Analysis of Cross-Domain Message Passing for OTFS Transmissions

TL;DR

This paper analyzes the performance of cross-domain iterative detection algorithms for OTFS transmissions, revealing their convergence behavior and error bounds through theoretical analysis and numerical validation.

Contribution

It introduces two novel CDID algorithms for OTFS, providing a detailed analysis of their error performance, convergence points, and bounds, which was not previously explored.

Findings

Extrinsic information passing converges to the matched filter bound.

A posteriori information passing has two potential convergence points.

Numerical results validate the analytical error performance analysis.

Abstract

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.