We consider a real-time monitoring system where a source node (with energy limitations) aims to keep the information status at a destination node as fresh as possible by scheduling status update transmissions over a set of channels. The freshness of information at the destination node is measured in terms of the Age of Information (AoI) metric. In this setting, a natural tradeoff exists between the transmission cost (or equivalently, energy consumption) of the source and the achievable AoI performance at the destination. This tradeoff has been optimized in the existing literature under the assumption of having a complete knowledge of the channel statistics. In this work, we develop online learning-based algorithms with finite-time guarantees that optimize this tradeoff in the practical scenario where the channel statistics are unknown to the scheduler. In particular, when the channel statistics are known, the optimal scheduling policy is first proven to have a threshold-based structure with respect to the value of AoI (i.e., it is optimal to drop updates when the AoI value is below some threshold). This key insight was then utilized to develop the proposed learning algorithms that surprisingly achieve an order-optimal regret (i.e., O(1)) with respect to the time horizon length.

Terahertz (THz) communication signals are susceptible to severe degradation because of the molecular interaction with the atmosphere in the form of subsequent absorption and re-radiation. Recently, reconfigurable intelligent surface (RIS) has emerged as a potential technology to assist in THz communications by boosting signal power or providing virtual line-of-sight (LOS) paths. However, the re-radiated energy has either been modeled as a scattering component or as additive Gaussian noise in the literature. Since the precise characterization is still a work in progress, this paper presents the first comparative investigation of the performance of an RIS-aided THz system under these two extreme re-radiation models. In particular, we first develop a novel parametric channel model that encompasses both models of the re-radiation through a simple parameter change, and then utilize that to design a robust block-coordinate descent (BCD) algorithmic framework which maximizes a lower bound on channel capacity while accounting for imperfect channel state information (CSI). In this framework, the original problem is split into two sub-problems: a) receive beamformer optimization, and b) RIS phase-shift optimization. As the latter sub-problem (unlike the former) has no analytical solution, we propose three approaches for it: a) semi-definite relaxation (SDR) (high complexity), b) signal alignment (SA) (low complexity), and c) gradient descent (GD) (low complexity). The time complexities associated with the proposed approaches are explicitly derived. We analytically demonstrate the limited interference suppression capability of a passive RIS by deriving the stationary points of signal-to-interference and noise ratio (SINR) of a one-element RIS system with one interferer. Our numerical results also demonstrate that slightly better throughput is achieved when the re-radiation manifests as scattering.

In this paper, we study a general setting of status updating systems in which a set of source nodes provide status updates about some physical process(es) to a set of monitors. The freshness of information available at each monitor is quantified in terms of the Age of Information (AoI), and the vector of AoI processes at the monitors (or equivalently the age vector) models the continuous state of the system. While the marginal distributional properties of each AoI process have been studied for a variety of settings using the stochastic hybrid system (SHS) approach, we lack a counterpart of this approach to systematically study their joint distributional properties. Developing such a framework is the main contribution of this paper. In particular, we model the discrete state of the system as a finite-state continuous-time Markov chain, and describe the coupled evolution of the continuous and discrete states of the system by a piecewise linear SHS with linear reset maps. Using the notion of tensors, we first derive first-order linear differential equations for the temporal evolution of both the joint moments and the joint moment generating function (MGF) for an arbitrary set of age processes. We then characterize the conditions under which the derived differential equations are asymptotically stable. The generality of our framework is demonstrated by recovering several existing results as special cases. Finally, we apply our framework to derive the stationary joint MGF in a multi-source updating system under the non-preemptive in service queueing discipline.

We study a general setting of status updating systems in which a set of source nodes provide status updates about some physical process(es) to a set of monitors. The freshness of information available at each monitor is quantified in terms of the Age of Information (AoI), and the vector of AoI processes at the monitors (or equivalently the age vector) models the continuous state of the system. While the marginal distributional properties of each AoI process have been studied for a variety of settings using the stochastic hybrid system (SHS) approach, we lack a counterpart of this approach to systematically study their joint distributional properties. Developing such a framework is the main contribution of this paper. In particular, we model the discrete state of the system as a finite-state continuous-time Markov chain, and describe the coupled evolution of the continuous and discrete states of the system by a piecewise linear SHS with linear reset maps. Using the notion of tensors, we first derive first-order linear differential equations for the temporal evolution of both the joint moments and the joint moment generating function (MGF) for an arbitrary set of age processes. We then characterize the conditions under which the derived differential equations are asymptotically stable. The generality of our framework is demonstrated by recovering several existing results as special cases. Finally, we apply our framework to derive closed-form expressions of the stationary joint MGF in a multi-source updating system under non-preemptive and source-agnostic/source-aware preemptive in service queueing disciplines.

This paper considers a multi-source updating system in which a transmitter powered by energy harvesting (EH) sends status updates about multiple sources of information to a destination, where the freshness of status updates is measured in terms of Age of Information (AoI). The harvested energy packets and the status updates of each source are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. Our focus is on understanding the distributional properties of AoI under a source-aware preemptive in service queueing discipline (which only allows preemption between the status updates generated by the same source to enhance fairness). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the moment generating function (MGF) and average of AoI. To the best of our knowledge, this paper is the first to characterize the AoI performance under a source-aware preemptive policy for the generic case where the transmitter has an arbitrary number of sources. The generality of our results is demonstrated by recovering several existing results for EH-powered single-source systems as special cases. Our results demonstrate that the proposed source-aware preemptive policy strikes a balance between minimizing the sum of average AoI values associated with different sources (average sum-AoI) and achieving fairness among the average AoI values of different sources.

We study a general setting of status updating systems in which a set of source nodes provide status updates about some physical process(es) to a set of monitors. The freshness of information available at each monitor is quantified in terms of the Age of Information (AoI), and the vector of AoI processes at the monitors (or equivalently the age vector) models the continuous state of the system. While the marginal distributional properties of each AoI process have been studied for a variety of settings using the stochastic hybrid system (SHS) approach, we lack a counterpart of this approach to systematically study their joint distributional properties. Developing such a framework is the main contribution of this paper. In particular, we model the discrete state of the system as a finite-state continuous-time Markov chain (MC), and describe the coupled evolution of the continuous and discrete states of the system by a piecewise linear SHS with linear reset maps. We start our analysis by deriving first-order linear differential equations for the temporal evolution of both the joint moments and the joint moment generating function (MGF) of all possible pairwise combinations formed by the age vector components. We then derive conditions under which the derived differential equations are asymptotically stable. Finally, we apply our framework to characterize the stationary joint MGF in a multi-source updating system under several queueing disciplines including non-preemptive and source-agnostic/source-aware preemptive in service queueing disciplines.

This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form ofstatus updatesto a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify thefreshnessof status updates when they reach the destination using the concept ofAge of Information (AoI). Unlike most of the existing analyses of AoI focusing on the evaluation of its average value when the transmitter is not subject to energy constraints, our analysis is focused on understanding thedistributional propertiesof AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and preemptive in service/waiting strategies. Using these MGF results, we further obtain closed-form expressions for the first and second moments of AoI in each queueing discipline. We demonstrate the generality of this analysis by recovering several existing results for the corresponding system with no energy constraints as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the necessity of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value.

In this paper, we consider a cellular-based Internet of things (IoT) network consisting of IoT devices that can communicate directly with each other in a device-to-device (D2D) fashion as well as send real-time status updates about some underlying physical processes observed by them. We assume that such real-time applications are supported by cellular networks where cellular base stations (BSs) collect status updates over time from a subset of the IoT devices in their vicinity. We characterize two performance metrics: i) the network throughput which quantifies the performance of D2D communications, and ii) the Age of Information which quantifies the performance of the real-time IoT-enabled applications. Concrete analytical results are derived using stochastic geometry by modeling the locations of IoT devices as a bipolar Poisson Point Process (PPP) and that of the BSs as another Independent PPP. Our results provide useful design guidelines on the efficient deployment of future IoT networks that will jointly support D2D communications and several cellular network-enabled real-time applications.

In this paper, we consider a large-scale wireless network consisting of source-destination (SD) pairs where the source nodes frequently send status updates about some underlying physical processes (observed by them) to their corresponding destination nodes. For this setup, we employ age of information (AoI) as a performance metric to quantify freshness of the status updates when they reach the destination nodes. While most of the existing works are focused on the analysis of the temporal mean AoI in deterministic network topologies, we aim to characterize the spatial AoI performance disparity that is inherently present in wireless networks. In particular, we treat the temporal mean AoI as a random variable over space as the update delivery rate of a wireless link is a function of the interference field observed by its receiver. Our objective is to characterize the spatial distribution of the temporal mean AoI observed by the SD pairs by modeling them as a Poisson bipolar process. We first derive accurate bounds on the moments of the successful transmission probability of a status update which are then used to derive tight bounds on the moments as well as the spatial distribution of the temporal mean peak AoI. Our results provide useful design guidelines on the appropriate selection of different system parameters to minimize the mean peak AoI.

This paper considers an energy harvesting (EH) real-time status update system in which an EH-powered transmitter node sends status updates about some physical process of interest to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the freshness of status updates when they reach the destination using the concept of Age of Information (AoI). Unlike most of the existing analyses of AoI that focus on characterizing its average when the transmitter has a reliable energy source and is hence not powered by EH (referred henceforth as a non-EH transmitter), our analysis is focused on understanding the distributional properties of AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under both nonpreemptive and preemptive in service queueing disciplines at the transmitter. We demonstrate the generality of this analysis by recovering several known results for the corresponding system with a non-EH transmitter as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the importance of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value.

In this article, an unmanned aerial vehicle (UAV)-assisted wireless network is considered in which a battery-constrained UAV is assumed to move towards energy-constrained ground nodes to receive status updates about their observed processes. The UAV's flight trajectory and scheduling of status updates are jointly optimized with the objective of minimizing the normalized weighted sum of Age of Information (NWAoI) values for different physical processes at the UAV. The problem is first formulated as a mixed-integer program. Then, for a given scheduling policy, a convex optimization-based solution is proposed to derive the UAV's optimal flight trajectory and time instants on updates. However, finding the optimal scheduling policy is challenging due to the combinatorial nature of the formulated problem. Therefore, to complement the proposed convex optimization-based solution, a finite-horizon Markov decision process (MDP) is used to find the optimal scheduling policy. Since the state space of the MDP is extremely large, a novel neural combinatorial-based deep reinforcement learning (NCRL) algorithm using deep Q-network (DQN) is proposed to obtain the optimal policy. However, for large-scale scenarios with numerous nodes, the DQN architecture cannot efficiently learn the optimal scheduling policy anymore. Motivated by this, a long short-term memory (LSTM)-based autoencoder is proposed to map the state space to a fixed-size vector representation in such large-scale scenarios while capturing the spatio-temporal interdependence between the update locations and time instants. A lower bound on the minimum NWAoI is analytically derived which provides system design guidelines on the appropriate choice of importance weights for different nodes. Furthermore, an upper bound on the UAV's minimum speed is obtained to achieve this lower bound value. The numerical results also demonstrate that the proposed NCRL approach can significantly improve the achievable NWAoI per process compared to the baseline policies, such as weight-based and discretized state DQN policies.

This paper considers a large-scale wireless network consisting of source-destination (SD) pairs, where the sources send time-sensitive information, termed status updates, to their corresponding destinations in a time-slotted fashion. We employ age of information (AoI) for quantifying the freshness of the status updates measured at the destination nodes under the preemptive and non-preemptive queueing disciplines with no storage facility. The non-preemptive queue drops the newly arriving updates until the update in service is successfully delivered, whereas the preemptive queue replaces the current update in service with the newly arriving update, if any. As the update delivery rate for a given link is a function of the interference field seen from the receiver, the temporal mean AoI can be treated as a random variable over space. Our goal in this paper is to characterize the spatial distribution of the mean AoI observed by the SD pairs by modeling them as a bipolar Poisson point process (PPP). Towards this objective, we first derive accurate bounds on the moments of success probability while efficiently capturing the interference-induced coupling in the activities of the SD pairs. Using this result, we then derive tight bounds on the moments as well as the spatial distribution of peak AoI (PAoI). Our numerical results verify our analytical findings and demonstrate the impact of various system design parameters on the mean PAoI.

This paper studies the interplay between device-to-device (D2D) communications and real-time monitoring systems in a cellular-based Internet of Things (IoT) network. In particular, besides the possibility that the IoT devices communicate directly with each other in a D2D fashion, we consider that they frequently send time-sensitive information/status updates (about some underlying physical processes observed by them) to their nearest cellular base stations (BSs). Specifically, we model the locations of the IoT devices as a bipolar Poisson Point Process (PPP) and that of the BSs as another independent PPP. For this setup, we characterize the performance of D2D communications using the average network throughput metric whereas the performance of the real-time applications is quantified by the Age of Information (AoI) metric. The IoT devices are considered to employ a distance-proportional fractional power control scheme while sending status updates to their serving BSs. Hence, depending upon the maximum transmission power available, the IoT devices located within a certain distance from the BSs can only send status updates. This association strategy, in turn, forms theJohnson-Mehl (JM)tessellation, such that the IoT devices located in theJM cellsare allowed to send status updates. The average network throughput is obtained by deriving the mean success probability for the D2D links. On the other hand, the temporal mean AoI of a given status update link can be treated as a random variable over space since its success delivery rate is a function of the interference field seen from its receiver. Thus, in order to capture the spatial disparity in the AoI performance, we characterize the spatial moments of the temporal mean AoI. In particular, we obtain these spatial moments by deriving the moments of both the conditional success probability and the conditional scheduling probability for status update links. Our results provide useful design guidelines on the efficient deployment of future massive IoT networks that will jointly support D2D communications and several cellular network-enabled real-time applications.

In this paper, we study a real-time monitoring system in which multiple source nodes are responsible for sending update packets to a common destination node in order to maintain the freshness of information at the destination. Since it may not always be feasible to replace or recharge batteries in all source nodes, we consider that the nodes are powered through wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy (referred to as the age-optimal policy) that jointly optimizes WET and scheduling of update packet transmissions with the objective of minimizing the long-term average weighted sum of Age of Information (AoI) values for different physical processes (observed by the source nodes) at the destination node, referred to as the sum-AoI. To solve this optimization problem, we first model this setup as an average cost Markov decision process (MDP) with finite state and action spaces. Due to the extreme curse of dimensionality in the state space of the formulated MDP, classical reinforcement learning algorithms are no longer applicable to our problem even for reasonable-scale settings. Motivated by this, we propose a deep reinforcement learning (DRL) algorithm that can learn the age-optimal policy in a computationally-efficient manner. We further characterize the structural properties of the age-optimal policy analytically, and demonstrate that it has a threshold-based structure with respect to the AoI values for different processes. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the age-optimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average weighted sum-AoI.

In this paper, we study a real-time Internet of Things (IoT)-enabled monitoring system in which a source node (e.g., IoTdevice or an aggregator located near a group of IoT devices) is responsible for maintaining the freshness of information status at a destination node by sending update packets. Since it may not always be feasible to replace or recharge batteries in all IoT devices, we consider that the source node is powered by wireless energy transfer (WET) by the destination. For this system setup, we investigate the optimal online sampling policy that minimizes the long-term average Age-of-Information (AoI), referred to as the age-optimal policy. The age- optimal policy determines whether each slot should be allocated for WET or update packet transmission while considering the dynamics of battery level, AoI, and channel state information (CSI). To solve this optimization problem, we model this setup as an average cost Markov Decision Process (MDP). After analytically establishing the monotonicity property of the value function associated with the MDP, the age-optimal policy is proven to be a thresholdbased policy with respect to each of the system state variables. We extend our analysis to characterize the structural properties of the policy that maximizes average throughput for our system setup, referred to as the throughput-optimal policy. Afterwards, we analytically demonstrate that the structures of the ageoptimal and throughput-optimal policies are different. We also numerically demonstrate these structures as well as the impact of system design parameters on the optimal achievable average AoI.

Unmanned aerial vehicles (UAVs) are expected to be a key component of the next-generation wireless systems. Due to their deployment flexibility, UAVs are being considered as an efficient solution for collecting information data from ground nodes and transmitting it wirelessly to the network. In this paper, a UAV-assisted wireless network is studied, in which energy-constrained ground nodes are deployed to observe different physical processes. In this network, a UAV that has a time constraint for its operation due to its limited battery, moves towards the ground nodes to receive status update packets about their observed processes. The flight trajectory of the UAV and scheduling of status update packets are jointly optimized with the objective of achieving the minimum weighted sum for the age- of-information (AoI) values of different processes at the UAV, referred to as weighted sum-AoI. The problem is modeled as a finite- horizon Markov decision process (MDP) with finite state and action spaces. Since the state space is extremely large, a deep reinforcement learning (RL) algorithm is proposed to obtain the optimal policy that minimizes the weighted sum-AoI, referred to as the age-optimal policy. Several simulation scenarios are considered to showcase the convergence of the proposed deep RL algorithm. Moreover, the results also demonstrate that the proposed deep RL approach can significantly improve the achievable sum- AoI per process compared to the baseline policies, such as the distance-based and random walk policies. The impact of various system design parameters on the optimal achievable sum-AoI per process is also shown through extensive simulations.

Owing to the ubiquitous availability of radio- frequency (RF) signals, RF energy harvesting is a promising candidate for powering IoT devices, some of which may be deployed at difficult-to-reach places thus making it inconvenient or even impossible to replace or recharge their batteries. In this paper, we model and analyze an IoT network which harvests RF energy and receives information from the same wireless network. In order to enable this operation, each time slot is partitioned into charging and information reception phases. For this setup, we characterize two performance metrics: (i) energy coverage, and (ii) joint signal-to-interference-plus-noise (SINR) and energy coverage. This analysis is performed using a spatial model that captures coupling between the locations of the IoT devices and the nodes of the wireless network (referred henceforth as the IoT gateways), which is usually ignored in the existing literature. In particular, we model the locations of the IoT devices using a general Poisson cluster process (PCP) and assume that the IoT gateways (GWs) are located at the cluster centers. Our results concretely demonstrate that both energy and joint coverage probabilities decrease as the size of the clusters increases. As expected, the performance converges to the case of modeling the locations of the IoT devices and the GWs as two independent PPPs when the cluster sizes go to infinity.

We characterize time and power allocations to optimize the sum-throughput of a Wireless Powered Communication Network (WPCN) with Non-Orthogonal Multiple Access (NOMA). In our setup, an Energy Rich (ER) source broadcasts wireless energy to several devices, which use it to simultaneously transmit data to an Access Point (AP) on the uplink. Differently from most prior works, in this paper we consider a generic scenario, in which the ER and AP do not coincide, i.e., are two separate entities. We study two NOMA decoding schemes, namely Low Complexity Decoding (LCD) and Successive Interference Cancellation Decoding (SICD). For each scheme, we formulate a sum-throughput optimization problem over a finite horizon. Despite the complexity of the LCD optimization problem, due to its non-convexity, we recast it into a series of geometric programs. On the other hand, we establish the convexity of the SICD optimization problem and propose an algorithm to find its optimal solution. Our numerical results demonstrate the importance of using successive interference cancellation in WPCNs with NOMA, and show how the energy should be distributed as a function of the system parameters.

This paper characterizes the performance of a generic -tier cache-aided heterogeneous network (CHN), in which the base stations (BSs) across tiers differ in terms of their spatial densities, transmission powers, pathloss exponents, activity probabilities conditioned on the serving link and placement caching strategies. We consider that each user connects to the BS which maximizes its average received power and at the same time caches its file of interest. Modeling the locations of the BSs across different tiers as independent homogeneous Poisson Point processes (HPPPs), we derive closed-form expressions for the coverage probability and local delay experienced by a typical user in receiving each requested file. We show that our results for coverage probability and delay are consistent with those previously obtained in the literature for a single tier system.

The optimal resource allocation scheme in a full-duplex Wireless Powered Communication Network (WPCN) composed of one Access Point (AP) and two wireless devices is analyzed and derived. AP operates in a full-duplex mode and is able to broadcast wireless energy signals in downlink and receive information data in uplink simultaneously. On the other hand, each wireless device is assumed to be equipped with Radio-Frequency (RF) energy harvesting circuitry which gathers the energy sent by AP and stores it in a finite capacity battery. The harvested energy is then used for performing uplink data transmission tasks. In the literature, the main focus so far has been on slot-oriented optimization. In this context, all the harvested RF energy in a given slot is also consumed in the same slot. However, this approach leads to sub-optimal solutions because it does not take into account the Channel State Information (CSI) variations over future slots. Differently from most of the prior works, in this paper we focus on the long-term weighted throughput maximization problem. This approach significantly increases the complexity of the optimization problem since it requires to consider both CSI variations over future slots and the evolution of the batteries when deciding the optimal resource allocation. We formulate the problem using the Markov Decision Process (MDP) theory and show how to solve it. Our numerical results emphasize the superiority of our proposed full-duplex WPCN compared to the half-duplex WPCN and reveal interesting insights about the effects of perfect as well as imperfect self-interference cancellation techniques on the network performance.

This paper studies optimal resource allocation in a wireless powered communication network with two groups of users; one is assumed to have radio frequency (RF) energy harvesting capability and no other energy sources, while the other group has legacy nodes that are assumed not to have RF energy harvesting capability and are equipped with dedicated energy supplies. First, the base-station (BS) with a constant power supply broadcasts an energizing signal over the downlink. Afterwards, all users transmit their data independently on the uplink using time division multiple access (TDMA). We propose two transmission schemes, namely OPIC and OPAC, subject to different energy constraints on the system. Within each scheme, we formulate two optimization problems with different objective functions, namely maximizing the sum throughput and maximizing the minimum throughput, for enhanced fairness. We establish the convexity of all formulated problems which opens room for efficient solution using standard techniques. Our numerical results show the superiority of our realistic system accommodating legacy nodes, along with RF harvesting nodes, compared to the baseline WPCN system with RF energy harvesting nodes only. Moreover, the results reveal new insights and throughput-fairness trade-offs unique to our new problem setting.