Optimality Analysis of RSMA Degenerating to SDMA Under Imperfect SIC

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.