Physical-Layer Sensing Privacy via Constellation Shaping for OFDM-ISAC Systems: Theory, Design, and Experiments

Abstract

The integration of sensing into communication networks introduces a new privacy risk, as a passive eavesdropper (Eve) may exploit ISAC data signals as signals of opportunity to perform unauthorized sensing of targets. In this paper, we develop a sensing-privacy-enhancing geometric constellation shaping (GCS) framework for OFDM-ISAC systems. The key observation is that constellation-dependent ranging performance is receiver-specific. For matched filtering at Eve, the ranging MSE is governed by the constellation kurtosis $\kurt$, whereas reciprocal filtering at the legitimate receiver (Alice) is governed by the inverse second-order moment $\ism$. Based on closed-form MSE expressions, we define sensing privacy as the ranging MSE gap between Eve and Alice and characterize its dependence on these two moments. The analysis shows that positive skewness of the symbol-power distribution is necessary for a positive intrinsic moment gap, namely $\kurt-\ism$. We further derive an exact skewness-based decomposition of the intrinsic moment gap and a canonical two-ring characterization, providing analytical guidelines for privacy-enhancing constellation geometries. We then formulate Eve-aware and Eve-agnostic GCS designs that balance sensing privacy and communication reliability through the minimum Euclidean distance (MED), with the Eve-agnostic design depending only on the intrinsic moment gap. Numerical results demonstrate scalable privacy--communication trade-offs, while over-the-air experiments show that the proposed constellation shaping substantially increases the ranging error gap between Eve and Alice with only a small communication throughput loss.