In this article, we consider an Industrial Internet of Things (IIoT) network operating under a carrier sense multiple access with collision avoidance (CSMA/CA) protocol. Latency-sensitive packets generated at multiple stations randomly are transmitted to a destination for decision making. To meet the strict timeliness constraint, the transmissions are carried by finite blocklength (FBL) codes, while the truncated hybrid automatic repeat request (HARQ) scheme is exploited to improve the reliability. For such unsaturated CSMA/CA networks, for the first time, we characterize the timeliness of packets utilized for decision-making via the age upon decisions (AuD) metric which emphasizes the information freshness at decision moments in comparison to age of information (AoI). To explicitly quantify the AuD performance, we develop an equivalent and tractable unsaturated Markov transfer model for the considered network and investigate the transmission probability and collision probability, respectively. Subsequently, the probability density functions of interarrival time and service time of the successfully transmitted packets are derived. We further derive a closed-form expression for the average AuD under a geometric decision process accordingly. Based on these characterizations, we aim at improving average AuD by jointly allocating the blocklength and transmit power. The formulated nonconvex problem is decomposed into subproblems, and we prove its joint convexity across all feasible intervals. Via simulations, we evaluate the performance of the considered network and conclude a series of design guidelines.

The promptness of decision-making is of paramount importance in coordinate decision-making communication systems. In this paper, we envision a system in which a sender transmits information to a receiver for decision-making. The decision-making process encompasses the extraction of decision-related information followed by subsequent computation. To assess the impact of communication delays, randomness of decision-making and computational time on the immediacy of decisions, we introduce a novel performance metric, namely the age of decision (AoD). Specifically, AoD is defined as the time elapsed since the generation of the update upon which the most recent decision is based. Considering the stochastic nature of decision-making, we analyze the average peak AoD in systems where the arrival and service processes follow general processes or Poisson processes. To facilitate our derivations, we introduce the concept of effective decisions to denote those decisions that can lead to the system’s peak AoD. Simulation results confirm the validity of our derivations and illustrate that appropriately increasing the rate of decision-making can significantly reduce the system’s average peak AoD.

We consider a wireless network where$N$nodes compete for a shared channel over the CSMA/CA protocol to deliver observed updates to a common remote monitor. For this network, we rate the information freshness of the CSMA/CA based network using the age of information (AoI). Different from previous work, the network we consider is unsaturated. To theoretically analyze the transmission behavior of the CSMA/CA based network, we, therefore, develop an equivalent and tractable Markov transmission model. Based on this newly developed model, the transmission probability, collision probability and average AoI of the network are obtained. Our numerical results show that as the packet rate and the number of nodes increase, both the transmission probability and collision probability are increasing; the average AoI first decreases and then increases as the packet rate increases and increases with the number of nodes.

In this article, we consider the timeliness of information transmissions in a three-node industrial wireless sensor network (IWSN) in terms of Age of Information (AoI). In this network, a sensor monitors the ambient environment and transmits the sensed information to a remote monitor directly or through a relay node. In particular, we are interested in how the timeliness of the system is changed by decomposing the long-distance transmission with a relay and by enabling parallel transmissions over the two hops with a packet buffer. To this end, we derive the average AoIs of the transmissions over the direct-link, the relay-links with and without a buffer in a closed form. The obtained results show that the relay-link with a buffer outperforms the other two links, while the relay-link without a buffer outperforms the direct-link only if the relay is properly placed and the sensor–monitor distance is relatively large. On the condition that the average transmission times over the direct-link and the relay-link without a buffer are equal, we further evaluate how fast the average AoI can be reduced by using a relay or a packet buffer, as the packet rate approaches the maximum feasible rate over the links. It is shown that, although the sensor–monitor distance dominates the average AoIs of the links, the gains of using the relay and the buffer do not change much with the distance and are approximately constant.

We consider an Internet-of-Things (IoT) system in which a sensor observes a phenomenon of interest with exponentially distributed intervals and delivers updates to a monitor with random service times. At the monitor, the received updates are used to make decisions with deterministic or random intervals. For this system, we investigate the freshness of the received updates at decision epochs using the age upon decisions (AuDs) metric. With the first-come-first-served (FCFS) policy, theoretical results show that: 1) when the decisions are made with exponentially distributed intervals, the average AuD of the system is smaller when the service time (e.g., transmission time) is uniformly distributed than when it is exponentially distributed and would be the smallest if it is deterministic; 2) when the decisions are made periodically, the average AuD of the system is larger than, and decreases with decision rate to, the average AuD of the corresponding system with Poisson decision intervals; and 3) the probability of missing to use a received update for any decisions is decreasing with the decision rate and is the smallest if the service time is deterministic. When the last-come-first-served (LCFS) policy with preemption is used, we observe that systems with Poisson service processes perform the best while systems with periodic service processes perform the worst. For IoT-based monitoring systems, therefore, it is suggested to use deterministic monitoring schemes, deterministic transmitting schemes, and Poisson decision schemes so that the received updates are as fresh as possible at the time they are used to make decisions.

The Internet of Things (IoT) has emerged as one of the key features of the next-generation wireless networks, where timely delivery of status update packets is essential for many real-time IoT applications. Age of Information (AoI) is a new metric to measure the freshness of update. The reduction of the violation probability that AoI of status updates exceeds a given age constraint is of great significance for guaranteeing the information freshness in IoT systems. By modeling the IoT networks as M/M/1 and M/D/1 queuing systems, this work focuses on characterizing the violation probability of peak AoI and AoI in IoT systems, where a sensor delivers updates to a monitor under M/M/1 and M/D/1 queues with first-come-first-served policy. From a time-domain perspective, we explore the correlation between interdeparture time and system time, by which the closed-form expressions of peak AoI distribution and the violation probability for any AoI constraint are derived. The obtained results induce accurate characterizations for probability distribution functions of peak AoI and AoI. Consequently, accurate characterizations of average AoI and the variance of AoI are obtained. Then, for peak AoI and AoI, the optimal generation rate of the status update that induces the minimal violation probability is also found. The numerical results show that the optimal update rate can significantly reduce the AoI violation probability for a wide range of AoI constraints. The theoretical findings and predictions are verified by numerical simulation results as well as provide guidance for the design of IoT networks.

Internet of Things (IoT) has emerged as one of the key features of the next-generation wireless networks, where timely delivery of status update packets is essential for many real-time IoT applications. Age of Information (AoI) is a new metric to measure the freshness of update. Reduction of the violation probability that AoI of status updates exceeds a given age constraint is of great significance for guaranteeing the data freshness in IoT systems. This work focuses on characterizing the violation probability of AoI in IoT systems where a sensor delivers updates to a monitor under M/M/1 queue with first-come-first-served (FCFS) policy. By exploring the correlation between inter-departure time and system time, the closed-form expression of the violation probability for any AoI constraint is derived. The obtained result induces an accurate characterization of the probability distribution function of AoI. The optimal generation rate of the status update that induces the minimal violation probability is also found. Numerical results show that the optimal update rate can significantly reduce the AoI violation probability for a wide range of AoI constraints.

In this article, we consider an Internet of Things (IoT) system in which a sensor delivers updates to a monitor with exponential service time and first-come-first-served (FCFS) discipline. We investigate the freshness of the received updates and propose a new metric termed as age upon decisions (AuD), which is defined as the time elapsed from the generation of each update to the epoch it is used to make decisions (e.g., estimations, inferences, and controls). Within this framework, we aim at improving the freshness of updates at decision epochs by scheduling the update arrival process and the decision-making process. The theoretical results show that: 1) when the decisions are made according to a Poisson process, the average AuD is independent of decision rate and will be minimized if the arrival process is periodic (i.e., deterministic); 2) when both the decision process and the arrival process are periodic, the average AuD is larger, but decreases with decision rate to, the average AuD of the corresponding system with the Poisson decisions (i.e., random); and 3) when both the decision process and the arrival process are periodic, the average AuD can be further decreased by optimally controlling the offset between the two processes. For practical IoT systems, therefore, it is suggested to employ periodic arrival processes and random decision processes. Nevertheless, making the periodical updates and decisions with properly controlled offset is also a promising solution, if the timing information of the two processes can be accessed by the monitor.

We consider an Internet of Things (IoT)-based sensing system, in which an energy harvesting powered sensor observes the phenomenon of interest and transmits its observations to a remote monitor through a Gaussian channel. Based on the received signals, the monitor makes estimations of source signals with some distortion requirement. We measure the timeliness of the recovered signals using the Age of Information (AoI), which could be reduced by transmitting observations more frequently (i.e., with shorter intervals). We evaluate the recovery distortion with the mean-squared-error (MSE) metric, which would be reduced if a larger transmit power and a larger source coding rate were used. Since the energy harvested by the sensor is quite limited, however, the frequency and power of transmissions cannot be increased at the same time. Thus, we shall investigate the timeliness-distortion tradeoff of the system by minimizing the average weighted sum AoI and distortion over all possible transmit powers and transmission intervals. First, we explicitly present the optimal transmit powers for the performance limit achieving save-and-transmit policy and the easy-implementing fixed power transmission policy. Second, we investigate the offline optimization of the system and propose a backward water-filling-based power allocation scheme, as well as a genetic-based joint transmission scheduling and power control algorithm. Third, we formulate the online power control as a Markov decision process (MDP) and solve the problem with an iterative algorithm, which closely approaches the tradeoff limit of the system. We show that the optimal transmit power is a monotonic and bivalued function of current AoI and distortion. Finally, we present our results via simulations and extend the results on the save-and-transmit policy to fading sensing systems.

This paper considers a two-way data exchanging system with a constant powered access point and an energyharvesting powered smart device. The access point simultaneously transmits information and energy to the smart device with fixed powers ρ̅Ptand ρPt, respectively. Upon collecting enough energy, the smart device performs one block of transmission immediately. We investigate the timeless of the two-way data exchange in terms of age of information (AoI). Specifically, we investigate the trade-off between downlink timeliness and uplink timeliness by optimizing the weighted-sum average AoI. Moreover, we provide a gradient based method to compute this ratio numerically. Our numerical results show that powersplitting based systems outperform time-splitting based systems in terms of timeliness in general.

We consider a wireless sensor network in which all the nodes wish to spread their updates over the network using CSMA/CA protocol. We investigate the age of information of the spreading process from a transmitter perspective, which is referred to as the broadcast age of information (BAoI). To be specific, BAoI is the age of the latest update successfully broadcasted to the one-hop neighbors of a node, and thus is suitable to measure the rapidity of the update spreading process. We establish an equivalent transmission model of the network by deriving the transmission probability and the collision probability of nodes. With this equivalent model, we then present the average BAoI of the network explicitly. Our results present the scaling laws of average BAoI with respect to node density and frame length, and are further illustrated through numerical results. As is shown, the average BAoI is increasing with node density and is convex in frame length, i.e., would be large when frame length is very small or very large.

This paper mainly focuses on the utilization frequency in receiving end of communication systems, which shows the inclination of the user about different symbols. When the using number is limited, a specific utility distribution is proposed on the best effort in term of fairness, which is also the closest one to occurring probability in the relative entropy. Similar to a switch, the parameter of this special utility distribution can be selected to make it satisfy the personalized user demands: negative parameter means the user focus on high-probability events and positive parameter means the user is interested in small-probability events. In fact, the utility distribution can be regraded as a measure of message importance in essence. It illustrates the meaning of message importance measure (MIM), and extend it to the general case by selecting the parameter. Based on it, we connect personalized user demands to the message importance. Numerical results show that this utility distribution characterizes the message importance like MIM and its parameter determines the concern of users like a switch.

We investigate the weighted-sum distortion minimization problem in transmitting two correlated Gaussian sources over Gaussian channels using two energy harvesting nodes. To this end, we develop off-line and online power control policies to optimize the transmit power of the two nodes. In the off-line case, we cast the problem as a convex optimization and investigate the structure of the optimal solution. We also develop a generalized waterfilling-based power allocation algorithm to obtain the optimal solution efficiently. For the online case, we quantify the distortion of the system using a cost function and show that the expected cost equals the expected weighted-sum distortion. Based on Banach's fixed point theorem, we further propose a geometrically converging algorithm to find the minimum cost via simple iterations. Simulation results show that our online power control outperforms the greedy power control where each node uses all the available energy in each slot and also performs close to that of the proposed off-line power control. Moreover, the performance of our off-line power control almost coincides with the performance limit of the system.

Message importance measure (MIM) is applicable to characterize the importance of information in the scenario of big data, similar to entropy in information theory. In fact, MIM with a variable parameter can make an effect on the characterization of distribution. Furthermore, by choosing an appropriate parameter of MIM, it is possible to emphasize the message importance of a certain probability element in a distribution. Therefore, parametric MIM can play a vital role in anomaly detection of big data by focusing on probability of an anomalous event. In this paper, we propose a parameter selection method of MIM focusing on a probability element and then present its major properties. In addition, we discuss the parameter selection with prior probability, and investigate the availability in a statistical processing model of big data for anomaly detection problem.

For a two-way relay network (TWRN) with three nodes, we discuss the performance optimization of digital network coding (DNC) and physical network coding (PNC) schemes under the energy harvesting (EH) constraints and peak power constraints. We also consider the energy transfer between nodes, which is referred to as energy co-operation. To find the maximal achievable performance, we first consider the case of offline scheduling, formulate the corresponding optimization problems, find the optimal solutions, as well as present some useful theoretical properties on optimality. Then we move to the online scheduling, and propose both dynamic programming and some intuitive policies to approach the performance of its offline counterpart. Numerical results show that PNC outperforms DNC due to the higher spectrum efficiency and the intrinsic coding gains, under the same conditions. Furthermore, it is observed that if the relay harvests much more energy and shares it with the two source nodes, DNC with energy co-operation scheme has the potential to perform comparable to or even better than PNC without energy co-operation scheme, which validates the importance of energy co-operation in contemporary communication systems.

We consider cluster-based routing protocols for energy harvesting wireless sensor networks. Since the energy harvesting process does not match the real energy demand, sensor nodes suffer from occasional energy shortages, especially when they serve as cluster head (CH) nodes. To address this problem, we propose a cluster-based routing protocol referred to as distance-and-energy-aware routing with energy reservation (DEARER). The DEARER protocol encourages nodes with high energy-arrival rate or being close to the sink to serve as CH nodes. Also, DEARER allows non-CH nodes to reserve a portion of the harvested energy for future use. In doing so, the DEARER selects “enabler” nodes as CH nodes and provides them with more energy, thereby mitigating the energy shortage events at CH nodes. By theoretical analysis and numerical experiments, we demonstrate that the DEARER protocol outperforms direct transmission and also approaches the genie-aided routing, where CH nodes are selected based on the real-time energy information of each node.

To meet the surging demand for throughput, 5G cellular networks need to be more heterogeneous and much denser, by deploying more and more small cells. In particular, the number of users in each small cell can change dramatically due to users' mobility, resulting in random and time varying uplink interference. This paper considers the uplink interference in a 5G heterogeneous network, which is jointly covered by one macro cell and several small cells. Based on the Lévy flight moving model, a mobility-aware interference model is proposed to characterize the uplink interference from macro cell users to small cell users. In this model, the total uplink interference is characterized by its moment generating function, for both closed subscriber group (CSG) and open subscriber group (CSG) femto cells. In addition, the proposed interference model is a function of basic step length, which is a key velocity parameter of Lévy flights. It is shown by both theoretical analysis and simulation results that the proposed interference model provides a flexible way of evaluating the system performance in terms of success probability and average rate.

Abstract To provide stable and high data rate wireless access for passengers in the train, it is necessary to properly deploy base stations along the railway. We consider this issue from the perspective of service, which is defined as the integral of the time‐varying instantaneous channel capacity. With large‐scale fading assumption, it will be shown that the total service of each base station is inversely proportional to the velocity of the train. Besides, we find that if the ratio of the service provided by a base station in its service region to its total service is given, the base station interval (i.e., the distance between two adjacent base stations) is a constant regardless of the velocity of the train. On the other hand, if a certain amount of service is required, the interval will increase with the velocity of the train. The aforementioned results apply not only to simple curve rails, like line rail and arc rail, but also to any irregular curve rail, provided that the train is traveling at a constant velocity. Furthermore, the new developed results are applied to analyze the on–off transmission strategy of base stations. Copyright © 2013 John Wiley & Sons, Ltd.

Two user Gaussian interference channel (GIC) consists of two source-destination pairs which transmit independent messages and interfere with each other. The best achievable rate region, referred to HK sum rate bound, requires the sources to split the information into public messages and private messages. As Gaussian signaling holds the potential of approaching the capacity, finding the HK sum rate achieved by Gaussian signaling is of great importance. However, The optimal power allocation over messages for Gaussian signaling are not known yet This work clearly describes the optimal power allocation and corresponding sum rate achieved by Gaussian signaling without time sharing (TS) in closed form. It lays a foundation for finding the TS strategy achieving the optimal sum rate. The obtained power allocation indicates that without TS, message splitting may not be always necessary. Besides, the conditions for using and not using message splitting are also characterized in detail.

Quality of service (QoS) requirements are usually different from user to user in a multiaccess system, and it is necessary to take the different requirements into account when allocating the shared resources of the system. In this paper, we consider one QoS criterion-average packet delay in a multiaccess system, and we combine information theory with queueing theory in an attempt to analyze whether a multiaccess system can meet the different delay requirements of all users. When the queue state information is not available to the central scheduler, we show that static rate allocation achieves the best performance. Based on this result, we provide a polynomial-time algorithm for deciding whether a system can meet the different delay requirements of all users. In cases where the system cannot meet the needs of all users, we prove that as long as the sum power is larger than a threshold, there is always an approach to adjust the transmission power of each user to make the system delay feasible if power reallocation is available.

In this paper, we consider one quality-of-service (QoS) criterion, average packet delay (queueing delay plus service time), in a multiaccess system and investigate the basic problem whether a multiaccess system can meet the different average packet delay requirements of all users by combining information theory with queueing theory. Two different cases of the central scheduler with and without queue state information (QSI) are discussed. If the QSI is not available to the central scheduler, we show that static rate allocation policies (SRAPs) can achieve better average packet delay performance than probabilistic rate allocation policies. Based on this conclusion, the delay feasibility checking process reduces to checking whether the required service rate vector lies in the multiaccess capacity region. We find that for users with equal transmit power, only N inequalities are necessary for the checking process, whereas for users with unequal transmit powers, we provide a polynomial-time algorithm for such a decision. Furthermore, if the system cannot satisfy the average packet delay requirements of all users, we prove that as long as the sum power is larger than a threshold, there is always an approach to adjust the transmit powers of different users to satisfy the average packet delay requirements. On the other hand, if the QSI is available to the central scheduler, we propose two dynamic scheduling algorithms to achieve proportional average packet delay and compare their performances with optimal SRAP by simulations.

ABSTRACT In this paper, we study the channel service process of a multiple‐input multiple‐output (MIMO) system over an independent and identically distributed (i.i.d.) fading channel. One key problem of communication over fading MIMO channels is what kind of service the MIMO channel can provide. In this paper, this problem is investigated in terms of channel service process. Assuming that the channel state information is available at the receiver, the channel service process S(t) is defined as the integral of the instantaneous channel capacity over a time interval of length t, which specifies the service provided by the channel during the period. Using the characteristic function approach and the infinitely divisible law, it is proved that the channel service process S(t) is a deterministic linear function of time t, other than any curve form or a stochastic process. Specifically, , where is a constant equal to the corresponding ergodic capacity. This result has two implications: (i) i.i.d. fading MIMO channels can support a constant rate traffic stream of rate without higher layer transmission delay; (ii) the ergodic capacity is the actual transmission capacity of the fading channel, other than only a statistical average value. Copyright © 2012 John Wiley & Sons, Ltd.

Analysis of effective information transmission rate over fading channels has attracted much attentions in the last few years. Ergodic capacity and outage capacity, as two conventional indices, have been widely investigated in various scenarios. However, there exists a gap between them for any fixed average signal to noise ratio. Thus, one problem is raised naturally: How to fill this gap? To answer it, we shall propose a new concept, є-overflow rate, which is used to characterize the transmission capability of a fading channel when a finite size buffer is employed at the transmitter. With this buffer, the constant rate source data stream is matched with the time varying channel status so that the fading channel can support a higher rate source data stream. It will be proved that the є-overflow rate is larger than the є-outage capacity under the same outage constraint and can converge to the ergodic capacity in all signal to noise ratio region.

In the paper, we study the service process S(t) of an independent and identically distributed (i.i.d.) Nakagami-m fading channel, which is defined as the amount of service provided, i.e., the integral of the instantaneous channel capacity over time t. By using the Moment Generation Function (MGF) approach and the infinitely divisible law, it is proved that, other than certain generally recognized curve form or a stochastic process, the channel service process S(t) is a deterministic linear function of time t, namely, S(t)=c_m* \cdot t where c_m* is a constant determined by the fading parameter m. Furthermore, we extend it to general i.i.d. fading channels and present an explicit form of the constant service rate c_p*. The obtained work provides such a new insight on the system design of joint source/channel coding that there exists a coding scheme such that a receiver can decode with zero error probability and zero high layer queuing delay, if the transmitter maintains a constant data rate no more than c_p*. Finally, we verify our analysis through Monte Carlo simulations.

ABSTRACT In this paper, we consider information transmission over a block Rayleigh fading channel, where a finite size buffer is employed to match the source traffic with the channel service capability. Given the buffer size, the transmission capability of a block fading Rayleigh channel is characterized from two aspects: (i) the buffer behavior when the input traffic rate is constant; and (ii) the traffic rate that can be supported by the channel for a given overflow probability constraint. For the first problem, the stationary distribution of the queue length in the buffer is derived by discretizing the queue length using a uniform quantization strategy. It is also shown that the overflow probability of the finite size buffer decreases exponentially with buffer size. An explicit upper bound on the overflow probability is also given. For the second one, a new concept of ε‐overflow rate is proposed to measure the transmission capability of a block fading channel under overflow probability constraints. It will be shown that the ε‐overflow rate is larger than the ε‐outage capacity under the same outage constraint and will meet the great gap between outage capacity and ergodic capacity as the overflow probability constraint varies. Copyright © 2012 John Wiley & Sons, Ltd.

Signal-Time Coding (STC), a novel transmission mechanism, was proposed recently. It combines the traditional encoding/modulation mode in the signal domain with the signal pulse phase modulation in the time domain and can achieve higher information flow rate in some cases for relay networks. However, there are still many fundamental problems to be investigated. This paper considers the implementing issue of STC in AWGN relay networks. Firstly, an energy detection based STC (ED-STC) scheme is proposed and the error probabilities of ED-STC in both the signal domain and the time domain are given. Secondly, a performance evaluation criterion, the reliable information per symbol (RIPS), is proposed to characterize the performance of STC in noisy wireless networks. Moreover, the performance bounds of the RIPS of ED-STC are derived. Numerical analysis show that ED-STC outperforms traditional transmission method in terms of effective information rate within some practical conditions.

In the paper, we study the channel service process of an independent and identically distributed (i.i.d.) Rayleigh channel. The channel service process S(t) is defined as the amount of service provided by the channel, i.e., integral of the instantaneous channel capacity over a time interval of length t. The channel side information (CSI) is assumed available at the receiver. Using the Moment Generation Function (MGF) approach and the infinitely divisible law, it is proved that the channel service process S(t) is a deterministic linear function of time t other than the generally recognized certain curve form, namely, S(t) = c* · t, where c* is a constant.

To maximize the life time of the energy limited Wireless Sensor Network, energy efficient routing algorithms are needed. These algorithms organize nodes into hierarchy and ensure collaboration among nodes. The clustering-based LEACH is one of the most classic protocols among them. In this paper, we provide a modified version of LEACH, mainly focusing on the selection of cluster-head nodes in the network. In the proposed PBEACP, we take into consideration of the remaining energy as well as nodes' geographic distribution in the selection of cluster-head nodes, leading to a more even distribution of the energy consumption among nodes. It also improves in guaranteeing the sensing coverage of cluster-head nodes, even if the topology of the network changes when there are nodes running out of energy. As is shown in our simulation results, the mean of nodes' life time is increased while the deviation is decreased. Also, the number of cluster-head nodes in the network is more stable.