The following material is devoted to the generalization of the chaos modeling to random fields in communication channels and its application on the space-time filtering for the incoherent paradigm; that is the purpose of this research. The approach, presented hereafter, is based on the “Markovian” trend in modeling of random fields, and it is applied for the first time to the chaos field modeling through the well-known concept of the random “treatment” of deterministic dynamic systems, first presented by A. Kolmogorov, M. Born, etc. The material presents the generalized Stratonovich-Kushner Equations (SKE) for the optimum filtering of chaotic models of random fields and its simplified quasi-optimum solutions. In addition to this, the application of the multi-moment algorithms for quasi-optimum solutions is considered and, it is shown, that for scenarios, when the covariation interval of the input random field is less than the distance between the antenna elements, the gain of the space-time algorithms against their “time” analogies is significant. This is the general result presented in the following.
References
[1]
Hasler, M., Mazzini, G., Ogorzalek, M., Rovatti, R. and Setti, G. (2002) Scanning the Special Issue—Special Issue on Applications of Nonlinear Dynamics to Electronic and Information Engineering. Proceedings of the IEEE, 90, 631-640.
[2]
Kontorovich, V., Lovtchikova, Z., et al. (2022) Effective Filtering of Weak Signals: Essential Solution for Their Measurement and Implementation. In: Yurish, S.Y., Ed., Advances in Measurement and Implementation, IFSA Publishing, 41-67.
[3]
Ji, S.Y., Yuan, F., Chen, K.Y. and Cheng, E. (2016) Application of Stochastic Resonance Technology in Underwater Acoustic Weak Signal Detection. OCEANS 2016—Shanghai, Shanghai, 10-13 April 2016, 1-5. https://doi.org/10.1109/oceansap.2016.7485567
[4]
Arditti, D., Alcocer, A., et al. (2014) Adaptive Mitigation of Platform-Generated Radio-Frequency Interference. USA Patent #141802219-1852.
[5]
Tzafestas, S.G. (1976) Nonlinear Distributed-Parameter Filtering Using the Forker-Planck Equation Approach. Journal of the Franklin Institute, 301, 429-449. https://doi.org/10.1016/0016-0032(76)90112-5
[6]
Eckmann, J. and Ruelle, D. (1985) Ergodic Theory of Chaos and Strange Attractors. Reviews of Modern Physics, 57, 617-656. https://doi.org/10.1103/revmodphys.57.617
[7]
Anischenko, V.S., et al. (2007) Non-Linear Dynamics of Chaotic and Stochastic Systems. Springer.
[8]
Shmelev, A. (1998) Markovian Approach to Random Fields Nonlinear Detection and Estimation Problems. EUSTPCO.
[9]
Shmelev, A. (1998) Principles of the Markovian Theory of Random Fields Nonlinear Processing. Moscow Institute of Physics and Technology Press. (In Russian)
[10]
Primak, S., Kontorovich, V. and Lyandres, V. (2004) Stochastic Methods and Their Applications to Communications. Wiley. https://doi.org/10.1002/0470021187
[11]
Pugachev, V. and Sinitsyn, I. (1987) Stochastic Differential Systems: Analysis and Filtering. John Wiley and Sons.
[12]
Stratonovich, R. (1963) Topics in the Theory of Random Noise. N.Y. Gordon and Beach.
[13]
Kushner, H. (1971) Dynamic Equations for Optimal Non-Linear Filtering. Journal of Differential Equations, 3, 170-180.
[14]
Yazwinski, A. (1970) Stochastic Processing and Filtering Theory. NY Academic.
[15]
Kontorovich, V. and Lovtchikova, Z. (2013) Nonlinear Filtering of Chaos for Real Time Applications. In: Kyamakya, K., Halang, W., Mathis, W., Chedjou, J. and Li, Z., Eds., SelectedTopicsinNonlinearDynamicsandTheoreticalElectricalEngineering, Springer, 41-59. https://doi.org/10.1007/978-3-642-37781-5_3
[16]
Hernández-Lemus, E. (2021) Random Fields in Physics, Biology and Data Science. Frontiers in Physics, 9, Article 641859. https://doi.org/10.3389/fphy.2021.641859
[17]
Kontorovich, V. (2022) Comments on SIC Design for SISO NOMA Systems over Doubly Selective Channels. IEEE Open Journal of Vehicular Technology, 3, 111-119. https://doi.org/10.1109/ojvt.2022.3162136
[18]
Kontorovich, V. (2023) The Incoherent Approach Might Be Opportunistic for the 6G Wireless Dense Networks Design? Theoretic View. IEEE Open Journal of Vehicular Technology, 4, 610-617. https://doi.org/10.1109/ojvt.2023.3311674
[19]
Kontorovich, V. (2023) Why the Incoherent Paradigm Is for the Future Wireless Networks? Communications and Network, 15, 65-82. https://doi.org/10.4236/cn.2023.153005
[20]
Kontorovich, V., et al. (2022) NOMA Transmission Systems: overview of SIC Design and New Findings. In: Mohammady, S., Ed., Multiplexing: Recent Advances and Novel Applications, Intech Open, 1-19.
[21]
Gershman, A. and Sidirofoulos, N. (2001) Space-Time processing for MIMO Communications. John Wiley and Sons.
[22]
Hopf, E. (1952) Statistical Hydromechanics and Functional Calculus. Indiana University Mathematics Journal, 1, 87-123. https://doi.org/10.1512/iumj.1952.1.51004
