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Optimality Analysis of RSMA Degenerating to SDMA Under Imperfect SIC

Xuejun Cheng, Qian Zhang, Yunnuo Xu, Zheng Dong, Ju Liu, Bruno Clerckx

TL;DR

This work analyzes RSMA in a RIS-assisted downlink under transceiver hardware impairments and imperfect SIC. By formulating SINR expressions that account for SIC residual interference and distortion, it proves that when the SIC imperfection coefficient $\delta_{\text{SIC}}$ approaches 1, there exists an optimal beamformer with $\mathbf{w}_c^{\star}=\mathbf{0}$, causing RSMA to degenerate to SDMA. The result holds for any system utility that is monotonically nondecreasing with SINR, providing a rigorous optimality justification for the observed convergence of RSMA performance to SDMA in SIC-limited regimes. Practically, this finding informs multi-access selection and robust design choices in SIC-constrained networks, including RIS-enhanced deployments.

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.

Optimality Analysis of RSMA Degenerating to SDMA Under Imperfect SIC

TL;DR

This work analyzes RSMA in a RIS-assisted downlink under transceiver hardware impairments and imperfect SIC. By formulating SINR expressions that account for SIC residual interference and distortion, it proves that when the SIC imperfection coefficient approaches 1, there exists an optimal beamformer with , causing RSMA to degenerate to SDMA. The result holds for any system utility that is monotonically nondecreasing with SINR, providing a rigorous optimality justification for the observed convergence of RSMA performance to SDMA in SIC-limited regimes. Practically, this finding informs multi-access selection and robust design choices in SIC-constrained networks, including RIS-enhanced deployments.

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 , 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.
Paper Structure (7 sections, 1 theorem, 19 equations)

This paper contains 7 sections, 1 theorem, 19 equations.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmit Signal Model
  4. Receive Signal Model
  5. SINR Expressions Under Imperfect SIC
  6. Limit Analysis and Core Proposition
  7. Conclusion

Key Result

Theorem 1

Consider a $K$-user downlink RSMA system. Under transceiver hardware impairments and imperfect SIC, the SINR of the private stream for user $k$ can be expressed as where When $\delta_{\mathrm{SIC}}\to 1$, for any system utility function that is monotonically nondecreasing with respect to the users' SINRs (which can characterize common performance metrics such as weighted sum rate, proportional f

Theorems & Definitions (2)

  • Theorem 1: Theorem 1
  • proof