People-Sensing Spatial Characteristics of RF Sensor Networks

An “RF sensor” network can monitor RSS values on links in the network and perform device-free localization, i.e., locating a person or object moving in the area in which the network is deployed. This paper provides a statistical model for the RSS variance as a function of the person’s position w.r.t. the transmitter (TX) and receiver (RX). We show that the ensemble mean of the RSS variance has an approximately linear relationship with the expected total affected power (ETAP). We then use analysis to derive approximate expressions for the ETAP as a function of the person’s position, for both scattering and reflection. Counterintuitively, we show that reflection, not scattering, causes the RSS variance contours to be shaped like Cassini ovals. Experimental tests reported here and in past literature are shown to validate the analysis.

💡 Research Summary

The paper presents a rigorous statistical framework that links the variance of received signal strength (RSS) on a wireless sensor link to the spatial position of a moving person relative to the transmitter (TX) and receiver (RX). The authors begin by modeling the complex baseband voltage as a sum of multipath components. When a person moves into the environment, only a subset of these components experiences random changes in phase and amplitude, while the remaining components stay constant. This decomposition yields a Ricean envelope for the received voltage, with a K‑factor defined as the ratio of the power in the unchanged components to the power in the affected components. Prior work has shown that the variance of RSS expressed in dB is approximately a linear function of the K‑factor (in dB) over a practical range (−2 dB < K < 10 dB). Leveraging this relationship, the authors derive an affine connection between the ensemble‑averaged RSS variance and the expected total affected power (ETAP), i.e., the expected sum of powers of the multipath components that are perturbed by the person’s presence.

To evaluate ETAP as a function of the person’s location, the paper adopts spatial multipath models originally developed for directional antenna analysis. Specifically, the geometrically‑based single‑bounce model (GBSBM) is employed, which assumes that each non‑line‑of‑sight (NLOS) path results from a single reflection off a scatterer located somewhere on an ellipse defined by the TX and RX positions. The authors distinguish two propagation mechanisms: scattering (diffuse interaction with small objects) and specular reflection (mirror‑like bounce from larger surfaces). For each mechanism they formulate probability density functions describing the spatial distribution of scatterers and derive closed‑form approximations for ETAP. In the scattering case, ETAP varies roughly proportionally to the distance from the person to the line joining TX and RX, producing roughly elliptical contours. In the reflection case, ETAP depends on the product of the distances from the person to TX and from the person to RX, i.e., ETAP ∝ |x_T − x|·|x_R − x|. This product defines a Cassini oval, a family of curves whose shape is determined by the constant product of distances to two foci. Consequently, the RSS variance contours generated by reflection alone assume the shape of Cassini ovals, a counter‑intuitive result because one might expect scattering to dominate variance shaping.

The theoretical predictions are validated against three data sets. First, the authors re‑examine contour plots from prior studies (e.g.,