Optimality Analysis of RSMA Degenerating to SDMA Under Imperfect SIC

2026-02-20

AI Summary

This work addresses the lack of theoretical understanding regarding the degradation of rate-splitting multiple access (RSMA) to space-division multiple access (SDMA) in the presence of transceiver hardware impairments and imperfect successive interference cancellation (SIC). By constructing a unified system model that jointly accounts for hardware distortions and residual SIC interference, the study rigorously proves—using optimization theory—that as the residual interference coefficient approaches unity, the optimal beamformer for the common stream in RSMA converges to zero. Consequently, the RSMA transmission structure naturally collapses into SDMA. This result provides the first optimality-based explanation for the empirically observed performance convergence between RSMA and SDMA under severe SIC failure, offering crucial theoretical guidance for selecting appropriate multiple access schemes in SIC-constrained systems.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

This document serves as supplementary material for our journal submission, providing detailed mathematical proofs and derivations that support the results presented in the main manuscript. Specifically, under a modeling framework that jointly considers transceiver hardware impairments and imperfect successive interference cancellation (SIC), we systematically derive and prove from an optimality perspective that: when the residual interference coefficient approaches 1 (i.e., SIC becomes severely ineffective), there exists an optimal solution such that the common stream beamformer satisfies $\bm w_c^\star=\bm 0$, and hence the optimal rate-splitting multiple access (RSMA) transmission structure degenerates into space division multiple access (SDMA). This conclusion provides a verifiable theoretical justification for the convergence phenomenon observed in simulations, namely that"the RSMA performance gradually approaches that of SDMA as SIC degrades", and can also serve as a reference for multiple-access selection and system design in SIC-limited scenarios.

Problem

• RSMA
• SDMA
• imperfect SIC
• hardware impairments
• optimality

Innovation

• RSMA
• SDMA
• imperfect SIC
• optimality analysis
• beamforming