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arxiv: 2604.18269 · v1 · submitted 2026-04-20 · 📡 eess.SP

Impact of CSIR, SIC, and Hardware Impairments on the Ergodic Rate of Downlink RSMA

Farjam Karim , Deepak Kumar , Prathapasinghe Dharmawansa , Nurul Huda Mahmood , Arthur Sousa de Sena , Matti Latva-aho This is my paper

Pith reviewed 2026-05-10 03:52 UTC · model grok-4.3

classification 📡 eess.SP
keywords RSMAergodic ratehardware impairmentsimperfect SICimperfect CSIRNOMA comparisonsum-ratefairness index
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The pith

Rate-splitting multiple access sustains higher ergodic rates, fairness, and sum-rate than non-orthogonal multiple access even under imperfect channel state information, imperfect successive interference cancellation, and hardware flaws.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper derives closed-form expressions for the ergodic rate, energy efficiency, sum-rate, and Jain's fairness index of downlink rate-splitting multiple access when receivers have imperfect channel state information, successive interference cancellation is imperfect, and hardware introduces distortions. It shows that rate-splitting multiple access outperforms non-orthogonal multiple access across these metrics even when the impairments are severe. The analysis identifies that imperfect channel state information limits performance most at low transmit powers, while hardware impairments become the main constraint at high powers and imperfect successive interference cancellation grows more relevant. These results position rate-splitting multiple access as a resilient option for future wireless networks that must handle practical non-idealities.

Core claim

Closed-form expressions for ergodic rate and related metrics are derived that jointly account for imperfect CSIR, imperfect SIC, and hardware impairments. These expressions and accompanying simulations establish that rate-splitting multiple access consistently outperforms non-orthogonal multiple access in ergodic rate, sum-rate, and fairness even under severe impairments. The work further shows that the dominant impairment shifts with transmit power: imperfect CSIR at low power, hardware impairments at high power, and imperfect SIC becoming more prominent as power rises.

What carries the argument

Closed-form analytical expressions for ergodic rate, energy efficiency, sum-rate, and Jain's fairness index that incorporate the combined effects of imperfect CSIR, imperfect SIC, and hardware impairments.

If this is right

  • At low transmit powers, imperfect CSIR is the dominant performance-limiting factor.
  • At high transmit powers, hardware impairments become the primary bottleneck.
  • Imperfect SIC grows more significant as a bottleneck when transmit power increases.
  • Rate-splitting multiple access delivers better fairness and sum-rate than non-orthogonal multiple access regardless of impairment severity.
  • Fairness should be treated as a core design objective alongside rate and energy efficiency.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The power-dependent shift in dominant impairments suggests that power allocation strategies could be tuned to the operating regime to further improve rate-splitting multiple access performance.
  • The robustness findings could motivate comparisons in multi-cell or uplink settings if similar expressions are obtained.
  • The emphasis on fairness implies that rate-splitting multiple access may reduce the need for additional scheduling layers in dense networks.

Load-bearing premise

The closed-form derivations rely on specific statistical models for the channel fading, the distributions of the impairments, and the imperfect successive interference cancellation error.

What would settle it

An experiment or simulation that uses measured hardware impairment statistics and correlated real-world channels and finds that non-orthogonal multiple access achieves higher ergodic rates or fairness than rate-splitting multiple access under the same conditions.

Figures

Figures reproduced from arXiv: 2604.18269 by Arthur Sousa de Sena, Deepak Kumar, Farjam Karim, Matti Latva-aho, Nurul Huda Mahmood, Prathapasinghe Dharmawansa.

Figure 1
Figure 1. Figure 1: Illustration of a general RSMA-aided Downlink Syste [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Impact of ξn on the user’s ergodic rate. 0 5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Fairness between RSMA and NOMA. 0 5 10 15 20 25 30 0 0.5 1 1.5 2 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

This work investigates the ergodic rate performance analysis of rate-splitting multiple access (RSMA) in a downlink communication system under practical impairments. Closed-form expressions are derived for key performance metrics such as ergodic rate, energy efficiency, sum-rate, and Jains fairness index, capturing the joint effects of imperfect channel state information at the receiver (CSIR), imperfect successive interference cancellation (SIC), and hardware impairments. Numerical simulations validate the accuracy of the analytical expressions and reveal several insightful trends. At low transmit powers, imperfect CSIR is the dominant performance-limiting factor, followed by hardware impairments and imperfect SIC. However, as the transmit power increases, hardware impairments become the primary bottleneck, with the impact of imperfect CSIR gradually diminishing, and imperfect SIC becoming a more prominent bottleneck. Moreover, RSMA consistently outperforms non-orthogonal multiple access (NOMA) in terms of ergodic rate, fairness, and sum-rate, even under severe non-idealities. These findings underscore the importance of incorporating fairness as a core design objective alongside rate and energy efficiency, positioning RSMA as a robust and strong multiple access candidate for next-generation wireless networks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript derives closed-form expressions for the ergodic rate, energy efficiency, sum-rate, and Jain's fairness index of downlink RSMA under the combined effects of imperfect CSIR, imperfect SIC, and hardware impairments. These expressions are obtained by averaging over standard Rayleigh fading, Gaussian impairment, and independent SIC-error distributions. Monte Carlo simulations are used to validate the analytics, and direct comparisons to NOMA under identical parameter settings show that RSMA achieves higher ergodic rates, improved fairness, and higher sum-rates even when non-idealities are severe. The work further reports that imperfect CSIR dominates at low transmit power while hardware impairments become the primary bottleneck at high power.

Significance. If the closed-form expressions hold, the paper supplies practical analytical tools for assessing RSMA in realistic downlink scenarios and identifies power-dependent impairment dominance, which is useful for 6G multiple-access design. Credit is due for the parameter-free derivations under standard models, the consistent numerical agreement between analysis and simulation across regimes, and the explicit RSMA-vs-NOMA comparisons that avoid fitted parameters.

major comments (2)
  1. [Abstract and §III] Abstract and performance-analysis section: the closed-form ergodic-rate expressions are stated to rely on post-hoc simplifications whose approximation steps and error bounds are not provided. This omission is load-bearing for the high-SNR conclusions (hardware impairments as dominant bottleneck) because the numerical match between analysis and simulation occurs only under the same modeling assumptions; without bounds it is unclear whether the reported trends remain accurate when the approximations are relaxed.
  2. [§III] §III, ergodic-rate derivation: the expressions average over independent Gaussian hardware-impairment and SIC-error models. While internally consistent, the central claim that RSMA outperforms NOMA “even under severe non-idealities” would be strengthened by a brief sensitivity check (e.g., correlated impairments or non-Gaussian SIC error) or an explicit statement that the outperformance holds only inside the adopted statistical framework.
minor comments (3)
  1. [§II] The system-model section would benefit from a compact table listing all impairment parameters (κ, ε, etc.) together with their physical meaning and typical ranges used in the numerical results.
  2. [Figures 1–4] Figure captions and legends should explicitly state the number of Monte-Carlo realizations and the exact parameter settings (e.g., number of users, power-splitting ratios) so that the plotted curves can be reproduced without consulting the main text.
  3. [Throughout] A few instances of inconsistent notation appear (e.g., the same symbol used for both the SIC error variance and a power-allocation coefficient); these should be unified.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. We address each major comment below with clarifications and indicate the changes we will incorporate to improve the manuscript.

read point-by-point responses

  1. Referee: [Abstract and §III] Abstract and performance-analysis section: the closed-form ergodic-rate expressions are stated to rely on post-hoc simplifications whose approximation steps and error bounds are not provided. This omission is load-bearing for the high-SNR conclusions (hardware impairments as dominant bottleneck) because the numerical match between analysis and simulation occurs only under the same modeling assumptions; without bounds it is unclear whether the reported trends remain accurate when the approximations are relaxed.

    Authors: We appreciate the referee drawing attention to the need for greater transparency in the derivation. The closed-form expressions in Section III are obtained by integrating over the joint distributions of Rayleigh fading, Gaussian hardware impairments, and independent SIC errors, followed by standard integral approximations to yield tractable closed forms. While the Monte Carlo results confirm accuracy under these models, we agree that the approximation steps and their impact on high-SNR trends should be made explicit. In the revised manuscript we will expand Section III with the full step-by-step derivation, including the specific integral simplifications employed, and add a brief asymptotic analysis at high SNR to bound the approximation error and confirm that hardware impairments remain the dominant bottleneck. revision: yes

  2. Referee: [§III] §III, ergodic-rate derivation: the expressions average over independent Gaussian hardware-impairment and SIC-error models. While internally consistent, the central claim that RSMA outperforms NOMA “even under severe non-idealities” would be strengthened by a brief sensitivity check (e.g., correlated impairments or non-Gaussian SIC error) or an explicit statement that the outperformance holds only inside the adopted statistical framework.

    Authors: We thank the referee for this observation. All derivations and RSMA-versus-NOMA comparisons are performed under the standard independent Gaussian models for impairments and SIC errors, which are conventional in the literature to enable closed-form analysis. The reported outperformance is therefore established within this framework. To strengthen the presentation we will insert an explicit clarifying statement in Section III noting that the conclusions hold under the adopted statistical assumptions. A comprehensive sensitivity study involving correlated or non-Gaussian impairments lies outside the scope of the present work but could be pursued in follow-on research; the current standard-model results nonetheless provide a rigorous baseline. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives closed-form ergodic-rate, sum-rate, energy-efficiency, and fairness expressions by direct statistical averaging over standard Rayleigh fading, Gaussian hardware-impairment, and independent SIC-error distributions. These expressions are validated by Monte-Carlo simulation under identical assumptions and compared to NOMA using the same parameter settings; no parameters are fitted to a data subset and then relabeled as predictions, no self-citations supply load-bearing uniqueness theorems, and no ansatz or definition is smuggled in via prior work. The derivation chain therefore remains self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The analysis rests on standard wireless assumptions (Rayleigh or Rician fading, additive Gaussian noise, independent impairment realizations) drawn from prior literature; no new free parameters, axioms, or invented entities are introduced beyond the impairment models already used in the field.

pith-pipeline@v0.9.0 · 5533 in / 1122 out tokens · 46997 ms · 2026-05-10T03:52:06.789255+00:00 · methodology

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Reference graph

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