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Dynamic Thinning Strategy for Adaptive Nulling in Planar Antenna Arrays Paolo Rocca 1 and Randy L. Haupt 2 1 ELEDIA Research Group, DISI - University of Trento Via Sommarive 14, 38123, Trento, Italy - [email protected] 2 Applied Research Laboratory, The Pennsylvania State University, PO Box 30, State College, PA, USA 16804 - [email protected] Abstract—An approach for the suppression of undesired signals impinging on a planar array is presented in this paper. The procedure is based on a dynamic thinning enforced to the array to move sidelobe nulls. Towards this aim, each element of the array is equipped with a radio- frequency switch which is used to connect/disconnect the element to the feeding network. While changing the thinning sequences, the number of active elements is kept as constant as possible to maintain unaltered the antenna gain. A set of representative results is reported to show the effectiveness of the approach. 1. INTRODUCTION A well known and effective strategy which has been frequently used for the minimization of the sidelobe level (SLL) is based on the thinning of uniform arrays [1, 2]. In thinned arrays, some elements belonging to a periodic lattice are turned off to create a low sidelobe density taper on the antenna aperture while approximately maintaining the same main beam width of the original array. Such a reduction of the number of radiating elements allows a non- negligible simplification of the antenna layout and complexity of beam forming network. Moreover, a suitable thinning limits the costs of manufacturing, reduces the weight and the power consumption of the antenna system. The design of thinned planar arrays has been studied have been proposed in the scientific literature [3]-[9]. The first computationally effective approach is based on the use of randomly spaced elements [3] or statistical density tapering strategies [4]. More recently, numerical optimization techniques have been preferred by virtue of the large computational resources offered by modern personal computers and the ability of these procedures to deal with non-convex problems. Among them, approaches based on genetic algorithms [5], simulated annealing [6], and particle swarm optimizers [7] have been effectively used. To avoid the computational and convergence issues in the synthesis of large arrays with many elements, hybrid techniques [8, 9] and sub-optimal, but fast, deterministic strategies [10] have been exploited. Thinning avoids the problem of implementing a low sidelobe amplitude taper that requires weights each element. Often times, though, adaptive nulling is needed in addition to the low sidelobes, and adaptive strategies have been proposed [11]. Unfortunately, placing adaptive weights at each of the elements somewhat negates the advantages of doing the thinning in the first place. In this framework, this study proposes an innovative approach for adaptive thinned arrays able to suppress the unwanted signals in the sidelobe region. Starting from a conventional filled array configuration, a radio-frequency (RF) switch is used in the beam forming network for each element of the array. Accordingly, the thinned configuration is obtained by controlling the on-off sequence of the RF switches. In case of interference impinging on the antenna aperture, the thinning configuration changes until the unwanted signals are placed in nulls of the radiation pattern. In order to correctly receive the desired signal in the main lobe region, the number of elements which are “on” is kept as constant as possible between the different thinning configurations to prevent distortion to the main lobe. The paper is organized as follows. The synthesis problem is mathematically formulated in Section 2 and some preliminary results are shown in Section 3 in order to prove the effectiveness of the proposed approach. Finally, conclusions are drawn in Section 4. 2. MATHEMATICAL FORMULATION Without loss of generality for the application of the proposed approach, let us consider a concentric ring array laying on the y x − plane with a single element at the center and elements uniformly spaced on each ring. Mathematically, the array factor is given by (1) where r N and n N are the number of rings and the number of elements in the n -th ring, respectively, n w is the element weight for the n -th ring, and n r is the radius of ring n . Moreover, λ π 2 = k is the free-space wave number, λ being the wavelength, and the couple of values ( ) φ ϑ, identifies the angular direction. The position of a generic i -th element on the antenna aperture is given by the radius of the ring to which the element belongs and the angular position as ( ) ( ) m n m n i i r r y x φ φ sin , cos , = , n m N m / ) 1 ( 2 − = π φ . 978-1-4244-5128-9/10/$26.00 ©2010 IEEE 995
