Synthesis of Pencil Beam Pattern with a Multiple Concentric Circular Ring Array Antenna with Minimum Side Lobe Level and Fixed First Null Beamwidth A.Chatterjee and G.K.Mahanti Department of Electronics & Communication Engg. National Institute of Technology Durgapur, India E-mail: snanirban@gmail.com E-mail: gautammahanti@yahoo.com A.Chakraborty Department of Electronics & Electrical Communication Engineering Indian Institute of Technology Kharagpur, India E-mail: bassein@ece.iitkgp.ernet.in Abstract—In this paper, the authors present a method based on modified particle swarm optimization for generating pencil beam in the vertical plane with minimum side lobe level and fixed first null beamwidth. The first null beamwidth is made equal to that of a uniformly excited and uniformly spaced multiple concentric circular ring array of same number of elements and same number of rings. The excitation amplitude is radially varied and optimized to achieve the goal. Example illustrates the potential of the method. Keywords-Concentric circular array; particle swarm optimization;first null beamwidth;side lobe level I. INTRODUCTION Circular antenna arrays find various applications in sonar, radar, mobile and commercial satellite communications systems [1–5]. It consists of a number of elements arranged on a circle [1] with uniform spacing and can be used for beam forming in the azimuth plane for example at the base stations of the mobile radio communications system [2-5]. A very popular type of antenna arrays is the circular array that has several advantages over other type of array antenna configurations; such as all-azimuth scan capability, invariant beam pattern in every φ-cut. Concentric Circular Antenna Array (CCAA) that contains many concentric circular rings of different radii and number of elements have several advantages such as φ-symmetric pattern, flexibility in array pattern synthesis etc.[2-5]. Uniform CCA (UCCA) is one of the most important configurations of the CCA [2] where the inter-element spacing in individual ring is kept almost half of the wavelength and all the elements in the array are uniformly excited. The side lobe in the UCCA drops to about 17.5 dB, especially at larger number of rings [2] with uniform excitation. Uniformly excited and equally spaced antenna arrays [1, 2] have high directivity but they usually suffer from high side lobe level. To reduce the side lobe level further, the array is made aperiodic by altering the positions of the antenna elements with all excitation amplitudes being uniform. Another possibility is to use an equally spaced array with radially tapered amplitude distribution [3, 4]. Particle swarm optimization (PSO) is an evolutionary algorithm and has been successfully used in the design of antenna arrays [5-11]. The PSO algorithm [12] has been shown to be an effective alternative to other evolutionary algorithms [13, 14] such as Genetic Algorithms (GA), Ant Colony Optimization (ACO) etc. in handling certain kinds of optimization problems. In this paper, we vary and optimize amplitude distribution radially that will produce pencil beam in the vertical plane with minimum side lobe level and fixed first null beamwidth. The first null beamwidth is made equal to a uniformly excited and uniformly spaced multiple concentric circular ring array of same number of elements and and same number of rings as reported in the article [15]. Optimization is done with the help of modified particle swarm optimization [11]. II. PROBLEM FORMULATION The arrangement of elements in planar circular arrays [2, 3] contains multiple concentric circular rings, which differ in radius and number of elements. Figure1 shows the configuration of multiple concentric circular arrays [2,3] in XY plane in which there are M concentric circular rings. The m-th ring has a radius r m and number of isotropic elements N m , where m = 1, 2 . . . M. Elements are equally placed along a common circle. All the elements on a circle have the same amplitude distribution but they vary from circle to circle, i.e. vary radially. The far-field pattern [1,15] in free space for such CCCA with a central element is given by: ) cos( sin 1 1 1 ) , ( mn m m r jk M m N n m e I E φ φ θ φ θ - = = ∑∑ + = (1) Normalized absolute power pattern, P(θ,φ) in dB can be expressed as follows: ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ = max 2 max ) , ( ) , ( 10 log 20 ) , ( ) , ( 10 log 10 ) , ( φ θ φ θ φ θ φ θ φ θ E E E E P (2) Where r m = radius of m-th ring =N m d m /2π, d m = inter-element arc spacing of m-th circle, m mn N n / 2 π φ = =angular position of mn-th element with 1≤ n ≤ N m ,θ,φ = polar, azimuth angle, k = wave number = 2π/λ , λ=wave length, I m = excitation amplitude of elements on m-th circular ring, j=complex number. 71 978-1-4244-7406-6/10/$26.00 c 2010 IEEE