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Project Seminar Radio Communications

Lecture: Direction of Arrival (DOA) Estimation

The lecture will teach the theoretical basics required for the study of scientific publications in the field of direction of arrival estimation. Furthermore, some state of the art direction of arrival estimation techniques will be discussed.


  • direction of arrival estimation [1]

Linear Algebra

  • matrices
  • Hermitian matrices
  • Singular Value Decomposition (SVD)


  • phasor notation
  • antenna arrays
  • random signals [2]
  • normal distribution


  • correlation matrix
  • measurements
  • correlated sources [3, 4]

Parametric Methods

  • Maximum Likelihood Estimator (MLE)
  • Deterministic Maximum Likelihood (DML) [5]

Conventional Methods

  • beamforming network
  • conventional beamformer [6]
  • Capon’s beamformer (Minimum Variance Distortionless Response, MVDR) [7]

Subspace Methods

  • MUltiple SIgnal Classification (MUSIC) [8]
  • Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) [9]

General References for the Lecture

mathematical basics: [10, 11]

estimation theory: [12]

spectral analysis, array signal processing: [13, 14, 15]

Lab: Radar Signal Processing

Radar signal processing is an important application of direction of arrival estimation. From a mathematical perspective, direction of arrival estimation as well as range estimation and velocity estimation are spectral estimation problems. The lab activities are described in the lab manual. Also have a look at the introduction to FMCW radar [16, 17, 18, 19].

  1. Range-Doppler-Processing
  2. Beamforming
  3. MUSIC

General References for the Lab

radar: [20]

digital signal processing: [21]

Matlab: [22]


The student shall give a talk on a given topic. As a starting point a paper will be recommended. However, the talk shall not be a mere summary of this paper. It shall rather comprise an original presentation of the theory linked to the lecture and own simulation results.

  1. Pisarenko Method [23]
  2. Stochastic Maximum Likelihood (SML) [24]
  3. Minimum Norm Method [25]
  4. Unitary ESPRIT [26]
  5. Single Frequency Estimator [27]
  6. Root MUSIC [28]
  7. Alternating Projection Algorithm (APA) [29]
  8. TLS ESPRIT [30]
  9. Unitary Root MUSIC [31]


[1] H. Krim and M. Viberg, "Two decades of array signal processing research: The parametric approach," Signal Processing Magazine, IEEE, vol. 13, no. 4, pp. 67-94, July 1996.
[2] R. T. Hoctor and S. A. Kassam, "The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging," Proceedings of the IEEE, vol. 78, no. 4, pp. 735-752, April 1990.
[3] T.-J. Shan, M. Wax, and T. Kailath, "On spatial smoothing for direction-of-arrival estimation of coherent signals," Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 33, no. 4, pp. 806-811, August 1985.
[4] S. U. Pillai and B. H. Kwon, "Forward/backward spatial smoothing techniques for coherent signal detection," Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 37, no. 1, pp. 8-15, January 1989.
[5] J. F. Böhme, "Estimation of source parameters by maximum likelihood and nonlinear regression," presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'84), San Diego, CA, March, 1984.
[6] M. S. Bartlett, "Smoothing periodograms from time-series with continuous spectra," Nature, vol. 161, pp. 686-687, May 1948.
[7] J. Capon, "High-resolution frequency-wavenumber spectrum analysis," Proceedings of the IEEE, vol. 57, no. 8, pp. 1408-1418, August 1969.
[8] R. O. Schmidt, "Multiple emitter location and signal parameter estimation," Antennas and Propagation, IEEE Transactions on, vol. 34, no. 3, pp. 276-280, March 1986.
[9] R. Roy and T. Kailath, "ESPRIT-Estimation of signal parameters via rotational invariance techniques," Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 37, no. 7, pp. 984-995, July 1989.
[10] T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing. Upper Saddle River, NJ: Prentice Hall, 2000.
[11] G. Strang, Introduction to Linear Algebra, 5. ed. Wellesley, MA: Wellesley-Cambridge Press, 2016.
[12] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Upper Saddle River, NJ: Prentice Hall, 1993.
[13] D. H. Johnson and D. E. Dudgeon, Array Signal Processing: Concepts and Techniques. Upper Saddle River, NJ: PTR Prentice-Hall, 1993.
[14] P. Stoica and R. Moses, Spectral Analysis of Signals. Upper Saddle River, NJ: Pearson Prentice Hall, 2005.
[15] H. L. Van Trees, Detection, Estimation, and Modulation Theory: Part 4: Optimum Array Processing. New York, NY: Wiley-Interscience, 2002.
[16] S. Patole, M. Torlak, D. Wang, and M. Ali, "Automotive radars: A review of signal processing techniques," Signal Processing Magazine, IEEE, vol. 34, no. 2, pp. 22-35, March 2017.
[17] V. Winkler, "Range Doppler detection for automotive FMCW radars," presented at the 4th European Microwave Conference, München, October, 2007.
[18] F. C. Robey, S. Coutts, D. Weikle, J. C. McHarg, and K. Cuomo, "MIMO radar theory and experimental results," presented at the 38th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, November, 2004.
[19] P. Häcker and B. Yang, "Single snapshot DOA estimation," Advances in Radio Science, vol. 8, pp. 251-256, 2010.
[20] M. A. Richards, Fundamentals of Radar Signal Processing, 2. ed. New York, NY: McGraw-Hill Education, 2014.
[21] K.-D. Kammeyer and K. Kroschel, Digitale Signalverarbeitung: Filterung und Spektralanalyse mit MATLAB-Übungen, 8. ed. Wiesbaden: Springer Vieweg, 2012.
[22] F. Thuselt and F. P. Gennrich, Praktische Mathematik mit MATLAB, Scilab und Octave: für Ingenieure und Naturwissenschaftler. Berlin: Springer Spektrum, 2013.
[23] V. F. Pisarenko, "The retrieval of harmonics from a covariance function," Geophys. J. Roy. Astronom. Soc., vol. 33, pp. 347-366, 1973.
[24] A. G. Jaffer, "Maximum likelihood direction finding of stochastic sources: A separable solution," presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'88), New York, NY, April, 1988.
[25] R. Kumaresan and D. W. Tufts, "Estimating the angles of arrival of multiple plane waves," Aerospace and Electronic Systems, IEEE Transactions on, vol. AES-19, no. 1, pp. 134-139, January 1983.
[26] M. D. Zoltowski, M. Haardt, and C. P. Mathews, "Closed-form 2-D angle estimation with rectangular arrays in element space or beamspace via unitary ESPRIT," Signal Processing, IEEE Transactions on, vol. 44, no. 2, pp. 316-328, February 1996.
[27] S. Kay, "A fast and accurate single frequency estimator," Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 37, no. 12, pp. 1987-1990, December 1989.
[28] A. J. Barabell, "Improving the resolution performance of eigenstructure-based direction-finding algorithms," presented at the IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP'83), Boston, MA, April, 1983.
[29] I. Ziskind and M. Wax, "Maximum likelihood localization of multiple sources by alternating projection," Acoustics, Speech and Signal Processing, IEEE Transactions on, vol. 36, no. 10, pp. 1553-1560, October 1988.
[30] B. Ottersten, M. Viberg, and T. Kailath, "Performance analysis of the total least squares ESPRIT algorithm," Signal Processing, IEEE Transactions on, vol. 39, no. 5, pp. 1122-1135, May 1991.
[31] M. Pesavento, A. B. Gershman, and M. Haardt, "Unitary root-MUSIC with a real-valued eigendecomposition: A theoretical and experimental performance study," Signal Processing, IEEE Transactions on, vol. 48, no. 5, pp. 1306-1314, May 2000.