Time, Simultaneity, and Causality in Wireless Networks with Sensing and Communications

TL;DR

A model that incorporates Temporal Window of Integration (TWI) to emulate human multisensory perception is introduced and the implications for setting timing constraints in real-time applications and enabling temporal forensics are discussed.

Abstract

Wireless systems beyond 5G evolve towards embracing both sensing and communication, resulting in increased convergence of the digital and the physical world. The existence of fused digital-physical realms raises critical questions regarding temporal ordering, causality, and the synchronization of events. This paper addresses the temporal challenges arising from the fact that the wireless infrastructure becomes an entity with multisensory perception. With the growing reliance on real-time interactions and applications such as digital twins, extended reality, and the metaverse, the need for accurate timestamping and temporal forensics becomes crucial. The paper introduces a model that incorporates Temporal Windows of Integration (TWI) to emulate human multisensory perception and discusses the implications for setting timing constraints in real-time applications and enabling temporal forensics. The analysis explores trade-offs, probabilities, and bounds for simultaneity and causality violation in the context of wireless systems evolving towards perceptive networks. This work underscores the significance of timestamping in the evolving wireless landscape, provide insights into system-level implications, and points out new research avenues for systems that combine sensing and communications.

Figures (10)

• Figure 1: An example of chronological discrepancy. Acoustic event ${\cal{E}}_1$ causes the event ${\cal{E}}_2$ at a later time. $B$ receives ${\cal{E}}_1$ as ${\cal{D}}_{B,1}$, communicated by an acoustic sensor (microphone) $S$, and later on receives ${\cal{E}_2}$ as ${\cal{S}}_{B,2}$ by using its radar sensing. $R$ receives at first ${\cal{E}}_2$ as ${\cal{D}}_{R,2}$, an image sent by $Z$, and after that receives ${\cal{E}}_1$ as ${\cal{S}}_{R,1}$ via its own acoustic sensor.
• Figure 2: Illustration of light cones and the impact of information processing. The event ${\cal E}_i$ for $i=A, B, C$ occurs at the location $x_i$. ${\cal E}_A$ is received as ${\cal E}^{\prime}_{A}$ via digital link, while ${\cal E}_C$ is detected as ${\cal E}^{\prime}_{C}$ as a sensing event. The Base Station (BS) is placed at $x_B$. (a) Reception with instantaneous processing. The chronology observed by the BS is ${\cal E}^{\prime}_A \rightarrow {\cal E}^{\prime}_C \rightarrow {\cal E}_B$. (b) Reception of ${\cal E}_A$ with data size $D_A$ at a rate $R_A$ and detection of ${\cal E}_C$ with a sensor detection time $T_s$. The chronology observed by the BS is ${\cal E}^{\prime}_C \rightarrow {\cal E}_B \rightarrow {\cal E}^{\prime}_A$.
• Figure 3: Illustration of temporal ordering in various processes. (a) Synchronous sensor. (b) Asynchronous sensor. (c) Communication between digital processes. (d) Integrated process of sensing and communication. (e) Temporal window of integration (TWI) applied to the integrated process from (d).
• Figure 4: A physical event that is detected by two asynchronous sensors. (a) Use of asynchronous temporal window of integration that starts with the start of the detection of the first sensor. (b) Synchronous windows of integration with $W<t_{S_2}-t_{S_1}$. (c) Synchronous windows of integration with $W \geq t_{S_2}-t_{S_1}$.
• Figure 5: Physical event triggers a digital transmission. Example of causality violation at device $B$ when the event ${\cal D}$ of decoding the data from $A$ precedes the sensing event ${\cal S}$ and the events are timestamped such that $s(t_{D})=s(t_S)-1$.

Theorems & Definitions (7)

• Definition 2.1
• Lemma 1
• Theorem 1
• Theorem 2
• proof
• proof
• proof