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.

翻译：本文档作为我们期刊投稿的补充材料，提供了支持主稿件中所述结果的详细数学证明与推导。具体而言，在联合考虑收发机硬件损伤与非理想连续干扰消除（SIC）的建模框架下，我们从最优性角度系统推导并证明了：当残余干扰系数趋近于1（即SIC严重失效）时，存在最优解使得公共流波束成形器满足$\bm w_c^\star=\bm 0$，从而最优速率分割多址接入（RSMA）传输结构退化为空分多址接入（SDMA）。该结论为仿真中观察到的“RSMA性能随SIC劣化逐渐趋近于SDMA”这一收敛现象提供了可验证的理论依据，也可为SIC受限场景下的多址接入选择与系统设计提供参考。