GA-BASED PREDICTION OF ANTENNA RADIATION PATTERNS FROM PLANAR NEAR-FIELD SAMPLES J. R. Pe ´ rez and J. Basterrechea Department of Communications Engineering University of Cantabria Avda. de Los Castros s/n 39005 Santander, Spain Received 12 November 2002 ABSTRACT: In this paper, a genetic-algorithm (GA) based approach for predicting the far-field pattern of an antenna under test (AUT) from planar near-field samples is presented. The method reconstructs the an- tenna radiation pattern from an optimized equivalent model of the AUT consisting of electric and magnetic short dipoles. Numerical results showing predicted far-field patterns are reported and discussed. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 235–236, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10880 Key words: near field; far field; antenna measurements; genetic algo- rithms INTRODUCTION Among the most well-known planar near-field (NF) to far-field (FF) transformation techniques [1, 2], the fast-Fourier-transform (FFT) based method is the most popular one, involving a low degree of mathematical and computational complexity. In this paper, another approach based on a global optimization technique is proposed as a powerful and versatile alternative to classical methods. The method is applicable to NF–FF transformation, making it possible to estimate the far-field pattern of the antenna under test (AUT) from the tangential components of its near field, measured or computed over a planar surface. Basically, it uses near-field data to determine the excitation of a set of dipoles distributed over a fictitious planar surface that encompasses the AUT. Then, the far-field radiation pattern can be estimated from these equivalent dipoles. DESCRIPTION OF THE METHOD Using the equivalence principle, the radiation of an AUT can be modeled using equivalent electric and magnetic current densities distributed over a surface enclosing the source. In this approach, these current densities are modeled by means of electric and magnetic short dipoles, uniformly spaced on a surface S e that encompasses the antenna aperture, as shown in Figure 1. The goal is to optimize the equivalent model in such a way that it radiates as close as possible to the original AUT, using the information provided by the grid of near-field samples S f as a reference. Let us suppose N electric and magnetic dipoles are used to reproduce the radiation pattern of an AUT from L near-field samples, E l . The spherical components of the electric field radiated by the whole set of dipoles at each near-field point are given by E d = E e + E m =  i=1 N/2 [R i ] -1 [T i ] -1 E ei +  i=1 N/2 [R i ] -1 [T i ] -1 E mi , (1) where [R i ] and [T i ] represent the rotation and translation matrixes used to express the fields in the global coordinate system as a function of the fields radiated by an isolated and z -directed electric or magnetic dipole, E ei and E mi , given by E eir =  2  M i  e jPi  cos  i R i, l 2   1 + 1 jkR i, l   e -jkRi,l , (2) E ei = j k 4  M i  e jPi  sin  i R i, l   1 + 1 jkR i, l - 1 kR i, l  2  e -jkRi,l , (3) E mi = -jk 4  M i  e jPi  sin  i R i, l   1 + 1 jkR i, l   e -jkRi,l , (4) where M i and P i are the amplitude and phase (respectively) of the dipolar moment for the dipole i , R i , l is the distance between the source point i and the observation point l ,  is the free-space impedance, and k is the wave number. The number, type, location, and orientation for each dipole are known parameters, which depend on the AUT and the frequency. Thus, the only parameters in Eqs. (1)–(4) available to shape the radiation pattern of the AUT are the dipolar moments. The optimization is carried out using genetic algorithms (GAs) [3], in which a set of chromosomes or potential solutions is made to evolve as the result of the pressure exerted by three mechanisms: selection, crossover, and mutation. Each chromosome C in Eq. (5) represents a vector to be optimized: C = M 1 , P 1 ,..., M i , P i ,..., M N , P N . (5) The aim is to maximize the fitness function given by Eq. (6), linking the near-field data E l and the near-field radiated by the equivalent model E d (C), so as to find that vector C which best fits the L near-field samples. Once the GA-based process reaches an accurate solution, the far-field pattern can be computed from Eqs. (1)–(4) under far-field conditions. F =  l=1 L 1 1 + | E l - E d (C)| 2 (6) The main parameters of the binary GA used [4] are listed in Table 1. The accuracy of the method depends mainly on the type of AUT to be analyzed, on the near-field data, and on the number, spacing, and type of dipoles used. Figure 1 Equivalent model for the AUT MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 37, No. 4, May 20 2003 235