MIMO Radar Array Configuration with Enhanced Degrees of Freedom and Increased Array Aperture


This paper presents a new antenna array design approach for multiple-input multiple-output (MIMO) radar. The geometry exhibits increased degrees of freedom (DOFs) with precise antenna locations for direction-of-arrival (DOA) estimation of sources. The enhancement is realized by using the method of sum coarray of the difference coarray (SCDC). By effectively increasing the inter-element spacing of the transmitting array, a larger hole-free SCDC uniform linear array (ULA) is obtained. This increment provides more DOFs and extended virtual array aperture (VAA) for intended geometry. The transmitting and receiving sensor positions are based on the maximum inter-element spacing constraint (MISC) principle. The MISC composition involves three sparse ULAs with two separate antennas placed appropriately. The mathematical expressions are presented to validate the designed model. Moreover, arbitrary and optimized antenna scenarios for the transmitter and receiver are investigated in terms of DOFs and VAA. The advantages of the proposed configuration are demonstrated by conducting rigorous Monte Carlo simulations. The experimental results of DOFs, VAA, number of resolvable sources, Cram\(\acute{\hbox {e}}\)r–Rao bound performance, detection, and resolution ability reveal that the proposed sensor array design approach is suitable for MIMO radar which is also capable of estimating the DOAs of multiple sources efficiently in underdetermined scenarios.

This is a preview of subscription content, access via your institution.

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


  1. 1.

    E. BouDaher, F. Ahmad, M.G. Amin, Sparsity-based direction finding of coherent and uncorrelated targets using active nonuniform arrays. IEEE Signal Process. Lett. 22(10), 1628–1632 (2015)

    Article  Google Scholar 

  2. 2.

    C.Y. Chen, P.P. Vaidyanathan, Minimum redundancy MIMO radars, in Proceedings of IEEE International Symposium on Circuits and System, pp. 45–48 (2008)

  3. 3.

    W. Chen, K. Wong, J. Reilly, Detection of the number of signals, a predicted eigen-threshold approach. IEEE Trans. Signal Process. 39, 1088–1098 (1991)

    Article  Google Scholar 

  4. 4.

    J. Dai, X. Bao, N. Hu, C. Chang, W. Xu, A recursive RARE algorithm for DOA estimation with unknown mutual coupling. IEEE Antennas Wirel. Propag. Lett. 13, 1593–1596 (2014)

    Article  Google Scholar 

  5. 5.

    J. Dong, J. Yang, W. Lei, R. Shi, Y. Guo, Antenna array design in MIMO radar using cyclic difference sets and simulated annealing, in Proceedings of International Conference on Microwave and Millimeter Wave Technology, ICMMT 2012, pp. 237–240 (2012)

  6. 6.

    J. Dong, R. Shi, Y. Guo, W. Lei, Antenna array design in MIMO radar using cyclic difference sets and genetic algorithm, in 10th International Symposium on Antennas, Propagation and EM Theory, ISAPE, pp. 26–29 (2012)

  7. 7.

    J. Dong, Q. Li, W. Guo, A combinatorial method for antenna array design in minimum redundancy MIMO radars. IEEE Antennas Wirel. Propag. Lett. 8(3), 1150–1153 (2009)

    MathSciNet  Article  Google Scholar 

  8. 8.

    E. Fishler, A. Haimovich, R.S. Blum, L.J. Cimini, D. Chizhik, R.A. Valenzuela, Spatial diversity in radars–models and detection performance. IEEE Trans. Signal Process. 54(3), 823–838 (2006)

    Article  Google Scholar 

  9. 9.

    I. Gupta, A. Ksienski, Effect of mutual coupling on the performance of adaptive arrays antennas propagation. IEEE Trans. 31, 785–791 (1983)

    Article  Google Scholar 

  10. 10.

    Y. Huang, G. Liao, J. Li, H. Wang, Sum and difference coarray based MIMO radar array optimization with its application for DOA estimation. Multidimens. Syst. Signal Process. 28(4), 1183–1202 (2017)

    MathSciNet  Article  Google Scholar 

  11. 11.

    H. Jiang, J.K. Zhang, K.M. Wong, Joint DOD and DOA estimation for bistatic MIMO radar in unknown correlated noise. IEEE Trans. Veh. Technol. 64(11), 5113–5125 (2015)

    Article  Google Scholar 

  12. 12.

    A. Kirschner, J. Guetlein, J. Detlefsen, MIMO radar setups by nesting braced minimum redundancy arrays, in german microwave conference, Aachen, Germany, pp. 10–13 (2014)

  13. 13.

    G. Liao, M. Jin, J. Li, A two-step approach to construct minimum redundancy MIMO radars, in International Radar Conference “Surveillance for a Safer World”, pp. 1–4 (2009)

  14. 14.

    J. Li, P. Stoica, MIMO radar with colocated antennas. IEEE Signal Process. Mag. 24, 106–114 (2007)

    Article  Google Scholar 

  15. 15.

    J. Li, D. Jiang, X. Zhang, DOA estimation based on combined unitary ESPRIT for coprime MIMO radar. IEEE Commun. Lett. 21(1), 96–99 (2017)

    Article  Google Scholar 

  16. 16.

    J. Li, P. Stoica, Y. Xie, On probing signal design for MIMO radar, in The Asilomar Conference on Signals, Systems, and Computers, pp. 31–35 (2006)

  17. 17.

    C.L. Liu, P.P. Vaidyanathan, Super nested arrays: linear sparse arrays with reduced mutual coupling—part I: fundamentals. IEEE Trans. Signal Process. 64(15), 3997–4012 (2016)

    MathSciNet  Article  Google Scholar 

  18. 18.

    C.L. Liu, P.P. Vaidyanathan, Hourglass arrays and other novel 2-D sparse arrays with reduced mutual coupling. IEEE Trans. Signal Process. 65(13), 3369–3383 (2017)

    MathSciNet  Article  Google Scholar 

  19. 19.

    A.T. Moffet, Minimum-redundancy linear arrays. IEEE Trans. Antennas Propag. 16(2), 172–175 (1968)

    Article  Google Scholar 

  20. 20.

    G. Oliveri, F. Caramanica, M.D. Migliore, A. Massa, Synthesis of nonuniform MIMO arrays through combinatorial sets. IEEE Antennas Wirel. Propag. Lett. 11, 728–731 (2012)

    Article  Google Scholar 

  21. 21.

    P. Pal, P.P. Vaidyanathan, Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 58(8), 4167–4181 (2010)

    MathSciNet  Article  Google Scholar 

  22. 22.

    S. Qin, Y.D. Zhang, M.G. Amin, DOA estimation of mixed coherent and uncorrelated signals exploiting a nested MIMO system, in 2014 IEEE Benjamin Franklin Symposium on Microwave and Antenna Sub-systems for Radar, Telecommunications, and Biomedical Applications (BenMAS), Philadelphia, PA, pp. 1–3 (2014)

  23. 23.

    S. Qin, Y.D. Zhang, M.G. Amin, DOA estimation of mixed coherent and uncorrelated targets exploiting coprime MIMO radar. Dig. Signal Process. 61, 26–34 (2017)

    Article  Google Scholar 

  24. 24.

    Z. Shi, C. Zhou, Y. Gu, N.A. Goodman, F. Qu, Source estimation using coprime array: a sparse reconstruction perspective. IEEE Sens. J. 17(3), 755–765 (2017)

    Article  Google Scholar 

  25. 25.

    J. Shi, G. Hu, X. Zhang, F. Sun, H. Zhou, Sparsity-based two-dimensional DOA estimation for coprime array: from sum-difference coarray viewpoint. IEEE Trans. Signal Process. 65(21), 5591–5604 (2017)

    MathSciNet  Article  Google Scholar 

  26. 26.

    J. Shi, G. Hu, X. Zhang, F. Sun, W. Zheng, Y. Xiao, Generalized co-prime MIMO radar for DOA estimation with enhanced degrees of freedom. IEEE Sens. J. 18(3), 1203–1212 (2018)

    Article  Google Scholar 

  27. 27.

    P.P. Vaidyanathan, P. Pal, Sparse sensing with co-prime samplers and arrays. IEEE Trans. Signal Process. 59(2), 573–586 (2011)

    MathSciNet  Article  Google Scholar 

  28. 28.

    X. Wang, L. Wan, M. Huang, C. Shen, K. Zhang, Polarization channel estimation for circular and non-circular signals in massive MIMO systems. IEEE J. Sel. Top. Signal Process. 13(5), 1001–1016 (2019)

    Article  Google Scholar 

  29. 29.

    M. Wang, A. Nehorai, Coarrays, MUSIC, and the Cram\(\acute{\text{ e }}\)r-rao bound. IEEE Trans. Signal Process. 65, 933–946 (2017)

    MathSciNet  Article  Google Scholar 

  30. 30.

    F. Wen, J. Shi, Z. Zhang, Joint 2D-DOD, 2D-DOA, and polarization angles estimation for bistatic EMVS-MIMO radar via PARAFAC analysis. IEEE Trans. Veh. Technol. 69(2), 1626–1638 (2020)

    Article  Google Scholar 

  31. 31.

    C. Weng, P.P. Vaidyanathan, Nonuniform sparse array design for active sensing, in The Asilomar Conference on Signals, Systems, and Computers, pp. 1062–1066 (2011)

  32. 32.

    M. Yang, L. Sun, X. Yuan, B. Chen, A new nested MIMO array with increased degrees of freedom and hole-free difference coarray. IEEE Signal Process. Lett. 25(1), 40–44 (2018)

    Article  Google Scholar 

  33. 33.

    M. Yang, L. Sun, X. Yuan, B. Chen, Improved nested array with hole-free DCA and more degrees of freedom. Electron. Lett. 52(25), 2068–2070 (2016)

    Article  Google Scholar 

  34. 34.

    Z. Zheng, Y. Huang, W. Wang, H.C. So, Spatial smoothing PAST algorithm for DOA tracking using difference coarray. IEEE Signal Process. Lett. 26(11), 1623–1627 (2019)

    Article  Google Scholar 

  35. 35.

    Z. Zheng, W.Q. Wang, Y. Kong, Y.D. Zhang, M.I.S.C. Array, A new sparse array design achieving increased degrees of freedom and reduced mutual coupling effect. IEEE Trans. Signal Process. 67(7), 1728–1741 (2019)

    MathSciNet  Article  Google Scholar 

  36. 36.

    Z. Zheng, Y. Huang, W. Wang, H.C. So, Direction-of-arrival estimation of coherent signals via coprime array interpolation. IEEE Signal Process. Lett. 27, 585–589 (2020)

    Article  Google Scholar 

  37. 37.

    Z. Zheng, T. Yang, W. Wang, S. Zhang, Robust adaptive beamforming via coprime coarray interpolation. Signal Process. 169, 107382 (2020)

    Article  Google Scholar 

  38. 38.

    C. Zhou, Z. Shi, Y. Gu, X. Shen, DECOM: DOA estimation with combined MUSIC for coprime array, in 2013 International Conference on Wireless Communications and Signal Processing, Hangzhou, pp. 1–5 (2013)

  39. 39.

    C. Zhou, Y. Gu, Y.D. Zhang, Z. Shi, T. Jin, X. Wu, Compressive sensing-based coprime array direction-of-arrival estimation. IET Commun. 11(11), 1719–1724 (2017)

    Article  Google Scholar 

  40. 40.

    C. Zhou, Y. Gu, X. Fan, Z. Shi, G. Mao, Y.D. Zhang, Direction-of-arrival estimation for coprime array via virtual array interpolation. IEEE Trans. Signal Process. 66(22), 5956–5971 (2018)

    MathSciNet  Article  Google Scholar 

Download references


This work was supported in part by the Natural Science Foundation of China under Grant Nos. 61971221 and 61971220, in part by the Six Talent Peaks Project in Jiangsu, China, and in part by the Fundamental Research Funds for the Central Universities of China NP2020104

Author information



Corresponding author

Correspondence to Abdul Hayee Shaikh.

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

Shaikh, A.H., Dang, X., Ahmed, T. et al. MIMO Radar Array Configuration with Enhanced Degrees of Freedom and Increased Array Aperture. Circuits Syst Signal Process 40, 375–400 (2021). https://doi.org/10.1007/s00034-020-01478-8

Download citation


  • MIMO radar
  • Direction-of-arrival
  • Sensor arrays
  • Virtual array aperture
  • Degrees of freedom