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Table Of Integrals Series And Products

Matrix Differential Calculus with Applications in Statistics and Econometrics

The fifth generation (5G) wireless communication networks are being deployed worldwide from 2020 and more capabilities are in the process of being standardized, such as mass connectivity, ultra-reliability, and guaranteed low latency. However, 5G will not meet all requirements of the future in 2030 and beyond, and sixth generation (6G) wireless communication networks are expected to provide global coverage, enhanced spectral/energy/cost efficiency, better intelligence level and security, etc. To meet these requirements, 6G networks will rely on new enabling technologies, i.e., air interface and transmission technologies and novel network architecture, such as waveform design, multiple access, channel coding schemes, multi-antenna technologies, network slicing, cell-free architecture, and cloud/fog/edge computing. Our vision on 6G is that it will have four new paradigm shifts. First, to satisfy the requirement of global coverage, 6G will not be limited to terrestrial communication networks, which will need to be complemented with non-terrestrial networks such as satellite and unmanned aerial vehicle (UAV) communication networks, thus achieving a space-air-ground-sea integrated communication network. Second, all spectra will be fully explored to further increase data rates and connection density, including the sub-6 GHz, millimeter wave (mmWave), terahertz (THz), and optical frequency bands. Third, facing the big datasets generated by the use of extremely heterogeneous networks, diverse communication scenarios, large numbers of antennas, wide bandwidths, and new service requirements, 6G networks will enable a new range of smart applications with the aid of artificial intelligence (AI) and big data technologies. Fourth, network security will have to be strengthened when developing 6G networks. This article provides a comprehensive survey of recent advances and future trends in these four aspects. Clearly, 6G with additional technical requirements beyond those of 5G will enable faster and further communications to the extent that the boundary between physical and cyber worlds disappears.

/pdf/towards-6g-wireless-communication-networks-vision-enabling-2tj7a36yux.pdf

Towards 6G wireless communication networks: vision, enabling technologies, and new paradigm shifts

Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

In this chapter we deal with the following nonlinear fractional programming problem: 

$$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$

where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Nonlinear Fractional Programming

Node localization is essential to most applications of wireless sensor networks (WSNs). In this paper, we consider both range-based node localization and range-free node localization with uncertainties in range measurements, radio range, and anchor positions. First, a greedy optimization algorithm, named sequential greedy optimization (SGO) algorithm, is presented, which is more suitable for distributed optimization in networks than the classical nonlinear Gauss-Seidel algorithm. Then a unified optimization framework is proposed for both range-based localization and range-free localization, and two convex localization formulations are obtained based on semidefinite programming (SDP) relaxation techniques. By applying the SGO algorithm to the edge-based SDP relaxation formulation, we propose a second-order cone programming (SOCP)-based distributed node localization algorithm. Two distributed refinement algorithms are also proposed by using the SGO algorithm to nonconvex localization formulations. The proposed localization algorithms all can be implemented partially asynchronously in networks. Finally, extensive simulations are conducted to demonstrate the efficiency and accuracy of the proposed distributed localization algorithms.

Distributed Wireless Sensor Network Localization Via Sequential Greedy Optimization Algorithm

A one-dimensional iterative chaotic map with infinite collapses within symmetrical region [-1, O)/spl cup/(O, +1] is proposed. The stability of fixed points and that around the singular point are analyzed. Higher Lyapunov exponents of proposed map show stronger chaotic characteristics than some iterative and continuous chaotic models usually used. There exist inverse bifurcation phenomena and special main periodic windows at certain positions shown in the bifurcation diagram, which can explain the generation mechanism of chaos. The chaotic model with good properties can be generated if choosing the parameter of the map properly. Stronger inner pseudorandom characteristics can also be observed through /spl chi//sup 2/ test on the supposition of even distribution. This chaotic model may have many advantages in practical use.

Chaotic characteristics of a one-dimensional iterative map with infinite collapses

In this paper, a novel interference coordination scheme based softer frequency reuse (SerFR) to mitigate inter-cell interference in Orthogonal Frequency Division Multiple Access (OFDMA) cellular systems is presented. In OFDMA systems, inter-cell interference is the most important interference source. Inter-cell interference coordination is considered to improve coverage and increase date rate at cell edge. Soft Frequency Reuse (SFR) interference coordination scheme is proposed in 3GPP Long Term Evolution (LTE). But the scheme cause frequency selective scheduling gain loss, and the peak rate for cell edge users is low because the cell edge users only can use a fraction of the entire frequency band. However, in SerFR scheme, cell edge users can use the entire frequency band, so there are more frequency selective scheduling garn and more peak date rate than SFR scheme.

Inter-cell interference coordination based on softer frequency reuse in OFDMA cellular systems

In this paper, we propose a novel vertical handoff decision algorithm for overlay wireless networks consisting of cellular and wireless local area networks (WLANs). The target network is selected using a fuzzy logic-based normalized quantitative decision algorithm which, in addition to usual parameters such as the current received signal strength (RSS) and the available bandwidth, also takes a prediction of the RSS into account, resulting in a more accurate handoff. The RSS prediction is obtained using a differential prediction algorithm that has good accuracy. Furthermore, to reduce system load, a pre-decision method is employed before actual handoff decision to filter out users with high mobility or low RSS from using the WLAN. Simulation results show that the proposed algorithm can reduce the call-dropping probability as well as unnecessary handoffs in heterogeneous network environments.

/pdf/a-novel-fuzzy-logic-vertical-handoff-algorithm-with-aid-of-2hcd2lcbc2.pdf

A Novel Fuzzy Logic Vertical Handoff Algorithm with Aid of Differential Prediction and Pre-Decision Method

We propose a novel spectrum-sensing method for cognitive radio (CR) based on stochastic resonance (SR). The spectral power of primary users (PUs) can be amplified, and the signal-to-noise ratio (SNR) of a received signal can be increased using SR. This ensures that the detection probability of the proposed approach is higher than that of the traditional energy detector. The detection probability of the proposed method is also theoretically derived under a constant false-alarm rate (CFAR). Performance analyses and computer simulation results show that the effectiveness of the proposed SR-based spectrum-sensing approach, particularly under low SNR circumstances, is better than that of the traditional energy-detection method. The computational complexity of the proposed approach can also be guaranteed to be comparable with the traditional spectrum-sensing methods.

Lingge Jiang

Papers

Distributed Wireless Sensor Network Localization Via Sequential Greedy Optimization Algorithm

Chaotic characteristics of a one-dimensional iterative map with infinite collapses

Inter-cell interference coordination based on softer frequency reuse in OFDMA cellular systems

A Novel Fuzzy Logic Vertical Handoff Algorithm with Aid of Differential Prediction and Pre-Decision Method

A Novel Spectrum-Sensing Technique in Cognitive Radio Based on Stochastic Resonance