Optimal Sampling for Data Freshness: Unreliable Transmissions With Random Two-Way Delay
Optimal Sampling for Data Freshness: Unreliable Transmissions With Random Two-Way Delay
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DOI：
10.1109/tnet.2022.3194417
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
Jiayu Pan;A. Bedewy;Yin Sun;N. Shroff
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文献类型：
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作者：
Jiayu Pan;A. Bedewy;Yin Sun;N. Shroff
在本文中，我们的目标是为系统设计一个最佳采样器，其中信号（源）的新鲜样本通过不可靠的通道发送到远程估计器，并通过反馈通道发回确认。由于时变信道条件，前向和反馈信道都可能具有随机传输时间。在分布式传感的推动下，估计器可以通过组合通过通道接收的信号样本和从本地传感器收集的噪声信号观测值来估计源信号的实时值。我们证明估计误差是接收信号样本的信息年龄（AoI）的非递减函数，并设计了一种最佳采样策略，可以在采样率约束下最小化长期平均估计误差。该采样策略对于最小化 AoI 的一般非递减函数的长期平均值也是最佳的。最佳采样器设计遵循随机阈值策略：如果上次传输成功，源将等待，直到传输时的预期估计误差超过阈值，然后发出新样本。如果最后一次传输失败，源立即发送新的样本，无需等待。阈值是定点方程的根，可以以低复杂度求解（例如，通过二分搜索）。最优采样策略适用于前向和反馈信道的一般传输时间分布。提供数值模拟来比较不同的采样策略。
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.