Lagrange Programming Neural Network Approach for Frequency Diverse Array Beampattern Synthesis

  • 45 Accesses


Different from traditional phased array radar, frequency diverse array (FDA) radar uses a small frequency increment across the array elements; thus, the beampattern of FDA can be performed in both range and angle domains. Nevertheless, the transmit beampattern of conventional FDA is coupled in range and angle domains, which is not suitable for target detection. In this paper, we propose a multi-carrier FDA framework to generate the range-angle-decoupled beampattern. To focus the transmit energy at the desired position and suppress the interference at the undesired position, we then propose a beampattern synthesis approach based on Lagrange programming neural network, which can be implemented by hardware easily. Numerical simulation results demonstrate the effectiveness of the proposed method.

This is a preview of subscription content, log in to check access.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13


  1. 1.

    P. Antonik, M.C. Wicks, H.D. Griffiths, C.J.Baker, Frequency diverse array radars, in Proceedings of the IEEE Radar Conference, Verona, NY 2006, pp. 215–217. IEEE

  2. 2.

    S. Arik, An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans. Neural Netw. 13(5), 1239–1242 (2002)

  3. 3.

    A. Basit, W. Khan, S. Khan, I.M. Qureshi, Development of frequency diverse array radar technology: a review. IET Radar Sonar Navig. 12(2), 165–175 (2018)

  4. 4.

    A. Basit, I.M. Qureshi, W. Khan, A.N. Malik, Range–angle-dependent beamforming for cognitive antenna array radar with frequency diversity. Cogn. Comput. 8(2), 1–13 (2015)

  5. 5.

    N.M. Botros, M. Abdul-Aziz, Hardware implementation of an artificial neural network using field programmable gate arrays (FPGA’s). IEEE Trans. Ind. Electron. 41(6), 665–667 (2002)

  6. 6.

    V. Boyd, Faybusovich: convex optimization. IEEE Trans. Autom. Control 51(11), 1859 (2006)

  7. 7.

    J. Cao, J. Wang, Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 50(1), 34–44 (2003)

  8. 8.

    S.L. Chi, J. Sum, H.C. So, A.G. Constantinides, F.K.W. Chan, Lagrange programming neural networks for time-of-arrival-based source localization. Neural Comput. Appl. 24(1), 109–116 (2014)

  9. 9.

    K. Gao, W.Q. Wang, J. Cai, J. Xiong, Decoupled frequency diverse array range–angle-dependent beampattern synthesis using non-linearly increasing frequency offsets. IET Microw. Antennas Propag. 10(8), 880–884 (2016)

  10. 10.

    K. Gao, W.Q. Wang, H. Chen, J. Cai, Transmit beamspace design for multi-carrier frequency diverse array sensor. IEEE Sens. J. 16(14), 5709–5714 (2016)

  11. 11.

    P. Gong, Z. Shao, G. Tu, C. Qin, Transmit beampattern design based on convex optimization for MIMO radar systems. Signal Process. 94(1), 195–201 (2014)

  12. 12.

    S. Haykin, Cognitive radar: a way of the future. IEEE Signal Process. Mag. 23(1), 30–40 (2006)

  13. 13.

    W. Khan, I.M. Qureshi, A. Basit, M. Zubair, A double pulse MIMO frequency diverse array radar for improved range-angle localization of target. Wirel. Pers. Commun. 82(4), 1–15 (2015)

  14. 14.

    W. Khan, I.M. Qureshi, S. Saeed, Frequency diverse array radar with logarithmically increasing frequency offset. IEEE Antennas Wirel. Propag. Lett. 14(1), 499–502 (2015)

  15. 15.

    F. Li, Delayed Lagrangian neural networks for solving convex programming problems. Neurocomputing 73(10), 2266–2273 (2010)

  16. 16.

    H. Liu, L. Dong, Z. Yi, T.K. Truong, Simultaneous radio frequency and wideband interference suppression in SAR signals via sparsity exploitation in time-frequency domain. IEEE Trans. Geosci. Remote Sens. PP(99), 1–14 (2018)

  17. 17.

    R.J. Mailloux, Phased Array Antenna Handbook. Artech House Antennas and Propagation Library, 2nd edn. (Artech House, Boston, 2005)

  18. 18.

    L. Qingshan, C. Jinde, X. Youshen, A delayed neural network for solving linear projection equations and its analysis. IEEE Trans. Neural Netw. 16(4), 834–843 (2005)

  19. 19.

    P.F. Sammartino, C.J. Baker, Developments in the frequency diverse bistatic system, in Radar Conference 2009, pp. 1–5

  20. 20.

    M. Secmen, S. Demir, A. Hizal, T. Eker, Frequency diverse array antenna with periodic time modulated pattern in range and angle, in IEEE Radar Conference 2007, pp. 427–430

  21. 21.

    H.Z. Shao, J. Dai, J. Xiong, H. Chen, W.Q. Wang, Dot-shaped range-angle beampattern synthesis for frequency diverse array. IEEE Antennas Wirel. Propag. Lett. 15, 1703–1706 (2016)

  22. 22.

    W.Q. Wang, Cognitive frequency diverse array radar with situational awareness. IET Radar Sonar Navig. 10(2), 359–369 (2016)

  23. 23.

    J. Xu, S. Zhu, G. Liao, Range ambiguous clutters suppression for airborne FDA-STAP radar. IEEE J. STSP 9(8), 1620–1631 (2015)

  24. 24.

    Y. Xu, X. Shi, J. Xu, L. Huang, W. Li, Range–angle-decoupled beampattern synthesis with subarray-based frequency diverse array ☆. Digit Signal Process. 64, 49–59 (2017)

  25. 25.

    S. Zhang, A.G. Constantinides, Lagrange programming neural networks. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 39(7), 441–452 (1992)

Download references

Author information

Correspondence to Tianfang Chen.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, T., Xia, D. Lagrange Programming Neural Network Approach for Frequency Diverse Array Beampattern Synthesis. Circuits Syst Signal Process 39, 439–455 (2020).

Download citation


  • Frequency diverse array (FDA)
  • Beampattern synthesis
  • Range-angle-decoupled
  • Multi-carrier frequency
  • Lagrange programming neural network