Related papers: Division Algebras and Wireless Communication
We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
The recently commercialized fifth-generation (5G) wireless communication networks achieved many improvements, including air interface enhancement, spectrum expansion, and network intensification by several key technologies, such as massive…
Recent developments of Baxter algebras have lead to applications to combinatorics, number theory and mathematical physics. We relate Baxter algebras to Stirling numbers of the first kind and the second kind, partitions and multinomial…
It is widely perceived that leveraging the success of modern machine learning techniques to mobile devices and wireless networks has the potential of enabling important new services. This, however, poses significant challenges, essentially…
In this paper we will first present a generalization of the wedge product of association schemes to table algebras and give a necessary and sufficient condition for a table algebra to be the wedge product of two table algebras. Then we show…
Intelligent communication is gradually considered as the mainstream direction in future wireless communications. As a major branch of machine learning, deep learning (DL) has been applied in physical layer communications and has…
We describe the role of algebraic extensions in the theory of commutative, unital normed algebras, with special attention to uniform algebras. We shall also compare these constructions and show how they are related to each other.
We consider arbitrary dense wireless networks, in which $n$ nodes are placed in an arbitrary (deterministic) manner on a square region of unit area and communicate with each other over Gaussian fading channels. We provide inner and outer…
We classify finite dimensional division real associative $\mathcal{Z}_2$-algebras, introduce composition $\mathcal{Z}_2$-algebras, and extend the Campbell-Baker-Hausdorff series and Lie correspondence in the context of linear Hu-Liu Leibniz…
We study the classical version of supersymmetric $W$-algebras. Using the second Gelfand-Dickey Hamiltonian structure we work out in detail $W_2$ and $W_3$-algebras.
Mathematical optimization is now widely regarded as an indispensable modeling and solution tool for the design of wireless communications systems. While optimization has played a significant role in the revolutionary progress in wireless…
We survey a number of results regarding the representation theory of $W$-algebras and their connection with the resent development of the four dimensional $N=2$ superconformal field theories in physics.
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting…
Wireless receiver design is critical to the overall system performance. In this work, we apply the techniques of mixed-integer programming to formulate a unified receiver in relay networks with only partial channel information. We also…
We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We…
This paper provides an overview of the features of fifth generation (5G) wireless communication systems now being developed for use in the millimeter wave (mmWave) frequency bands. Early results and key concepts of 5G networks are…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
The challenge to in-band full-duplex wireless communication is managing self-interference. Many designs have employed spatial isolation mechanisms, such as shielding or multi-antenna beamforming, to isolate the self-interference wave from…
In extending results from Lie to Leibniz algebras, it is helpful to have techniques which translate results from the former to the latter without having to repeat the (perhaps modified) arguments. Such a technique is developed in this work,…