Modeling Beam forming in Circular Antenna Array with Directional Emitters
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1 International Journal of Research in Engineering and Science (IJRES) ISSN (Online): , ISSN (Print): Volue 5 Issue 3 ǁ Mar ǁ PP Modeling Bea foring in Circular Antenna Array with Directional Eitters Nechaev Yu.B. 1,Alkhafaji Sarad K.D. 1,Peshkov I.W. 2 1 (Inforation Systes Departent, Voronezh State University, Russia) 2 (Radio Electronics And Coputer Techniques Departent, Bunin Yelets State University, Russia) ABSTRACT: The article discusses the functioning of the radio direction-finding and beaforing ethods in the syste of circular antenna arrays fored fro the designed radiators, directional factor which is not equal to 1. Evaluation of foring of spatial pattern of cylindrical antenna array using phased ethod is fulfilled. Dolph- Chebyshev window is used to reduce the side lobe level. Keywords : Antenna, Cylindrical antenna; Direction-Finding; Digital Processing; Dolph-Chebyshev; Phased array; Super resolution. I. INTRODUCTION Adaptive beaforing of antenna arrays (AR) can significantly increase the ratio of the transitting signal power to interference and noise power. One way it is beaforing based on an assessent of the angular coordinates of radio sources. In such probles, the required nuber of priary odules processing the received signals and analog-to-digital converters can reach high values [1]. The different configurations are used today, but ones with the patch antennas which have the directive factor higher that one took great interest. One of the ost faous configuration is cylindrical antenna arrays. II. PROBLEM FORMULATION Let an antenna array consist of N antenna eleents (AE). Let s assue, that M radio signals arriving on the antenna array fro distinct directions M, 1 0. For an arbitrary geoetry configuration antenna array a coplex output signal vector can be written as: [1]: xt As( t) n( t), (1) where x t T N-diensional vector describing output signals of each antenna eleent, s(t) M-diensional signal vector; n t N-diensional noise vector of spatial channel and receiver; A NM atrix of steering vectors, th colun of the atrix describes phase distribution of th signal source inside antenna array. Assue that the antenna eleents in the circular antenna array are identical and have a axiu radial direction fro 2n the center of the array, g, n 0,1,, N 1. In this case, the steering vector is defined as [2]: N 2N 1 jr cos j r N cos 2 1 N a g e g e, (2) N 2 where - wave nuber (λ wave length), g - aplitude response of the antenna eleent (i.e., antenna gain) in the direction of θ. It should be noted that since the direction vector (2) represents the aplitude and phase responses of the antennas in the coposition of the lattice (1) fro different incident waves, the gain g is the voltage gain (or current) relative to the values that could be taken hypothetical isotropic antenna. Antennas are typically defined in ters of their radiated (or received) power in a certain direction with respect to an isotropic antenna. If the radiation pattern of the antenna power to designate as a linear gain G (θ) relative to an isotropic antenna, then g G. To investigate the effect of the directivity of the accuracy of the direction-finding is necessary to have a odel of a hypothetical radiation pattern of the antenna. In this article the probles and liitations of the antennas of the developent process are not considered, the purpose of the work to investigate the effect of NAM focus on the accuracy of radio direction finding. Model pattern of the antenna eleent in the far zone has T 1 Page
2 Modeling Beaforing In Circular Antenna Array With Directional Eitters 1 cos response in the aziuthal plane, where directivity control. Such NAM has CPV, which increases with increasing and has a axiu gain at θ = 0. This odel is a close approxiation of the antennas which have the radiation on the back side, such as a icrostrip antenna with a finite ground. Furtherore, it is assued that a syetric Na diensional plane, then the noralized diagra for eitters arranged in a ring, looks like [4, 5]: 1 2n Un, 1 sin 1 cos, 0,1,, 1 2 n N (3) 2 N It should be noted that the axiu of each eleent extends radially fro the center of the ring are uniforly distributed AR. Using a atheatical odel DN (3) directional coefficient of each antenna eleent in the coposition calculated as the lattice [4, 5]: 22 2 D (4) 2 1 sin 1 cos sin dd 0 0 For an isotropic antenna, = 0 and D = 1 in the expression (4), and by increasing the D orientation also increases. For exaple, when 2.7, D = 4 and when 8,7, direction D = 10, etc. Fro the expression (4) can be derived on a theoretical odel DV power in the far field at plane φ = 90 relative to an isotropic antenna, assuing that the antennas are perfectly atched and lossless [4, 5]: D 2n G 1 cos, 0,1,, n N N Fig. 1 shows the theoretical Na hypothetical antenna for φ = 90 fro the directional coefficients D = 2, 4, 10, 25, 50 (i.e., fro 3 dbi to 17 dbi) and isotropic AE NAM for coparison. Fig. 1. Curves for different spatial patterns D = 1, 2, 4, 10, 25, 50, φ = 90. The research of beaforing ethod via coposed of circular antenna arrays depending on the directivity of the antenna eleents is fulfilled. Such antenna arrays coposed of directed radiators, called conforal. Range the directive factor wipe fro 1 (onidirectional transitter) up to 30. If the nuber of eitters equal to eight, and taking into account that the width of the substrate λ/2, take radius as r 1 2 / 4, then gap ( Gap ) between the eleents is epty (Fig. 2), also consider the configuration of radius λ. 2 Page
3 Modeling Beaforing In Circular Antenna Array With Directional Eitters Fig. 2. The circuit array of eight designed radiators, consisting of a substrate ( "Substrate") and the radiator ( "Patch"). In telecounication systes, when the output signal of tie k is obtained as data by linear cobination with N antenna eleents [3]: y( k) w H x ( k), where w vector of weights. While changing w, the bea pattern can be positioned in any direction of the radiation pattern and adaptively control its shape to the total power of interference and additive noise was inial with inial distortion of the useful signal, i.e..: in E H { w x in}, при w H a 1 1 w where x signal fro the antenna eleents of the array, containing only interference and noise. In this bea in shaper the weight vector is selected to be equal to the steering vector of the desired signal, i.e. [3]: w a ( 1 ). Here, the radiation pattern coprises a axiu in the direction θ 1. This usually has high side lobes, then weighting vector required (here we use the Chebyshev window to reduce the sidelobe level to -30 db). The presence of sidelobes eans that the array is radiating energy in untended directions. Additionally, due to reciprocity, the array is receiving energy fro unintended directions. In a ultipath environent, the sidelobes can receive the sae signal fro ultiple angles. This is the basis for fading experienced in counications. The sidelobes can be suppressed by weighting, shading, or windowing the array eleents [3]. Then the vector of weights: w a 0 t, where t windowing vector. Using Dolph-Chebyshev ethod of windowing for eight eleent antenna array allows coputing the following coefficients: , , , , , , , In this case, the radiating eleents in the opposite direction fro the signal source just off (Fig. 3). Fig. 3. Window of Dolph-Chebyshev 3 Page
4 Modeling Beaforing In Circular Antenna Array With Directional Eitters a) b) Fig. 4. The radiation pattern a) without windowing b) with window function of Dolph-Chebyshev As can be seen fro Fig. 4, beaforing without using the soothing window function side-lobe level is several ties higher than that with Dolph-Chebyshev window. Consider the radiation pattern of circular antenna arrays when you turn on the ain bea of 20. a) b) Fig. 5. The radiation pattern a) without windowing b) with window function of Dolph-Chebyshev Fro Fig. 5 it seen that when you turn the ain lobe of the radiation pattern using the Dolph- Chebyshev windows side-lobe level is also significantly reduced relative to conventional beaforing. The difference between the levels of the side lobes reaches 10dB and higher. III. CONCLUSIONS The paper analyzes the foring of the pattern of the circular antenna array coposed of eight radiators with directional factor equal to ten. When using the ethod according to the soothing window Dolph- Chebyshev the sidelobe level is greatly reduced as in the radiation aziuth 0, and in turn, in particular by Page
5 Modeling Beaforing In Circular Antenna Array With Directional Eitters REFERENCES [1]. Kri H. Two decades of array signal processing research / H. Kri, M. Viberg // IEEE Signal Processing Magazine Vol. 7. P [2]. Jackson B. R. Direction of Arrival Estiation Using Directive Antennas in Unifor Circular Arrays / Jackson Brad R., Rajan Sreeraan, Liao Bruce J., Wang Sichun // EEE Transactions on Antennas and Propagation. - vol. 63, issue 2. - pp [3]. Gross F.B Sart antennas for wireless counications : with Matlab / F.B. Gross. New York : McGraw-Hill Professional, p. [4]. Jackson B. R. Direction of Arrival Estiation Using Directive Antennas in Unifor Circular Arrays / Jackson Brad R., Rajan Sreeraan, Liao Bruce J., Wang Sichun // EEE Transactions on Antennas and Propagation. - vol. 63, issue 2. - pp [5]. J. D. Kraus, Antennas. McGraw-Hill, Page
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