Measuring Discrete Sensing Capability for ISAC via Task Mutual Information

TL;DR

The paper addresses the lack of a priori performance metrics for ubiquitous RF sensing in ISAC by introducing a discrete sensing model with $m$ target states and $n$ independent features, and defines discrete task mutual information (DTMI) $I(X^n;Y^n)$ to quantify sensing capability. It derives a lower bound $P_E^n \ge \frac{H(W)-I(X^n;Y^n)-H(P_E^n)}{\log m}$ and an upper bound $P_E^n \le \varepsilon + \sum_{k} p(w_k) \sum_{j\neq k} 2^{3n\varepsilon-\sum I(X_i(w_j);Y_i(w_k))}$, tied to a decoding rule based on a jointly matching set, and provides a sufficient condition for lossless sensing. Corollaries explain why multimodal sensing improves performance, how to compare sensing features via DTMI, and why preprocessing alone cannot guarantee perfect sensing under certain information-theoretic constraints. The authors validate the framework on binary and multi-class tasks (e.g., WiFi/RFID sensing, direction estimation, device identification), showing DTMI tracks accuracy with high correlation (up to PCC ~ 0.9) and enabling DTMI-based bounds to guide ISAC design; the work is complemented by open-source code to reproduce the results.

Abstract

6G technology offers a broader range of possibilities for communication systems to perform ubiquitous sensing tasks, including health monitoring, object recognition, and autonomous driving. Since even minor environmental changes can significantly degrade system performance, and conducting long-term posterior experimental evaluations in all scenarios is often infeasible, it is crucial to perform a priori performance assessments to design robust and reliable systems. In this paper, we consider a discrete ubiquitous sensing system where the sensing target has \(m\) different states \(W\), which can be characterized by \(n\)-dimensional independent features \(X^n\). This model not only provides the possibility of optimizing the sensing systems at a finer granularity and balancing communication and sensing resources, but also provides theoretical explanations for classical intuitive feelings (like more modalities and more accuracy) in wireless sensing. Furthermore, we validate the effectiveness of the proposed channel model through real-case studies, including person identification, displacement detection, direction estimation, and device recognition. The evaluation results indicate a Pearson correlation coefficient exceeding 0.9 between our task mutual information and conventional experimental metrics (e.g., accuracy). The open source address of the code is: https://github.com/zaoanhh/DTMI

Figures (11)

• Figure 1: Sensing channel encoder.
• Figure 2: For independent sequences $X^n$ and $Y^n$, the number of elements in their jointly matching set is approximately $2^{\sum_{i=1}^n H(X_i,Y_i)}$. We decode the channel embedding as $\hat{w}_k$ when $Y^n$ forms a joint matching sequence with only one feature $X^n(w_k)$.
• Figure 3: The sensing channel of multi-modal sensing system.
• Figure 4: The sensing system with data pre-processing.
• Figure 5: Human detection in home environments based on WiFi. (a) Experimental environment and device deployment. (b) Human detection algorithm based on thresholding method. (c) Channel embedding extraction.

Theorems & Definitions (22)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Theorem 1
• proof
• Lemma 1
• proof