BANANI BASU AND G. K. MAHANTI: CONSTRICTED PARTICLE SWARM OPTIMIZATION FOR DESIGN OF COLLINEAR ARRAY OF UNEQUAL LENGTH DIPOLE ANTENNAS DOI: 10.21917/ijsc.2010.0007 42 CONSTRICTED PARTICLE SWARM OPTIMIZATION FOR DESIGN OF COLLINEAR ARRAY OF UNEQUAL LENGTH DIPOLE ANTENNAS Banani Basu 1 and G. K. Mahanti 2 Department of Electronics & Communication Engineering, National Institute of Technology, Durgapur, India E-mail: basu_banani@yahoo.co.in 1 , gautammahanti@yahoo.com 2 Abstract A method based on constricted Particle Swarm Optimization (CPSO) algorithm to design a non-uniformly spaced collinear array of thin dipole antennas of unequal height is proposed. This paper presents a method for computing the appropriate excitation and geometry of individual array elements to generate a pencil beam in the vertical plane with minimum Standing Wave Ratio (SWR) and fixed Side Lobe Level (SLL). Coupling effect between any two collinear center- fed thin dipole antennas having sinusoidal current distributions is analyzed using induced EMF method and minimized in terms of SWR. DRR of excitation distribution is fixed at a lower value for further mitigation of the coupling effect. Phase distribution for all the elements is kept at zero degree for broadside array. Optimization results show the effectiveness of the algorithm for the design of the array. Moreover method seems very conducive for estimating the mutual impedance between any two collinear center-fed thin dipole antennas having sinusoidal current distributions. Keywords: Constricted Particle Swarm Optimization (CPSO), Collinear Dipole Array, Standing Wave Ratio (SWR), Induced EMF Method, Dynamic Range Ratio (DRR) 1. INTRODUCTION Array pattern synthesis is achieved by appropriately computing the excitation and geometric configuration of its radiating elements. Many methods have been used to achieve specified radiation pattern for non-uniformly excited, non- uniformly spaced linear arrays [1-12]. The analysis of non- uniformly spaced linear arrays was proposed by Unz[1], who developed a matrix formulation to obtain the current distribution necessary to generate a desired radiation pattern [1]. Skolnik [2] employed dynamic programming to design a unequally spaced array. Mailloux and Cohen [3] utilized the statistical thinning of arrays with quantized element weights to improve side lobe level performance. Different global optimization algorithms such as Genetic Algorithm (GA), Simulated Annealing (SA) and pattern search algorithm were used to thin an array [4–8]. Non- uniformly spaced array was further synthesized by randomly positioning the array element along the desired direction. Harrington developed an iterative method to reduce the sidelobe level of uniformly excited linear arrays by employing unequal spacing [9]. His method reduces the sidelobe level effectively without increasing the beamwidth of the mainbeam as obtained by uniformly spaced linear array. Literature described in [10-12] proposed different conventional and soft computing techniques for synthesis of non-uniformly spaced array. In article [10], the particle swarm optimization was applied for optimization of non-uniformly spaced antenna arrays and side lobe level was reduced. Neural Network (NN) and least mean square technique was used to design non-uniformly spaced array [11,12]. However most of the works consider the minimization of the side lobe level without considering mutual coupling effect. In recent works driving point impedance matching has been derived with unequal spacing of elements [13,14]. King [15] presented a method for evaluating the real and imaginary components of mutual impedance between any two thin dipole antennas, with an emphasis on antennas having sinusoidal current distributions. In the proposed work, we synthesize a non-uniformly spaced array consists of radiators of unequal heights. In our wok, CPSO is used for the synthesis of pencil beam pattern with specified SLL, DRR and minimum SWR value by optimizing the excitation and geometry of the individual array element. Coupling effect is compensated by minimizing standing wave ratio along with fixing dynamic ranges of excitation current amplitude distributions to a lower value. Impedance matrix is calculated using induced EMF method [15, 16]. 2. THEORETICAL FORMULATION We consider an array of 2N collinear wire dipoles oriented in the vertical direction. All the dipoles are assumed non-identical and have very thin radii. The radiation pattern in the vertical plane depends on the geometry of the array as well as on the excitation currents applied at the center of the dipoles. The geometry of the array is specified by the lengths n l (n = 1,…., N) of the dipoles and the inter element spacing 1 ,  n n d (n = 2,. . . , N) between them. Array elements are placed symmetrically on each side of the origin. Excitation and geometry both are assumed symmetric with respect to the origin. Assuming sinusoidal current distribution of a very thin dipole antenna directed along Z-axis, the element pattern is given by Eq. (1).     sin 2 cos 2 cos cos               n n kl kl Elepat (1) The far-field pattern [16] F(θ) in the vertical plane considering the element pattern with symmetric amplitude distributions is given by Eq.(2)        Elepat N n n kp n I F     1 cos cos 2 (2) Normalized power pattern in dB can be expressed as follows.                        max 10 2 max 10 log 20 log 10      F F F F P (3)