Optimality Analysis of RSMA Degenerating to SDMA Under Imperfect SIC

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.

💡 Research Summary

This paper provides a rigorous optimality‑based proof that, in a downlink multi‑antenna system employing Rate‑Splitting Multiple Access (RSMA) with RIS assistance, the optimal transmission strategy collapses to conventional Space Division Multiple Access (SDMA) when successive interference cancellation (SIC) becomes completely ineffective. The authors model both transmitter and receiver hardware impairments (HWI) as additive Gaussian distortion noises whose powers are proportional to the transmitted signal power (parameter m_t) and to the undistorted received signal power (parameter m_r). The transmitted signal consists of a common stream s_c and K private streams s_k, each weighted by beamforming vectors w_c and w_k, respectively.

At the receiver, each user first decodes the common stream while treating all private streams as interference, then attempts to cancel the decoded common stream before decoding its own private stream. Because SIC is imperfect, a residual self‑interference term proportional to δ_SIC^2 |h_k^H w_c|^2 remains, where δ_SIC∈