Vol. 25

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2010-09-16

Synthesis of Optimal Narrow Beam Low Sidelobe Linear Array with Constrained Length

By Jean-Jacques Fuchs and Benjamin Fuchs
Progress In Electromagnetics Research B, Vol. 25, 315-330, 2010
doi:10.2528/PIERB10070607

Abstract

The synthesis of optimal narrow beam low sidelobe linear array is addressed. Only the length of the array is constrained. The number, the positions and the weightings of the elements are left free. It is proven, that the optimal design is always an array with a small number of elements. One first demonstrates that among equally spaced linear arrays of given length, the sparsest Dolph-Chebyshev design, i.e., the one with the largest admissible inter-element distance, is the optimal one. Then, the restriction to equally spaced elements is removed, and the general problem is solved and discussed. It is shown that the sparsest Dolph-Chebyshev designs are optimal for array lengths in given specified intervals and close to optimal for all other lengths.

Citation


Jean-Jacques Fuchs and Benjamin Fuchs, "Synthesis of Optimal Narrow Beam Low Sidelobe Linear Array with Constrained Length," Progress In Electromagnetics Research B, Vol. 25, 315-330, 2010.
doi:10.2528/PIERB10070607
http://jpier.org/PIERB/pier.php?paper=10070607

References


    1. Dolph, C. L., "A current distribution for broadside arrays which optimizes the relationship between beam width and sidelobe level," Proc. IRE, Vol. 34, 335-348, June 1946.
    doi:10.1109/JRPROC.1946.225956

    2. Riblet, H. J., "Discussion of Dolphs paper," Proc. IRE, Vol. 35, 489-492, May 1947.
    doi:10.1109/JRPROC.1947.232940

    3. McNamara, D. A., "An exact formulation for the synthesis of broadside Chebyshev arrays of 2N elements with interelement spacing d < λ/2," Microwave and Optical Technology Letters, Vol. 48, No. 3, 457-463, March 2006.
    doi:10.1002/mop.21378

    4. Skolnik, M. I., "Nonuniform arrays," Collin-Zucker Antenna Theory, Chapter 6, McGraw-Hill, New York, 1969.

    5. Kumar, B. P. and G. R. Branner, "Design of unequally spaced arrays for performance improvment," IEEE Transactions on Antennas and Propagation, Vol. 47, No. 3, 511-523, March 1999.
    doi:10.1109/8.768787

    6. Lee, K.-C. and J.-Y. Jhang, "Application of particle swarm algorithm to the optimization of unequally spaced antenna arrays," Journal of Electromagnetic Wave and Applications, Vol. 20, No. 14, 2001-2012, 2006.
    doi:10.1163/156939306779322747

    7. Oraizi, H. and M. Fallahpour, "Non uniformly spaced linear array design for the specified beamwidth/sidelobe level or specified directivity/sidelobe level with coupling considerations," Progress In Electromagnetics Research M, Vol. 4, 185-209, 2008.
    doi:10.2528/PIERM08072302

    8. Bevelacqua, P. J. and C. A. Balanis, "Minimum sidelobe levels for linear arrays," IEEE Transactions on Antennas and Propagation, Vol. 55, No. 12, 3442-3449, December 2007.
    doi:10.1109/TAP.2007.910490

    9. Lebret, H. and S. Boyd, "Antenna pattern synthesis via convex optimization," IEEE Transactions on Signal Processing, Vol. 45, No. 3, 526-531, March 1997.
    doi:10.1109/78.558465

    10. Fuchs, B. and J. J. Fuchs, "Optimal narrow beam low sidelobe synthesis of arbitrary arrays," IEEE Transactions on Antennas and Propagation, Vol. 58, No. 6, 2130-2135, June 2010.
    doi:10.1109/TAP.2010.2046863

    11. Luenberger, D. G., Introduction to Linear and Nonlinear Programming, Addison Wesley, 1973.