In this paper, we investigate the performance of the cross-domain iterative detection (CDID) framework with orthogonal time frequency space (OTFS) modulation, where two distinct CDID algorithms are presented. The proposed schemes estimate/detect the information symbols iteratively across the frequency domain and the delay-Doppler (DD) domain via passing either the a posteriori or extrinsic information. Building upon this framework, we investigate the error performance by considering the bias evolution and state evolution. Furthermore, we discuss their error performance in convergence and the DD domain error state lower bounds in each iteration. Specifically, we demonstrate that in convergence, the ultimate error performance of the CDID passing the a posteriori information can be characterized by two potential convergence points. In contrast, the ultimate error performance of the CDID passing the extrinsic information has only one convergence point, which, interestingly, aligns with the matched filter bound. Our numerical results confirm our analytical findings and unveil the promising error performance achieved by the proposed designs.

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