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SIC-Free Rate-Splitting Multiple Access: Constellation-Constrained Optimization and Application to Large-Scale Systems

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Under optimized precoders, SIC-free RSMA nearly matches SIC-based RSMA, keeping most of the sum-rate and fairness gains with a simpler receiver.

desk verdict Competent extension of SIC-free RSMA to optimized precoders, but the headline comparison likely rides on an unvalidated Jensen approximation; worth refereeing with a demand for exact-rate checks. read the letter →

arxiv 2506.12668 v2 pith:YTROPG5X submitted 2025-06-15 cs.IT eess.SPmath.IT

Sibo Zhang , Bruno Clerckx , David Vargas This is my paper · ORCID
classification cs.ITeess.SPmath.IT MSC 94A1594A4090C26
keywords rate-splittingmultipleaccessfinite-alphabetsignalingSIC-freereceiversprecoderoptimizationweightedsum-ratemax-minfairnessmassiveMIMOconstellation-constrainedrates
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether rate-splitting multiple access (RSMA) can forgo successive interference cancellation (SIC) without costly performance loss when signals are drawn from finite constellations rather than Gaussian alphabets. It derives exact and approximate constellation-constrained rate expressions for both receiver types with no restriction on the precoders, then optimizes precoders under weighted sum-rate and max-min fairness objectives. Numerical results show that SIC-free RSMA preserves most of the superiority of SIC-based RSMA over SDMA and NOMA, with only minor losses, across small-scale and large-scale massive MIMO settings. If true, this makes SIC-free RSMA a practical candidate for future wireless systems where receiver simplicity, low latency, and small buffers matter.

What carries the argument

The load-bearing machinery is the Jensen-based approximation of the constellation-constrained mutual information, which replaces the exact conditional-entropy expression with a tractable closed form involving distances between constellation points, together with projected subgradient ascent for the non-convex precoder optimization. Around this core sit a closed-form global optimal common-stream allocation (Algorithm 3), a log-sum-exp smoothing of the max-min objective, and, for large-scale systems, user grouping with null-space projection plus a low-dimensional subspace property that collapses the per-group precoder dimension to two. These components convert an exponentially complex finite-alphabet design problem into one whose per-iteration cost scales linearly with the number of users.

What would settle it

Evaluate the exact constellation-constrained mutual information at the precoders returned by the proposed algorithms for a small case (e.g., NT = 2, K = 2, QPSK) across the SNR range 5–30 dB and compare it with the approximate rates used in optimization; a large gap would indicate that the optimized precoders and reported SIC-free gains do not reflect true rates.

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Extended reading notes

Core claim

The central claim is that, once precoders are optimized using the finite-constellation structure, SIC-free RSMA achieves nearly the same weighted sum-rate and max-min fairness as SIC-based RSMA, even though the two require markedly different precoders and power splits. The paper establishes this by deriving rate expressions for the common and private streams under finite-alphabet inputs without assuming zero-forcing private precoders, and by proving that for weighted sum-rate maximization only the most weighted user's message needs to be split—an allocation result that holds for any input distribution. The accompanying projected subgradient ascent algorithms, combined with a closed-form optimal common-stream allocation, show that the SIC-free loss is minor under optimized designs, extending earlier SIC-free conclusions from low-complexity precoders to fully optimized ones and from sum-rate to fairness criteria.

Load-bearing premise

The optimization uses the Jensen-based approximation to the constellation-constrained mutual information as a stand-in for the true rate, and the paper does not report whether final performance numbers evaluate the exact or approximate expressions.

Editorial extensions

If this is right

  • If SIC-free RSMA indeed loses little performance under optimized precoders, receiver hardware for RSMA can drop SIC blocks, reducing latency, buffer size, and implementation complexity without sacrificing most of the spectral-efficiency gains.
  • Dedicated precoding matters: since SIC-free and SIC-based RSMA converge to similar rates with very different precoders and common-stream power allocations, deploying SIC-free RSMA requires re-optimizing precoders rather than reusing SIC-based designs.
  • For massive MIMO regimes, the user-grouping and null-space-projection approach makes finite-constellation RSMA optimization computationally feasible, so the SIC-free advantage can be assessed and exploited in systems with many antennas and users.
  • Under max-min fairness, SIC-free RSMA also preserves most of the SIC-based gain, meaning fairness-oriented deployments need not pay a large receiver-complexity premium.
  • The global optimal common-stream allocation for weighted sum-rate maximization implies that only one user's message needs to be split when the goal is sum-rate, reducing control signaling in practical RSMA implementations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper reports approximate rates as the optimization surrogate but does not state whether final figures use the exact or approximate expressions; an editorial read is that the exact-versus-approximate gap at optimized operating points deserves a dedicated comparison before the minor-loss conclusion is taken as quantitative.
  • The non-monotonic effect of finite-alphabet interference cited in the paper suggests SIC-free RSMA may also be robust in other interference-dominated regimes, such as heterogeneous networks or overloaded cells, where strong structured interference can be less harmful than Gaussian models predict.
  • The dimensionality-reduction trick could transfer to other finite-alphabet precoding problems beyond RSMA, since the low-dimensional subspace property holds for any objective depending only on the channel-range directions.
  • A testable extension is to run the proposed algorithms with exact mutual information evaluations in the objective, which would reveal whether the reported SIC-free loss widens, shrinks, or stays unchanged when the Jensen surrogate is removed.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies downlink rate-splitting multiple access (RSMA) under finite-alphabet inputs and compares two receiver architectures: SIC-based and SIC-free. It derives constellation-constrained rate expressions for both architectures (Eqs. (7)-(9)), introduces a Jensen-based approximation (Eqs. (14)-(16)), and proposes projected subgradient ascent (PSGA) algorithms for weighted sum-rate and max-min fairness optimization, with closed-form common-rate allocations in Propositions 1 and 2. To handle large-scale systems, it adds user grouping, null-space projection, and dimensionality reduction. Numerical results claim that SIC-free RSMA incurs only minor losses relative to SIC-based RSMA under optimized precoders, extending prior conclusions from low-complexity designs to fully optimized ones.

Significance. If the numerical conclusion is confirmed, the paper is valuable: it extends the SIC-free RSMA literature from heuristic low-complexity precoders to optimized precoders, covers both WSR and MMF objectives, and offers a practical complexity-reduction path for large-scale systems. The rate derivations and the closed-form common-rate allocations (Propositions 1 and 2) are sound and are useful beyond finite constellations. The large-scale complexity analysis is also a strength. However, the central performance claim currently rests on an unvalidated surrogate: the paper does not state whether the final figures use exact rates or the Jensen approximation, and no code or exact-rate validation is provided. The comparison between SIC and SIC-free receivers is therefore not yet established at the level the abstract claims.

major comments (3)
  1. [VI.C and VI.E, with Eqs. (14)-(16)] The paper never states whether Figures 3, 6, 7, 8, and 9 plot the exact rate expressions (7)-(9) or the Jensen-approximate expressions (14)-(16). Section IV explicitly says the approximation is used 'during the optimization process,' but Section VI contains no corresponding statement for the evaluation phase. If the plotted curves use (14)-(16), then the headline SIC-free-versus-SIC comparison is between two surrogates, and the receiver-dependent approximation error could either create or mask the reported 'minor losses.' Please state explicitly which rates are plotted, and re-run the key figures with the exact rates (7)-(9) at least for the operating SNRs and constellation modes used in Figures 3, 7, 8, and 9.
  2. [III.A, Eq. (6), and VI] The approximation in Eq. (6) is obtained by moving the noise expectation inside the logarithm and rescaling the squared distance by 1/2; it is not exact, and its error depends on SNR, constellation cardinality, and the interference structure. No experiment in Section VI quantifies the gap between (14)-(16) and (7)-(9) at the operating points. Because the approximation error can differ between SIC and SIC-free receivers, a validation figure or table is needed to show that the optimized precoders and the reported rate gaps reflect the true constellation-constrained mutual information rather than an artifact of the surrogate.
  3. [V.B, Proposition 3] Proposition 3 states that every non-trivial stationary point of P1 and P3 lies in the range of [h1,...,hK]. This claim is stronger than what the dimensionality reduction requires and is false as stated. For example, with K=1, h=[1;0]^T, and P=[0;1]^T, the objective depends only on h^H P, which vanishes, so the gradient with respect to P is zero and P is a stationary point, yet P is outside the range. The argument only needs existence of a global optimum in the range, which is true by projecting the orthogonal component to zero and renormalizing. Please restate the proposition in the existential form and provide the proof rather than omitting it.
minor comments (5)
  1. [VI.A] The sentence describing the channel model contains a duplicated word: 'non-LoS channel component and and the Rician factor.'
  2. [III.B, Eq. (18)] The mutual information expressions in Eq. (18) omit the conditioning on h_k^H P that is used consistently in Eqs. (10)-(13); adding it would improve notational consistency.
  3. [Appendix B] The proof of Proposition 2 assumes Rp,1 < Rp,2 < ... < Rp,K without discussing ties. Algorithm 3 appears to handle ties, but the proof should state how equal private rates are treated.
  4. [Tables III-VI] The transmission-mode dictionaries use constellations such as '8QAM' and '512QAM' that are not standard square QAM; please define these constellations or cite the specific signal sets used.
  5. [Figure 5] Figure 5 plots CPU time rather than iteration count; the convergence claim would be easier to interpret if iteration counts were also reported, or if the machine and implementation details were given.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the rates follow from standard chain-rule identities, and the SIC-free loss emerges from simulation rather than by construction; the main caveat is that final figures may rely on the Jensen-approximate rates (14)-(16), a verifiability gap rather than a circular one.

full rationale

No equation in the paper reduces to its own input by construction. The constellation-constrained rates in (7)-(9) are expanded from the chain rule of mutual information in (10)-(13), with the conditional-entropy formula (5) credited to the external work [29]; the citation to the authors' own [19] for the form of the expansion ('the achievable rate of the common stream at user- k, k ∈ K, can be derived as [19]') is not load-bearing because the full expansion is displayed in the paper and rests on the standard chain rule [36]. The Jensen approximation in (6) and its rate-level versions (14)-(16) are adopted from the external reference [35] and used, in the paper's words, 'by using the approximation given by (14)-(16) during the optimization process' (Section IV-A); this is a surrogate objective, not a parameter fitted to the reported rates, so the SIC-free-versus-SIC comparison is not forced by any fitted input. Self-citations are motivational rather than evidentiary: the limit in (19), cited to the same-author preprint [37], is invoked to argue that SIC-free rates can approach SIC-based rates under strong finite-alphabet interference, but the numerical claims in Figures 3 and 6-9 are computed from the paper's own rate expressions under optimized precoders, so the central comparison does not reduce to [37]. Flagged limitation, weighed in the verdict: Section IV-A says only that (14)-(16) are used 'during the optimization process', and Section VI does not state whether the reported figures use the exact rates (7)-(9) or the approximations (14)-(16); since (6) is obtained by moving the noise expectation inside the logarithm and rescaling the squared distance by 1/2, its error is SNR-, constellation-, and interference-dependent and differs between the SIC-based and SIC-free expressions, so if the figures use (14)-(16) the 'minor loss' could reflect approximation error rather than true achievable rates. This is a correctness and reproducibility risk outside the circularity definition, because no target quantity is fitted and no equation is self-defined. The omitted proof of Proposition 3 is justified by the observation that precoder components outside the range of [h1,...,hK] 'do not affect the objective function of P1 and P3'; this is a standard range-space argument, not a self-referential step. Overall, the derivation chain is self-contained, and the modest score reflects only the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The rate expressions rest on the standard finite-alphabet mutual information formula and the paper's channel and CSI assumptions. No parameters are fitted to data, and no new entities are postulated. The main ledger items are the Jensen approximation used during optimization and the omitted proof of the low-dimensional subspace property.

assumptions (4)
  • standard math Mutual information expression for finite-alphabet Gaussian channels (Eq. (5) from [29]).
    The constellation-constrained rate expressions (7)-(16) are built directly on this formula.
  • domain assumption Jensen-based approximation in Eq. (6) is accurate enough to serve as the optimization objective.
    Used in Algorithms 1 and 4; fidelity to exact rate is not validated in numerical results.
  • domain assumption Perfect CSI, infinite block length, Gaussian noise, and independent zero-mean unit-variance symbols.
    Assumptions in Section II; needed for the rate expressions and for the claim that rates are achievable.
  • domain assumption Low-dimensional subspace property (Proposition 3): any non-trivial stationary point lies in the range of [h1,...,hK].
    Proof omitted as trivial; used to justify dimensionality reduction in Section V-B.

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Cite this review

Pith. "Pith review of SIC-Free Rate-Splitting Multiple Access: Constellation-Constrained Optimization and Application to Large-Scale Systems." pith.science (2026). https://pith.science/paper/YTROPG5X

@misc{pith2026250612668,
  author       = {Pith},
  title        = {Pith review of: SIC-Free Rate-Splitting Multiple Access: Constellation-Constrained Optimization and Application to Large-Scale Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YTROPG5X}},
  note         = {Machine review of arXiv:2506.12668}
}
read the original abstract

Rate-Splitting Multiple Access (RSMA) has been recognized as a promising multiple access technique for future wireless communication systems. Recent research demonstrates that RSMA can maintain its superiority without relying on Successive Interference Cancellation (SIC) receivers. In practical systems, SIC-free receivers are more attractive than SIC receivers because of their low complexity and latency. This paper evaluates the theoretical limits of RSMA with and without SIC receivers under finite constellations. We first derive the constellation-constrained rate expressions for RSMA. We then design algorithms based on projected subgradient ascent to optimize the precoders and maximize the weighted sum-rate or max-min fairness among users. To apply the proposed optimization algorithms to large-scale systems, one challenge lies in the exponentially increasing computational complexity brought about by the constellation-constrained rate expressions. In light of this, we propose methods to avoid such computational burden. Numerical results show that, under optimized precoders, SIC-free RSMA leads to minor losses in both weighted sum-rate and max-min fairness in comparison to RSMA with SIC receivers, making it a viable option for future implementations.

Figures

Figures reproduced from arXiv: 2506.12668 by the authors.

Figure 1
Figure 1. Single-layer RSMA with SIC and SIC-free receivers. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Illustration of user grouping. partitioned into K 2 groups, and each group contains two users. The elimination of inter-group interference is illustrated since signals carrying the common and private streams intended for a particular user do not propagate to other groups, although intra-group interference, i.e., interference caused by the private stream intended for a co-group user, potentially exists. In contrast t… view at source ↗
Figure 3
Figure 3. Ergodic SR performance. 0 5 10 15 20 25 30 35 40 SNR (dB) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Common stream power ratio SIC-based RSMA, 6 bits SIC-free RSMA, 6 bits SIC-based RSMA, 8 bits SIC-free RSMA, 8 bits [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Convergence of PSGA and GQMP. E. Performance in Large-Scale Systems We consider a large-scale rectangular antenna array with NT = 128, with 16 antennas in each row along the y-axis and 8 antennas in each column along the z-axis, serving 64 users. Figures 8 and 9 depict…
Figure 6
Figure 6. Figure 6: Rate region with NT = 2 and K = 2, {θ az 1 , θaz 2 } = {0, π/9}, K = 10 dB. served that the conclusions drawn from small-scale systems as discussed previously, i.e., RSMA schemes outperform SDMA in both sum-rate and MMF, and SIC-free RSMA preserves most of the superior…
Figure 7
Figure 7. Figure 7: Ergodic MMF performance. 5 10 15 20 25 30 SNR (dB) 40 60 80 100 120 140 160 180 200 CC sum-rate (bits per channel use) SIC-based RSMA (ordered) SIC-free RSMA (ordered) SDMA (ordered) SIC-based RSMA (unordered) SIC-free RSMA (unordered) SDMA (unordered) [PITH_FULL_IMAG…
Figure 8
Figure 8. Figure 8: Ergodic sum-rate performance in large-scale systems with [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

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Forward citations

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.