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arxiv: 2501.19019 · v1 · submitted 2025-01-31 · 📡 eess.SP

Uplink Rate Splitting Multiple Access with Imperfect Channel State Information and Interference Cancellation

Farjam Karim , Nurul Huda Mahmood , Arthur S. de Sena , Deepak Kumar , Bruno Clerckx , Matti Latva-aho This is my paper

Pith reviewed 2026-05-23 04:51 UTC · model grok-4.3

classification 📡 eess.SP
keywords uplink RSMAimperfect CSIRimperfect SICoutage probabilityNOMA comparisonthroughputtwo-user scenario
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The pith

Uplink RSMA manages imperfect receiver channel information and cancellation errors more effectively than NOMA by splitting each user's message.

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

The paper studies uplink rate splitting multiple access for two users when the receiver has imperfect channel state information and successive interference cancellation is imperfect. It derives closed-form expressions for outage probability, throughput, and high-power asymptotic behavior, then validates them with simulations. The results show that channel estimation errors dominate performance loss at low transmit power while cancellation errors dominate at high power, and that strategic message splitting gives RSMA an edge over standard NOMA under these imperfections.

Core claim

In the two-user uplink, RSMA splits each user's message into a common part and a private part; closed-form outage expressions that incorporate both imperfect CSIR and residual SIC interference demonstrate lower outage than NOMA for the same power and rate allocation, with the advantage arising because the common stream absorbs part of the uncertainty.

What carries the argument

Message splitting into common and private streams together with closed-form outage probability expressions that fold in statistical models of CSIR error and SIC residual interference.

If this is right

  • At low transmit power, imperfect CSIR degrades outage more than imperfect SIC.
  • At high transmit power, imperfect SIC becomes the dominant performance limiter.
  • Changing the rate allocation factor between common and private streams trades off the two users' outage probabilities.
  • RSMA exhibits lower outage than NOMA across the examined range of imperfect CSIR and SIC conditions.

Where Pith is reading between the lines

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

  • The two-user closed forms could be used as building blocks for larger user counts if the splitting ratios can be optimized jointly.
  • Hardware calibration that reduces CSIR error variance would shift the operating regime where SIC errors dominate to lower powers.
  • The power-dependent crossover between CSIR and SIC dominance suggests an adaptive power-control policy that could further improve robustness.

Load-bearing premise

The derivations assume exactly two users and particular statistical distributions for the channel estimation errors and SIC error terms.

What would settle it

Outage measurements collected from a real two-user uplink testbed whose channel estimation error variance and SIC residual statistics differ from the paper's models would falsify the closed-form expressions.

Figures

Figures reproduced from arXiv: 2501.19019 by Arthur S. de Sena, Bruno Clerckx, Deepak Kumar, Farjam Karim, Matti Latva-aho, Nurul Huda Mahmood.

Figure 2
Figure 2. Figure 2: Ξi Effect on Outage vs SNR. δ values for evaluating Ωhie ∀i ∈ {1, 2} in (12). Additionally, by setting Ξ2 = 0, P Out 2 for the perfect SIC case can also be obtained. Corollary 2. The throughput of U2 with imperfect CSIR and imperfect SIC can be evaluated as T2 = [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: NOMA vs RSMA Comparison. SIC factor (Ξi) with perfect CSIR. It is clearly evident from the figures that P Out 1 and P Out 2 expressions derived in (7) and (12) are in close agreement with simulated results for all values of δ and Ξi . An increase in the value of δ from 0.2 to 0.9 can significantly reduce the outage probability for both users before approaching the floor. This improvement is due to the enha… view at source ↗
read the original abstract

This article investigates the performance of uplink rate splitting multiple access (RSMA) in a two-user scenario, addressing an under-explored domain compared to its downlink counterpart. With the increasing demand for uplink communication in applications like the Internet-of-Things, it is essential to account for practical imperfections, such as inaccuracies in channel state information at the receiver (CSIR) and limitations in successive interference cancellation (SIC), to provide realistic assessments of system performance. Specifically, we derive closed-form expressions for the outage probability, throughput, and asymptotic outage behavior of uplink users, considering imperfect CSIR and SIC. We validate the accuracy of these derived expressions using Monte Carlo simulations. Our findings reveal that at low transmit power levels, imperfect CSIR significantly affects system performance more severely than SIC imperfections. However, as the transmit power increases, the impact of imperfect CSIR diminishes, while the influence of SIC imperfections becomes more pronounced. Moreover, we highlight the impact of the rate allocation factor on user performance. Finally, our comparison with non-orthogonal multiple access (NOMA) highlights the outage performance trade-offs between RSMA and NOMA. RSMA proves to be more effective in managing imperfect CSIR and enhances performance through strategic message splitting, resulting in more robust communication.

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 / 2 minor

Summary. The manuscript analyzes a two-user uplink RSMA system under imperfect CSIR and imperfect SIC. It derives closed-form expressions for outage probability, throughput, and high-SNR asymptotic outage behavior, validates them against Monte Carlo simulations, examines the relative impact of the two impairments as a function of transmit power and rate allocation factor, and compares outage performance against uplink NOMA, concluding that RSMA is more robust to imperfect CSIR via strategic message splitting.

Significance. If the derivations hold under the stated models, the closed-form outage and throughput expressions together with the Monte Carlo validation constitute a concrete analytical contribution for evaluating uplink RSMA in the presence of realistic receiver impairments. The power-dependent trade-off between CSIR and SIC errors and the explicit comparison with NOMA supply design-relevant insights for IoT-style uplink scenarios. The work does not claim parameter-free results or machine-checked proofs, but the analytic-plus-simulation approach is a standard strength when the models are accepted.

major comments (2)
  1. [System Model / Derivations] System model and derivation sections: the closed-form outage expressions rest on the assumption that the CSIR estimation error is circularly symmetric complex Gaussian whose variance scales linearly with SNR (or 1/SNR) and that the residual SIC interference is an independent term with its own fixed or power-dependent variance. These modeling choices are load-bearing for both the analytic results and the subsequent claim that RSMA outperforms NOMA in managing imperfect CSIR; no robustness checks against non-Gaussian, correlated, or hardware-induced error distributions (e.g., phase-noise floors) are provided.
  2. [Numerical Results / Comparison with NOMA] Numerical results and comparison sections: the outage curves and the headline statement that “RSMA proves to be more effective in managing imperfect CSIR” are obtained exclusively under the two error models above and a two-user topology. Because the ordering versus NOMA can reverse under alternative error statistics, the comparative claim requires either a sensitivity study or an explicit statement of the modeling assumptions under which it holds.
minor comments (2)
  1. Notation for the rate allocation factor and the power scaling of the error variances should be introduced once and used consistently; occasional re-definition of symbols across sections reduces readability.
  2. The Monte Carlo simulation description should include the number of trials, the exact generation procedure for the imperfect CSIR and residual SIC terms, and any data-exclusion rules so that the validation can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of the modeling assumptions and the scope of the comparative claims. We address each point below and propose targeted revisions to clarify the context of our results.

read point-by-point responses

  1. Referee: [System Model / Derivations] System model and derivation sections: the closed-form outage expressions rest on the assumption that the CSIR estimation error is circularly symmetric complex Gaussian whose variance scales linearly with SNR (or 1/SNR) and that the residual SIC interference is an independent term with its own fixed or power-dependent variance. These modeling choices are load-bearing for both the analytic results and the subsequent claim that RSMA outperforms NOMA in managing imperfect CSIR; no robustness checks against non-Gaussian, correlated, or hardware-induced error distributions (e.g., phase-noise floors) are provided.

    Authors: The closed-form expressions are derived under the standard assumption of circularly symmetric complex Gaussian CSIR errors with variance inversely proportional to SNR, together with an independent residual SIC term; these choices follow common practice in the literature to obtain tractable analytics. Monte Carlo simulations confirm the expressions under exactly these models. We will add an explicit paragraph in the System Model section stating the assumptions and noting that all analytic and comparative results hold specifically under Gaussian error statistics. A full robustness study against non-Gaussian or hardware-specific distributions would require new derivations outside the present scope. revision: partial

  2. Referee: [Numerical Results / Comparison with NOMA] Numerical results and comparison sections: the outage curves and the headline statement that “RSMA proves to be more effective in managing imperfect CSIR” are obtained exclusively under the two error models above and a two-user topology. Because the ordering versus NOMA can reverse under alternative error statistics, the comparative claim requires either a sensitivity study or an explicit statement of the modeling assumptions under which it holds.

    Authors: The RSMA-versus-NOMA comparison is performed under the same Gaussian error models and two-user topology used for the derivations. We will revise the abstract, introduction, and conclusion to qualify the claim explicitly as holding under the considered CSIR and SIC error statistics. This clarification, together with the added modeling discussion, makes the scope of the result transparent without requiring additional sensitivity simulations. revision: partial

Circularity Check

0 steps flagged

No circularity: derivations start from standard channel models and produce independent closed-form results

full rationale

The paper derives outage probability, throughput, and asymptotic expressions for a two-user uplink RSMA system directly from the assumed statistical models of imperfect CSIR (additive complex Gaussian) and residual SIC interference. These expressions are validated by Monte Carlo simulation and compared to NOMA under identical assumptions; no step reduces a fitted parameter to a prediction, invokes a self-citation as a uniqueness theorem, or renames a known result. The central claims therefore remain independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the central claim rests on standard wireless fading models and specific statistical characterizations of CSIR and SIC errors that are not detailed here.

free parameters (1)
  • rate allocation factor
    Mentioned as affecting user performance; treated as a design choice whose value is not derived from first principles.
axioms (1)
  • domain assumption Two-user uplink channel with imperfect CSIR and imperfect SIC
    Invoked throughout the derivation of outage and throughput expressions.

pith-pipeline@v0.9.0 · 5776 in / 1272 out tokens · 19111 ms · 2026-05-23T04:51:09.508601+00:00 · methodology

discussion (0)

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Reference graph

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