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 $Ω(\ln k)$. 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 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 maximu…
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…
We consider the following communication scenario. An encoder causally observes the Wiener process and decides when and what to transmit about it. A decoder makes real-time estimation of the process using causally received codewords. We determine the causal encoding and decoding policies that jointly minimize the mean-square estimation error, under the long-term communication rate constraint of $R$ bits per second. We show that an optimal encoding policy can be implemented as a causal sampling policy followed by a causal compressing policy. We prove that the optimal encoding policy samples the …
In this study, we generalize a problem of sampling a scalar Gauss Markov Process, namely, the Ornstein-Uhlenbeck (OU) process, where the samples are sent to a remote estimator and the estimator makes a causal estimate of the observed realtime signal. In recent years, the problem is solved for stable OU processes. We present solutions for the optimal sampling policy that exhibits a smaller estimation error for both stable and unstable cases of the OU process along with a special case when the OU process turns to a Wiener process. The obtained optimal sampling policy is a threshold policy. Howev…
The age of information, as a metric for evaluating information freshness, has received a lot of attention. Recently, an interesting 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 extend a previous study by investigating a problem of sampling a stationary Gauss…
In this paper, we study the stochastic optimization of cloud radio access networks (C-RANs) by joint remote radio head (RRH) activation and beamforming in the downlink. Unlike most previous works that only consider a static optimization framework with full traffic buffers, we formulate a dynamic optimization problem by explicitly considering the effects of random traffic arrivals and time-varying channel fading. The stochastic formulation can quantify the tradeoff between power consumption and queuing delay. Leveraging on the Lyapunov optimization technique, the stochastic optimization problem…
We consider a mobile cloud computing system with multiple users, a remote cloud server, and a computing access point (CAP). The CAP serves both as the network access gateway and a computation service provider to the mobile users. It can either process the received tasks from mobile users or offload them to the cloud. We jointly optimize the offloading decisions of all users, together with the allocation of computation and communication resources, to minimize the overall cost of energy consumption, computation, and maximum delay among users. The joint optimization problem is formulated as a mix…
The problem of joint source-channel coding is considered for a stationary remote (noisy) Gaussian source and a Gaussian channel. The encoder and decoder are assumed to be causal and their combined operations are subject to a delay constraint. It is shown that, under the mean-square error distortion metric, an optimal encoder-decoder pair from the linear and time-invariant (LTI) class can be found by minimization of a convex functional and a spectral factorization. The functional to be minimized is the sum of the well-known cost in a corresponding Wiener filter problem and a new term, which is …
From Freshness to Effectiveness: Goal-Oriented Sampling for Remote Decision Making
Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；Guangdong Provincial Key Laboratory of Aerospace Communication and Networking Technology（广东省航空航天通信与网络技术重点实验室）；Institute for Infocomm Research, Agency for Science, Technology and Research（新加坡科技研究局信息通信研究所）；Peng Cheng Laboratory（鹏城实验室）
This paper investigates the problem of minimizing the Age of Incorrect Information (AoII) when the communication channel has a random delay. We consider a slotted-time system where a transmitter observes a dynamic source and decides when to send updates to a remote receiver through a channel with random delay. The receiver maintains estimates of the state of the dynamic source based on the received updates. In this paper, we adopt AoII as the performance metric and investigate the problem of optimizing the transmitter's action in each time slot to minimize AoII. We first characterize the consi…
We investigate remote estimation over a Gilbert-Elliot channel with feedback. We assume that the channel state is observed by the receiver and fed back to the transmitter with one unit delay. In addition, the transmitter gets ACK/NACK feedback for successful/unsuccessful transmission. Using ideas from team theory, we establish the structure of optimal transmission and estimation strategies and identify a dynamic program to determine optimal strategies with that structure. We then consider first-order autoregressive sources where the noise process has unimodal and symmetric distribution. Using …
We study the problem of optimizing the decisions of a preemptively capable transmitter to minimize the Age of Incorrect Information (AoII) when the communication channel has a random delay. We consider a slotted-time system where a transmitter observes a Markovian source and makes decisions based on the system status. In each time slot, the transmitter decides whether to preempt or skip when the channel is busy. When the channel is idle, the transmitter decides whether to send a new update. A remote receiver estimates the state of the Markovian source based on the update it receives. We consid…
In cyber-physical systems, as in 5G and beyond, multiple physical processes require timely online monitoring at a remote device. There, the received information is used to estimate current and future process values. When transmitting the process data over a communication channel, source-channel coding is used in order to reduce data errors. During transmission, a high data resolution is helpful to capture the value of the process variables precisely. However, this typically comes with long transmission delays reducing the utilizability of the data, since the estimation quality gets reduced ove…
This paper analyzes wireless network control for remote estimation of linear time-invariant dynamical systems under various Hybrid Automatic Repeat Request (HARQ) packet retransmission schemes. In conventional HARQ, packet reliability increases gradually with additional packets; however, each retransmission maximally increases the Age of Information and causes severe degradation in estimation mean squared error (MSE) performance. We optimize standard HARQ schemes by allowing partial retransmissions to increase the packet reliability gradually and limit the AoI growth. In incremental redundancy…
