/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Real and Complex Analysis

Due to the broadcast nature of radio propagation, the wireless air interface is open and accessible to both authorized and illegitimate users. This completely differs from a wired network, where communicating devices are physically connected through cables and a node without direct association is unable to access the network for illicit activities. The open communications environment makes wireless transmissions more vulnerable than wired communications to malicious attacks, including both the passive eavesdropping for data interception and the active jamming for disrupting legitimate transmissions. Therefore, this paper is motivated to examine the security vulnerabilities and threats imposed by the inherent open nature of wireless communications and to devise efficient defense mechanisms for improving the wireless network security. We first summarize the security requirements of wireless networks, including their authenticity, confidentiality, integrity, and availability issues. Next, a comprehensive overview of security attacks encountered in wireless networks is presented in view of the network protocol architecture, where the potential security threats are discussed at each protocol layer. We also provide a survey of the existing security protocols and algorithms that are adopted in the existing wireless network standards, such as the Bluetooth, Wi-Fi, WiMAX, and the long-term evolution (LTE) systems. Then, we discuss the state of the art in physical-layer security, which is an emerging technique of securing the open communications environment against eavesdropping attacks at the physical layer. Several physical-layer security techniques are reviewed and compared, including information-theoretic security, artificial-noise-aided security, security-oriented beamforming, diversity-assisted security, and physical-layer key generation approaches. Since a jammer emitting radio signals can readily interfere with the legitimate wireless users, we also introduce the family of various jamming attacks and their countermeasures, including the constant jammer, intermittent jammer, reactive jammer, adaptive jammer, and intelligent jammer. Additionally, we discuss the integration of physical-layer security into existing authentication and cryptography mechanisms for further securing wireless networks. Finally, some technical challenges which remain unresolved at the time of writing are summarized and the future trends in wireless security are discussed.

/pdf/a-survey-on-wireless-security-technical-challenges-recent-3uamoalvot.pdf

A Survey on Wireless Security: Technical Challenges, Recent Advances, and Future Trends

In this paper, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information , or simply age , which is defined as how old the freshest received update is, since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semi-Markov decision problem with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if: 1) the age penalty function grows quickly with respect to the age; 2) the packet transmission times over the channel are positively correlated over time; or 3) the packet transmission times are highly random (e.g., following a heavy-tail distribution).

Update or Wait: How to Keep Your Data Fresh

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

In this paper, we consider the problem of minimizing the age of information in a multi-source system, where samples are taken from multiple sources and sent to a destination via a channel with random delay. Due to interference, only one source can be scheduled at a time. We consider the problem of finding a decision policy that determines the sampling times and transmission order of the sources for minimizing the total average peak age (TaPA) and the total average age (TaA) of the sources. Our investigation of this problem results in an important separation principle: The optimal scheduling strategy and the optimal sampling strategy are independent of each other. In particular, we prove that, for any given sampling strategy, the Maximum Age First (MAF) scheduling strategy provides the best age performance among all scheduling strategies. This transforms our overall optimization problem into an optimal sampling problem, given that the decision policy follows the MAF scheduling strategy. While the zero-wait sampling strategy (in which a sample is generated once the channel becomes idle) is shown to be optimal for minimizing the TaPA, it does not always minimize the TaA. We use Dynamic Programming (DP) to investigate the optimal sampling problem for minimizing the TaA. Finally, we provide an approximate analysis of Bellman's equation to approximate the TaA-optimal sampling strategy by a water-filling solution which is shown to be very close to optimal through numerical evaluations.

Age-optimal Sampling and Transmission Scheduling in Multi-Source Systems

In this paper, we consider a problem of sampling a Wiener process, with samples forwarded to a remote estimator via a channel that consists of a queue with random delay. The estimator reconstructs a real-time estimate of the signal from causally received samples. Motivated by recent research on age-of-information, we study the optimal sampling strategy that minimizes the mean square estimation error subject to a sampling frequency constraint. We prove that the optimal sampling strategy is a threshold policy, and find the optimal threshold. This threshold is determined by the sampling frequency constraint and how much the Wiener process varies during the channel delay. An interesting consequence is that even in the absence of the sampling frequency constraint, the optimal strategy is not zero-wait sampling in which a new sample is taken once the previous sample is delivered; rather, it is optimal to wait for a non-zero amount of time after the previous sample is delivered, and then take the next sample. Further, if the sampling times are independent of the observed Wiener process, the optimal sampling problem reduces to an age-of-information optimization problem that has been recently solved. Our comparisons show that the estimation error of the optimal sampling policy is much smaller than those of age-optimal sampling, zero-wait sampling, and classic uniform sampling.

Remote Estimation of the Wiener Process over a Channel with Random Delay

We study timely status updates of a real-time system in an adversarial setting. The system samples a physical process, and sends the samples from the source (e.g., a sensor) to the destination (e.g, a control center) through a channel. For real-time monitoring/control tasks, it is crucial for the system to update the status of the physical process “timely”. We measure the timeliness of status updates by the time elapsed since the latest update at the destination was generated at the source, and define the time elapsed as age of information, or age in short. To sabotage the system, an attacker aims to maximize the age by jamming the channel and hence causing delay in status updates. The system aims to minimize the age by judiciously choosing when to sample and send the updates. We model the ongoing repeated interaction between the attacker and the system as a dynamic game. In each stage game, the attacker chooses the jamming time according to the jamming time distribution, and the system responds by delaying the sampling according to the sampling policy. We prove that there exists a unique stationary equilibrium in the game, and provide a complete analytical characterization of the equilibrium. Our results shed lights on how the attacker sabotages the system and how the system should defend against the attacker.

A dynamic jamming game for real-time status updates

Inequalities for the generalized Marcum Q-function

One key requirement for storage clouds is to be able to retrieve data quickly. Recent system measurements have shown that the data retrieving delay in storage clouds is highly variable, which may result in a long latency tail. One crucial idea to improve the delay performance is to retrieve multiple data copies by using parallel downloading threads. However, how to optimally schedule these downloading threads to minimize the data retrieving delay remains to be an important open problem. In this paper, we develop low-complexity thread scheduling policies for several important classes of data downloading time distributions, and prove that these policies are either delay-optimal or within a constant gap from the optimum delay performance. These theoretical results hold for an arbitrary arrival process of read requests that may contain finite or infinite read requests, and for heterogeneous MDS storage codes that can support diverse storage redundancy and reliability requirements for different data files. Our numerical results show that the delay performance of the proposed policies is significantly better than that of First-Come-First-Served (FCFS) policies considered in prior work.

Yin Sun

Papers

Age-optimal Sampling and Transmission Scheduling in Multi-Source Systems

Remote Estimation of the Wiener Process over a Channel with Random Delay

A dynamic jamming game for real-time status updates

Inequalities for the generalized Marcum Q-function

Provably delay efficient data retrieving in storage clouds