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Wireless communications advance hand-in-hand with artificial intelligence (AI), indicating an interconnected advancement where each facilitates and benefits from the other. This synergy is particularly evident in the development of the sixth-generation technology standard for mobile networks (6G), envisioned to be AI-native. Generative-AI (GenAI), a novel technology capable of producing various types of outputs, including text, images, and videos, offers significant potential for wireless communications, with its distinctive features. Traditionally, conventional AI techniques have been employed for predictions, classifications, and optimization, while GenAI has more to offer. This article introduces the concept of strategic demand-planning through demand-labeling, demand-shaping, and demand-rescheduling. Accordingly, GenAI is proposed as a powerful tool to facilitate demand-shaping in wireless networks. More specifically, GenAI is used to compress and convert the content of various kind (e.g., from a higher bandwidth mode to a lower one, such as from a video to text), which subsequently enhances performance of wireless networks in various usage scenarios such as cell-switching, user association and load balancing, interference management, and disaster scenarios management. Therefore, GenAI can serve a function in saving energy and spectrum in wireless networks. With recent advancements in AI, including sophisticated algorithms like large-language-models and the development of more powerful hardware built exclusively for AI tasks, such as AI accelerators, the concept of demand-planning, particularly demand-shaping through GenAI, becomes increasingly relevant. Furthermore, recent efforts to make GenAI accessible on devices, such as user terminals, make the implementation of this concept even more straightforward and feasible.

This study aims to introduce the cell load estimation problem of cell switching approaches in cellular networks specially-presented in a high-altitude platform station (HAPS)-assisted network. The problem arises from the fact that the traffic loads of sleeping base stations for the next time slot cannot be perfectly known, but they can rather be estimated, and any estimation error could result in divergence from the optimal decision, which subsequently affects the performance of energy efficiency. The traffic loads of the sleeping base stations for the next time slot are required because the switching decisions are made proactively in the current time slot. Two different Q-learning algorithms are developed; one is full-scale, focusing solely on the performance, while the other one is lightweight and addresses the computational cost. Results confirm that the estimation error is capable of changing cell switching decisions that yields performance divergence compared to no-error scenarios. Moreover, the developed Q-learning algorithms perform well since an insignificant difference (i.e., 0.3%) is observed between them and the optimum algorithm.

It is crucial to deploy temporary non-terrestrial networks (NTN) in disaster situations where terrestrial networks are no longer operable. Deploying uncrewed aerial vehicle base stations (UAV-BSs) can provide a radio access network (RAN); however, the backhaul link may also be damaged and unserviceable in such disaster conditions. In this regard, high-altitude platform stations (HAPS) spark attention as they can be deployed as super macro base stations (SMBS) and data centers. Therefore, in this study, we investigate a three-layer heterogeneous network with different topologies to prolong the lifespan of the temporary network by using UAV-BSs for RAN services and HAPS-SMBS as a backhaul. Furthermore, a two-layer clustering algorithm is proposed to handle the UAV-BS ad-hoc networking effectively.

This study investigates the integration of a high altitude platform station (HAPS), a non-terrestrial network (NTN) node, into the cell-switching paradigm for energy saving. By doing so, the sustainability and ubiquitous connectivity targets can be achieved. Besides, a delay-aware approach is also adopted, where the delay profiles of users are respected in such a way that we attempt to meet the latency requirements of users with a best-effort strategy. To this end, a novel, simple, and lightweight Q-learning algorithm is designed to address the cell-switching optimization problem. During the simulation campaigns, different interference scenarios and delay situations between base stations are examined in terms of energy consumption and quality-of-service (QoS), and the results confirm the efficacy of the proposed Q-learning algorithm.

Nonlinear distortion stemming from low-cost power amplifiers may severely affect wireless communication performance through out-of-band (OOB) radiation and in-band distortion. The distortion is correlated between different transmit antennas in an antenna array, which results in a beamforming gain at the receiver side that grows with the number of antennas. In this paper, we investigate how the strength of the distortion is affected by the frequency selectivity of the channel. A closed-form expression for the received distortion power is derived as a function of the number of multipath components (MPCs) and the delay spread, which highlight their impact. The performed analysis, which is verified via numerical simulations, reveals that as the number of MPCs increases, distortion exhibits distinct characteristics for in-band and OOB frequencies. It is shown that the received in-band and OOB distortion power is inversely proportional to the number of MPCs, and it is reported that as the delay spread gets narrower, the in-band distortion power is beamformed towards the intended user, which yields higher received in-band distortion compared to the OOB distortion., Comment: This paper is presented in ICC 2023

In this paper, we propose an adaptive approach, based on mesh refinement or parametric enrichment with polynomial degree adaption, for numerical solution of convection dominated equations with random input data. A parametric system emerged from an application of stochastic Galerkin approach is discretized by using a symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term in the spatial domain. We derive a residual-based error estimator contributed by the error due to the SIPG discretization, the (generalized) polynomial chaos discretization in the stochastic space, and data oscillations. Then, the reliability of the proposed error estimator, an upper bound for the energy error up to a multiplicative constant, is shown. Moreover, to balance the errors stemmed from spatial and stochastic spaces, the truncation error coming from Karhunen--Lo\`{e}ve expansion is also considered in the numerical simulations. Last, several benchmark examples including a random diffusivity parameter, a random velocity parameter, random diffusivity/velocity parameters, and a random (jump) discontinuous diffusivity parameter, are tested to illustrate the performance of the proposed estimator., Comment: 26 pages, 19 figures, 5 tables

Providing a stable connectivity in maritime communications is of utmost importance to unleash the full potential of smart ports. Nonetheless, due to the crowded nature of harbor environments, it is likely that some ships are shadowed by others, resulting in reduced received power that subsequently diminishes their data rates-even threatens basic connectivity requirements. Given that uncrewed aerial vehicles (UAVs) have been regarded as an integral part of future generations of wireless communication networks, they can be employed in maritime communications as well. In this paper, we investigate the use of UAV-mounted relays in order to help mitigate the reduced data rates of blocked links in maritime communications. Various communication architectures are considered based on the positioning mechanism of the UAV; in this regard, fixed, k-means algorithm-based, and landing spot-based positioning approaches are examined. Additionally, since UAVs are predominantly battery-operated, the energy consumption performances of these approaches are also measured. Results reveal that the landing spot-based UAV relay positioning approach finds the best trade-off between the data rate and energy consumption.

There is a consensus in the literature that cell-switching is a viable solution to tackle the draconian increase in the energy consumption of cellular networks. Although the literature is full of works addressing the energy consumption problem via cell-switching, where small cells with low or no load are turned off and the traffic is offloaded to either adjacent base stations or macro cells, in terrestrial communication networks, they may not be feasible when there is either a lack of infrastructure or insufficient capacity due to high demand. The integration of non-terrestrial networks (NTN) into the cell-switching process can be considered as a visionary approach to handle this problem. In this regard, high altitude platform station (HAPS) draws considerable attention with its massive footprint, high capacity, and ubiquitous connectivity. The aim of this study is to show the potential benefits of using HAPS in cell-switching methods by being a bountiful host for offloaded users from cell-switching operations. More specifically, HAPS is included in the network so that it can increase the switching off opportunities by providing extra coverage and capacity. The simulation results demonstrate that a significant amount of reduction in energy consumption (as high as 16%) is obtained while ensuring quality-of-service (QoS) requirements.

A subalgebra $B$ of a Leibniz algebra $L$ is called a weak c-ideal of $L$ if there is a subideal $C$ of $L$ such that $L=B+C$ and $B\cap C\subseteq B_{L}$ where $B_{L}$ is the largest ideal of $L$ contained in $B.$ This is analogous to the concept of a weakly c-normal subgroup, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Leibniz algebras generalising previous results for Lie algebras. We note that one-dimensional weak c-ideals are c-ideals, and show that a result of Turner classifying Leibniz algebras in which every one-dimensional subalgebra is a c-ideal is false for general Leibniz algebras, but holds for symmetric ones., Comment: arXiv admin note: substantial text overlap with arXiv:2006.05234

We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing uncertainties into a large system of deterministic problems, is applied to discretize the stochastic domain, while a discontinuous Galerkin method is preferred for the spatial discretization due to its better convergence behaviour for optimization problems governed by convection dominated PDEs. Error analysis is done for the state and adjoint variables in the energy norm, while the estimates of deterministic control is obtained in the $L^2$--norm. Large matrix system emerging from the stochastic Galerkin method is addressed by the low--rank version of GMRES method, which reduces both the computational complexity and the memory requirements by employing Kronecker--product structure of the obtained linear system. Benchmark examples with and without control constraints are presented to illustrate the efficiency of the proposed methodology., Comment: 41 pages, 8 figures, 7 tables

Proportionate type algorithms were developed and excessively used in the echo cancellation problems due to sparse characteristics of the echo channels. In the past, most of the attention was paid to a particular type of proportionate approach, which assigns step-sizes to filter coefficients proportional to the magnitude of the corresponding coefficient. In this letter, we propose a new proportionate type algorithm, which takes dynamic behavior of the estimated filter coefficient into account while assigning individual step-sizes to each coefficient. Proposed algorithm introduces an effective way to assign individual step-sizes using the time derivatives of the filter coefficients. Computational complexity of the proposed algorithm is similar to those of previously proposed algorithms. Simulation results have shown the improvements in the convergence rate achieved by the proposed algorithm.

We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of deterministic convection diffusion equations, is used to handle the stochastic domain in this study, whereas discontinuous Galerkin method is used to discretize spatial domain due to its local mass conservativity. A priori error estimates of the stationary problem and stability estimate of the unsteady model problem are derived in the energy norm. To address the curse of dimensionality of Stochastic Galerkin method, we take advantage of the low--rank Krylov subspace methods, which reduce both the storage requirements and the computational complexity by exploiting a Kronecker--product structure of system matrices. The efficiency of the proposed methodology is illustrated by numerical experiments on the benchmark problems., Comment: 50 pages, 9 figures, 9 tables

A subalgebra B of a Lie algebra L is called a weak c-ideal of L if there is a subideal C of L such that L = B+C and B\cap C \subseteq B_L where B_L is the largest ideal of L contained in B. This is analogous to the concept of weakly c- normal subgroups, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also note that one-dimensional weak c-ideals are c-ideals., Comment: arXiv admin note: substantial text overlap with arXiv:0811.2689

A frequency domain method is proposed to reduce the sidelobe level of a uniformly weighted uniform linear array in direction-of-arrival estimation. The development is based on the nonlinear method of spatially variant apodization originally proposed for spectral analysis and synthetic aperture radar imagery., Comment: 4 pages 5 figures

The number of Frattini chief factors or of chief factors which are complemented by a maximal subalgebra of a finite-dimensional Lie algebra $L$ is the same in every chief series for $L$, by \cite[Theorem 2.3]{[11]}. However, this is not the case for the number of chief factors which are simply complemented in $L$. In this paper we determine the possible variation in that number.