We study a setting where an intelligent model (e.g., a pre-trained neural network) infers the real-time value of a target signal using data samples transmitted from a remote source. The transmission scheduler decides (i) the freshness of packets, (ii) their length (i.e., the number of samples they contain), and (iii) when they should be transmitted. The freshness is quantified using the Age of Information (AoI), and the inference quality for a given packet length is a general function of AoI. Previous works assumed i.i.d. transmission delays with immediate feedback or were restricted to the case where inference performance degrades as the input data ages. Our formulation, in addition to capturing non-monotone age dependence, also covers Markovian delay on both forward and feedback links. We model this as an infinite-horizon average-cost Semi-Markov Decision Process. We obtain a closed-form solution that decides on (i) and (iii) for any constant packet length. The solution for when to transmit is an index-based threshold policy, where the index function is expressed in terms of the delay state and AoI at the receiver. In contrast, the freshness of the selected packet is a function of only the delay state. We then separately optimize the value of the constant packet length. Moreover, we also develop an indexbased threshold policy for the time-variable packet length case, which allows a complexity reduction. In simulation results, we observe that our goal-oriented scheduler drops inference error down to one-sixth with respect to the age-based scheduling of unit-length packets.

We study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times are i.i.d. across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-armed Bandit (RMAB) problem with a continuous state space. We prove that the bandits are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation of Gauss-Markov processes. Our results unite two theoretical frameworks that were used for remote estimation and AoI minimization: threshold-based sampling and Whittle index-based scheduling. In the single-source, single-channel scenario, we demonstrate that the optimal solution to the sampling and scheduling problem can be equivalently expressed as both a threshold-based sampling strategy and a Whittle index-based scheduling policy. Notably, the Whittle index is equal to zero if and only if two conditions are satisfied: (i) the channel is idle, and (ii) the estimation error is precisely equal to the threshold in the threshold-based sampling strategy. Moreover, the methodology employed to derive threshold-based sampling strategies in the single-source, single-channel scenario plays a crucial role in establishing indexability and evaluating the Whittle index in the more intricate multi-source, multi-channel scenario. Our numerical results show that the proposed policy achieves high-performance gain over the existing policies when some of the Gauss-Markov processes are highly unstable.

Reinforcement learning (RL) holds great promise for network control problems, yet its deployment in real-world systems remains limited due to the instability and unpredictability of RL policies during training. To address this challenge, we propose a two-phase conservative RL framework that combines domain expertise from classical network optimization with modern deep RL techniques. Our key idea is to initialize the learning process with a stable base policy, derived from expert knowledge, and then apply conservative fine-tuning under a Kullback–Leibler (KL) divergence constraint to safely explore improved behaviors. We apply this framework to the problem of covert multi-hop routing, where the objective is to optimize data throughput while minimizing detectability by adversaries. In Phase I, we construct a reliable base policy by imitating the back-pressure algorithm, which guarantees throughput-optimal behavior and stable queue dynamics. Phase II fine-tunes this policy to improve covert performance, as measured by the Detection Error Probability (DEP), while preserving training-time stability. Empirical evaluations on a grid network show that our method enables more reliable learning than pure RL. While pure RL (e.g., PPO) can sometimes achieve higher covert performance, it frequently suffers from large queues and collapsed throughput during training. In our experiments, our conservative RL framework reduces the worst-case training-time queue length by over 99% while maintaining comparable covert communication performance.

We consider a remote inference system with multiple modalities, where a multimodal machine learning (ML) model performs real-time inference using features collected from remote sensors. When sensor observations evolve dynamically over time, fresh features are critical for inference tasks. However, timely delivery of features from all modalities is often infeasible because of limited network resources. Towards this end, in this paper, we study a two-modality scheduling problem that seeks to minimize the ML model’s inference error, expressed as a penalty function of the Age of Information (AoI) vector of the two modalities. We develop an index-based threshold policy and prove its optimality. Specifically, the scheduler switches to the other modality once the current modality’s index function exceeds a predetermined threshold. We show that both modalities share the same threshold and that the index functions and the threshold can be computed efficiently. Our optimality results hold for general AoI functions (which could be non-monotonic and non-separable) and heterogeneous transmission times across modalities. To demonstrate the importance of considering a task-oriented AoI function, we conduct numerical experiments based on robot state prediction and compare our policy with round-robin and uniform random policies (both are oblivious to the AoI and the inference error). The results show that our policy reduces inference error by up to 55% compared with these baselines.

We study the design of a goal-oriented sampling and scheduling strategy through a channel with highly variable two-way random delay, which can exhibit memory (e.g., Delay and Disruption Tolerant Networks). The objective of the communication is to optimize the performance of remote inference, where an inference algorithm (e.g., a trained neural network) on the receiver side predicts a time-varying target signal using the data samples transmitted by a sensor. Previous formulations to this problem either assumed a channel with IID transmission delay, neglecting feedback delay or considered the monotonic relation that the performance only gets worse as the input information ages. We show how, with delayed feedback, one can effectively exploit the knowledge about delay memory through an index-based threshold policy. This policy minimizes the expected time-average inference error that can be monotone or non-monotone in age. The index function is expressed in terms of the Age of Information (AoI) on the receiver side and a parameter regarding the distribution of subsequent transmission delay, both of which can readily be tracked.

In this paper, we analyze the impact of data freshness on remote inference systems, where a pre-trained neural network infers a time-varying target (e.g., the locations of vehicles and pedestrians) based on features (e.g., video frames) observed at a sensing node (e.g., a camera). One might expect that the performance of a remote inference system degrades monotonically as the feature becomes stale. Using an information-theoretic analysis, we show that this is true if the feature and target data sequence can be closely approximated as a Markov chain, whereas it is not true if the data sequence is far from being Markovian. Hence, the inference error is a function of Age of Information (AoI), where the function could be non-monotonic. To minimize the inference error in real-time, we propose a new “selection-from-buffer” model for sending the features, which is more general than the “generate-at-will” model used in earlier studies. In addition, we design low-complexity scheduling policies to improve inference performance. For single-source, single-channel systems, we provide an optimal scheduling policy. In multi-source, multi-channel systems, the scheduling problem becomes a multi-action restless multi-armed bandit problem. For this setting, we design a new scheduling policy by integrating Whittle index-based source selection and duality-based feature selection-from-buffer algorithms. This new scheduling policy is proven to be asymptotically optimal. These scheduling results hold for minimizing general AoI functions (monotonic or non-monotonic). Data-driven evaluations demonstrate the significant advantages of our proposed scheduling policies.

In this paper, we study an online sampling problem of the Wiener process. The goal is to minimize the mean squared error (MSE) of the remote estimator under a sampling frequency constraint when the transmission delay distribution is unknown. The sampling problem is reformulated into an optional stopping problem, and we propose an online sampling algorithm that can adaptively learn the optimal stopping threshold through stochastic approximation. We prove that the cumulative MSE regret grows with rate$\mathcal{O}(\ln k)$, where$k$is the number of samples. Through Le Cam’s two point method, we show that the worst-case cumulative MSE regret of any online sampling algorithm is lower bounded by$\Omega(\ln k)$. Hence, the proposed online sampling algorithm is minimax order-optimal. Finally, we validate the performance of the proposed algorithm via numerical simulations.

In this paper, we study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times are i.i.d. across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-armed Bandit (RMAB) problem with a continuous state space. We prove that the bandits are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation of Gauss-Markov processes. We further investigate signal-agnostic remote estimation and develop a Whittle index policy for multi-source Age of Information (AoI) minimization over parallel channels with i.i.d. random transmission times. Our results unite two theoretical frameworks for remote estimation and AoI minimization: threshold-based sampling and Whittle index-based scheduling. In the single-source, single-channel scenario, we demonstrate that the optimal solution to the sampling and scheduling problem can be equivalently expressed as both a threshold-based sampling strategy and a Whittle index-based scheduling policy. Notably, the Whittle index is equal to zero if and only if two conditions are satisfied: (i) the channel is idle, and (ii) the estimation error is precisely equal to the threshold in the threshold-based sampling strategy. Moreover, the methodology employed to derive threshold-based sampling strategies in the single-source, single-channel scenario plays a crucial role in establishing indexability and evaluating the Whittle index in the more intricate multi-source, multi-channel scenario. Our numerical results show that the proposed policy achieves high performance gain over the existing policies when some of the Gauss-Markov processes are highly unstable.

We consider the problem of minimizing the age of information when a source can transmit status updates over two heterogeneous channels. Our work is motivated by recent developments in 5 G mmWave technology, where transmissions may occur over an unreliable but fast (e.g., mmWave) channel or a slow reliable (e.g., sub-6 GHz) channel. The unreliable channel is modeled as a time-correlated Gilbert-Elliot channel at a high rate when the channel is in the “ON” state. The reliable channel provides a deterministic but lower data rate. The scheduling strategy determines the channel to be used for transmission in each time slot, aiming to minimize the time-average age of information (AoI). The optimal scheduling problem is formulated as a Markov Decision Process (MDP), which is challenging to solve because super-modularity does not hold in a part of the state space. We address this challenge and show that a multi-dimensional threshold-type scheduling policy is optimal for minimizing the age. By exploiting the structure of the MDP and analyzing the discrete time Markov chains (DTMCs) of the threshold-type policy, we devise a low-complexity bisection algorithm to compute the optimal thresholds. We compare different scheduling policies using numerical simulations.

In this paper, we aim to design an optimal sampler for a system in which fresh samples of a signal (source) are sent through an unreliable channel to a remote estimator, and acknowledgments are sent back over a feedback channel. Both the forward and feedback channels could have random transmission times due to time varying channel conditions. Motivated by distributed sensing, the estimator can estimate the real-time value of the source signal by combining the signal samples received through the channel and the noisy signal observations collected from a local sensor. We prove that the estimation error is a non-decreasing function of the Age of Information (AoI) for the received signal samples and design an optimal sampling strategy that minimizes the long-term average estimation error subject to a sampling rate constraint. The sampling strategy is also optimal for minimizing the long-term average of general non-decreasing functions of the AoI. The optimal sampler design follows a randomized threshold strategy: If the last transmission was successful, the source waits until the expected estimation error upon delivery exceeds a threshold and then sends out a new sample. If the last transmission fails, the source immediately sends out a new sample without waiting. The threshold is the root of a fixed-point equation and can be solved with low complexity (e.g., by bisection search). The optimal sampling strategy holds for general transmission time distributions of the forward and feedback channels. Numerical simulations are provided to compare different sampling policies.

In this paper, we study a sampling problem in which fresh samples of a signal (source) are sent through an unreliable channel to a remote estimator, and acknowledgments are sent back over a feedback channel. Both the forward and feedback channels are subject to random transmission times. Motivated by distributed sensing, the estimator can estimate the real-time value of the source signal by combining the signal samples received through the channel and noisy signal observations collected from a local sensor. We prove that the estimation error is a non-decreasing function of the Age of Information (AoI) for received signal samples and design an optimal sampling strategy that minimizes the long-term average estimation error. The optimal sampler design follows a threshold strategy: If the last transmission was successful, the source waits until the expected estimation error upon delivery exceeds a threshold and then sends out a new sample. If the last transmission fails, the source immediately sends out a new sample without waiting. The threshold is the unique root of a fixed-point equation and can be solved with low complexity (e.g., by bisection search). In addition, the proposed sampling strategy is also optimal for minimizing the long-term average of general non-decreasing functions of the AoI. Its optimality holds for general transmission time distributions of the forward and feedback channels.

In this paper, we analyze the impact of data freshness on real-time supervised learning, where a neural network is trained to infer a time-varying target (e.g., the position of the vehicle in front) based on features (e.g., video frames) observed at a sensing node (e.g., camera or lidar). One might expect that the performance of real-time supervised learning degrades monotonically as the feature becomes stale. Using an information-theoretic analysis, we show that this is true if the feature and target data sequence can be closely approximated as a Markov chain; it is not true if the data sequence is far from Markovian. Hence, the prediction error of real-time supervised learning is a function of the Age of Information (AoI), where the function could be non-monotonic. Several experiments are conducted to illustrate the monotonic and non-monotonic behaviors of the prediction error. To minimize the inference error in real-time, we propose a new "selection-from-buffer" model for sending the features, which is more general than the "generate-at-will" model used in earlier studies. By using Gittins and Whittle indices, low-complexity scheduling strategies are developed to minimize the inference error, where a new connection between the Gittins index theory and Age of Information (AoI) minimization is discovered. These scheduling results hold (i) for minimizing general AoI functions (monotonic or non-monotonic) and (ii) for general feature transmission time distributions. Data-driven evaluations are presented to illustrate the benefits of the proposed scheduling algorithms.

In this paper, we study an online sampling problem of the Wiener process. The goal is to minimize the mean squared error (MSE) of the remote estimator under a sampling frequency constraint when the transmission delay distribution is unknown. The sampling problem is reformulated into a renewal reward optimization problem, and we propose an online sampling algorithm that can adaptively learn the optimal sampling policy through stochastic approximation. We show that the cumulative MSE regret grows with rate O(ln k), where k is the number of samples. Through Le Cam's two point method, we show that the worst-case cumulative MSE regret of any online sampling algorithm is lower bounded by Ω (ln k). Hence, the proposed online sampling algorithm is minimax order-optimal. Finally, we validate the performance of the proposed algorithm via numerical simulations.

In this paper, we consider a scheduling problem, in which several streams of status update packets with different priority levels are sent through a shared channel to their destinations. We introduce a notion oflexicographic age optimality, or simplylex-age-optimality, to evaluate the performance of multi-class status update policies. In particular, a lex-age-optimal scheduling policy first minimizes the Age of Information (AoI) metrics for high-priority streams, and then, within the set of optimal policies for high-priority streams, achieves the minimum AoI metrics for low-priority streams. We propose a new scheduling policy named Preemptive Priority, Maximum Age First, Last-Generated, First-Served (PP-MAF-LGFS), and prove that the PP-MAF-LGFS scheduling policy is lex-age-optimal. This result holds (i) for minimizing any time-dependent, symmetric, and non-decreasing age penalty function; (ii) for minimizing any non-decreasing functional of the stochastic process formed by the age penalty function; and (iii) for the cases where different priority classes have distinct arrival traffic patterns, age penalty functions, and age penalty functionals. For example, the PP-MAF-LGFS scheduling policy is lex-age-optimal for minimizing the probability of age violation of a high-priority stream and the time-average age of a low-priority stream. Numerical results are provided to illustrate our theoretical findings.

In this paper, we study the problem of minimizing the age of information when a source can transmit status updates over two heterogeneous channels. Our work is motivated by recent developments in 5G mmWave technology, where transmissions may occur over an unreliable but fast (e.g., mmWave) channel or a slow reliable (e.g., sub-6GHz) channel. The unreliable channel is modeled as a time-correlated Gilbert-Elliot channel, where information can be transmitted at a high rate when the channel is in the "ON" state. The reliable channel provides a deterministic but lower data rate. The scheduling strategy determines the channel to be used for transmission with the aim to minimize the time-average age of information (AoI). The optimal scheduling problem is formulated as a Markov Decision Process (MDP), which in our setting poses some significant challenges because e.g., supermodularity does not hold for part of the state space. We show that there exists a multi-dimensional threshold-based scheduling policy that is optimal for minimizing the age. A low-complexity bisection algorithm is further devised to compute the optimal thresholds. Numerical simulations are provided to compare different scheduling policies.

We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications.

We consider a joint sampling and scheduling problem for optimizing data freshness in multi-source systems. Data freshness is measured by a non-decreasing penalty function of age of information, where all sources have the same age-penalty function. Sources take turns to generate update packets, and forward them to their destinations one-by-one through a shared channel with random delay. There is a scheduler, that chooses the update order of the sources, and a sampler, that determines when a source should generate a new packet in its turn. We aim to find the optimal scheduler-sampler pairs that minimize the total-average age-penalty at delivery times (Ta-APD) and the total-average age-penalty (Ta-AP). We prove that the Maximum Age First (MAF) scheduler and the zero-wait sampler are jointly optimal for minimizing the Ta-APD. Meanwhile, the MAF scheduler and a relative value iteration with reduced complexity (RVI-RC) sampler are jointly optimal for minimizing the Ta-AP. The RVI-RC sampler is based on a relative value iteration algorithm whose complexity is reduced by exploiting a threshold property in the optimal sampler. Finally, a low-complexity threshold-type sampler is devised via an approximate analysis of Bellman's equation. This threshold-type sampler reduces to a simple water-filling sampler for a linear age-penalty function.

We consider the problem of optimizing the freshness of status updates that are sent from a large number of low-power sources to a common access point. The source nodes utilize carrier sensing to reduce collisions and adopt an asynchronized sleep-wake scheduling strategy to achieve a target network lifetime (e.g., 10 years). We useage of information(AoI) to measure the freshness of status updates, and design sleep-wake parameters for minimizing the weighted-sum peak AoI of the sources, subject to per-source battery lifetime constraints. When the sensing time (i.e., the time duration of carrier sensing) is zero, this sleep-wake design problem can be solved by resorting to a two-layer nested convex optimization procedure; however, for positive sensing times, the problem is non-convex. We devise a low-complexity solution to solve this problem and prove that, for practical sensing times that are short, the solution is within a small gap from the optimum AoI performance. When the mean transmission time of status-update packets is unknown, we devise a reinforcement learning algorithm that adaptively performs the following two tasks in an “efficient way”: a) it learns the unknown parameter, b) it also generates efficient controls that make channel access decisions. We analyze its performance by quantifying its “regret”, i.e., the sub-optimality gap between its average performance and the average performance of a controller that knows the mean transmission time. Our numerical and NS-3 simulation results show that our solution can indeed elongate the batteries lifetime of information sources, while providing a competitive AoI performance.

Recently, a connection between the age of information and remote estimation error was found in a sampling problem of Wiener processes: If the sampler has no knowledge of the signal being sampled, the optimal sampling strategy is to minimize the age of information; however, by exploiting causal knowledge of the signal values, it is possible to achieve a smaller estimation error. In this paper, we generalize the previous study by investigating a problem of sampling a stationary Gauss-Markov process named the Ornstein-Uhlenbeck (OU) process, where we aim to find useful insights for solving the problems of sampling more general signals. The optimal sampling problem is formulated as a constrained continuous-time Markov decision process (MDP) with an uncountable state space. We provide an exact solution to this MDP: The optimal sampling policy is a threshold policy oninstantaneous estimation errorand the threshold is found. Further, if the sampler has no knowledge of the OU process, the optimal sampling problem reduces to an MDP for minimizing anonlinearage of information metric. The age-optimal sampling policy is a threshold policy onexpected estimation errorand the threshold is found. In both problems, the optimal sampling policies can be computed by low-complexity algorithms (e.g., bisection search and Newton’s method), and the curse of dimensionality is circumvented. These results hold for (i) general service time distributions of the queueing server and (ii) sampling problems both with and without a sampling rate constraint. Numerical results are provided to compare different sampling policies.

We consider the problem of tracking an unstable stochastic process Xtby using causal knowledge of another stochastic process Yt. We obtain necessary conditions and sufficient conditions for maintaining a finite tracking error. We provide necessary conditions as well as sufficient conditions for the success of this estimation, which is defined as order m moment trackability. By-products of this study are connections between statistics such as Rényi entropy, Gallager’s reliability function, and the concept of anytime capacity.

In this paper, we consider the problem of optimizing the freshness of status updates that are sent from a large number of low-power source nodes to a common access point. The source nodes utilize carrier sensing to reduce collisions and adopt an asychronized sleep-wake strategy to achieve an extended battery lifetime (e.g., 10-15 years). We use age of information (AoI) to measure the freshness of status updates, and design the sleep-wake parameters for minimizing the weighted-sum peak AoI of the sources, subject to per-source battery lifetime constraints. When the sensing time is zero, this sleep-wake design problem can be solved by resorting to a two-layer nested convex optimization procedure; however, for positive sensing times, the problem is non-convex. We devise a low-complexity solution to solve this problem and prove that, for practical sensing times that are short and positive, the solution is within a small gap from the optimum AoI performance. Our numerical and NS-3 simulation results show that our solution can indeed elongate the batteries lifetime of information sources, while providing a competitive AoI performance.

In this paper, we consider a problem of sampling a Wiener process, with samples forwarded to a remote estimator over a channel that is modeled as a queue. The estimator reconstructs an estimate of the real-time signal value from causally received samples. We study the optimal online sampling strategy that minimizes the mean square estimation error subject to a sampling rate constraint. We prove that the optimal sampling strategy is a threshold policy, and find the optimal threshold. This threshold is determined by how much the Wiener process varies during the random service time and the maximum allowed sampling rate. Further, if the sampling times are independent of the observed Wiener process, the above sampling problem for minimizing the estimation error is equivalent to a sampling problem for minimizing the age of information. This reveals an interesting connection between the age of information and remote estimation error. Our comparisons show that the estimation error achieved by the optimal sampling policy can be much smaller than those of age-optimal sampling, zero-wait sampling, and periodic sampling.

We study the sensitivity of multi-user scheduling performance to channel magnitude misreporting in systems with massive antennas. We consider the round-robin scheduler combined with max-min and waterfilling power controls, respectively. We show that user scheduling combined with power allocation, in general, dampens the negative effect of channel misreporting compared to the purely physical layer analysis of channel misreporting without scheduling. We discover several interesting results. First, we observe a periodicity in rate-loss behavior as the number of misreporting users increases. Second, we find that the waterfilling power control is more robust to channel misreporting compared with max-min power control. Third, for homogeneous users with equal average signal-to-noise ratios (SNRs), channel underreporting is harmful but overreporting is beneficial for max-min power control; the opposite impact is found for waterfilling power control. For heterogeneous users with various average SNRs, however, both underreporting and overreporting harm the system for both power control policies, demonstrating the complex interactions across network layers due to channel misreporting.

One fundamental challenge in 5G URLLC is how to optimize massive MIMO systems for achieving low latency and high reliability. A natural design choice to maximize reliability and minimize retransmission is to select the lowest allowed target error rate. However, the overall latency is the sum of queueing latency and retransmission latency, hence choosing the lowest target error rate does not always minimize the overall latency. In this paper, we minimize the overall latency by jointly designing the target error rate and transmission rate adaptation, which leads to a fundamental tradeoff point between queueing and retransmission latency. This design problem can be formulated as a Markov decision process, which is theoretically optimal, but its complexity is prohibitively high for real-system deployments. We managed to develop a low-complexity closed-form policy named Large-arraY Reliability and Rate Control (LYRRC), which is proven to be asymptotically latency-optimal as the number of antennas increases. In LYRRC, the transmission rate is twice of the arrival rate, and the target error rate is a function of the antenna number, arrival rate, and channel estimation error. With simulated and measured channels, our evaluations find LYRRC satisfies the latency and reliability requirements of URLLC in all the tested scenarios.

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

Recently, a connection between the age of information and remote estimation error was found in a sampling problem of Wiener processes: If the sampler has no knowledge of the signal being sampled, the optimal sampling strategy is to minimize the age of information; however, by exploiting causal knowledge of the signal values, it is possible to achieve a smaller estimation error. In this paper, we generalize the previous study by investigating a problem of sampling a stationary Gauss-Markov process named the Ornstein-Uhlenbeck (OU) process, where we aim to find useful insights for solving the problems of sampling more general signals. The optimal sampling problem is formulated as a constrained continuous-time Markov decision process (MDP) with an uncountable state space. We provide an exact solution to this MDP: The optimal sampling policy is a threshold policy on instantaneous estimation error and the threshold is found. Further, if the sampler has no knowledge of the OU process, the optimal sampling problem reduces to an MDP for minimizing a nonlinear age of information metric and the age-optimal sampling policy is a threshold policy on expected estimation error and the threshold is found. In both problems, the optimal sampling policies can be computed by bisection search, and the curse of dimensionality is circumvented. These results hold for (i) general service time distributions of the queueing server and (ii) sampling problems both with and without a sampling rate constraint. Numerical results are provided to compare different sampling policies.

In this paper, we investigate scheduling policies that minimize the age of information in single-hop queueing systems. We propose a Last-Generated, First-Serve (LGFS) scheduling policy, in which the packet with the earliest generation time is processed with the highest priority. If the service times are i.i.d. exponentially distributed, the preemptive LGFS policy is proven to be age-optimal in a stochastic ordering sense. If the service times are i.i.d. and satisfy a New-Better-than-Used (NBU) distributional property, the non-preemptive LGFS policy is shown to be within a constant gap from the optimum age performance. These age-optimality results are quite general: (i) they hold for arbitrary packet generation times and arrival times (including out-of-order packet arrivals); (ii) they hold for multi-server packet scheduling with the possibility of replicating a packet over multiple servers; (iii) and they hold for minimizing not only the time-average age and mean peak age, but also for minimizing the age stochastic process and any non-decreasing functional of the age stochastic process. If the packet generation time is equal to the packet arrival time, the LGFS policies reduce to the Last-Come, First-Serve (LCFS) policies. Hence, the age optimality results of LCFS-type policies are also established.

Information updates in multihop networks such as Internet of Things (IoT) and intelligent transportation systems have received significant recent attention. In this paper, we minimize the age of a single information flow in interference-free multihop networks. When preemption is allowed and the packet transmission times are exponentially distributed, we prove that a preemptive last-generated, first-served (LGFS) policy results in smaller age processes across all nodes in the network than any other causal policy (in a stochastic ordering sense). In addition, for the class of new-better-than-used (NBU) distributions, we show that the non-preemptive LGFS policy is within a constant age gap from the optimum average age. In contrast, our numerical result shows that the preemptive LGFS policy can be very far from the optimum for some NBU transmission time distributions. Finally, when preemption is prohibited and the packet transmission times are arbitrarily distributed, the non-preemptive LGFS policy is shown to minimize the age processes across all nodes in the network among all work-conserving policies (again in a stochastic ordering sense). Interestingly, these results hold under quite general conditions, including (1) arbitrary packet generation and arrival times, and (2) for minimizing both the age processes in stochastic ordering and any non-decreasing functional of the age processes.

Maintaining reliable millimeter wave (mmWave) connections to many fast-moving mobiles is a key challenge in the theory and practice of 5G systems. In this paper, we develop a new algorithm that can jointly track the beam direction and channel coefficient of mm Wave propagation paths using phased antenna arrays. Despite the significant difficulty in this problem, our algorithm can simultaneously achieve fast tracking speed, high tracking accuracy, and low pilot overhead. In static scenarios, this algorithm can converge to the minimum Cramér-Rao lower bound of beam direction with high probability. Simulations reveal that this algorithm greatly outperforms several existing algorithms. Even at SNRs as low as 5dB, our algorithm is capable of tracking a mobile moving at an angular velocity of 5.45 degrees per second and achieving over 95% of channel capacity with a 32-antenna phased array, by inserting only 10 pilots per second.

A fundamental challenge in wireless multicast has been how to simultaneously achieve high-throughput and low-delay for reliably serving a large number of users. In this paper, we show how to harness substantial throughput and delay gains by exploiting multi-channel resources. We develop a new scheme called Multi-Channel Moving Window Codes (MC-MWC) for multi-channel multi-session wireless multicast. The salient features of MC-MWC are three-fold. (i) High throughput: we show that MC-MWC achieves order-optimal throughput in the many-user many-channel asymptotic regime. Moreover, the number of channels required by a conventional channel-allocation based scheme is shown to be doubly-exponentially larger than that required by MC-MWC. (ii) Low delay: using large deviations theory, we show that the delay of MC-MWC decreases linearly with the number of channels, while the delay reduction of conventional schemes is no more than a finite constant. (iii) Low feedback overhead: the feedback overhead of MC-MWC is a constant that is independent of both the number of receivers in each session and the number of sessions in the network. Finally, our trace-driven simulation and numerical results validate the analytical results and show that the implementation complexity of MC-MWC is low.

The robustness of system throughput with scheduling is a critical issue. In this paper, we analyze the sensitivity of multi-user scheduling performance to channel misreporting in systems with massive antennas. The main result is that for the round-robin scheduler combined with max-min power control, the channel magnitude misreporting is harmful to the scheduling performance and has a different impact from the purely physical layer analysis. Specifically, for the homogeneous users that have equal average signal-to-noise ratios (SNRs), underreporting is harmful, while overreporting is beneficial to others. In under-reporting, the asymptotic rate loss on others is derived, which is tight when the number of antennas is huge. One interesting observation in our research is that the rate loss “periodically” increases and decreases as the number of misreporters grows. For the heterogeneous users that have various SNRs, both underreporting and overreporting can degrade the scheduler performance. We observe that strong misreporting changes the user grouping decision and hence greatly decreases some users' rates regardless of others gaining rate improvements, while with carefully designed weak misreporting, the scheduling decision keeps fixed and the rate loss on others is shown to grow nearly linearly with the number of misreporters.

We study the problem of minimizing the time-average expected Age of Information for status updates sent by an energy-harvesting source with a finite-capacity battery. In prior literature, optimal policies were observed to have a threshold structure under Poisson energy arrivals, for the special case of a unit-capacity battery. In this paper, we generalize this result to any (integer) battery capacity, and explicitly characterize the threshold structure. We provide the expressions relating the threshold values on the age to the average age. One of these results, that we derive from these expressions, is the unexpected equivalence of the minimum average AoI and the optimal threshold for the highest energy state.

The problem of reducing the age-of-information has been extensively studied in single-hop networks. In this paper, we minimize the age-of-information in general multihop networks. If the packet transmission times over the network links are exponentially distributed, we prove that a preemptive Last Generated First Served (LGFS) policy results in smaller age processes at all nodes of the network (in a stochastic ordering sense) than any other causal policy. In addition, for arbitrary distributions of packet transmission times, the non-preemptive LGFS policy is shown to minimize the age processes at all nodes among all non-preemptive work-conserving policies (again in a stochastic ordering sense). It is surprising that such simple policies can achieve optimality of the joint distribution of the age processes at all nodes even under arbitrary network topologies, as well as arbitrary packet generation and arrival times. These optimality results not only hold for the age processes, but also for any non-decreasing functional of the age processes.

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

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

Coordinated Multipoint (CoMP) techniques have promised substantial throughput improvement by exploiting the cooperation across base stations in cellular networks. In addition to the high computation and implementation complexity, existing CoMP proposals also require different base stations to exchange co-channel condition information through backhaul links. Such cooperation incurs additional costs in pilots and backhaul bandwidth, which in turn reduces the resource allocated to data transmission. Therefore, the promised throughput gain is greatly degraded in practical applications. Aiming to overcome this limitation, we develop a novel coordinated power control scheme for uplink cellular networks, named Checks and Balances (C&B), which can realize the potential benefits of CoMP with minimum complexity and cost. C&B checks the signal strength of one user and its generated interference to neighboring base stations, and tries to balance the two. We evaluate the throughput performance of C&B on an LTE system-level simulation platform, which is carefully calibrated with Huawei. Our simulation results suggest that C&B achieves up to 52% increase in average throughput, and up to 156% increase in edge-user throughput, compared to existing power control schemes.

In this work we study how to manage the freshness of status updates sent from a source to a remote monitor via a network server. A proper metric of data freshness at the monitor is the age-of-information, which is defined as how old the freshest update is since the moment this update was generated at the source. A logical policy is the zero-wait policy, i.e., the source submits a fresh update once the server is free, which achieves the maximum throughput and the minimum average delay. Surprisingly, this zero-wait policy does not always minimize the average age. This motivates us to study how to optimally control the status updates to keep data fresh and to understand when the zero-wait policy is optimal. We introduce a penalty function to characterize the level of “dissatisfaction” on data staleness, and formulate the average age penalty minimization problem as a constrained semi-Markov decision process (SMDP) with an uncountable state space. Despite of the difficulty of this problem, we develop efficient algorithms to find the optimal status update policy. We show that, in many scenarios, the optimal policy is to wait for a certain amount of time before submitting a new update. In particular, the zero-wait policy can be far from the optimum if (i) the penalty function grows quickly with respect to the age, and (ii) the update service times are highly random and positive correlated. To the best of our knowledge, this is the first optimal control policy which is proven to minimize the age-of-information in status update systems.

In this work, we investigate the design of information-update systems, where incoming update packets are forwarded to a remote destination through multiple servers (each server can be viewed as a wireless channel). One important performance metric of these systems is the data freshness at the destination, also called the age-of-information or simply age, which is defined as the time elapsed since the freshest packet at the destination was generated. Recent studies on information-update systems have shown that the age-of-information can be reduced by intelligently dropping stale packets. However, packet dropping may not be appropriate in many applications, such as news and social updates, where users are interested in not just the latest updates, but also past news. Therefore, all packets may need to be successfully delivered. In this paper, we study how to optimize age-of-information without throughput loss. We consider a general scenario where incoming update packets do not necessarily arrive in the order of their generation times. We prove that a preemptive Last Generated First Served (LGFS) policy simultaneous optimizes the age, throughput, and delay performance in infinite buffer queueing systems. We also show age-optimality for the LGFS policy for any finite queue size. These results hold for arbitrary, including non-stationary, arrival processes.

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

A major challenge of wireless multicast is being able to support a large number of users while simultaneously maintaining low delay and low feedback overhead. In this paper, we develop a joint coding and feedback scheme named moving window network coding with anonymous feedback (MWNC-AF) that simultaneously achieves constant decoding delay and constant feedback overhead, irrespective of the number of receivers n, without sacrificing either throughput or reliability. We explicitly characterize the asymptotic decay rate of the tail probability of the decoding delay and prove that injecting a fixed amount of information bits into the MWNC-AF encoder buffer in each time slot (called “constant data injection process”) achieves the fastest decay rate, thus showing how to obtain delay optimality in a large deviation sense. We then investigate the average decoding delay of MWNC-AF and show that, when the traffic load approaches capacity, the average decoding delay under the constant injection process is at most one half of that under a Bernoulli injection process. We prove that the per-packet encoding and decoding complexities of MWNC-AF both scale as O(logn) and are thus insensitive to the increase of the number of receivers n. Our simulations further underscore the performance of our scheme through comparisons with existing schemes and show that the delay, encoding, and decoding complexities are low even for a large number of receivers, demonstrating the efficiency, scalability, and ease of implementability of MWNC-AF.

Storage clouds, such as Amazon S3, are being widely used for web services and Internet applications. It has been observed that the delay for retrieving data from and placing data into the clouds is quite random, and exhibits weak correlations between different read/write requests. This inspires us to investigate a key problem: can we reduce the delay by transmitting data replications in parallel or using powerful erasure codes? In this paper, we study the problem of reducing the delay of downloading data from cloud storage systems by leveraging multiple parallel threads, assuming that the data has been encoded and stored in the clouds using fixed rate forward error correction (FEC) codes with parameters (n, k). That is., each file is divided into k equal-sized chunks, which are then expanded into n chunks such that any k chunks out of the n are sufficient to successfully restore the original file. The model can be depicted as a multiple-server queue with arrivals of data retrieving requests and a server corresponding to a thread. However, this is not a typical queueing model because a server can terminate its operation, depending on when other servers complete their service (due to the redundancy that is spread across the threads). Hence, to the best of our knowledge, the analysis of this queueing model remains quite uncharted. Real traces from Amazon S3 show that the time to retrieve a fixed size chunk is random and can be accurately approximated as an i.i.d. exponentially distributed random variable. We show that any work-conserving scheme is delay-optimal when k = 1. When k > 1, we find that a simple greedy scheme, which allocates all available threads to the head of line request, is delay optimal, which appears surprising.

Many opportunistic scheduling techniques are impractical because they require accurate channel state information (CSI) at the transmitter. In this paper, we investigate the scheduling of unicast and multicast services in a downlink network with a very limited amount of feedback information. Specifically, unicast users send imperfect (or no) CSI and infrequent acknowledgements (ACKs) to a base station, and multicast users only report infrequent ACKs to avoid feedback implosion. We consider the use of physical-layer rateless codes, which not only combats channel uncertainty, but also reduces the overhead of ACK feedback. A joint scheduling and power allocation scheme is developed to realize multiuser diversity gain for unicast service and multicast gain for multicast service. We prove that our scheme achieves a near-optimal throughput region. Our simulation results show that our scheme significantly improves the network throughput over schemes employing fixed-rate codes or using only unicast communications.

Wireless network scheduling and control techniques (e.g., opportunistic scheduling) rely heavily on access to Channel State Information (CSI). However, obtaining this information is costly in terms of bandwidth, time, and power, and could result in large overhead. Therefore, a critical question is how to optimally manage network resources in the absence of such information. To that end, we develop a cross-layer solution for downlink cellular systems with imperfect (and possibly no) CSI at the transmitter. We use rateless codes to resolve channel uncertainty. To keep the decoding complexity low, we explicitly incorporate time-average block-size constraints, and aim to maximize the system utility. The block-size of a rateless code is determined by both the network control decisions and the unknown CSI of many time slots. Therefore, unlike standard utility maximization problems, this problem can be viewed as a constrained partial observed Markov decision problem (CPOMDP), which is known to be hard due to the “curse of dimensionality.” However, by using a modified Lyapunov drift method, we develop a dynamic network control scheme, which yields a total network utility within O(1/Lav) of utility-optimal point achieved by infinite block-size channel codes, where Lavis the enforced value of the time-average block-size of rateless codes. This opens the door of being able to trade complexity/delay for performance gains in the absence of accurate CSI. Our simulation results show that the proposed scheme improves the network throughput by up to 68% over schemes that use fixed-rate codes.

This paper considers reliable communications over a multiple-input multiple-output (MIMO) Gaussian channel, where the channel matrix is within a bounded channel uncertainty region around a nominal channel matrix, i.e., an instance of the compound MIMO Gaussian channel. We study the optimal transmit covariance design to achieve the capacity of compound MIMO Gaussian channels, where the channel uncertainty region is characterized by the spectral norm. This design problem is a challenging non-convex optimization problem. However, in this paper, we reveal that this design problem has a hidden convexity property, and hence it can be simplified as a convex optimization problem. Towards this goal, we first prove that the optimal transmit design is to diagonalize the nominal channel, and then show that the duality gap between the capacity of the compound MIMO Gaussian channel and the minimal channel capacity is zero, which proves the conjecture of Loyka and Charalambous (IEEE Trans. Inf. Theory, vol. 58, no. 4, pp. 2048-2063, 2012). The key tools for showing these results are a novel matrix determinant inequality and some unitarily invariant properties.

This paper considers reliable communications over a multiple-input multiple-output (MIMO) Gaussian channel, where the channel matrix is within a bounded channel uncertainty region around a nominal channel matrix, i.e., an instance of the compound MIMO Gaussian channel. We study the optimal transmit covariance matrix design to achieve the capacity of compound MIMO Gaussian channels, where the channel uncertainty region is characterized by the spectral norm. This design problem is a challenging nonconvex optimization problem. However, in this paper, we reveal that this problem has a hidden convexity property, which can be exploited to map the problem into a convex optimization problem. We first prove that the optimal transmit design is to diagonalize the nominal channel, and then show that the duality gap between the capacity of the compound MIMO Gaussian channel and the min-max channel capacity is zero, which proves and generalizes a conjecture of Loyka and Charalambous. The key tools for showing these results are a new matrix determinant inequality and some unitarily invariant properties.

Most of the existing works on two-way frequency division multiplexing (OFDM) relay channels was centered on per-subcarrier decode-and-forward (DF) relaying, where each subcarrier is treated as a separate channel, and channel coding is performed separately over each subcarrier. In this paper, we show that this per-subcarrier DF relay strategy is suboptimal. More specifically, we present a multi-subcarrier DF relay strategy which achieves a larger rate region by adopting cross-subcarrier channel coding. Then we develop an optimal resource allocation algorithm to characterize the achievable rate region of the proposed multi-subcarrier DF relay strategy. Compared to standard Lagrangian duality optimization algorithms, our algorithm has a much smaller computational complexity due to the use of the structure property of the optimal resource allocation solution. We further prove that our multi-subcarrier DF relay strategy tends to achieve the capacity region of the two-way OFDM relay channels in the low signal-to-noise ratio (SNR) regime, and the amplify-and-forward (AF) relay strategy tends to achieve the multiplexing gain region of the two-way OFDM relay channels in the high SNR regime. Our theoretical analysis and numerical results demonstrate that DF relaying has better performance in the low to moderate SNR regime, while AF relaying is more appropriate in the high SNR regime.

Optimal power allocation for orthogonal frequency division multiplexing (OFDM) wiretap channels with Gaussian channel inputs has already been studied in some previous works from an information theoretical viewpoint. However, these results are not sufficient for practical system designs. One reason is that discrete channel inputs, such as quadrature amplitude modulation (QAM) signals, instead of Gaussian channel inputs, are deployed in current practical wireless systems to maintain moderate peak transmission power and receiver complexity. In this paper, we investigate the power allocation and artificial noise design for OFDM wiretap channels with discrete channel inputs. We first prove that the secrecy rate function for discrete channel inputs is nonconcave with respect to the transmission power. To resolve the corresponding nonconvex secrecy rate maximization problem, we develop a low-complexity power allocation algorithm, which yields a duality gap diminishing in the order of O(1/√N), where N is the number of subcarriers of OFDM. We then show that independent frequency-domain artificial noise cannot improve the secrecy rate of single-antenna wiretap channels. Towards this end, we propose a novel time-domain artificial noise design which exploits temporal degrees of freedom provided by the cyclic prefix of OFDM systems to jam the eavesdropper and boost the secrecy rate even with a single antenna at the transmitter. Numerical results are provided to illustrate the performance of the proposed design schemes.

This paper investigates the distributed power allocation problem for coordinated multipoint (CoMP) transmissions in distributed antenna systems (DAS). Traditional duality-based optimization techniques cannot be directly applied to this problem, because the non-strict concavity of the CoMP transmission's achievable rate with respect to the transmission power induces that the local power allocation subproblems have non-unique optimum solutions. We propose a distributed power allocation algorithm to resolve this non-strict concavity difficulty. This algorithm only requires local information exchange among neighboring base stations serving the same user, and is thus flexible with respect to network size and topology. The step-size parameters of this algorithm are determined by only local user access relationship (i.e., the number of users served by each antenna), but do not rely on channel coefficients. Therefore, the convergence speed of this algorithm is quite robust to channel fading. We rigorously prove that this algorithm converges to an optimum solution of the power allocation problem. Simulation results are presented to demonstrate the effectiveness of the proposed power allocation algorithm.

This paper presents a novel two-way decode-and-forward (DF) relay strategy for Orthogonal Frequency Division Multiplexing (OFDM) relay networks. This DF relay strategy employs multi-subcarrier joint channel coding to leverage frequency selective fading, and thus can achieve a higher data rate than the conventional per-subcarrier DF relay strategies. We further propose a low-complexity, optimal power allocation strategy to maximize the data rate of the proposed relay strategy. Simulation results suggest that our strategy obtains a substantial gain over the per-subcarrier DF relay strategies, and also outperforms the amplify-and-forward (AF) relay strategy in a wide signal-to-noise-ratio (SNR) region.

This paper studies a spectrum sharing scenario between a cooperative relay network (CRN) and a nearby ad-hoc network. In particular, we consider a dynamic spectrum access and resource allocation problem of the CRN. Based on sensing and predicting the ad-hoc transmission behaviors, the ergodic traffic collision time between the CRN and ad-hoc network is minimized subject to an ergodic uplink throughput requirement for the CRN. We focus on real-time implementation of spectrum sharing policy under practical computation and signaling limitations. In our spectrum sharing policy, most computation tasks are accomplished off-line. Hence, little real-time calculation is required which fits the requirement of practical applications. Moreover, the signaling procedure and computation process are designed carefully to reduce the time delay between spectrum sensing and data transmission, which is crucial for enhancing the accuracy of traffic prediction and improving the performance of interference mitigation. The benefits of spectrum sensing and cooperative relay techniques are demonstrated by our numerical experiments.

In this paper, we study a cognitive coexistence strategy for heterogeneous networks. While a lot of previous works focused on spectrum underlay approaches for weak interference scenarios, a high power infrastructure (IS) transmitter creates a large dead zone for nearby ad-hoc (AH) links using the same spectrum. To address this problem, we propose to utilize a half-duplex decode-and-forward (DF) relay node to assist the IS transmitter. The transmission time and power of relay-assisted IS network is optimized to reduce its generated interference while still guaranteeing its quality-of-service (QoS) level. The resource allocation problem of relay-assisted IS network is formulated as a convex optimization problem, for which a tailored dual optimization method is proposed. Our numerical results show that our relay-assisted scheme can produce less interference and/or achieve a higher QoS level.

In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and NuttallQ-functions. More precisely, a simple probabilistic method is first given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized MarcumQ-function and its deformations is established with respect to each of the three parameters. Since the NuttallQ-function has similar probabilistic interpretations as the generalized MarcumQ-function, we deduce the log-concavity of the NuttallQ-function. By exploiting the log-concavity of these two functions, we propose new tight lower and upper bounds for the generalized Marcum and NuttallQ-functions. Our proposed bounds are much tighter than the existing bounds in the literature in most of the cases. The relative errors of our proposed bounds converge to0asb\ura ¿. The numerical results show that the absolute relative errors of the proposed bounds are less than 5% in most of the cases. The proposed bounds can be effectively applied to the outage probability analysis of interference-limited systems such as cognitive radio and wireless sensor network, in the study of error performance of various wireless communication systems operating over fading channels and extracting the log-likelihood ratio for differential phase-shift keying (DPSK) signals.

In this paper, we study the joint power and channel resource allocation problem for a multiuser F/TDMA decode-and-forward (DF) relay network under per-node power constraints and a total channel resource constraint. Our goal is to maximize the total throughput achieved by the systems. To that end, we formulate a joint power and channel resource allocation problem. We develop an iterative optimization algorithm to solve this problem, whose convergence and optimality are guaranteed. Due to the per-node power constraints, more than one relay node may be needed for a single data stream. Our solution also provides a way of finding the optimal relays among the assisting relay nodes.

In this paper, we study the generalized MarcumQ-functionQnu(a,b), wherea, nu > 0 andbges 0. Our aim is to extend the results of Corazza and Ferrari (IEEETrans.Inf.Theory, vol. 48, pp. 3003-3008, 2002) to the generalized MarcumQ-function in order to deduce some new tight lower and upper bounds. The key tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind and some classical inequalities, i.e., the Cauchy-Buniakowski-Schwarz and Chebyshev integral inequalities. These bounds are shown to be very tight for largeb, i.e., the relative errors of our bounds converge to zero asbincreases. Both theoretical analysis and numerical results are provided to show the tightness of our bounds.

In this paper, we manage to prove the log-concavity of the generalized Marcum Q-function Qnu(a, b) with respect to its order nu on (1, infin). The proof relies on a powerful mathematical concept named total positivity. Based on the recursion relation of the generalized Marcum Q-function, a new intuitive formula for Qnu(a,b) is proposed, where nu is an odd multiple of 0.5. After these results, we derive upper and lower bounds for the generalized Marcum Q-function of positive integer order m. Numerical results show that in most of the cases our proposed bounds are much tighter than the existing bounds in the literature. It is surprising to see that the relative errors of the proposed bounds converge to 0 when b approaches infinite.