Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2021. No. 1

Full text in Russian (pdf)

Russian page


DOI https://doi.org/10.30898/1684-1719.2021.1.3

UDC 621.391


Generalization of super-resolution minimal polynomial method for direction of arrival estimation under spatially colored noise and interference conditions


O. A. Shmonin

Lobachevsky State University of Nizhny Novgorod, Gagarin avenue str., 23, Nizhny Novgorod, 603950 Russia


The paper was received on December 21, 2020


Abstract. The article is dedicated to super-resolution and direction of arrival (DOA) estimation problems under spatially colored noise and interference conditions. Super-resolution minimal polynomial method (MPM) is considered. The base method uses a signal received by antenna array assuming that noise in each array element is independent and has certain power. It also supposes that there are only signals which directions of arrival need to be estimated. In other words, there is no interference. The practice shows that these assumptions may not be satisfied in real-world systems. Interference problem arises both in radar and radio communication applications. In a dense scattering environment (e.g. the urban) there is multipath propagation effect. It makes interference spatially-distributed and decreases DOA estimation algorithms resolution ability. In order to overcome these problems the generalized minimal polynomial method (GMPM) is developed and proposed in this paper. Two approaches for generalization are considered. The first is based on features of the signal subspace forming under spatially colored noise conditions. The second is relied on the signal transformation which leads to identity noise correlation matrix. Theoretical description is presented for both approaches. Furthermore, the approaches equivalence is proved. Efficiency of the proposed algorithm is investigated in comparison with base MPM. It is shown that in case of spatially-distributed interference the proposed method gives opportunity to achieve a sufficient gain in resolution ability and DOA estimation accuracy in comparison with the base MPM algorithm.

Key words: antenna array, super-resolution, bearing, direction of arrival estimation, spatially colored noise, interference.


1.   Shirman J.D. Radioelektronnye sistemy. Osnovy postroeniya i teoriya: spravochnik. [Radioelectronic systems. Base of the design and theory: reference manual]. Moscow, Radiotekhnika Publ. 2007. 512 p. (In Russian)

2.   Ratynskij M.V. Adaptaciya i sverhrazreshenie v antennyh reshetkah [Adaptation and super-resolution in antenna arrays]. Moscow, Radio i svyaz' Publ. 2004. 199 p. (In Russian)

3.   Ermolayev V.T., Flaksman A.G. Teoreticheskie osnovy obrabotki signalov v besprovodnyh sistemah svyazi. [Theoretical base of signal processing in wireless communication systems]. Nizhny Novgorod, UNN Publ. 2011. 368 p. (In Russian)

4.   Godara L.C. Smart antennas. London, CRC Press Publ. 2004. 472 p.

5.   Tuncer T.E., Friedlander B. Classical and Modern Direction-of-Arrival Estimation. London, Elsevier Inc. 2009. 429 p.

6.   Ermolayev V.T., Flaksman A.G., Anurin A.A. Estimation of parameters of signals received by antenna array. Radiophysics and quantum electronics. 1996. Vol.39. No.9. P.765-776. https://doi.org/10.1007/BF02120859

Available at: https://link.springer.com/content/pdf/10.1007/BF02120859.pdf

7.   Roy R., Kailath T. Esprit - Estimation Of Signal Parameters Via Rotational Invariance Techniques. IEEE Trans. Acoustics, Speech and Signal Processing. 1989. Vol. 37, No. 7. P. 984995. https://doi.org/10.1109/29.32276. Available at: https://pdfs.semanticscholar.org/831e/d2a5f40861866b4ebfe60257b997701e38e2.pdf

8.   Ermolayev V.T., Flaksman A.G., Eloknin A.V., Shmonin O.A. Angular superresolution of the antenna-array signals using the root method of minimum polynomial of the correlation matrix. Radiophysics and quantum electronics. 2018. Vol.61. No.3. P.232-241. https://doi.org/10.1007/s11141-018-9884-5. Available at: https://link.springer.com/content/pdf/10.1007/s11141-018-9884-5.pdf

9.   Gantmakher F.R. Teoriya matric. [The Theory of Matrices]. Moscow, Nauka Publ. 1967. 576 p. (In Russian)

10Parlett B. N. The symmetric eigenvalue problem. Philadelphia, Society for Industrial and Applied Mathematics. 1998. 345 p.

11. Ermolayev V.T., Flaksman A.G., Eloknin A.V., Shmonin O.A. An experimental study of the angular superresolution of two correlated signals using the minimum-polynomial method. Radiophysics and quantum electronics. 2019. Vol.61. No.11. P. 841-852. https://doi.org/10.1007/s11141-019-09941-6. Available at: https://link.springer.com/content/pdf/10.1007/s11141-019-09941-6.pdf

12. Shmonin O.A. Angular super-resolution of radiation sources by antenna array generalization of minimal polynomial method for the case of spatially colored noise. Proceedings of XXIV International Sci-Tech Conference Informacionnye sistemy i tekhnologii [Information systems and technology]. Nizhny Novgorod. 2018. P. 214-219. (In Russian)

13. Ermolayev V.T., Shmonin O.A. Generalization of super-resolution minimal polynomial method for the case of spatially colored noise. Proceedings of XXII Scientific Conference on Radiophysics. Nizhny Novgorod, UNN. 2018. P. 381-384. (In Russian)

14. Bevan D.D.N., Ermolayev V.T., Flaksman A.G., Averin I.M. Gaussian channel model for mobile multipath environment. EURASIP Journal on appled Signal Processing. 2004, No. 9. P. 13211329. https://doi.org/10.1155/S1110865704404028. Available at: https://link.springer.com/content/pdf/10.1155%2FS1110865704404028.pdf

15. Monzingo R.A., Miller T. W. Introduction to Adaptive Arrays. New York, Wiley Publ. 1980. 543 p.

16. Prasolov V.V. Zadachi i teoremy linejnoj algebry. [Exercises and theorems of linear algebra]. Moscow, Nauka Publ. 1996. 304 p. (In Russian)

17. Vergbitskiy V.M. Osnovy chislennyh metodov. [The base of numerical methods]. Moscow, Vysshaya shkola Publ. 2009. 840 p. (In Russian)

18. Ermolayev V.T. Evaluation of parameters for the minimal polynomial of the signal-correlation matrix of a multichannel adaptive receiving system. Radiophysics and quantum electronics. 1995. Vol.38. No.8. P.551-561. https://doi.org/10.1007/BF01037705. Available at: https://link.springer.com/content/pdf/10.1007/BF01037705.pdf


For citation:

Shmonin O.A. Generalization of super-resolution minimal polynomial method for direction of arrival estimation under spatially colored noise and interference conditions. Zhurnal Radioelektroniki [Journal of Radio Electronics]. 2021. No.1. https://doi.org/10.30898/1684-1719.2021.1.3 (In Russian)