Skip to main content
SpringerLink
Log in

Adaptive Complex Singular Spectrum Analysis with Application to Modern Superresolution Methods

  • Chapter
  • First Online:
Data-Centric Business and Applications

Part of the book series: Lecture Notes on Data Engineering and Communications Technologies ((LNDECT,volume 48))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Proakis G, Salehi M (2008) Digital communications, 5th edn. McGraw-Hill, NewYork

    Google Scholar 

  2. Trees HLV (2002) Optimum array processing. Part IV of detection, estimation and modulation theory. Wiley-Interscience

    Google Scholar 

  3. Marple SL (2018) Digital spectral analysis, 2nd edn. Dover Publication Inc, Maniola, New York

    Google Scholar 

  4. Small M (2005) Applied nonlinear time series analysis applications in physics, physiology and finance. World Scientific Publishing Co. Pte. Ltd

    Google Scholar 

  5. Golyandina N, Zhigljavsky A (2013) Singular spectrum analysis for time series. Springer

    Google Scholar 

  6. Sanei S, Hassani H (2016) Singular spectrum analysis of biomedical signals. CRC Press, London

    Google Scholar 

  7. Yanai H, Takeuchi K, Takane Y (2011) Projection matrices, generalized inverse matrices, and singular value decomposition. Springer Science

    Google Scholar 

  8. Aivazyan SA, Buchstaber VM, Enyukov IS, Meshalkin LD (1989) Applied statistics. Classification and reduction of dimensionality. Finances and statistics. Moscow

    Google Scholar 

  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. https://doi.org/10.1109/PROC.1982.12367

    Article  Google Scholar 

  10. Cadzow JA (1988) Signal enhancement—a composite property mapping algorithm. IEEE Trans ASSP 36:49–62. https://doi.org/10.1109/29.1488

    Article  MATH  Google Scholar 

  11. Broomhead D, King G (1986) Extracting qualitative dynamics from experimental data. Phys D 20:217–236. https://doi.org/10.1016/0167-2789(86)90031-X

    Article  MathSciNet  MATH  Google Scholar 

  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, Bristol

    Google Scholar 

  13. Scharf LL (1991) The SVD and reduced rank signal processing. Sig Process 25:113–133. https://doi.org/10.1016/0165-1684(91)90058-Q

    Article  MATH  Google Scholar 

  14. Ephraim Y, Trees HLV (1995) A signal subspace approach for speech enhancement. IEEE Trans Speech Audio Process 3:251–266. https://doi.org/10.1109/89.397090

    Article  Google Scholar 

  15. van der Veen AJ, Deprettere EF, Swindlehurst AL (1993) Subspace based signal analysis using singular value decomposition. Proc IEEE 81:1277–1308. https://doi.org/10.1109/5.237536

  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)

    MathSciNet  Google Scholar 

  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. https://doi.org/10.3103/S0735272715080038

    Article  Google Scholar 

  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. https://doi.org/10.3103/S0735272715030036

    Article  Google Scholar 

  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 2016

    Google Scholar 

  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. https://doi.org/10.1109/TCOMM.2003.820761

    Article  Google Scholar 

  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 2018

    Google Scholar 

  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. https://doi.org/10.1016/j.dsp.2017.10.025

    Article  MathSciNet  Google Scholar 

  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. https://doi.org/10.1109/TSP.2017.2752720

    Article  MATH  Google Scholar 

  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. https://doi.org/10.1007/s11277-018-5811-5

    Article  Google Scholar 

  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. https://doi.org/10.1109/TSP.2002.808102

    Article  MathSciNet  MATH  Google Scholar 

  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 2007

    Google Scholar 

  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. https://doi.org/10.1364/JOSA.73.001799

    Article  Google Scholar 

  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. Ltd

    Google Scholar 

  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. https://doi.org/10.1049/iet-spr.2011.0260

  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. https://doi.org/10.1016/j.chemolab.2008.06.002

    Article  Google Scholar 

  31. Dologlou I, Carayannis G (1991) Physical interpretation of signal reconstruction from reduced rank matrices. IEEE Trans Signal Process 39(7):1681–1682. https://doi.org/10.1109/78.134407

  32. Hansen PC, Jensen SH (1998) FIR filter representations of reduction-rank noise reduction. IEEE Trans Signal Process 46(6):1737–1741. https://doi.org/10.1109/78.678511

    Article  Google Scholar 

  33. Van Huffel S (1993) Enhanced resolution based on minimum variance estimation and exponential data modeling. Sig Process 33:333–355. https://doi.org/10.1016/0165-1684(93)90130-3

    Article  Google Scholar 

  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 2007

    Google Scholar 

  35. Moskvina V, Schmidt KM (2003) Approximate projectors in singular spectrum analysis. SIAM J Matrix Anal Appl 24(4):932–942. https://doi.org/10.1137/S0895479801398967

    Article  MathSciNet  MATH  Google Scholar 

  36. Vasylyshyn V (2013) Removing the outliers in root-MUSIC via pseudo-noise resampling and conventional beamformer. Sig Process 93:3423–3429. https://doi.org/10.1016/j.sigpro.2013.05.026

  37. Li J, Liu G, Giannakis GB (2001) Carrier frequency offset estimation for OFDM-based WLANs. IEEE Signal Process Lett 8(3):80–82. https://doi.org/10.1109/97.905946

    Article  Google Scholar 

  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 2015

    Google Scholar 

  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. https://doi.org/10.1109/JPROC.2018.2820126

  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. https://doi.org/10.1615/TelecomRadEng.v73.i15.30

    Article  Google Scholar 

  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 2018

    Google Scholar 

  42. Ageyev DV, Salah MT (2016) Parametric synthesis of overlay networks with self-similar traffic. Telecommun Radio Eng 75(14):1231–124 https://doi.org/10.1615/TelecomRadEng.v75.i14.10

Download references

Author information

Authors and Affiliations

  1. Ivan Kozhedub Kharkiv National Air Force University, Kharkiv, Ukraine

    V. Vasylyshyn

Authors
  1. V. Vasylyshyn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Vasylyshyn .

Editor information

Editors and Affiliations

  1. V.V. Popovskyy department of Infocommunication Engineering, Faculty of Infocommunication, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    Tamara Radivilova

  2. V.V. Popovskyy department of Infocommunication Engineering, Faculty of Infocommunication, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine

    Dmytro Ageyev

  3. Department of e-Business, Faculty of Business, Economics and Statistics, University of Vienna, Vienna, Austria

    Natalia Kryvinska

Rights and permissions

Reprints and permissions

Copyright information

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

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vasylyshyn, V. (2021). Adaptive Complex Singular Spectrum Analysis with Application to Modern Superresolution Methods. In: Radivilova, T., Ageyev, D., Kryvinska, N. (eds) Data-Centric Business and Applications. Lecture Notes on Data Engineering and Communications Technologies, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-030-43070-2_3

Download citation

Publish with us

Policies and ethics

Search

Navigation