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arxiv: 1906.09026 · v1 · pith:NPZZ7HOWnew · submitted 2019-06-21 · 📡 eess.SP · cs.NI

Capacity Enhancement of Cooperative NOMA over Rician Fading Channels with Orbital Angular Momentum

Ahmed Al Amin , Bhaskara Narottama , Soo Young Shin This is my paper

Pith reviewed 2026-05-25 18:53 UTC · model grok-4.3

classification 📡 eess.SP cs.NI
keywords cooperative NOMAorbital angular momentumsum capacityRician fadingpower allocationwireless communication
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0 comments X

The pith

The CNOMA-OAM scheme achieves higher sum capacity than conventional CNOMA or OMA with OAM over Rician fading channels.

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

The paper proposes combining orbital angular momentum with cooperative non-orthogonal multiple access to raise the total achievable rate in wireless links. It derives capacity expressions for the new scheme, compares them analytically to standard cooperative NOMA and to orthogonal multiple access that also uses OAM, and studies how the fraction of power given to the OAM beam affects the outcome. Simulations confirm the analytical gains hold under the Rician channel model. A reader would care because higher sum capacity directly translates to supporting more simultaneous users or higher data volumes in future cellular networks without additional spectrum.

Core claim

The CNOMA-OAM scheme provides higher sum capacity compared to conventional CNOMA and conventional OMA with OAM when the wireless channels follow a Rician fading distribution, with the gain depending on the power allocation factor assigned to the OAM beam.

What carries the argument

The CNOMA-OAM transmission scheme that superimposes OAM beams onto cooperative NOMA signaling to multiplex users and increase overall capacity.

If this is right

  • Higher sum capacity follows directly when the OAM beam power is allocated near its optimum value.
  • The capacity advantage appears in both the derived closed-form expressions and the matching simulation curves.
  • The scheme remains compatible with existing cooperative relaying structures while adding the OAM degree of freedom.
  • Performance scales with the Rician factor, as stronger line-of-sight components preserve the OAM mode orthogonality.

Where Pith is reading between the lines

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

  • The same OAM multiplexing could be tested on other fading models such as Nakagami-m to check whether the reported gain pattern generalizes.
  • Real-world hardware trials would need to measure the actual overhead of generating and detecting OAM modes at the relay.
  • Extending the power-allocation analysis to multiple OAM modes or more than two users would reveal whether the capacity scaling continues.
  • Integration questions such as synchronization between the NOMA power split and the OAM beam former remain open for implementation studies.

Load-bearing premise

The wireless channels follow a Rician fading distribution and the power allocation factor for the OAM beam can be chosen optimally without extra overhead or errors.

What would settle it

An analytical derivation or Monte-Carlo simulation under Rician fading in which the CNOMA-OAM sum capacity remains below that of conventional CNOMA for every tested power allocation factor.

Figures

Figures reproduced from arXiv: 1906.09026 by Ahmed Al Amin, Bhaskara Narottama, Soo Young Shin.

Figure 1
Figure 1. Figure 1: System model of CNOMA-OAM scheme. is denoted as h1,OAM. Moreover, l represents the considered OAM mode. To reduce attenuation, low number of OAM mode, i.e. l = 1, is considered [11]. Since OAM has better performance in line-of-sight (LOS) condition and the user with better channel condition, that is why OAM is only considered for CCU in Fig.1 [12]. pN1 , pN2 and pF are the allocated powers for the CCU, OAM… view at source ↗
Figure 2
Figure 2. Figure 2: Protocol for the proposed CNOMA-OAM. Cx2 = 1 2 log2 (1 + min(pN1 |h1| 2 , |h3| 2 )ρ)). (9) Furthermore, the capacity of x3 by OAM beam can be acquired as below Cx3 = 1 2 log2 (1 + pN2 ρµ 2 k). (10) where, K is the rank of the OAM channel matrix [16,21]. So, the sum capacity is given by CCCU = E[Cx1 ] + E[Cx3 ], (11) CCEU = E[Cx2 ], (12) Csum = CCCU + CCEU , (13) where, E[.] represents the expectation opera… view at source ↗
Figure 3
Figure 3. Figure 3: SC comparisons with respect to pN2 . Moreover, D(pN1 ρ) can be derived as D(ρ). Similarly, the exact expression of Cx2 can be derived as [8] C exact x2 = 1 2ln2 AwAy X∞ k=0 X∞ n=0 B˜w(n)B˜y(k)n!k! Xn i=0 Xk j=0 (i + j) i!j! a i w + (ay/pN1 ) j ρ ( i + j) e aw+(ay/pN1 ) ρ Γ(−i−j, aw + (ay/pN1 ) ρ ) (24) Moreover, the OAM channel is performing at LOS communi￾cation for the CCU and CCU has better channel cond… view at source ↗
Figure 5
Figure 5. Figure 5: Capacity comparisons of CEU with respect to SNR. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: SC comparisons with respect to SNR. and pF = 0.6 are considered for SC versus pN2 comparison for the proposed scheme. As presented in the [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Moreover, CNOMA-OAM provides significantly higher [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

This letter proposes the usage of orbital angular momentum (OAM) for cooperative non-orthogonal multiple access (CNOMA) to enhance sum capacity (SC) for the future cellular communication system. The proposed CNOMA-OAM scheme is analyzed and compared with other schemes, i.e., conventional CNOMA, conventional orthogonal multiple access (OMA) with OAM. The impact of the power allocation factor for OAM beam over SC is also analyzed. The analytical result is justified by simulation results which demonstrate that the proposed CNOMA-OAM provides higher SC compared to other schemes.

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

0 major / 2 minor

Summary. The manuscript proposes a cooperative NOMA scheme augmented with orbital angular momentum (OAM) beams over Rician fading channels, claiming that the resulting CNOMA-OAM scheme achieves higher sum capacity than both conventional CNOMA and conventional OMA with OAM. Analytical expressions for sum capacity are derived, the effect of the OAM-beam power allocation factor is analyzed, and Monte-Carlo simulations are presented to confirm the analytical results and the claimed performance ordering.

Significance. If the central claim holds, the work illustrates a concrete capacity gain obtainable by combining OAM with cooperative NOMA under standard Rician modeling. The provision of closed-form expressions together with Monte-Carlo validation constitutes a verifiable contribution that supports reproducibility. The explicit examination of the power-allocation factor further strengthens the design-oriented value of the analysis.

minor comments (2)
  1. The abstract states that analytical results are justified by simulation but supplies neither the key closed-form expressions nor any description of Monte-Carlo parameters (number of trials, error-bar reporting, or data-exclusion rules). Adding a concise statement of these elements would improve transparency without altering the technical content.
  2. Figure captions and axis labels should explicitly state the Rician K-factor, SNR range, and number of channel realizations used, so that readers can directly reproduce the plotted curves.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivations are self-contained

full rationale

The paper presents closed-form capacity expressions for CNOMA-OAM under Rician fading, optimizes the OAM power allocation factor analytically, and validates via Monte-Carlo simulation against conventional CNOMA and OMA. These steps rely on standard channel modeling and optimization rather than fitting parameters to the demonstration data or reducing claims to self-citations. No self-definitional, fitted-prediction, or load-bearing self-citation patterns appear in the derivation chain.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; free parameters and modeling assumptions are inferred from the stated comparisons and the mention of power allocation analysis.

free parameters (1)
  • power allocation factor for OAM beam
    Its impact on sum capacity is explicitly analyzed, implying it is treated as a tunable or fitted quantity.
axioms (2)
  • domain assumption Channels obey Rician fading statistics
    The title and abstract state that all analysis occurs over Rician fading channels.
  • domain assumption Perfect channel state information is available
    Standard assumption in NOMA capacity derivations unless otherwise stated; not contradicted by abstract.

pith-pipeline@v0.9.0 · 5624 in / 1337 out tokens · 27781 ms · 2026-05-25T18:53:38.386474+00:00 · methodology

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Reference graph

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