Adaptive Complex Singular Spectrum Analysis with Application to Modern Superresolution Methods

  • V. VasylyshynEmail author
Part of the Lecture Notes on Data Engineering and Communications Technologies book series (LNDECT, volume 48)


The adaptive variant of the Singular Spectrum Analysis (SSA) approach for complex-valued signal model is obtained. It is related with the estimation of the noise variance using the results of the random matrix theory. Application of the adaptive complex SSA approach as preprocessing (denoising) step to modern methods of spectral analysis (subspace-based methods) is considered in the paper. The data sequence obtained after adaptive SSA approach is used as the input information for the superresolution method. The results of simulation demonstrate the performance improvement of the subspace-based methods in the conditions of low signal-to-noise ratio (SNR) when using the proposed approach. The performance of the subspace-based methods without and with the use of the adaptive SSA is comparable at high SNR. Furthermore, the performance of adaptive SSA approach depends on the quality of the noise variance estimate. The application of extended data matrix with specific structure obtained from the filtered data matrix is proposed. The directions of further investigations and possible applications of presented approach in communication systems are considered.


Singular value decomposition Adaptive singular spectrum analysis Superresolution methods 


  1. 1.
    Proakis G, Salehi M (2008) Digital communications, 5th edn. McGraw-Hill, NewYorkGoogle Scholar
  2. 2.
    Trees HLV (2002) Optimum array processing. Part IV of detection, estimation and modulation theory. Wiley-InterscienceGoogle Scholar
  3. 3.
    Marple SL (2018) Digital spectral analysis, 2nd edn. Dover Publication Inc, Maniola, New YorkGoogle Scholar
  4. 4.
    Small M (2005) Applied nonlinear time series analysis applications in physics, physiology and finance. World Scientific Publishing Co. Pte. LtdGoogle Scholar
  5. 5.
    Golyandina N, Zhigljavsky A (2013) Singular spectrum analysis for time series. SpringerGoogle Scholar
  6. 6.
    Sanei S, Hassani H (2016) Singular spectrum analysis of biomedical signals. CRC Press, LondonGoogle Scholar
  7. 7.
    Yanai H, Takeuchi K, Takane Y (2011) Projection matrices, generalized inverse matrices, and singular value decomposition. Springer ScienceGoogle Scholar
  8. 8.
    Aivazyan SA, Buchstaber VM, Enyukov IS, Meshalkin LD (1989) Applied statistics. Classification and reduction of dimensionality. Finances and statistics. MoscowGoogle Scholar
  9. 9.
    Tufts DW, Kumaresan R, Kirsteins I (1982) Data adaptive signal estimation by singular value decomposition of a data matrix. Proc IEEE 70:684–685. Scholar
  10. 10.
    Cadzow JA (1988) Signal enhancement—a composite property mapping algorithm. IEEE Trans ASSP 36:49–62. Scholar
  11. 11.
    Broomhead D, King G (1986) Extracting qualitative dynamics from experimental data. Phys D 20:217–236. Scholar
  12. 12.
    Broomhead D, Jones R, King G, Pike E (1987) Singular system analysis with application to dynamical systems. In: Pike ER, Lugiato LA (eds) Chaos, noise and fractals. Adam Hilger, BristolGoogle Scholar
  13. 13.
    Scharf LL (1991) The SVD and reduced rank signal processing. Sig Process 25:113–133. Scholar
  14. 14.
    Ephraim Y, Trees HLV (1995) A signal subspace approach for speech enhancement. IEEE Trans Speech Audio Process 3:251–266. Scholar
  15. 15.
    van der Veen AJ, Deprettere EF, Swindlehurst AL (1993) Subspace based signal analysis using singular value decomposition. Proc IEEE 81:1277–1308.
  16. 16.
    Vasylyshyn VI (2014) The signal preprocessing with using the SSA method in the spectral analysis problems. Appl Radio Electron 14(1):43–50 (in Russian)MathSciNetGoogle Scholar
  17. 17.
    Kostenko PYu, Vasylyshyn V (2015) Surrogate data generation technology using the SSA method for enhancing the effectiveness of signal spectral analysis. Radioelectron Commun Syst 58:356–361. Scholar
  18. 18.
    Vasylyshyn V (2015) Adaptive variant of the surrogate data technology for enhancing the effectiveness of signal spectral analysis using eigenstructure methods. Radioelectron Commun Syst 58(3):116–126. Scholar
  19. 19.
    Choi J, Evans BL, Gatherer A (2016) Space-time fronthaul compression of complex baseband uplink LTE signals. Paper presented at 2016 IEEE international conference on communications, Kuala Lumpur, 22–27 May 2016Google Scholar
  20. 20.
    Nilsson R, Sjöberg F, LeBlanc JPA (2003) Rank-reduced LMMSE canceller for narrowband interference suppression in OFDM-based systems. IEEE Trans Commun 51(12):2126–2140. Scholar
  21. 21.
    Vasylyshyn V, Lyutov V (2018) Signal denoising using modified complex SSA method with application to frequency estimation. Paper presented at 2018 5th international scientific-practical conference problems of infocommunications. Science and technology, Kharkiv, 9–12 Oct 2018Google Scholar
  22. 22.
    Leles MCR, Sansão JPH, Mozelli LA, Guimarães HN (2018) Improving reconstruction of time-series based in singular spectrum analysis: a segmentation approach. Digit Signal Proc 77:63–76. Scholar
  23. 23.
    Harmouche J, Fourer D, Auger F, Borgnat P, Flandrin P (2018) The sliding singular spectrum analysis: a data-driven non-stationary signal decomposition tool. IEEE Trans Signal Process 66(1):1–13. Scholar
  24. 24.
    Krishna EH, Sivani K, Reddy K (2018) New channel estimation method using singular spectrum analysis for OFDM systems. Wireless Pers Commun 101(4):2193–2207. Scholar
  25. 25.
    Besson O, Stoica P (2003) On parameter estimation of MIMO flat-fading channels with frequency offsets. IEEE Trans Signal Process 51(3):602–613. Scholar
  26. 26.
    da Costa JPCL, Haardt M, Rmer F, del Galdo G (2007) Enhanced model order estimation using higher-order arrays. Paper presented at 41st Asilomar conference on signals, systems, and computers, Pacific Grove, 4–7 Nov 2007Google Scholar
  27. 27.
    Kung SY, Arun KS, Bhaskar Rao DV (1983) State-space and singular-value decomposition methods for the harmonic retrieval problem. J Opt Soc Am 77:1799–1811. Scholar
  28. 28.
    Zhidong B, Zhaoben F, Yingchang L (2014) Spectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics. World Scientific Publishing Co. Pte. LtdGoogle Scholar
  29. 29.
    Yazdian E, Gazor S, Bastani H (2012) Source enumeration in large arrays using moments of eigenvalues and relatively few samples. IET Signal Process 6(7):689–696.
  30. 30.
    Kritchman S, Nadler B (2008) Determining the number of components in a factor model from limited noisy data. Chemometr Intell Lab Syst 94:19–32. Scholar
  31. 31.
    Dologlou I, Carayannis G (1991) Physical interpretation of signal reconstruction from reduced rank matrices. IEEE Trans Signal Process 39(7):1681–1682.
  32. 32.
    Hansen PC, Jensen SH (1998) FIR filter representations of reduction-rank noise reduction. IEEE Trans Signal Process 46(6):1737–1741. Scholar
  33. 33.
    Van Huffel S (1993) Enhanced resolution based on minimum variance estimation and exponential data modeling. Sig Process 33:333–355. Scholar
  34. 34.
    Vasylyshyn V (2007) Antenna array signal processing with high-resolution by modified beamspace MUSIC algorithm. Paper presented at 6th international conference on antenna theory and techniques, Sevastopol, 17–21 Sept 2007Google Scholar
  35. 35.
    Moskvina V, Schmidt KM (2003) Approximate projectors in singular spectrum analysis. SIAM J Matrix Anal Appl 24(4):932–942. Scholar
  36. 36.
    Vasylyshyn V (2013) Removing the outliers in root-MUSIC via pseudo-noise resampling and conventional beamformer. Sig Process 93:3423–3429.
  37. 37.
    Li J, Liu G, Giannakis GB (2001) Carrier frequency offset estimation for OFDM-based WLANs. IEEE Signal Process Lett 8(3):80–82. Scholar
  38. 38.
    Volosyuk VK, Kravchenko VF, Kutuza BG, Pavlikov VV (2015) Review of modern algorithms for high resolution imaging with passive radar. Paper presented at the international conference on antenna theory and techniques, Kiev, 21–24 Apr 2015Google Scholar
  39. 39.
    Ortega A, Frossard P, Kovačević J, Moura JMF, Vandergheynst P (2018) Graph signal processing: overview, challenges and applications. Proc IEEE 106(5):808–828.
  40. 40.
    Lemeshko AV, Evseeva OYu, Garkusha SV (2014) Research on tensor model of multipath routing in telecommunication network with support of service quality by greater number of indices. Telecommun Radio Eng 73(15):1339–1360. Scholar
  41. 41.
    Bulakh V, Kirichenko L, Radivilova T (2018) Time series classification based on fractal properties. Paper presented at the 2018 IEEE second international conference on data stream mining & processing (DSMP), Lviv, 21–25 Aug 2018Google Scholar
  42. 42.
    Ageyev DV, Salah MT (2016) Parametric synthesis of overlay networks with self-similar traffic. Telecommun Radio Eng 75(14):1231–124

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Ivan Kozhedub Kharkiv National Air Force UniversityKharkivUkraine

Personalised recommendations