Development of the Two Real Signals Blind Separation Method Using Fourth-Order Cumulants

Currently, blind signal separation methods are used in various fields of human activity, including wireless communication systems, radar and direction finding. This paper describes a method for blindly separating two material radio signals. Blind separation of signals implies that no information about the radio signal other than the received samples is unknown. The solution to this problem is based on two fundamental assumptions performed in real conditions. The first assumption is that the observed signal linearly depends on the source signal. The second assumption is that the radio sources are statistically independent. The general structure of blind source separation methods can be represented as a combination of a contrast function and a method for its optimization. In known methods, the solution of the SRS problem is carried out by iterative methods. As a criterion for the separation of radio signals in this work, we selected the reduction of the second and fourth order cumulants of the output signals to zero. The proposed analytical solution makes it possible to find a unmixing matrix W for any independent s1 and s2 signals in addition to those for which the fourth order cumulants are equal to zero. For such quantities, this method can only bring their mixture to two uncorrelated signals. In contrast to existing iterative methods, the proposed blind source separation method provides guaranteed convergence of the problem in given constraints. To test the operability of the method, a model of mixing and separation of signals was created, the efficiency of the method was tested at various powers of intrinsic noise in the receiving channels. As a result of modeling the proposed method, a dependence of the signal separation level on the power of intrinsic noise was constructed. The efficiency of the method was demonstrated with a ratio of input signal noise to useful signal power of less than 0,2 dB.

Keywords

blind signal separation; digital signal processing; cumulant; mathematical modelling; separation level.

References

1. Cardoso J.-F. Blind Signal Separation: Statistical Principles. Proceedings of the IEEE, 1998, vol. 86, no. 10, pp. 2009-2025.
2. Hyvarinen A. Syrvey on Independent Component Analysis. Neural Computing Surveys, 1999, no. 2, pp. 94-128.
3. Wu Xing-Jie, Hu Yun-an, Li Ming, Zeng Ling-Li, Shen Hui, Hu Dewen. An Improved Group BSS-CCA Method for Blind Source Separation of Functional MRI Scans of the Human Brain. Procedings ICBDA, 2017, pp. 758-761.
4. Bhandari R., Jadhav S. A Literature Survey on BSS Approaches for MIMO-OFDM Detection. Proceedings ICCUBEA, 2015, pp. 238-241.
5. Chao-Cheng Tu, Champagne B. Subspace. Blind MIMO-OFDM Channel Estimation with Short Averaging Periods: Performance Analysis. IEEE Wireless Communications and Networking Conference, 2008, pp. 24-29.
6. Sarperi L., Zhu X., Nandi A.K. Blind OFDM Receiver Based on Independent Component Analysis for Multiple-Input Multiple-Output Systems. IEEE Transactions on Wireless Communications, 2007, vol. 6, pp. 4079-4089.
7. Sahroni A., Setiawan H., Marfianti E. Performance of Blind Source Separation (BSS) Techniques for Mixed Source Signals of EEG, ECG, and Voice Signal. Proceedings IWCIA, 2014, pp. 213-217.
8. Li Hongyi, Lin Wei, Zhao Di. A Single-Channel BSS Method Based on ICEEMDAN and FastICA and Its Application in EMI Analysis. Proceedings ICCSE, 2019, pp. 780-784.
9. Adzhemov S.S., Kuchumov A.A., Savost'janov D.V. [Blind Separation of Signals Based on Shear Statistics]. T-Comm: Telekommunikacii i transport, 2009, Special, pp. 16-19. (in Russian)
10. Kuchumov A.A., Miroshnikova N.E. [Efficiency of Using Blind Processing Algorithms to Separate Signals with Different Types of Modulation]. T-Comm: Telekommunikacii i transport, 2016, vol. 10, no. 5, pp. 17-20. (in Russian)
11. Belouchrani A., Abed-Meraim K., Cardoso J.-F., Moulines E. Second-Order Blind Separation of Temporally Correlated Sources. Proccedings International Conference on Digital Signal Process, 1993, pp. 346-351.
12. Cardoso J.-F., Souloumiac A. Blind Beamforming from Non-Gaussian Signals. Proceedings of the Institution of Electrical Engineers, 1993, vol. 140, no. 6, pp. 362-370.
13. Tong Lang, Soon Vic, Huang Yih-Fang, Liu Raymond. Indeterminacy and Identifiability of Blind Identification. IEEE Transactions on Circuits and Systems, 1991, vol. 38, pp. 499-509.
14. Koldovsk'y Z., Tichavsk'y P., Oja E. Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the Cram'er-Rao Lower Bound. IEEE Transactions on Neural Networks, 2006, vol. 17, no. 5, pp. 1265-1277.
15. Priputin V.S. [The Method of Blind Separation of Signals Based on Second-Order Statistics in the Problem of Spatial Polarization Selection]. T-Comm: Telekommunikacii i transport, 2014, no. 6, pp. 36-39. (in Russian)
16. Kuchumov A.A., Liberovskiy N.Y., Priputin V.S. Blind Two Real Signals Separation Method Based on Third Order Cumulants. Proceedings Systems of Signals Generating and Processing in the Field of on Board Communications, 2019, pp. 1-4.
17. Malahov A.N. Kumuljantnyj analiz sluchajnyh negaussovyh processov i ih preobrazovanij [Cumulative Analysis of Random Non-Gaussian Processes and Their Transformations]. Moscow, Sovetskoe radio, 1978. (in Russian)
18. Levin B.R. Teoreticheskie osnovy statisticheskoj radiotehniki [Theoretical Foundations of Statistical Radio Engineering]. Moscow, Radio i svjaz', 1989. (in Russian)
19. Stratonovich R.L. Principy adaptivnogo priema [Adaptive Admission Principles]. Moscow, Sovetskoe radio, 1973. (in Russian)
20. Mesloub A., Abed-Meraim K., Belouchrani A. A New Algorithm for Complex Non-Orthogonal Joint Diagonalization Based on Shear and Givens Rotations. IEEE Transactions on Signal Processing, 2014, vol. 62, no. 8, pp. 1913-1925.