Inside the Channel: A Stochastic Analysis of the CSI for Wi-Fi Sensing

With the widespread interest in Joint Communication and Sensing, a key point of new generations of wireless networks, comes the need for a thorough analysis of the information that sensing tools leverage. Although multiple works focus on the use of Wi-Fi Channel State Information (CSI) to implement ambient sensing techniques and tools, a statistical characterization of CSI structure and behavior across variable environmental conditions is still missing. This work analyzes the fundamental properties of the CSI through a focus on the long-term behavior of its amplitude and its interpretation as a stochastic process. We show that the short-term amplitude variations, the increments, are accurately modeled by a heavy-tailed T Location Scale distribution across a wide range of real-world experimental conditions, regardless of bandwidth, hardware, and environmental dynamics. The analysis of amplitude autocorrelation further reveals the presence of residual memory beyond the mean value in the amplitude process, indicating a non-Markovian evolution. The increments autocorrelation, which exhibits one-step memory, is analytically consistent with this finding. Building on this stochastic characterization, we introduce a formal framework to uniform CSI representation and we define a simple distance-based metric to support the comparison of CSI samples collected under heterogeneous experimental conditions. The metric is then used by a proof-of-concept lightweight sensing method presented in the final part of the study: amenable to implementation on resource-constrained devices typical of the Internet of Things, the algorithm is able to accurately discriminate static from dynamic environments showing how the stochastic characterization of CSI’s can inform training-free passive CSI-based sensing with Wi-Fi without requiring complex learning models.