Bayesian Cramér-Rao Bound for Sensing Performance in Meta-Backscatter Systems

Meta-backscatter system that utilizes meta-material sensors is a promising enabler for future environmental sensing, offering distinct advantages such as low cost, zero-power consumption, and robustness. Specifically, the electromagnetic response of the sensor, typically characterized by a frequency-selective absorption profile, is affected by the environmental conditions, allowing the estimation of these conditions from the reflected signal. However, it remains unclear what estimation accuracy can be achieved fundamentally. Motivated by this gap, we quantify this accuracy limit using the Bayesian Cramér-Rao bound (BCRB), which provides a lower bound on the mean-squared error for the environmental condition. Establishing this limit is challenging because the electromagnetic response of the sensor is distorted by the channel fading, while the channel estimation is infeasible since the sensors cannot be configured to predefined states to generate training data. To address this challenge, we consider the joint BCRB of the channel coefficient and the environmental condition in a multicarrier framework. The BCRB of the environmental condition is then obtained by selecting the corresponding element from the joint BCRB. An analysis of the derived BCRB reveals the impact of the absorption peak shape and the number of subcarriers. The derivation and analysis of the BCRB are verified through simulations.