Robust Security Beamforming for SWIPT-Assisted Relay System with Channel Uncertainty

This paper considers the physical layer security (PLS) of a simultaneous wireless information and power transfer (SWIPT) relay communication system composed of a legitimate source–destination pair and some eavesdroppers. Supposing a disturbance of channel status information (CSI) between relay and eavesdroppers in a bounded ellipse, we intend to design a robust beamformer to maximum security rate in the worst case on the constraints of relay energy consumption. To handle this non-convex optimization problem, we introduce a slack variable to transform the original problem into two sub-problems firstly, then an algorithm employing a semidefinite relaxation (SDR) technique and S-procedure is proposed to tackle above two sub-problems. Although our study was conducted in the scene of a direct link among source, destination, and eavesdroppers that is non-existing, we demonstrate that our conclusions can be easily extended to the scene for which a direct link among source, destination and eavesdroppers exist. Numerical simulation results compared with the benchmark scheme are provided to prove the effectiveness and superior performance of our algorithm.

Age-Aware Utility Maximization in Relay-Assisted Wireless Powered Communication Networks

This article investigates a relay-assisted wireless powered communication network (WPCN), where the access point (AP) inspires the auxiliary nodes to participate together in charging the sensor, and then the sensor uses its harvested energy to send status update packets to the AP. An incentive mechanism is designed to overcome the selfishness of the auxiliary node. In order to further improve the system performance, we establish a Stackelberg game to model the efficient cooperation between the AP–sensor pair and auxiliary node. Specifically, we formulate two utility functions for the AP–sensor pair and the auxiliary node, and then formulate two maximization problems respectively. As the former problem is non-convex, we transform it into a convex problem by introducing an extra slack variable, and then by using the Lagrangian method, we obtain the optimal solution with closed-form expressions. Numerical experiments show that the larger the transmit power of the AP, the smaller the age of information (AoI) of the AP–sensor pair and the less the influence of the location of the auxiliary node on AoI. In addition, when the distance between the AP and the sensor node exceeds a certain threshold, employing the relay can achieve better AoI performance than non-relaying systems.

Factorization of Noncommutative Polynomials and Nullstellensätze for the Free Algebra

This article gives a class of Nullstellensätze for noncommutative polynomials. The singularity set of a noncommutative polynomial $f=f(x_1,\dots ,x_g)$ is $\mathscr{Z}(\,f)=(\mathscr{Z}_n(\,f))_n$, where $\mathscr{Z}_n(\,f)=\{X \in{\operatorname{M}}_{n}({\mathbb{C}})^g \colon \det f(X) = 0\}.$ The 1st main theorem of this article shows that the irreducible factors of $f$ are in a natural bijective correspondence with irreducible components of $\mathscr{Z}_n(\,f)$ for every sufficiently large $n$. With each polynomial $h$ in $x$ and $x^*$ one also associates its real singularity set $\mathscr{Z}^{{\operatorname{re}}}(h)=\{X\colon \det h(X,X^*)=0\}$. A polynomial $f$ that depends on $x$ alone (no $x^*$ variables) will be called analytic. The main Nullstellensatz proved here is as follows: for analytic $f$ but for $h$ dependent on possibly both $x$ and $x^*$, the containment $\mathscr{Z}(\,f) \subseteq \mathscr{Z}^{{\operatorname{re}}} (h)$ is equivalent to each factor of $f$ being “stably associated” to a factor of $h$ or of $h^*$. For perspective, classical Hilbert-type Nullstellensätze typically apply only to analytic polynomials $f,h $, while real Nullstellensätze typically require adjusting the functions by sums of squares of polynomials (sos). Since the above “algebraic certificate” does not involve a sos, it seems justified to think of this as the natural determinantal Hilbert Nullstellensatz. An earlier paper of the authors (Adv. Math. 331 (2018): 589–626) obtained such a theorem for special classes of analytic polynomials $f$ and $h$. This paper requires few hypotheses and hopefully brings this type of Nullstellensatz to near final form. Finally, the paper gives a Nullstellensatz for zeros ${\mathcal{V}}(\,f)=\{X\colon f(X,X^*)=0\}$ of a hermitian polynomial $f$, leading to a strong Positivstellensatz for quadratic free semialgebraic sets by the use of a slack variable.

Assessing the Middle East Top Container Ports Relative Technical Efficiency

Middle East main container ports are developing rapidly with a lot of investments. This is due to their geographical location in the main East-West trade route. Accordingly, it is important to assess their relative technical efficiency to make them visible and stand out in such a development. This research will assess the relative technical efficiency based on the infrastructure of the main container ports in the Middle East by the aid of data envelopment analysis (DEA) for the year 2017. This will be performed by using the DEA four models based on the input oriented mode CCR model, BCC model, Supper efficiency and the Slack variable analyses. Results of the research highlight that nearly 80% of the studied ports are, with an increasing return to scale approach to the study ports, suffering from a surplus in their infrastructure that should be considered in future investments.

Innovative assessment scheme of navigation risk based on improved multi-source information fusion techniques

To deal with highly time complexity and unstable assessments for conflicting evidences from various navigation factors, we put forward an innovative assessment scheme of navigation risk based on the improved multi-source information fusion techniques. Different from the existing studies, we first deduce the nonlinear support vector machine classification model for the general scenario. The slack variable is adaptively computed based on the Euclidean distance ratio. Considering the unsatisfactory characteristics of the standard Dempster–Shafer evidence theory, the optimal combination rule is derived step by step. What"s more, the lowly dimensional Kalman filter is applied to forecast the navigation risk. Simultaneously, the time complexity of each technique is analyzed. With respect to the vessel navigation risk, the assessment results are provided to indicate the reliability and efficiency of the proposed scheme.