Inference-Aware State Reconstruction for Industrial Metaverse under Synchronous/Asynchronous Short-Packet Transmission

TL;DR

The spatial-temporal correlation of the sensor data of interest is used to infer the real-time data of the target sensor to reduce the mean squared error (MSE) of reconstruction for industrial metaverse under short-packet transmission (SPT).

Abstract

We consider a real-time state reconstruction system for industrial metaverse. The time-varying physical process states in real space are captured by multiple sensors via wireless links, and then reconstructed in virtual space. In this paper, we use the spatial-temporal correlation of the sensor data of interest to infer the real-time data of the target sensor to reduce the mean squared error (MSE) of reconstruction for industrial metaverse under short-packet transmission (SPT). Both synchronous and asynchronous transmission modes for multiple sensors are considered. It is proved that the average MSE of reconstruction and average block error probability (BLEP) have a positive correlation under inference with synchronous transmission scheme, and they have a negative correlation in some conditions under inference with asynchronous transmission scheme. Also, it is proved that the average MSE of reconstruction with inference can be significantly lower than that without inference, even under weak mean squared spatial correlation (MSSC). In addition, closed-form MSSC thresholds are derived for the superiority regions of the inference with synchronous transmission and inference with asynchronous transmission schemes, respectively. Adaptations of blocklength and time shift of asynchronous transmission are conducted to minimize the average MSE of reconstruction. Simulation results show that the two schemes significantly outperform the no inference case, with an average MSE reduction of more than 50%.

Figures (12)

• Figure 1: The inference-aware real-time state reconstruction system model in the industrial metaverse.
• Figure 2: Sampling and reconstruction with and without inference under synchronous transmission mode. The noisy sample $Y_{m,{\text{t}_{\text{2}}}}$ of sensor ${\text{S}}_m$ is lost in the second transmission period. With inference, the cloud server uses the fresh noisy sample $Y_{\text{1},{\text{t}_{\text{2}}}}$ from sensor ${\text{S}}_{\text{1}}$ to reconstruct the real-time data of sensor ${\text{S}}_m$, which leads to a lower MSE of reconstruction than the case of no inference.
• Figure 3: Sampling and reconstruction with and without inference under asynchronous transmission mode. With inference, the cloud server at the reception time of every sensor uses the latest successfully received noisy sample to reconstruct the real-time data of sensor $\text{S}_m$, which leads to a lower MSE of reconstruction than the case of no inference.
• Figure 4: Joint impact of average BLEP and MSSC on average MSE of reconstruction by inference with synchronous transmission scheme at transmission period $T=150$ ms.
• Figure 5: Joint impact of average BLEP and MSSC on average MSE of reconstruction by inference with asynchronous transmission scheme at transmission period $T=150$ ms and time shift (a)-(b) $h=$ 5 ms and (c)-(d) $h=\frac{T}{M}=$ 30 ms.