THINNED HEXAGONAL ARRAYS FOR SATELLITE APPLICATIONS. OPTIMIZED WITH GENETIC ALGORITHMS. M.C. Vigano'. 1. , G. Toso. 1. , S. Selleri. 2.
THINNED HEXAGONAL ARRAYS FOR SATELLITE APPLICATIONS OPTIMIZED WITH GENETIC ALGORITHMS M.C. Vigano’1, G. Toso1, S. Selleri2, C. Mangenot1, P. Angeletti1, G. Pelosi2 1
European Space Agency ESA ESTEC, Keplerlaan 1, PB 299, 2200 AG Noordwijk, The Netherlands, {carolina.vigano; giovanni.toso; cyril.mangenot; piero.angeletti}@esa.int 2
Department of Electronics and Telecommunications, University of Florence Via C. Lombroso 6/17, I-50134 Florence, Italy {stefano.selleri; giuseppe.pelosi}@unifi.it
ABSTRACT This paper addresses the problem of the optimization of a transmit Direct Radiating Array (DRA) in Ka-band for generating a multibeam coverage from a geostationary orbit. By mean of Genetic Algorithms (GA) evolutionary optimization, more than 30% of the elements of the initial fully populated array may be switched off while maintaining the array compliant with stringent radiation constraints. INTRODUCTION Present and future generation of communication satellites will use multiple beam antennas providing down link and uplink coverages over a field of view for personal communication, direct broadcast or mobile communication applications. High gain multiple overlapping spot beams, adopting both frequency and polarization reuse, will provide the needed coverage. In order to generate high gain spot beams, electrically large antenna apertures are required. These apertures may be generated by either reflectors or phased arrays. Most of the reflector-based multiple beam antennas adopt one feed per beam architectures with adjacent beams generated by different reflectors fed by a cluster of horns [1]. This leads to three to four reflector antennas for European or CONUS coverage receive functions and the same number for transmit. A possible solution to generate a multi-beam coverage using a single aperture is the Focal Array Fed Reflector (FAFR) described in [2]. The beam generation is performed by illuminating together individual feeds using a beamforming network and the overlapped beam footprint in obtained reusing some of the reflector focal plane feeds for several beams. The FAFR is quite complex at focal array level but offers the main advantage of using only one antenna (array + reflector) to generate the full set of beams. Both the previous concepts suffer from severe accommodation or implementation difficulties. In a long term perspective, solutions based on a single aperture are more appealing and could offer important advantages especially in terms of costs, mass and spacecraft accommodation. Phased arrays would be a natural choice to generate multiple beams but they have been often dismissed essentially because of their complexity and cost [3]. One way to reduce the price of the array consists in reducing as much as possible the number of active elements (thinning the array) maintaining under control the main radiative characteristics of the array itself.
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In this paper, Genetic Algorithms (GA) are used to thin an initially fully populated hexagonal array. In most of the papers published on thinned arrays [4] [5] the objective is only the maximization of the number of elements to be switched off while guarantying the minimum sidelobe level (SLL) for the array. In this paper the optimization is a multi-parametric. Besides increasing as much as possible the thinning factor of the array, the array should guarantee a fixed gain value at the end of coverage (EOC) of each beam, and a maximum interfering isolation (C/I) in adjacent beams reusing the same frequency and polarization. HEXAGONAL THINNED ARRAY OPTIMIZATION The transmitting antenna considered in this study is operating in Ka-band (19.5-20 GHz) and should have a maximum diameter of 1.3 meters. The basic idea is that of using a hexagonal direct radiating array with dimensions sufficient to provide the required maximum gain and a beamwidth of less than 1 degree. The initial array is fully populated i.e. has elements in all the positions of the hexagonal lattice. The array should generate 64 spot beams. The total band is subdivided into 4 sub-bands, and each is assigned to a spot (see Fig.1) such that there are no adjacent spots with the same characteristics. Fig. 1 shows the footprint on the Earth of the 64 spots and the relative requirements. Spots number 64 Spot diameter 0.65° Inter-spot 0.56° distance Tx band 19.7 – 20.2 GHz Frequency reuse 1:4 EOC gain > 43.8 dBi Single Entry C/I
> 20 dB
Fig. 1 – European coverage with 64 spots, and technical requirements for the antenna. The coverage and the technical requirements in Fig. 1 have been provided by Alcatel Alenia Space (F) and have been used for the ESA Domino II mission. In Fig. 2, on the right, the EOC and C/I values are indicated in the multibeams pattern; the two black beams have the same operating frequency while the intermediate green one works at a different frequency. The optimum distance between the elements in the hexagonal array is the range 3-4 λ; these values take into account not only the positions of the grating lobes with respect to the required geostationary coverage, but also the scanning losses caused by the antenna elements. In the case of a 4 λ distance, antenna elements may be rectangular horns with dimension 4λ × 2 3λ . Considering the typical aperture efficiencies of these horns, each of them may guarantee a gain around 21 dBi. With this choice, a hexagonal array with 11 rings around a central element, with
(
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)
a total number of 397 elements, could satisfy the initial requirement on the EOC gain while the C/I level of 20 dB is not satisfied with a uniform amplitude distribution.
Fig. 2 – Array geometry and visual representation of the requested spot characteristics. The optimization aim is hence to reduce as much as possible the total number of active elements, keeping satisfied the EOC requirements and satisfying as well the C/I isolation. The application of Genetic Algorithms to array thinning is particularly straightforward, since GA, in their standard implementation, deal with binary data and the thinning problem is inherently binary [6]. The main problem in the implementation of GA consists in the selection of an appropriate cost function. In particular, the selected cost function includes constraints on the EOC and C/I values, and on the number of active elements. Fig. 3 presents one of the best results obtained after a long trade-off: a hexagonal array with 68% of the elements switched on and no constraints on the alimentation of the central part of the array elements. In Fig. 4 several cuts of the pattern are presented demonstrating the compliance of the pattern with respect to the initial requirements. In Fig. 5 and 6, results obtained with the same number of element switched on, but distributed with GA on 12 instead of 11 rings are shown. In this last case, because the number of possible configurations has increased, the SLL improves and the requirements are satisfied with a larger margin. CONCLUSIONS In this paper the optimization of a transmit array for satellite applications has been considered. Resorting to GA several elements of the array have been switched off. More than 30% of the initial elements may be switched off satisfying the technical requirements. The optimized configuration permits reducing drastically the cost of the array and improving the C/I level with respect to the initial fully populated array. Improvements may be achieved refining further the cost function, and optimizing the element factor.
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Fig. 3 – 11-rings thinned array optimized with GA (coordinates in meters).
Fig. 4 – 11-rings optimised array: pattern showing the beam in the boresight direction in different azimuth cuts
Fig. 5 – 12-rings thinned array optimized with GA (coordinates in meters).
Fig. 6 – 12-rings optimised array: pattern showing the beam in the boresight direction in different azimuth cuts
REFERENCES [1] Y. Cailloce, G. Caille, I. Albert, J.M. Lopez, “Ka-band Antennas providing multiple beams for a multimedia via satellite mission,” Alcatel Space Industries and Centre National d’Etudes Spatiales Technical Report. [2] C. Mangenot, P. Lepeltier, J.L. Cazaux, J. Maurel, “Ka-band fed array focal reflector receive antenna design and development using MEMS switches”, JINA Conference 2002, November 12-14 2002, invited presentation, Vol. II, pag. 337-345. [3] R.J. Mailloux, Phased Array Antenna Handbook, Artech House, Boston (MA), 2005. [4] R.L. Haupt , “Thinned Arrays Using Genetic Algorithms”, IEEE Trans. Antennas Propagat., Vol. 41, No. 2, Feb. 1993, pp. 993-999. [5] J.O. Erstad, S. Holm, “An Approach to Design of Sparse Array Systems”, Proc. 1994 IEEE Symp. Ultrasonic, Cannes, France, 1-4 Oct. 1994, pp. 1507-10. [6] D.E. Golberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading (MA), 1989.
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