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arxiv: 2604.14754 · v1 · submitted 2026-04-16 · 📡 eess.SP

Utilizing Improper Gaussian Signaling for Downlink Rate-Splitting Multiple Access with Imperfect Successive Interference Cancellation

Wanting Shi , Hao Cheng , Zhe Li , Yili Xia , Wenjiang Pei This is my paper

Pith reviewed 2026-05-10 10:46 UTC · model grok-4.3

classification 📡 eess.SP
keywords rate-splitting multiple accessimproper Gaussian signalingimperfect successive interference cancellationdownlinkSISOsum-rate maximizationreinforcement learning
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The pith

Improper Gaussian signaling on the common stream counters residual interference in RSMA with imperfect SIC.

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

The paper demonstrates that improper Gaussian signaling applied only to the common stream in a SISO rate-splitting multiple access system reduces the impact of residual interference caused by imperfect successive interference cancellation. Proper Gaussian signaling is retained for the private streams. For private rate maximization the optimal impropriety degree reaches its highest allowed value, while closed-form solutions exist for common rate maximization when monotonicity conditions hold. A soft actor-critic algorithm addresses the non-convex sum-rate problem. Numerical evaluations show consistent rate gains over proper Gaussian signaling, with the advantage growing as SIC imperfection increases.

Core claim

By applying improper Gaussian signaling exclusively to the common stream while using proper Gaussian signaling for private streams in a basic SISO downlink RSMA setup, the residual interference from imperfect SIC is effectively mitigated. The optimal impropriety degree for private rate maximization attains its maximum. Closed-form optimal solutions are derived for common rate maximization under rigorous monotonicity conditions. A soft actor-critic algorithm optimizes the non-convex sum-rate maximization problem. Numerical results confirm that this IGS approach outperforms PGS, with the performance gap widening as the level of SIC imperfection increases.

What carries the argument

Improper Gaussian signaling (IGS) with non-zero pseudo-variance applied selectively to the common stream to suppress residual interference after imperfect SIC in RSMA.

If this is right

  • Private rates reach their maximum when the impropriety degree on the common stream is set to its upper limit.
  • Closed-form expressions for the optimal impropriety degree exist for common-rate maximization whenever the relevant rate functions satisfy the stated monotonicity conditions.
  • The soft actor-critic algorithm yields practical solutions for the joint sum-rate optimization.
  • Rate gains from IGS widen steadily as the SIC imperfection factor increases.

Where Pith is reading between the lines

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

  • The SISO findings may extend to MIMO RSMA if independent control of stream impropriety remains feasible under spatial correlation.
  • IGS could complement rather than replace advanced SIC techniques in practical deployments.
  • Hardware tests with real IQ imbalance would clarify whether the reported gains survive non-ideal transmitter effects.
  • The signaling strategy might transfer to other multiple-access schemes that suffer from imperfect decoding.

Load-bearing premise

The impropriety degree on the common stream can be controlled independently of the private streams without violating power constraints or SISO channel assumptions.

What would settle it

A simulation or measurement in the same SISO setup where the sum rate at maximum common-stream impropriety falls below the proper Gaussian signaling baseline even at high SIC imperfection levels would disprove the core effectiveness claim.

Figures

Figures reproduced from arXiv: 2604.14754 by Hao Cheng, Wanting Shi, Wenjiang Pei, Yili Xia, Zhe Li.

Figure 1
Figure 1. Figure 1: Comparison of sum private rate curves for different SNR. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of common rate curves versus κ under different λ and Rmin [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Optimal κ values under different λ values. (a) Rmin = 0.2 (b)Rmin = 0.5. [2] Y. Mao, O. Dizdar, B. Clerckx, R. Schober, P. Popovski, and H. V. Poor, “Rate-splitting multiple access: Fundamentals, survey, and future research trends,” IEEE Commun. Surv. Tutor., vol. 24, no. 4, pp. 2073– 2126, 2022. [3] M. Soleymani, I. Santamaria, and E. A. Jorswieck, “Rate splitting in MIMO RIS-assisted systems with hardwar… view at source ↗
read the original abstract

To mitigate the residual interference from imperfect successive interference cancellation (SIC) in Rate-Splitting Multiple Access (RSMA), this paper incorporates improper Gaussian signaling (IGS) into the downlink RSMA framework. Unlike existing RSMA--IGS works that embed impropriety within IQ-imbalanced frameworks, we show that IGS alone effectively counters SIC-induced residual interference. For a basic SISO setup with IGS on the common stream and PGS on private streams, we establish three key results: the optimal impropriety degree for private rate maximization attains its maximum; closed-form optimal solutions with rigorous monotonicity conditions are derived for common rate maximization; and a soft actor-critic (SAC) algorithm is developed for the non-convex sum rate problem. Numerical results show that IGS consistently outperforms PGS, with the gain widening as SIC imperfection increases.

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

1 major / 2 minor

Summary. The paper claims that applying improper Gaussian signaling (IGS) only to the common stream (with proper Gaussian signaling on private streams) in a basic SISO downlink RSMA setup mitigates residual interference from imperfect SIC. It derives that the optimal impropriety degree for private-rate maximization is the maximum value; provides closed-form optimal solutions for common-rate maximization under stated monotonicity conditions on the impropriety parameter; develops a soft actor-critic (SAC) algorithm for the non-convex sum-rate maximization; and shows numerically that IGS outperforms PGS with the performance gap widening as SIC imperfection increases.

Significance. If the derivations and monotonicity conditions hold under the stated assumptions, the work provides a practical, hardware-light enhancement to RSMA by using IGS to counter imperfect SIC without embedding it in IQ-imbalance models. Credit is due for the closed-form expressions (with explicit monotonicity conditions), the SAC optimizer for the sum-rate problem, and the numerical validation demonstrating consistent gains. These elements could inform low-complexity transceiver design in multi-user downlink scenarios where SIC errors are non-negligible.

major comments (1)
  1. [§IV.B] §IV.B (common-rate maximization): the closed-form optimal impropriety degree rests on rigorous monotonicity conditions with respect to the impropriety parameter. When IGS is applied solely to the common stream while private streams remain PGS, the residual interference term after imperfect SIC depends on the common signal's pseudo-variance; this couples the effective covariance matrix to the impropriety degree and may violate the assumed monotonicity for nonzero SIC imperfection factors, undermining the closed-form claim.
minor comments (2)
  1. [§II] The SISO assumption and independent control of impropriety on the common stream (without side effects on private streams or channel statistics) should be stated explicitly in the system model section to clarify the scope.
  2. [§V] Numerical results section: report standard deviations or confidence intervals on the plotted rate gains to allow assessment of statistical reliability across Monte Carlo trials.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the sole major comment below, providing clarification on the derivations in Section IV.B while maintaining the integrity of our claims.

read point-by-point responses

  1. Referee: [§IV.B] §IV.B (common-rate maximization): the closed-form optimal impropriety degree rests on rigorous monotonicity conditions with respect to the impropriety parameter. When IGS is applied solely to the common stream while private streams remain PGS, the residual interference term after imperfect SIC depends on the common signal's pseudo-variance; this couples the effective covariance matrix to the impropriety degree and may violate the assumed monotonicity for nonzero SIC imperfection factors, undermining the closed-form claim.

    Authors: We appreciate the referee highlighting this potential coupling. In deriving the closed-form solution for common-rate maximization in §IV.B, the monotonicity conditions explicitly incorporate the dependence of the residual interference on the common stream's pseudo-variance. The effective SINR after imperfect SIC is expressed as a function of both the covariance and pseudo-covariance matrices, with the SIC error factor multiplying the pseudo-variance term. The proof proceeds by computing the derivative of the common rate w.r.t. the impropriety degree κ and showing that, under the stated assumptions (non-negative channel gains, fixed power split, and the given bounds on κ), this derivative does not change sign even when the residual term is included. The conditions ensure the desired-signal benefit from IGS dominates any increase in residual interference. These steps are rigorous within the SISO setup and have been cross-verified numerically for nonzero SIC imperfection. We are prepared to expand the appendix with an explicit derivative expression if that would aid clarity. revision: partial

Circularity Check

0 steps flagged

Derivation chain remains self-contained with no reductions to inputs by construction.

full rationale

The paper's key results—optimal impropriety degree for private rates, closed-form common-rate solutions under stated monotonicity conditions, and SAC-based sum-rate optimization—follow from standard mutual-information expressions for IGS/PGS under imperfect SIC in SISO RSMA. Rate formulas are derived from conventional covariance and pseudo-covariance matrices without redefining quantities in terms of the target optima or fitting parameters to the same data being predicted. No load-bearing self-citations, uniqueness theorems imported from the authors' prior work, or ansatzes smuggled via citation appear in the abstract or described derivation steps. The monotonicity conditions are presented as derived properties rather than assumed inputs, keeping the chain independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the work relies on standard domain assumptions in wireless communications such as additive noise and channel models; no new entities are introduced and no free parameters are explicitly fitted beyond optimization variables. Full details unavailable.

axioms (1)
  • domain assumption Standard assumptions on additive white Gaussian noise and perfect channel state information at transmitter for rate calculations
    Implicit in all rate expressions and optimization for RSMA and IGS.

pith-pipeline@v0.9.0 · 5457 in / 1331 out tokens · 51885 ms · 2026-05-10T10:46:51.470884+00:00 · methodology

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Reference graph

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