Cramer-Rao Lower Bound Analysis for OTFS and OFDM Modulation Systems

The orthogonal time frequency space (OTFS) modulation as a promising signal representation attracts growing interest for integrated sensing and communication (ISAC), yet its merits over orthogonal frequency division multiplexing (OFDM) remain controversial. This paper devotes to a comprehensive comparison of OTFS and OFDM for sensing from the perspective of Cramér-Rao lower bounds (CRLB) analysis. To this end, we develop the cyclic prefix (CP)-Free and CP-added models for OFDM, while for OTFS, we consider the Zak transform based and the Two-Steps conversion based models, respectively. Then we rephrase these four models into a unified matrix format to derive the CRLB of the delays and Doppler shifts for multipath scenario. Numerical results demonstrate the superiority of OTFS modulation for sensing, and the effect of physical parameters for performance achievement.