On the Value of Information in Status Update Systems

The age of information (AoI) is now well established as a metric that measures the freshness of information delivered to a receiver from a source that generates status updates. This paper is motivated by the inherent value of packets arising in many cyber-physical applications (e.g., due to precision of the information content or an alarm message). In contrast to AoI, which considers all packets are of equal importance or value, we consider status update systems with update packets carrying values as well as their generated time stamps. A status update packet has a random initial value at the source and a deterministic deadline after which its value vanishes (called ultimate staleness). In our model, the value of a packet either remains constant until the deadline or decreases in time (even after reception) starting from its generation to the deadline when it vanishes. We consider two metrics for the value of information (VoI) at the receiver: sum VoI is the sum of the current values of all packets held by the receiver, whereas packet VoI is the value of a packet at the instant it is delivered to the receiver. We investigate various queuing disciplines under potential dependence between value and service time and provide closed form expressions for both average sum VoI and packet VoI at the receiver. Numerical results illustrate the average VoI for different scenarios and relations between average sum VoI and average packet VoI.     

Joint Optimization of Data Freshness and Fidelity for Selection Combining-Based Transmissions

Motivated by big data applications in the Internet of Things (IoT), abundant information arrives at the fusion center (FC) waiting to be processed. It is of great significance to ensure data freshness and fidelity simultaneously. We consider a wireless sensor network (WSN) where several sensor nodes observe one metric and then transmit the observations to the FC using a selection combining (SC) scheme. We adopt the age of information (AoI) and minimum mean square error (MMSE) metrics to measure the data freshness and fidelity, respectively. Explicit expressions of average AoI and MMSE are derived. After that, we jointly optimize the two metrics by adjusting the number of sensor nodes. A closed-form sub-optimal number of sensor nodes is proposed to achieve the best freshness and fidelity tradeoff with negligible errors. Numerical results show that using the proposed node number designs can effectively improve the freshness and fidelity of the transmitted data.     

Optimal Information Update for Energy Harvesting Sensor with Reliable Backup Energy

The timely delivery of status information collected from sensors is critical in many real-time applications, e.g., monitoring and control. In this paper, we consider a scenario where a wireless sensor sends updates to the destination over an erasure channel with the supply of harvested energy and reliable backup energy. We adopt the metric age of information (AoI) to measure the timeliness of the received updates at the destination. We aim to find the optimal information updating policy that minimizes the time-average weighted sum of the AoI and the reliable backup energy cost. First, when all the environmental statistics are assumed to be known, the optimal information updating policy exists and is proved to have a threshold structure. Based on this special structure, an algorithm for efficiently computing the optimal policy is proposed. Then, for the unknown environment, a learning-based algorithm is employed to find a near-optimal policy. The simulation results verify the correctness of the theoretical derivation and the effectiveness of the proposed method.     

Channel Quality-Based Optimal Status Update for Information Freshness in Internet of Things

This paper investigates the status updating policy for information freshness in Internet of things (IoT) systems, where the channel quality is fed back to the sensor at the beginning of each time slot. Based on the channel quality, we aim to strike a balance between the information freshness and the update cost by minimizing the weighted sum of the age of information (AoI) and the energy consumption. The optimal status updating problem is formulated as a Markov decision process (MDP), and the structure of the optimal updating policy is investigated. We prove that, given the channel quality, the optimal policy is of a threshold type with respect to the AoI. In particular, the sensor remains idle when the AoI is smaller than the threshold, while the sensor transmits the update packet when the AoI is greater than the threshold. Moreover, the threshold is proven to be a non-increasing function of channel state. A numerical-based algorithm for efficiently computing the optimal thresholds is proposed for a special case where the channel is quantized into two states. Simulation results show that our proposed policy performs better than two baseline policies.     

Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.     

Optimizing Age Penalty in Time-Varying Networks with Markovian and Error-Prone Channel State

In this paper, we consider a scenario where the base station (BS) collects time-sensitive data from multiple sensors through time-varying and error-prone channels. We characterize the data freshness at the terminal end through a class of monotone increasing functions related to Age of information (AoI). Our goal is to design an optimal policy to minimize the average age penalty of all sensors in infinite horizon under bandwidth and power constraint. By formulating the scheduling problem into a constrained Markov decision process (CMDP), we reveal the threshold structure for the optimal policy and approximate the optimal decision by solving a truncated linear programming (LP). Finally, a bandwidth-truncated policy is proposed to satisfy both power and bandwidth constraint. Through theoretical analysis and numerical simulations, we prove the proposed policy is asymptotic optimal in the large sensor regime.     

Age of Information Minimization for Radio Frequency Energy-Harvesting Cognitive Radio Networks

The Age of Information (AoI) measures the freshness of information and is a critic performance metric for time-sensitive applications. In this paper, we consider a radio frequency energy-harvesting cognitive radio network, where the secondary user harvests energy from the primary users’ transmissions and opportunistically accesses the primary users’ licensed spectrum to deliver the status-update data pack. We aim to minimize the AoI subject to the energy causality and spectrum constraints by optimizing the sensing and update decisions. We formulate the AoI minimization problem as a partially observable Markov decision process and solve it via dynamic programming. Simulation results verify that our proposed policy is significantly superior to the myopic policy under different parameter settings.     

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.     

A UoI-Optimal Policy for Timely Status Updates with Resource Constraint

Timely status updates are critical in remote control systems such as autonomous driving and the industrial Internet of Things, where timeliness requirements are usually context dependent. Accordingly, the Urgency of Information (UoI) has been proposed beyond the well-known Age of Information (AoI) by further including context-aware weights which indicate whether the monitored process is in an emergency. However, the optimal updating and scheduling strategies in terms of UoI remain open. In this paper, we propose a UoI-optimal updating policy for timely status information with resource constraint. We first formulate the problem in a constrained Markov decision process and prove that the UoI-optimal policy has a threshold structure. When the context-aware weights are known, we propose a numerical method based on linear programming. When the weights are unknown, we further design a reinforcement learning (RL)-based scheduling policy. The simulation reveals that the threshold of the UoI-optimal policy increases as the resource constraint tightens. In addition, the UoI-optimal policy outperforms the AoI-optimal policy in terms of average squared estimation error, and the proposed RL-based updating policy achieves a near-optimal performance without the advanced knowledge of the system model.     

On the Age of Information in a Two-User Multiple Access Setup

This work considers a two-user multiple access channel in which both users have Age of Information (AoI)-oriented traffic with different characteristics. More specifically, the first user has external traffic and cannot control the generation of status updates, and the second user monitors a sensor and transmits status updates to the receiver according to a generate-at-will policy. The receiver is equipped with multiple antennas and the transmitters have single antennas; the channels are subject to Rayleigh fading and path loss. We analyze the average AoI of the first user for a discrete-time first-come-first-served (FCFS) queue, last-come-first-served (LCFS) queue, and queue with packet replacement. We derive the AoI distribution and the average AoI of the second user for a threshold policy. Then, we formulate an optimization problem to minimize the average AoI of the first user for the FCFS and LCFS with preemption queue discipline to maintain the average AoI of the second user below a given level. The constraints of the optimization problem are shown to be convex. It is also shown that the objective function of the problem for the first-come-first-served queue policy is non-convex, and a suboptimal technique is introduced to effectively solve the problem using the algorithms developed for solving a convex optimization problem. Numerical results illustrate the performance of the considered optimization algorithm versus the different parameters of the system. Finally, we discuss how the analytical results of this work can be extended to capture larger setups with more than two users.     

Age Analysis of Status Updating System with Probabilistic Packet Preemption

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.     

Internet of Things: The Optimal Generation Rates under Preemption Strategy in a Multi-Source Queuing System

With the rapid development and wide application of the Internet of Things (IoT), how to provide timely and fresh information for strategic analysis and decision-making has become a key issue. Recent studies have shown that preemption strategies are of great importance to the improvement of information freshness. In view of this, we focus on the multi-source preemptive queuing model and investigate how to control the generation rate of each source to achieve the optimal overall information freshness. Specifically, we consider two typical preemption strategies: self-preemption strategy and global-preemption strategy. Noting that the urgency requirements of the systems on the data of each source are different, we propose the weighted average age of information (AoI) to characterize the overall information freshness of the system. For the self-preemption strategy, we prove that the optimal generation rate allocation is a convex problem and present an efficient algorithm to find the optimal solution. Additionally, we also derive a closed-form approximate optimal solution under light load cases to meet the demands for rapid deployment. For the global-preemption strategy, we directly derive the closed-form optimal solution of the corresponding problem. By comparing the optimized weighted average AoIs, the performance achieved by the global-preemption system was better than that achieved by the self-preemption system in terms of the overall timeliness. The numerical analysis verified the correctness of the theoretical analysis and that the proposed approximate solution had high accuracy not only under light load cases but also under other cases.     

Scheduling Strategy Design Framework for Cyber–Physical System with Non-Negligible Propagation Delay

Cyber–physical systems (CPS) have been widely employed as wireless control networks. There is a special type of CPS which is developed from the wireless networked control systems (WNCS). They usually include two communication links: Uplink transmission and downlink transmission. Those two links form a closed-loop. When such CPS are deployed for time-sensitive applications such as remote control, the uplink and downlink propagation delay are non-negligible. However, existing studies on CPS/WNCS usually ignore the propagation delay of the uplink and downlink channels. In order to achieve the best balance between uplink and downlink transmissions under such circumstances, we propose a heuristic framework to obtain the optimal scheduling strategy that can minimize the long-term average control cost. We model the optimization problem as a Markov decision process (MDP), and then give the sufficient conditions for the existence of the optimal scheduling strategy. We propose the semi-predictive framework to eliminate the impact of the coupling characteristic between the uplink and downlink data packets. Then we obtain the lookup table-based optimal offline strategy and the neural network-based suboptimal online strategy. Numerical simulation shows that the scheduling strategies obtained by this framework can bring significant performance improvements over the existing strategies.     

Scheduling to Minimize Age of Incorrect Information with Imperfect Channel State Information

In this paper, we study a slotted-time system where a base station needs to update multiple users at the same time. Due to the limited resources, only part of the users can be updated in each time slot. We consider the problem of minimizing the Age of Incorrect Information (AoII) when imperfect Channel State Information (CSI) is available. Leveraging the notion of the Markov Decision Process (MDP), we obtain the structural properties of the optimal policy. By introducing a relaxed version of the original problem, we develop the Whittle’s index policy under a simple condition. However, indexability is required to ensure the existence of Whittle’s index. To avoid indexability, we develop Indexed priority policy based on the optimal policy for the relaxed problem. Finally, numerical results are laid out to showcase the application of the derived structural properties and highlight the performance of the developed scheduling policies.     

Free-space laser communications with adaptive optics: Atmospheric compensation experiments

Refractive index inhomogeneities of the turbulent air cause wave-front distortions of optical waves propagating through the atmosphere, leading to such effects as beam spreading, beam wander, and intensity fluctuations (scintillations). These distortions are responsible for severe signal fading in free-space optical communications systems and therefore compromise link reliability. Wave-front distortions can be mitigated, in principle, with adaptive optics, i.e., real-time wave-front control, reducing the likeliness of signal fading. However, adaptive optics technology, currently primarily used in astronomical imaging, needs to be adapted to the requirements of free-space optical communication systems and their specific challenges.In this chapter we discuss a non-conventional adaptive optics approach that has certain advantages with respect to its incorporation into free-space optical communication terminals. The technique does not require wave-front measurements, which are difficult under the strong scintillation conditions typical for communication scenarios, but is based on the direct optimization of a performance quality metric, e.g., the communication signal strength, with a stochastic parallel gradient descent (SPGD) algorithm.We describe an experimental adaptive optics system that consists of a beam-steering and a higher-resolution wave-front correction unit with a 132-actuator MEMS piston-type deformable mirror controlled by a VLSI system implementing the SPGD algorithm. The system optimizes the optical signal that could be coupled into a single-mode fiber after propagating along a 2.3-km near-horizontal atmospheric path. We investigate characteristics of the performance metric under different atmospheric conditions and evaluate the effect of the adaptive system. Experiments performed under strong scintillation conditions with beam-steering only as well as with higher-resolution wave-front control demonstrate the mitigation of wave-front distortions and the reduction of signal fading.     

Secure communications over opportunistic-relay channels

In this paper, we derive information-theoretic performance limits for secure communications over two classes of discrete memoryless relay channels. We consider two different communication scenarios over a four node wireless network comprising a source–destination pair, a relay node and a malicious node eavesdropping on the link between the relay and the destination. In both scenarios, the relay is (1) opportunistic in the sense that, it utilizes the communication opportunity to transmit its own message to the destination; and (2) constrained to secure its communication from the external eavesdropper. We present a novel achievability scheme, namely layered coding, to simultaneously deal with cooperation, cognition and confidentiality. We derive inner bounds on the capacity region for the two communication scenarios, and characterize the rate-penalty for satisfying the security constraints on the messages. Outer bounds are derived using auxiliary random variables which enable single-letter characterization. We also compare the opportunistic-relay models to the classical cognitive radio network setup. Finally, we discuss some of the advantages and drawbacks of our coding strategy in comparison to those in the existing literature, which provides interesting insights into the relative merits of the methods employed in this work for obtaining the capacity bounds.     

Simultaneous two-way classical communication and measurement-device-independent quantum key distribution on oceanic quantum channels

Simultaneous two-way classical and quantum (STCQ) communication combines both continuous classical coherent optical communication and continuous-variable quantum key distribution (CV-QKD), which eliminates all detection-related imperfections by being measurement-device-independent (MDI). In this paper, we propose a protocol relying on STCQ communication on the oceanic quantum channel, in which the superposition-modulation-based coherent states depend on the information bits of both the secret key and the classical communication ciphertext. We analyse the encoding combination in classical communication and consider the probability distribution transmittance under seawater turbulence with various interference factors. Our numerical simulations of various practical scenarios demonstrate that the proposed protocol can simultaneously enable two-way classical communication and CV-MDI QKD with just a slight performance degradation transmission distance compared to the original CV-MDI QKD scheme. Moreover, the asymmetric situation outperforms the symmetric case in terms of transmission distance and optical modulation variance. We further take into consideration the impact of finite-size effects to illustrate the applicability of the proposed scheme in practical scenarios. The results show the feasibility of the underwater STCQ scheme, which contributes toward developing a global quantum communication network in free space.     

Analysis of telescope array receivers for deep-space inter-planetary optical communication link between Earth and Mars

Optical communication technology shows promising prospects to fulfill the large bandwidth communication requirements of future deep-space exploration missions that are launched by NASA and various other international space agencies. At Earth, a telescope with a large aperture diameter is required to capture very weak optical signals that are transmitted from distant planets and to support large bandwidth communication link. A single large telescope has the limitations of cost, single point failure in case of malfunction, difficulty in manufacturing high quality optics, maintenance, and trouble in providing communication operations when transmitting spacecraft is close to the Sun. An array of relatively smaller-sized telescopes electrically connected to form an aggregate aperture area equivalent to a single large telescope is a viable alternative to a monolithic gigantic aperture. In this paper, we present the design concept and analysis of telescope array receivers for an optical communication link between Earth and Mars. Pulse-position modulation (PPM) is used at the transmitter end and photon-counting detectors along with the direct-detection technique are employed at each telescope element in the array. We also present the optimization of various system parameters, such as detector size (i.e., receiver field of view), PPM slot width, and the PPM order M, to mitigate the atmospheric turbulence and background noise effects, and to maximize the communication system performance. The performance of different array architectures is evaluated through analytical techniques and Monte-Carlo simulations for a broad range of operational scenarios, such as, Earth-Mars conjunction, Earth-Mars opposition, and different background and turbulence conditions. It is shown that the performance of the telescope array-based receiver is equivalent to a single large telescope; and as compared to current RF technology, telescope array-based optical receivers can provide several orders of magnitude greater data rates for deep-space communication with Mars.     

An Information-Theoretic View of Mixed-Delay Traffic in 5G and 6G

Fifth generation mobile communication systems (5G) have to accommodate both Ultra-Reliable Low-Latency Communication (URLLC) and enhanced Mobile Broadband (eMBB) services. While eMBB applications support high data rates, URLLC services aim at guaranteeing low-latencies and high-reliabilities. eMBB and URLLC services are scheduled on the same frequency band, where the different latency requirements of the communications render their coexistence challenging. In this survey, we review, from an information theoretic perspective, coding schemes that simultaneously accommodate URLLC and eMBB transmissions and show that they outperform traditional scheduling approaches. Various communication scenarios are considered, including point-to-point channels, broadcast channels, interference networks, cellular models, and cloud radio access networks (C-RANs). The main focus is on the set of rate pairs that can simultaneously be achieved for URLLC and eMBB messages, which captures well the tension between the two types of communications. We also discuss finite-blocklength results where the measure of interest is the set of error probability pairs that can simultaneously be achieved in the two communication regimes.     

Scheduling for end-to-end performance in multi-rate CDMA/HDR systems

An interesting feature of the third generation (3G) cellular networks is their ability to support multiple data rates for data services. Thus, it is important to understand the end-to-end delay and throughput performance over these multi-rate cellular systems. In this work, we consider a multi-rate system such as High Data Rate (HDR) and represent the possible data rates using a Markov chain. Using a M/G/1 queuing model, we calculate the expected data rate and the corresponding link layer delay for each of the initial states. We study the effects of various link layer scheduling techniques for the radio link protocol (RLP) frames destined for multiple user. Though the commonly used link layer scheduling techniques work well, they do not provide the best performance for when end-to-end semantics need to be maintained. In this regard, we propose a scheduling algorithm that aids the transport protocol, for example TCP. Our research shows that the proposed remaining frames first scheduler enhances the transport layer performance compared to the commonly used “best channel scheduler”. Comparative results, based on simulations, are shown with respect to radius of cell, distance of user, number of users, and varying bit error rate.