Ziv-Zakai Bound for Mixture Distribution Parameters Estimation in OTFS-ISAC System

The Cramér-Rao bound (CRB), a classical lower bound, provides inaccurate performance predictions for channel parameter estimation under low signal-to-noise ratio (SNR) conditions in orthogonal time frequency space (OTFS)-based integrated sensing and communication (ISAC) systems. This paper derives a novel Ziv-Zakai bound (ZZB) for mixture distribution parameters in OTFS-ISAC. First, we analyze existing ZZBs for single-distribution parameter estimation and the properties of mixture distributions. Then, by leveraging boundary conditions of channel parameters, we prove that the equally likely hypothesis still holds in the ZZB derivation for mixture distributions. Finally, we derive the ZZB expression for the mixture distribution parameters estimation. The derived ZZB serves as an effective benchmark for evaluating parameter estimation (e.g., uniform/ non-uniform Gaussian parameters) in OTFS-ISAC systems under challenging conditions. The simulation results demonstrate that the derived ZZB is tighter than the classical CRB in low SNRs region, where different superimposed pilot structures, prior distributions, and dimension of the delay- Doppler (DD) domain grid are tested.