Share This Article:

Antenna Array Pattern Synthesis via Coordinate Descent Method

Abstract Full-Text HTML XML Download Download as PDF (Size:2183KB) PP. 168-177
DOI: 10.4236/jemaa.2015.75018    4,428 Downloads   5,357 Views   Citations

ABSTRACT

This paper presents an array pattern synthesis algorithm for arbitrary arrays based on coordinate descent method (CDM). With this algorithm, the complex element weights are found to minimize a weighted L2 norm of the difference between desired and achieved pattern. Compared with traditional optimization techniques, CDM is easy to implement and efficient to reach the optimum solutions. Main advantage is the flexibility. CDM is suitable for linear and planar array with arbitrary array elements on arbitrary positions. With this method, we can configure arbitrary beam pattern, which gives it the ability to solve variety of beam forming problem, e.g. focused beam, shaped beam, nulls at arbitrary direction and with arbitrary beam width. CDM is applicable for phase-only and amplitude-only arrays as well, and furthermore, it is a suitable method to treat the problem of array with element failures.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Wang, Y. , He, X. , Wang, J. , Berezin, S. and Mathis, W. (2015) Antenna Array Pattern Synthesis via Coordinate Descent Method. Journal of Electromagnetic Analysis and Applications, 7, 168-177. doi: 10.4236/jemaa.2015.75018.

References

[1] Lebret, H. and Boyd, S. (1997) Antenna Array Pattern Synthesis via Convex Optimization. IEEE Transactions on Signal Processing, 45, 526-532.
http://dx.doi.org/10.1109/78.558465
[2] Schelkunoff, S.A. (1943) A Mathematical Theory of Linear Arrays. Bell System Technical Journal, 22, 80-107.
http://dx.doi.org/10.1002/j.1538-7305.1943.tb01306.x
[3] Dolph, C.L. (1946) A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level. Proceedings of the IRE, 34, 335-348.
http://dx.doi.org/10.1109/JRPROC.1946.225956
[4] Taylor, T.T. (1955) Design of Line-Source Antennas for Narrow Beamwidth and Low Side Lobes. Transactions of the IRE Professional Group on Antennas and Propagation, 3, 16-28.
http://dx.doi.org/10.1109/TPGAP.1955.5720407
[5] Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Professional, Boston.
[6] Storn, R. and Price, K. (1997) Differential Evolution—A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, 11, 341-359.
http://dx.doi.org/10.1023/A:1008202821328
[7] Kennedy, J. and Eberhart, R. (1995) Particle Swarm Optimization. IEEE International Conference on Neural Networks, 4, 1942-1948.
http://dx.doi.org/10.1109/icnn.1995.488968
[8] Taguchi, G., Chowdhury, S. and Wu, Y. (2004) Taguchi’s Quality Engineering Handbook. Wiley-Interscience, Hoboken.
[9] Weng, W.-C., Yang, F. and Elsherbeni, A.Z. (2007) Linear Antenna Array Synthesis Using Taguchi’s Method: A Novel Optimization Technique in Electromagnetics. IEEE Transactions on Antennas and Propagation, 55, 723-730.
http://dx.doi.org/10.1109/TAP.2007.891548
[10] Fuchs, B., Skrivervik, A. and Mosig, J.R. (2013) Shaped Beam Synthesis of Arrays via Sequential Convex Optimizations. IEEE Antennas and Wireless Propagation Letters, 12, 1049-1052.
http://dx.doi.org/10.1109/LAWP.2013.2280043
[11] Nongpiur, R.C. and Shpak, D.J. (2014) Synthesis of Linear and Planar Arrays with Minimum Element Selection. IEEE Transactions on Signal Processing, 62, 5398-5410.
http://dx.doi.org/10.1109/TSP.2014.2350966
[12] Subhashini, K.R. and Praveen Kumar, A.T. (2014) Comparative Analysis of Linear and Nonlinear Pattern Synthesis of Hemispherical Antenna Array Using Adaptive Evolutionary Techniques? International Journal of Antennas and Propagation, 2014, Article ID: 987140.
http://dx.doi.org/10.1155/2014/987140
[13] Haupt, R.L. (1994) Thinned Arrays Using Genetic Algorithms. IEEE Transactions on Antennas and Propagation, 42, 993-999.
http://dx.doi.org/10.1109/8.299602
[14] Haupt, R.L. and Johnson, J.M. (1999) Dynamic Phase-Only Array Beam Control Using a Genetic Algorithm. Proceedings of the 1st NASA/DoD Workshop on Evolvable Hardware, Pasadena, 19-21 July 1999, 217-224.
http://dx.doi.org/10.1109/EH.1999.785456
[15] Marcano, D. and Duran, F. (2000) Synthesis of Antenna Arrays Using Genetic Algorithms. IEEE Antennas and Propagation Magazine, 42, 12-20.
http://dx.doi.org/10.1109/74.848944
[16] Ares-Pena, F.J., Rodriguez-Gonzalez, J.A., Villanueva-Lopez, E. and Rengarajan, S.R. (1999) Genetic Algorithms in the Design and Optimization of Antenna Array Patterns. IEEE Transactions on Antennas and Propagation, 47, 506-510.
http://dx.doi.org/10.1109/8.768786
[17] Elkamchouchi, H.M. and Hassan, M.M. (2014) Array Pattern Synthesis Approach Using a Genetic Algorithm. IET Microwaves, Antennas & Propagation, 8, 1236-1240.
http://dx.doi.org/10.1049/iet-map.2013.0718
[18] Kurup, D.G., Himdi, M. and Rydberg, A. (2003) Synthesis of Uniform Amplitude Unequally Spaced Antenna Arrays Using the Differential Evolution Algorithm. IEEE Transactions on Antennas and Propagation, 51, 2210-2217.
http://dx.doi.org/10.1109/TAP.2003.816361
[19] Goudos, S.K., Siakavara, K., Samaras, T., Vafiadis, E.E. and Sahalos, J.N. (2011) Self-Adaptive Differential Evolution Applied to Real-Valued Antenna and Microwave Design Problems. IEEE Transactions on Antennas and Propagation, 59, 1286-1298.
http://dx.doi.org/10.1109/TAP.2011.2109678
[20] Guney, K. and Basbug, S. (2013) Null Synthesis of Time-Modulated Circular Antenna Arrays Using an Improved Differential Evolution Algorithm. IEEE Antennas and Wireless Propagation Letters, 12, 817-820.
http://dx.doi.org/10.1109/LAWP.2013.2271273
[21] Robinson, J. and Rahmat-Samii, Y. (2004) Particle Swarm Optimization in Electromagnetics. IEEE Transactions on Antennas and Propagation, 52, 397-407.
http://dx.doi.org/10.1109/TAP.2004.823969
[22] Boeringer, D.W. and Werner, D.H. (2004) Particle Swarm Optimization versus Genetic Algorithms for Phased Array Synthesis. IEEE Transactions on Antennas and Propagation, 52, 771-779.
http://dx.doi.org/10.1109/TAP.2004.825102
[23] Khodier, M.M. and Christodoulou, C.G. (2005) Linear Array Geometry Synthesis with Minimum Sidelobe Level and Null Control Using Particle Swarm Optimization. IEEE Transactions on Antennas and Propagation, 53, 2674-2679.
http://dx.doi.org/10.1109/TAP.2005.851762
[24] Donelli, M., Martini, A. and Massa, A. (2009) A Hybrid Approach Based on PSO and Hadamard Difference Sets for the Synthesis of Square Thinned Arrays. IEEE Transactions on Antennas and Propagation, 57, 2491-2495.
http://dx.doi.org/10.1109/TAP.2009.2024570
[25] Roy, S., Martinez, S.Z., Coello Coello, C.A. and Sengupta, S. (2012) A Multi-Objective Evolutionary Approach for Linear Antenna Array Design and Synthesis. Proceedings of the 2012 IEEE Congress on Evolutionary Computation (CEC), Brisbane, 10-15 June 2012, 1-8.
http://dx.doi.org/10.1109/CEC.2012.6252989
[26] Zangwill, W. (1969) Nonlinear Programming: A Unified Approach. Prentice-Hall, Englewood Cliffs.
[27] Kragh, T.J. (2006) Monotonic Iterative Algorithm for Minimum-Entropy Autofocus? Proceedings of the Adaptive Sensor Array Processing Workshop, Lexington, MA, 6-7 June 2006.
[28] Ash, J.N. (2012) An Autofocus Method for Backprojection Imagery in Synthetic Aperture Radar. IEEE Geoscience and Remote Sensing Letters, 9, 104-108.
http://dx.doi.org/10.1109/LGRS.2011.2161456
[29] Bouman, C.A. and Sauer, K. (1996) A Unified Approach to Statistical Tomography Using Coordinate Descent Optimization. IEEE Transactions on Image Processing, 5, 480-492.
http://dx.doi.org/10.1109/83.491321
[30] Shen, H.F., Zhang, L.P., Huang, B. and Li, P.X. (2007) A MAP Approach for Joint Motion Estimation, Segmentation, and Super Resolution. IEEE Transactions on Image Processing, 16, 479-490.
http://dx.doi.org/10.1109/TIP.2006.888334
[31] Nesterov, Y. (2012) Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems. SIAM Journal on Optimization, 22, 341-362.
http://dx.doi.org/10.1137/100802001
[32] Perini, J. and Idselis, M. (1971) Note on Antenna Pattern Synthesis Using Numerical Iterative Methods. IEEE Transactions on Antennas and Propagation, 19, 284-286.
http://dx.doi.org/10.1109/TAP.1971.1139919
[33] Bucci, O.M., Mazzarella, G. and Panariello, G. (1989) Reconfigurable Arrays by Phase-Only Control. Proceedings of the IEEE Antennas and Propagation Society International Symposium, San Jose, 26-30 June 1989, 142-145.
http://dx.doi.org/10.1109/APS.1989.134633
[34] Elliott, R.S. (1981) Antenna Theory and Design. Prentice-Hall, Englewood Cliffs.
[35] Peters, T.J. (1991) A Conjugate Gradient-Based Algorithm to Minimize the Sidelobe Level of Planar Arrays with Element Failures. IEEE Transactions on Antennas and Propagation, 39, 1497-1504.
http://dx.doi.org/10.1109/8.97381
[36] Yeo, B.-K. and Lu, Y. (1999) Array Failure Correction with a Genetic Algorithm. IEEE Transactions on Antennas and Propagation, 47, 823-828.
http://dx.doi.org/10.1109/8.774136
[37] Zainud-Deen, S.H., Ibrahem, M.S., Sharshar, H.A. and Ibrahem, S.M.M. (2004) Array Failure Correction with Orthogonal Method. Proceedings of the Twenty-First National Radio Science Conference, Cairo, 16-18 March 2004, B7-1-9.
[38] Mitilineos, S.A. and Capsalis, C.N. (2005) On Array Failure Mitigation Using Genetic Algorithms and a Priori Joint Optimization. IEEE Antennas and Propagation Magazine, 47, 227-232.
http://dx.doi.org/10.1109/MAP.2005.1599213
[39] Keizer, W.P.M.N. (2007) Element Failure Correction for a Large Monopulse Phased Array Antenna with Active Amplitude Weighting. IEEE Transactions on Antennas and Propagation, 55, 2211-2218.
http://dx.doi.org/10.1109/TAP.2007.902008
[40] Bucci, O.M., Capozzoli, A. and D’Elia, G. (2000) Diagnosis of Array Faults from Far-Field Amplitude-Only Data. IEEE Transactions on Antennas and Propagation, 48, 647-652.
http://dx.doi.org/10.1109/8.855482

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.