The Peano-Gosper fractal array

This paper investigates the radiation characteristics of a new type of array that is based on the family of space-filling and self-avoiding fractals known as Peano-Gosper curves. The elements of the fractal array are uniformly distributed along a Peano-Gosper curve, which leads to a planar array configuration with parallelogram cells that is bounded by a closed Koch curve. These unique properties are exploited in order to develop a design methodology for deterministic arrays that have no grating lobes even when the minimum spacing between elements is increased to at least one wavelength. This leads to a class of arrays that are relatively broad-band when compared to more conventional periodic planar arrays with square or rectangular cells and regular boundary contours. An efficient iterative procedure for calculating the radiation patterns of these Peano-Gosper fractal arrays to arbitrary stage of growth P is also introduced in this paper.

[1]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[2]  Randy L. Haupt.  Thinned arrays using genetic algorithms , 1994 .

[3]  D. Werner,et al.  The theory and design of fractal antenna arrays , 1999 .

[4]  M. T. Ma,et al.  Theory and application of antenna arrays , 1974 .

[5]  Douglas H. Werner,et al.  Matching network design using genetic algorithms for impedance constrained thinned arrays , 2002, IEEE Antennas and Propagation Society International Symposium (IEEE Cat. No.02CH37313).

[6]  Douglas H. Werner,et al.  Optimization of thinned aperiodic linear phased arrays using genetic algorithms to reduce grating lobes during scanning , 2002 .

[7]  V. Murino,et al.  Stochastic optimization of linear sparse arrays , 1999 .

[8]  C.H. Chen,et al.  Genetic algorithm optimization of antenna arrays with variable interelement spacings , 1998, IEEE Antennas and Propagation Society International Symposium. 1998 Digest. Antennas: Gateways to the Global Network. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.98CH36.

[9]  D.J. O'Neill.  Element placement in thinned arrays using genetic algorithms , 1994, Proceedings of OCEANS'94.

[10]  C. A. Meijer,et al.  Simulated annealing in the design of thinned arrays having low sidelobe levels , 1998, Proceedings of the 1998 South African Symposium on Communications and Signal Processing-COMSIG '98 (Cat. No. 98EX214).

[11]  Y. Kim,et al.  The fractal random array , 1986, Proceedings of the IEEE.

[12]  D.W. Boeringer,et al.  Thinned aperiodic linear phased array optimization for reduced grating lobes during scanning with input impedance bounds , 2001, IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.01CH37229).