On the View-and-Channel Aggregation Gain in Integrated Sensing and Edge AI

TL;DR

This work develops a theoretical framework to quantify End-to-End sensing performance in Integrated Sensing and Edge AI (ISEA) with multi-view sensing and AirComp-based aggregation. It models local features as a Gaussian mixture and shows that the aggregated feature distribution yields an exponential decrease in sensing uncertainty as the number of views grows, with the rate tied to a global discriminant gain. When wireless channels are present, the AirComp distortion reduces the exponential rate by a factor $A_{loss}$, but preserves the exponential scaling, enabling a view-and-channel aggregation gain that significantly improves edge sensing under low latency. The study also compares AirComp to analog orthogonal access, deriving a crossing point near $N \approx K$ and proposing adaptive access switching to optimize performance, with validation on synthetic data and real MVCNN ModelNet experiments, highlighting practical implications for fast, multi-view edge sensing.

Abstract

Sensing and edge artificial intelligence (AI) are two key features of the sixth-generation (6G) mobile networks. Their natural integration, termed Integrated sensing and edge AI (ISEA), is envisioned to automate wide-ranging Internet-of-Tings (IoT) applications. To achieve a high sensing accuracy, multi-view features are uploaded to an edge server for aggregation and inference using an AI model. The view aggregation is realized efficiently using over-the-air computing (AirComp), which also aggregates channels to suppress channel noise. At its nascent stage, ISEA still lacks a characterization of the fundamental performance gains from view-and-channel aggregation, which motivates this work. Our framework leverages a well-established distribution model of multi-view sensing data where the classic Gaussian-mixture model is modified by adding sub-spaces matrices to represent individual sensor observation perspectives. Based on the model, we study the End-to-End sensing (inference) uncertainty, a popular measure of inference accuracy, of the said ISEA system by a novel approach involving designing a scaling-tight uncertainty surrogate function, global discriminant gain, distribution of receive Signal-to-Noise Ratio (SNR), and channel induced discriminant loss. We prove that the E2E sensing uncertainty diminishes at an exponential rate as the number of views/sensors grows, where the rate is proportional to global discriminant gain. Given channel distortion, we further show that the exponential scaling remains with a reduced decay rate related to the channel induced discriminant loss. Furthermore, we benchmark AirComp against equally fast, traditional analog orthogonal access, which reveals a sensing-accuracy crossing point between the schemes, leading to the proposal of adaptive access-mode switching. Last, the insights from our framework are validated by experiments using real-world dataset.

Figures (8)

• Figure 1: A system integrating multi-view sensing and edge AI.
• Figure 2: Numerical validation on the surrogate sensing uncertainty, $\kappa_1 = \frac{1}{0.5M+1}$, $\kappa_2 = \frac{1}{M+1}$.
• Figure 3: Numerical validation of Lemma \ref{['Lemma:asymp_dist']}.
• Figure 4: Numerical validation on the crossing point between AirComp and analog orthogonal access. The parameters are set as $M=L=10$, $\mathbf{C} = 0.1\mathbf{I}_M$, $\mathsf{rank}(\mathbf{P}_k)=1$, $\gamma=10\mathrm{\ dB}$. The expectation is taken over channel distribution.
• Figure 5: (Linear classification) Comparison between E2E sensing uncertainty and accuracy for a variable number of sensors and different local observation DoFs.

Theorems & Definitions (18)

• Lemma 1: Distribution of Aggregated Feature Map
• proof
• Lemma 2: Global Discrimination Gain
• Proposition 1: Sensing Uncertainty
• proof
• Example 1: Numerical Validation
• Proposition 2: Surrogate Function Expansion
• proof
• Lemma 3
• proof