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. The approach is based on the "Markovian" trend in modeling of random fields,and it is applied to 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 applies the generalized Stratonovich-Kushner Equations (SKE) for the optimum filtering of chaotic models of random fields and its simplified quasioptimum 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 really significant.

This material is dedicated to the rather old, but always actual, topic in theoretical analysis of applied problems: how to simplify an analytical investigation by applying multidimensional Probability Density Functions (n-PDFs). A brief overview of the applied interpretations for n-PDF approximation is presented, which allows to make choice of the practically useful analytical presentations for n-PDFs. For analytical solutions, two approximations for the n-PDF were chosen: Poli-Gaussian approximation (mix of Gaussian PDF's) and Functional Approximation or Gaussian-like. The first one is found to be suitable (and is recommended) for the class of scenarios better described by the term "scenarios of random structure". The second seems to be more adequate for analysis of the numerical characteristics of the communication system's behavior Recommendations for validation of the models with given n-PDF approximations, based on goodness of fit criteria's can be found as well.

The material is dedicated to various aspects of graphene metasurface implementation of the Reconfigurable Intelligent Surface (RIS) in the framework of the incoherent paradigm for NOMA-RIS-MIMO transmission design. Digital coded model of the metasurface is considered in the framework of the general representation of the graphene metasurface as a planar antenna array (PA). The simplification of the PA in the form of the non-uniform ULA (n-ULA) array and uniform linear array (ULA) is explained as well. In this regard array orthogonalization was applied in the form of the universal Prolate Spheroidal Wave Functions (PSWF) eigenbasis and it was used for the formulation of the RIS controller algorithm.

This material is fully dedicated to the “Incoherent approach for Power NOMA-RIS-MIMO transmission in wireless channels”. Such kind of approach might be successfully applied in dense networks formed by high-speed-vehicles (HSV networks, etc.), as those scenarios take place in Doubly-Selective communication channels typical for such kind of radio networks. The proposal for the, hereafter presented, incoherent view (“paradigm”) is based on several basic principles: - Rejection of the Channel State Information (CSI, CSIT) approach, i.e. rejection of the “coherent” paradigm (ideology); - Application of the so-called “invariant” (in relation to the communication channel’s distortions) modulation technique; - Orthogonal channel decomposition by means of “universal” eigen-basis (in the form of Prolate Spheroidal Wave Functions, PSWF) as “artificial trajectories” of wave propagation. - Chaotic filtering (with chaos parameters settings as UE signatures) together with sequential multiuser parallel detection algorithms for users’ identification. It is shown that the proposed paradigm might provide an effective use of the radio-resource and it is relatively simple for implementation.

The approach (Paradigm) presented hereafter was inspired by two basic ideas: assuming the MIMO-RIS-NOMA communication channel as a dispersive channel with fading and representing the later by means of Generalized Kroneker Channel model (GKCM) applying the so-called “Orthogonalization Approach” based on the utilization of the “universal” eigenbasis in the form of Prolate  Spheroidal Wave Functions (PSWF). In other words, the essence of the approach lies in representing the MIMO-RIS-NOMA channel by means of the finite set of artificially created orthogonal trajectories for wave propagation (PSWF eigenbasis) depending to the Planar Antenna(PA) patterns at the Transmitting and Receiving terminals of MIMO systems, being connected between themselves by the so-called Coupling Matrix (CM) of the RIS. Certainly, the goal for RIS (by certain choice of the elements of CM) is to provide the system for the decoding of the NOMA users with the required values of SNR for each user to guarantee its successful decoding processing. Theoretical analysis of this paradigm is presented in the following material.

The impressive growth of the demand for wireless services for 5G and beyond, particularly encouraged by the Internet of Things, Internet of Everything, etc., raised up the importance of the problems related to the drastic increase (among others) of spectrum efficiency of the systems. In this regard two opportunistic trends were recently discussed by practical professionals and academicians: non-orthogonal spectrum sharing (NOMA transmission) for user equipment (UE) at physical layer level and decentralized Blockchain-enabled Radio Access (B-RAN) paradigm at network layer label. Both of them promise a significant growth on the transmission rate and the spectrum efficiency with low latency, etc. not only for 5G networks, but further, towards 6G networks and so on. Moreover, it is a fact that the number of published works for B-RAN (some of them considered hereafter) is very impressive, however, the attention to its modeling aspects is rather limited. The following material is dedicated to present several theoretical aspects of the small-scale modeling of B-RAN based on two well-known principles: continuous time Markov stochastic processes with discrete set of states for B-RAN modeling and self-similar processes for its traffic modeling.

Non-orthogonal multiple access principle applied in power domain (power-domain NOMA) enhances spectrum efficiency and connectivity of mobile communication systems through sharing between Orthogonal Multiple Access (OMA) and other multiple users. It is the almost main current trend for research and standards for 5G and beyond. Spectrum sharing generates multi-users interference (Multiple Access Interference, MAI) which destroys orthogonality in OMA systems. Meanwhile the so-called Successive Interference Cancellation (SIC) techniques are used to suppress MAI and the Cognitive Radio (CR) principle (CR-NOMA) for decoding order for multiple users inspired effective SIC algorithms. The CR-NOMA principle is applied in the present material as well, but with significant changes for SIC design as for Doubly Selective channels. Due to the above reasons, two original SIC design methods are proposed hereafter following the CR-NOMA principle. Regarding to it the OMA signal (primary user) is decoded first using a Chaos-based quasi-optimum Extended Kalman Filter (EKF). The set of “secondary users” (multiusers) are proposed to be decoded secondly by the following two different methods: - Chaos-based EKF filters or , - Sequential m hypothesis testing. The proposed approach for SIC design is rather simple, fast and accurate for practical implementation.