Multi-Domain Communication Systems and Networks: A Tensor-Based Approach

Most modern communication systems, such as those intended for deployment in IoT applications or 5G and beyond networks, utilize multiple domains for transmission and reception at the physical layer. Depending on the application, these domains can include space, time, frequency, users, code sequences, and transmission media, to name a few. As such, the design criteria of future communication systems must be cognizant of the opportunities and the challenges that exist in exploiting the multi-domain nature of the signals and systems involved for information transmission. Focussing on the Physical Layer, this paper presents a novel mathematical framework using tensors, to represent, design, and analyze multi-domain systems. Various domains can be integrated into the transceiver design scheme using tensors. Tools from multi-linear algebra can be used to develop simultaneous signal processing techniques across all the domains. In particular, we present tensor partial response signaling (TPRS) which allows the introduction of controlled interference within elements of a domain and also across domains. We develop the TPRS system using the tensor contracted convolution to generate a multi-domain signal with desired spectral and cross-spectral properties across domains. In addition, by studying the information theoretic properties of the multi-domain tensor channel, we present the trade-off between different domains that can be harnessed using this framework. Numerical examples for capacity and mean square error are presented to highlight the domain trade-off revealed by the tensor formulation. Furthermore, an application of the tensor framework to MIMO Generalized Frequency Division Multiplexing (GFDM) is also presented.

Gravitational waves on Earth and their warming effects

The gravity or reactive bundle energy is the outlet of the morphogenetic impact, known as “BIG BANG”, creating a bounded ordered/structured universe along with the solar system, including the EARTH-world with its human race. Post-impact, the huge kinetic energy is spread into stellar bodies associated with the light flux under strong mutual connections or gravitational bundle. Einstein’s general relativity theory including the gravitational field can be expressed under a condensed tensor formulation as E  R − Rg =  T where E defines the geometry via a curved space-time structure (R) over the gravity field (1/2Rg), embedded in a matter distribution T The fundamental (ten non-linear partial differential) equations of the gravitational field are a kind of the space-time machine using the curvature of a four-dimensional space-time to engender the gravity field carrying away material structures. Gravity according to the curved space-time theory is not seen as a gravitational force, but it manifests itself in the relativistic form of the space-time curvature needing the constancy of the light speed. But the constant light velocity makes the tidal wave/pulsating energy, a characteristic of solar energy, impossible. The Einstein’s field equation, expressed in terms of tensor formulation along with the constant light speed postulate, needs two special space-time tensors (curvature and torsion) in 4 dimensions, where for the simplicity the torsion/twist tensor is less well approximated (Bianchi identity) leading to a constant/frozen gravity (twist-free gravity).The non-zero torsion tensor plays a significant physical role in the planetary dynamics as a finest gear of a planet, where its spinning rotation is directly connected to the own work and space-time structure (or clock), controlled by light fluctuations (or tidal effect of gravity). The spin correction of Einstein’s gravitational field refers to the curvature-torsion effect coupled with fluctuating light speed. The mutual curvature-torsion bundle self-sustained by the quantum fluctuations of light speed engenders helical gravitational wave fields of a quantum nature where bodies orbit freely in the light speed field (cosmic wind). In contrast to the Einstein’s field equation describing a gravitational frozen field, a quantum tidal gravity model is proposed in the paper.

Unit vector template generator applied to a new control algorithm for an UPQC with instantaneous power tensor formulation, a simulation case study

<span>In this paper we present a new algorithm to generate the reference signals to control the series and parallel power inverters in an unified power quality conditioner “UPQC” to enhance power quality. The algorithm is based in the instantaneous power tensor formulation which it is obtained by the dyadic product between the instantaneous vectors of voltage and current in n-phase systems. The perfect harmonic cancelation algorithm “PHC” to estimate the current reference in a shunt active power filter was modified to make it hardy to voltage sags through unit vector template generation “UVGT” while from the same algorithm it extracts the voltage reference for series active power filter. The model was validated by mean of simulations in Matlab-Simulink®.</span>

Appraisal of magnetotelluric galvanic electric distortion by optimizing amplitude and phase tensor relations

The introduction of the phase tensor marked a major breakthrough in the analysis and treatment of electric field galvanic distortion in the magnetotellurics method. Recently, the phase tensor formulation has been extended to a complete impedance tensor decomposition by introducing the complementary amplitude tensor, and both tensors can be further parameterized to represent geometric properties such as dimensionality, strike angle, and macroscopic anisotropy. Both tensors are characteristic for the electromagnetic induction phenomenon in the conductive subsurface with its specific geometric structure. The central hypothesis is that this coupling should result in similarities in both tensor’s geometric parameters, skew, strike, and anisotropy. A synthetic example illustrates that the undistorted amplitude tensor parameters are more similar to the phase tensor than increasingly distorted ones and provides empiric evidence for the predictability of the proposed hypothesis. Conclusions drawn are reverse engineered to produce an objective function that minimizes when amplitude and phase tensor parameter dissimilarity is, along with any present distortion, minimal. A genetic algorithm with such an objective function is used to systematically seek the distortion parameters necessary to correct any affected amplitude tensor and, thus, impedance data. The successful correction of a large synthetic impedance data set with random distortion further supports the central hypothesis and serves as comparison to the state-of-the-art. The classic BC87 data set sites lit007/ lit008 and lit901/ lit902 have been noted by various authors to contain significant distortion and a 3D regional response, thus invalidating current distortion analysis methods and eluding geologic interpretation. Correction of the BC87 responses based on the present hypothesis conforms to the regional geology.

Stochastic electromagnetic field propagation— measurement and modelling

This paper reviews recent progress in the measurement and modelling of stochastic electromagnetic fields, focusing on propagation approaches based on Wigner functions and the method of moments technique. The respective propagation methods are exemplified by application to measurements of electromagnetic emissions from a stirred, cavity-backed aperture. We discuss early elements of statistical electromagnetics in Heaviside's papers, driven mainly by an analogy of electromagnetic wave propagation with heat transfer. These ideas include concepts of momentum and directionality in the realm of propagation through confined media with irregular boundaries. We then review and extend concepts using Wigner functions to propagate the statistical properties of electromagnetic fields. We discuss in particular how to include polarization in this formalism leading to a Wigner tensor formulation and a relation to an averaged Poynting vector. This article is part of the theme issue ‘Celebrating 125 years of Oliver Heaviside's ‘Electromagnetic Theory’’.

Uncertainty Quantification of NOx Emissions Induced Through the Prompt Route in Premixed Alkane Flames

Increasingly stringent regulations on emissions in the gas turbine industry require novel designs to minimize the environmental impact of oxides of nitrogen (NOx). The development of advanced low-NOx technologies depends on accurate and reliable thermochemical mechanisms to achieve emissions targets. However, current combustion models have high levels of uncertainty in kinetic rates that, when propagated through calculations, yield significant variations in predictions. A recent study identified and optimized nine elementary reactions involved in CH formation to accurately capture its concentration and improve prompt-NO predictions. The current work quantifies the uncertainty on peak CH concentration and NOx emissions generated by these nine reaction rates only, when propagated through the San Diego mechanism. Various non-intrusive spectral methods are used to study atmospheric alkane-air flames. 1st- and 2nd-order total-order expansions and tensor-product expansions are compared against a reference Monte Carlo analysis to assess the ability of the different techniques to accurately quantify the effect of uncertainties on the quantities of interest. Sparse grids, subsets of the full tensor-product expansion, are shown to retain the advantages of tensor formulation compared to total-order expansions while requiring significantly fewer collocation points to develop a surrogate model. The high resolution per dimension can capture complex probability distributions witnessed in radical species concentrations. The uncertainty analysis of lean to rich flames demonstrated a high variability in NOx predictions reaching up to 400 % of nominal predictions. Wider concentration intervals were observed in rich conditions where prompt-NOx is the dominant contributor to emissions. The high variability and scale of uncertainty in NOx emissions originating from these nine elementary reactions demonstrate the need for future experiments and data assimilation to constrain current models to accurately capture CH for robust NOx emissions predictions.