Securing the sensing functionality in ISAC: KLD-based ambiguity function shaping

Integrated sensing and communication (ISAC) systems introduce a sensing-privacy vulnerability because unauthorized sensing eavesdroppers (Eve) may exploit ISAC signals for independent passive sensing. This work addresses sensing-security for orthogonal frequency-division multiplexing (OFDM)- and orthogonal time frequency space (OTFS)-based ISAC waveforms from a target-detection perspective. We develop system models for the base station (BS), user equipment, and Eve, and define a Kullback-Leibler divergence-based detection metric that accounts for mainlobe, sidelobe, and noise components in ambiguity-function and range-Doppler maps. Building on this analysis, we formulate a sensing-secure signaling design problem that tunes a perturbation matrix to jointly control signal amplitude and phase in the time-frequency domain and solve it via simulated annealing. Simulation results show that the proposed scheme substantially degrades Eve's detection probability-from 79.4% to 37.4% for OTFS and from 94.3% to 33.0% for OFDM-while incurring only a small loss in BS sensing performance. The proposed scheme also enables controllable sensing-security and communication trade-offs.