Direction-of-Arrival Estimation Methods: A Performance-Complexity Tradeoff Perspective

  • Edno GentilhoJr.Email author
  • Paulo Rogerio Scalassara
  • Taufik Abrão


This work analyses the performance-complexity tradeoff for different direction of arrival (DoA) estimation techniques. Such tradeoff is investigated taking into account uniform linear array structures. Several DoA estimation techniques have been compared, namely the conventional Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR), Multiple Signal Classifier (MUSIC) subspace, Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT), Unitary-ESPRIT and Fourier Transform method (FT-DoA). The analytical formulation of each estimation technique as well the comparative numerical results are discussed focused on the estimation accuracy versus complexity tradeoff. The present study reveals the behavior of seven techniques, demonstrating promising ones for current and future location applications involving DoA estimation, especially for 5G massivemimo systems.


Direction-of-Arrival (DoA) Espacial estimation MUSIC ESPRIT Root-MUSIC 



This work was supported in part by the National Council for Scientific and Technological Development (CNPq) of Brazil under Grants 304066/2015-0, and in part by CAPES - Coordenaçá3o de Aperfeiçoamento de Pessoal de Nível Superior, Brazil (scholarship), and by the Londrina State University - Paraná State Government (UEL).


  1. 1.
    Godara, L.C. (2004). Smart Antennas, 1st edn. Boca Raton: CRC Press.CrossRefGoogle Scholar
  2. 2.
    Monzingo, R.A., Haupt, R.L., Miller, T.W. (2011). Introduction to Adaptive Arrays. Raleigh: Scitech.CrossRefGoogle Scholar
  3. 3.
    Fourtz, J., Spanias, A., Banavar, M.K. (2008). Narrowband Direction of Arrival Estimation for Antenna Arrays, 1st edn. Arizona: Morgan & Claypool.Google Scholar
  4. 4.
    Capon, J. (1969). High-Resolution Frequency-Wavenumber spectrum analysis. Proceedings of the IEEE, 57 (8), 1408–1418.CrossRefGoogle Scholar
  5. 5.
    Reddy, V.U., Paulraj, A., Kailath, T. (1987). Performance Analysis of The Optimum Beamformer in The Presence of Correlated Sources and Its Behavior Under Spatial Smoothing. IEEE Transactions on Acoustics, Speech, and Signal Processing, 35(7), 927–936.CrossRefGoogle Scholar
  6. 6.
    Schmidt, R.O. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3), 276–280.CrossRefGoogle Scholar
  7. 7.
    Godara, L.C. (1997). Application of antenna arrays to mobile communications, part II: Beam-forming and direction-of-arrival considerations. Proceedings of the IEEE, 85(8), 1195–1245.CrossRefGoogle Scholar
  8. 8.
    Haykin, S. (1996). Adaptative Filter Theory, 3rd edn. New York: Prentice Hall.Google Scholar
  9. 9.
    Liberti, J.C., & Rappaport, T.S. (1999). Smart Antennas for Wireless Communications - IS-95 and Third Generation CDMA Applications, 1st edn. Upper Saddle River: Prentice Hall.Google Scholar
  10. 10.
    Gross, F.B. (2015). Smart Antenna with MATLAB, 2nd edn. New York: NY.Google Scholar
  11. 11.
    Barabell, A.J. (1983). Improving the resolution performance of eigenstructure-based direction-finding algorithms. ICASSP ’83. IEEE International Conference on Acoustics, Speech, and Signal Processing, 8, 8–11.Google Scholar
  12. 12.
    Roy, R., & Kailath, T. (1989). ESPRIT - estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics Speech, and Signal Processing, 37(7), 984–995.CrossRefzbMATHGoogle Scholar
  13. 13.
    Haardt, M. (1997). Efficient One-, Two-, and Multidimensional High-Resolution Array Signal Processing, 1st edn. Munich: Shaker Verlag.Google Scholar
  14. 14.
    Balanis, C.A., & Ioannides, P.I. (2007). Introduction to Smart Antennas, 1st edn. Arizona: Morgan & Claypool.Google Scholar
  15. 15.
    Allen, B., & Ghavami, M. (2005). Adaptive array systems: Fundamentals and applications. West Sussex: Wiley.Google Scholar
  16. 16.
    Liang, J., & Liu, D. (2010). Passive Localization of Mixed Near-Field and Far-Field Sources Using Two-stage MUSIC Algorithm. IEEE Transactions on Signal Processing, 58(1), 108–120.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Liu, G., & Sun, X. (2014). Two-Stage matrix differencing algorithm for mixed Far-Field and Near-Field sources classification and localization. IEEE Sensors Journal, 14(6), 1957–1965.CrossRefGoogle Scholar
  18. 18.
    Pal, P., & Vaidyanathan, P.P. (2010). Nested arrays: A novel approach to array processing with enhanced degrees of freedom. IEEE Transactions on Signal Processing, 58(8), 4167–4181.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Zhang, Y.D., Qin, S., Amin, M.G. (2014). Doa estimation exploiting coprime arrays with sparse sensor spacing. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. Number 1 (pp. 2267–2271). Florence: IEEE.Google Scholar
  20. 20.
    Li, J., & Zhang, X. (2017). Direction of arrival estimation of quasi-stationary signals using unfolded coprime array. IEEE Access, 5, 1–1.CrossRefGoogle Scholar
  21. 21.
    Mailloux, R.J. (2005). Phased Array Antenna Handbook, 2nd edn. Vol. 1. Artech House: Norwood.Google Scholar
  22. 22.
    Yang, X., Liu, L., Wang, Y. (2016). A new low complexity DOA estimation algorithm for massive MIMO systems. In 2016 IEEE international conference on consumer electronics-china (ICCE-china) (pp. 1–4). Guangzhou: IEEE.Google Scholar
  23. 23.
    Meng, H., Zheng, Z., Yang, Y., Liu, K., Ge, Y. (2016). A low-complexity 2-d DOA estimation algorithm for massive MIMO systems. In 2016 IEEE/CIC international conference on communications in China (ICCC) (pp. 1–5). Chengdu: IEEE.Google Scholar
  24. 24.
    Ferreira, T.N., Netto, S.L., de Campos, M.L., Diniz, P.S. (2016). Low-complexity DoA estimation based on Hermitian EVDs. Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop (pp. 1–5).Google Scholar
  25. 25.
    Zhang, K., Ma, P., Zhang, J.Y. (2011). DOA estimation algorithm based on FFT in switch antenna array. Proceedings of 2011 IEEE CIE International Conference on Radar, 2(4), 1425–1428.CrossRefGoogle Scholar
  26. 26.
    Trench, W.F. (1989). Numerical Solution of the eigenvalue problem for hermitian toeplitz matrices. SIAM Journal Matrix Analisys Applications, 10(2), 135–146.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Hunger, R. (2007). Floating point operations in Matrix-Vector calculus. Technical report, Munich.Google Scholar
  28. 28.
    Cybenko, G. (1980). The numerical stability of the Levinson-Durbin algorithm for toeplitz systems of equations. SIAM Journal on Scientific Computing, 1(3), 303–319.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Haardt, M., Pesavento, M., Roemer, F., Nabil el korso, M. (2014). Subspace Methods and Exploitation of Special Array Structures. In Academic Press Library in Signal Processing: volume 3; Array and Statistical Signal Processing. 3rd edn. (pp. 651–717). Oxford: Academic Press.Google Scholar
  30. 30.
    Amdahl, G.M. (1967). Validity of the single processor approach to achieving large scale computing capabilities. Proceedings of the April 18-20, 1967, spring joint computer conference on - AFIPS ’67 (Spring) 483.Google Scholar
  31. 31.
    Culler, D., Singh, J.P., Gupta, A. (1997). Parallel computer architecture: a Hardware/Software approach Vol. 1. San Francisco: Morgan Kaufmann.Google Scholar
  32. 32.
    Golub, G.H., & Loan, C.F.V. (2013). Matrix Computations, 4th edn. Baltimore: Johns Hopkins University Press.zbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringFederal Institute of Technology of Paraná (IFPR)ParanavaíBrazil
  2. 2.Department of Electrical EngineeringFederal Technological University of Paraná (UTFPR)Cornélio ProcópioBrazil
  3. 3.Department of Electrical EngineeringState University of Londrina (UEL)LondrinaBrazil

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