In this paper, we consider a status update system, where an access point collects measurements from multiple sensors that monitor a common physical process, fuses them, and transmits the aggregated sample to the destination over an erasure channel. Under a typical information fusion scheme, the distortion of the fused sample is inversely proportional to the number of measurements received. Our goal is to minimize the long-term average age while satisfying the average energy and general age-based distortion requirements. Specifically, we focus on the setting in which the distortion requirement is stricter when the age of the update is older. We show that the optimal policy is a mixture of two stationary, deterministic, threshold-based policies, each of which is optimal for a parameterized problem that aims to minimize the weighted sum of the age and energy under the distortion constraint. We then derive analytically the associated optimal average age-cost function and characterize its performance in the large threshold regime, the results of which shed critical insights on the tradeoff among age, energy, and the distortion of the samples. We have also developed a closed-form solution for the special case when the distortion requirement is independent of the age, arguably the most important setting for practical applications.

In this paper, we consider transmission scheduling in a status update system, where updates are generated periodically and transmitted over a Gilbert-Elliott fading channel. The goal is to minimize the long-run average age of information (AoI) under a long-run average energy constraint. We consider two practical cases to obtain channel state information (CSI): (i) without channel sensing and (ii) with delayed channel sensing. For (i), CSI is revealed by the feedback (ACK/NACK) of a transmission, but when no transmission occurs, CSI is not revealed. Thus, we have to balance tradeoffs across energy, AoI, channel exploration, and channel exploitation. The problem is formulated as a constrained partially observable Markov decision process (POMDP). We show that the optimal policy is a randomized mixture of no more than two stationary deterministic policies each of which is of a threshold-type in the belief on the channel. For (ii), (delayed) CSI is available via channel sensing. Then, the tradeoff is only between the AoI and energy. The problem is formulated as a constrained MDP. The optimal policy is shown to have a similar structure as in (i) but with an AoI associated threshold. With these, we develop an optimal structure-aware algorithm for each case.

Millimeter wave (mmWave) communication has the potential to achieve very high data rates but is highly vulnerable to blockage. In this paper, we provision an integrated mmWavesub-6 GHz architecture to combat blockage and intermittent connectivity of the mmWave communications. To this end, we model the mmWave channel as a two-state Markov channel and investigate the problem of scheduling packets across the mmWave and sub-6 GHz interfaces such that the long-term average delay of system is minimized. We prove that the optimal policy is of a threshold-type with state-dependent thresholds, i.e., packets should always be routed to the mmWave interface as long as the number of packets in the system is smaller than the state-dependent threshold. Numerical results demonstrate that under heavy traffic, integrating sub-6 GHz with mmWave can reduce the average delay by over 70%. Moreover, considering the difficulty of tracking the mmWave channel state in practice, we develop heuristics of substituting a single fixed threshold (state-independent) for two state-dependent thresholds. Our simulation results indicate that the replacement only incurs a slight increase in average delay. Moreover, when system parameters are not known, we propose a certainty-equivalence threshold-based learning algorithm, and provide an upper bound on its regret.

In this paper, we consider transmission scheduling in a status update system, where updates are generated periodically and transmitted over a Gilbert-Elliott fading channel. The goal is to minimize the long-run average age of information (AoI) at the destination under an average energy constraint. The channel state is revealed by the feedback (Ack/Nack) of a transmission; while it remains unknown if there is no transmission. Thus, we have to design a scheduling policy that balances tradeoffs across energy, AoI, channel exploration, and channel exploitation. The problem is formulated as a constrained partially observable Markov decision process problem (POMDP). We show that the optimal policy is a randomized mixture of no more than two stationary deterministic policies each of which is of a threshold-type in the belief on the channel. We propose a finite-state approximation for our infinite-state belief MDP and show convergence. Based on the theoretical insights gained from studying this problem, we develop an optimal algorithm using the structure of the problem.

In this paper, we consider a status update system, in which update packets are sent to the destination via a wireless medium that allows for multiple rates, where a higher rate also naturally corresponds to a higher error probability. The data freshness is measured using age of information, which is defined as the age of the recent update at the destination. A packet that is transmitted with a higher rate, will encounter a shorter delay and a higher error probability. Thus, the choice of the transmission rate affects the age at the destination. In this paper, we design a low-complexity scheduler that selects between two different transmission rate and error probability pairs to be used at each transmission epoch. This problem can be cast as a Markov Decision Process. We show that there exists a threshold-type policy that is age-optimal. More importantly, we show that the objective function is quasi-convex or non-decreasing in the threshold, based on the system parameters values. This enables us to devise a low-complexity algorithm to minimize the age. These results reveal an interesting phenomenon: While choosing the rate with minimum mean delay is delay-optimal, this does not necessarily minimize the age.

Millimeter wave (mmWave) technologies have the potential to achieve very high data rates, but suffer from intermittent connectivity. In this paper, we provision an architecture to integrate sub-6 GHz and mmWave technologies, where we incorporate the sub-6 GHz interface as a fallback data transfer mechanism to combat blockage and intermittent connectivity of the mmWave communications. To this end, we investigate the problem of scheduling data packets across the mmWave and sub-6 GHz interfaces such that the average delay of system is minimized. This problem can be formulated as Markov Decision Process. We first investigate the problem of discounted delay minimization, and prove that the optimal policy is of the threshold-type, i.e., data packets should always be routed to the mmWave interface as long as the number of packets in the system is smaller than a threshold. Then, we show that the results of the discounted delay problem hold for the average delay problem as well. Through numerical results, we demonstrate that under heavy traffic, integrating sub-6 GHz with mmWave can reduce the average delay by up to 70%. Further, our scheduling policy substantially reduces the delay over the celebrated MaxWeight policy.

In the underwater environment exist marine mammals and underwater wireless sensor networks (UWSNs), both of which use acoustic signals for communication. However, most of existing researches only focus on the performance, such as energy efficiency, packet error rates and propagation delay, of acoustic communication in UWSNs, which seems not friendly to marine mammals. With the purpose of sharing the scarce acoustic spectrum with marine mammals in a friendly way, an environment-friendly spectrum decision strategy is proposed in this paper. The strategy features a localization scheme for marine mammals and an environment-friendly channel allocation scheme. Based on the estimated locations of marine mammals, the transmission power and available channels are jointly allocated to the contending users. In this way, the proposed strategy can maximize the network capacity while avoiding interference with marine mammals. Simulation results show that the localization scheme has a success rate of localization around 90% and a relatively small average localization error at about 10m; the environment-friendly channel allocation scheme can work effectively as the locations of marine mammals change.