 1027 – 1031.

[8] HERSCOVICI, N., SIPUS Z., KILDAL, P. The cylindrical omnidirectional patch antenna. IEEE AP-S International Symposium, 1997, vol. 2, p. 924 – 927.