Physical layer security using beamforming techniques for 5G and beyond networks: A systematic review

It has been predicted that by the year 2030, 5G and beyond 5G (B5G) networks are expected to provide hundreds of trillions of gigabytes of data for various emerging applications such as augmented, mixed, and virtual reality (AR/MR/VR), wireless computer-brain interfaces (WCBI), connected robotics and autonomous systems. Most of these applications share data with each other using an open channel, i.e., the Internet. The open and broadcast nature of wireless channel makes the communication susceptible to various types of attacks (e.g., eavesdropping, jamming). Thus, there is a strong requirement to enhance the secrecy of wireless channel to maintain the privacy and confidentiality of transmitted data. Physical layer security (PLS) has evolved as a novel concept and robust alternative to cryptography-based techniques, which have a number of drawbacks and practical issues for 5G and beyond networks. Beamforming is an energy-efficient PLS technique, that involves steering of the transmitted signal in a particular direction, while considering that an intruding user attempts to decode the transmitted data. Motivated from these points, this article summarizes various beamforming based PLS techniques for secure data transmission in 5G and B5G networks. We investigate the eight most promising techniques for beamforming in PLS: Non-Orthogonal Multiple Access (NOMA), Full-Duplex Networks, Massive Multiple-Input Multiple-Output (MIMO), Cognitive Radio (CR) Network, Relay Network, Simultaneous Wireless Information and Power Transfer (SWIPT), UAV Communication Networks and Space Information Networks, and Heterogeneous Networks. Moreover, various physical layer threats and countermeasures associated with 5G and B5G networks are subsequently covered. Lastly, we provide insights to the readers about constraints and challenges for the usage of beamforming-based PLS techniques in various upcoming future applications.     

A Measure of Simultaneous Approximation for Quasi-Modular Functions

We improve on a recent result of Saradha giving a transcendence measure for the quotient of a period of an elliptic curve defined over by its associated quasi-period. In an (almost successful) attempt to include in a single measure both this result and that obtained by Reyssat in 1980, we blend into the modular method ideas related to modular but also hypergeometric functions, as appearing e.g. in André's work, as well as some Galois considerations.     

State-Dependent Coupling in General Networks

In this paper we extend a result which holds for the class of networks of quasireversible nodes to a class of networks constructed by coupling Markov chains. We begin with a network in which the transition rates governing the stochastic behaviour of the individual nodes depend only on the state of the node. Assuming that the network has an invariant measure, we construct another network with transition rates at each node depending on the state of the entire network, and obtain its invariant measure.     

Convex curves, Radon transforms and convolution operators defined by singular measures

Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents.     

Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Given a subset E of convex functions from into which satisfy growth conditions of order p>1 and an open bounded subset of , we establish the continuity of a map μΦ_μ from the set of all Young measures on equipped with the narrow topology into a set of suitable functionals defined in and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization.     

量子点CdSe／ZnS的浓度对其荧光的影响研究

影响量子点荧光特性除了量子点尺寸因素外,其溶液浓度也会对其荧光特性起很重要的作用。但到目前,还未见到有关量子点 CdSe／ZnS 在溶液中浓度对其荧光影响的详细报道。为了掌握影响量子点CdSe／ZnS荧光特性的因素及其物理机制,利用紫外-可见吸收光谱仪和荧光光谱仪测量了尺寸为4 nm的量子点CdSe／ZnS在氯仿中不同浓度下的吸收光谱和荧光光谱,并侧重研究了量子点CdSe／ZnS的浓度对其发光特性的影响并分析了其物理机制。结果表明量子点对光谱的吸收随其浓度的增加而增大,但其发光却具有一个最佳浓度2μmol·L－1。当量子点的浓度＞2μmol·L－1时,量子点的荧光强度随着量子点浓度的增加而降低,而当量子点的浓度＜2μmol·L－1时,量子点的发光强度则随其浓度的降低而降低。其原因主要有两个：（1）荧光猝灭效应;（2）荧光发射与光吸收的竞争效应。当量子点的浓度＞2μmol·L－1时,由于量子点之间相距太近（仅为94 nm）而引起了荧光猝灭效应,且其荧光猝灭效应随量子点间距的减小而增大,且因为吸收过大,导致受激的量子点并未增加,因此,其荧光随浓度的增加而降低。而当量子点的浓度＜2μmol·L－1时,因为量子点之间的距离足够大,不再引起荧光猝灭效应,其荧光强度取决于单位体积内的量子点的个数,单位体积内量子点的个数越多,其发光强度越强。因此其发光强度随量子点溶液的浓度降低而降低。     

AC 1 make or break lemma

Mañé suggested the following question: Consider aC ^r flow on a compact manifold without boundary and suppose that the ω-limit set of a pointp intersets the α-limit set ofq, i.e. ω(p)∩α(q)≠Ø. Can the flow beC ^r-perturbed so that either (a)p is connected toq (p andq in the same orbit) or (b) ω(p)∩α(q)=Ø for the new flow? Here we solve positively a stronger version of this problem forC ¹ small perturbations of the original flow.     

利用电子散斑相移技术测量物体三维面形的方法

为了获得准确的面形测量,提出了一种相移电子散斑干涉技术测量物体面形的测量方法.利用电子散斑干涉产生载波条纹,该载波条纹受到物体表面高度的调制变得弯曲,引起载波条纹相位的变化,可运用相移技术提取物体的相位信息,最后根据高度和相位之间的关系得到物体的面形.介绍了该方法的原理,利用该方法对球冠物体进行了面形测量,证明该方法测量物体面形是可行性的.由于是采用散斑干涉的方法产生干涉条纹,因此该方法测量物体面形具有灵敏度高的优点.     

Some criteria for the existence of invariant measures and asymptotic stability for random dynamical systems on polish spaces

Tomasz Szarek presented interesting criteria for the existence of invariant measures and asymptotic stability of Markov operators on Polish spaces. Hans Crauel in his book presented the theory of random probabilistic measures on Polish spaces showing that notions of compactness and tightness for such measures are in one-to-one correspondence with such notions for non-random measures on Polish spaces, in addition to the criteria under which the space of random measures is itself a Polish space. This result allowed the transfer of results of Szarek to the case of random dynamical systems in the sense of Arnold. These criteria are interesting because they allow to use the existence of simple deterministic Lyapunov type function together with additional conditions to show the existence of invariant measures and asymptotic stability of random dynamical systems on general Polish spaces.