Derivation of CRB and Refined SINR Expressions for OTFS-RSMA LEO ISAC Systems

TL;DR

This paper derives CRB and refined SINR expressions for OTFS-RSMA LEO ISAC systems, considering imperfect CSI and SIC, to support analytical modeling in satellite integrated sensing and communication.

Contribution

It provides detailed derivations of CRB and SINR expressions for OTFS-RSMA systems under practical imperfections, enhancing analytical understanding.

Findings

Derived CRB expressions for sensing parameters.

Refined SINR formulas considering imperfect CSI and SIC.

Supports improved system modeling and analysis.

Abstract

This document provides detailed step-by-step derivations for the Cram\'er-Rao Bounds (CRB) for sensing parameters and the refined Signal-to-Interference-plus-Noise Ratio (SINR) expressions under imperfect Channel State Information (CSI) and imperfect Successive Interference Cancellation (SIC) for the Orthogonal Time Frequency Space (OTFS) Rate-Splitting Multiple Access (RSMA) framework presented in our main work "An Integrated OTFS-RSMA Framework for LEO Satellite ISAC: Modeling, Metrics, and Potential". These derivations support the analytical expressions and models in the broad main discussion.