Rethinking Estimation Rate for Wireless Sensing: A Rate-Distortion Perspective

Wireless sensing has been recognized as a key enabling technology for numerous emerging applications. For decades, the sensing performance was mostly evaluated from a reliability perspective, with the efficiency aspect widely unexplored. Motivated from both backgrounds of rate-distortion theory and optimal sensing waveform design, a novel efficiency metric, namely, the sensing estimation rate (SER), is defined to unify the information- and estimation- theoretic perspectives of wireless sensing. Specifically, the active sensing process is characterized as a virtual lossy data transmission through non-cooperative joint source-channel coding. The bounds of SER are analyzed based on the data processing inequality, followed by a detailed derivation of achievable bounds under the special cases of the Gaussian linear model (GLM) and semi-controllable GLM. As for the intractable non-linear model, a computable upper bound is also given in terms of the Bayesian Cram\'er-Rao bound (BCRB). Finally, we show the rationality and effectiveness of the SER defined by comparing to the related works.