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arxiv: 1907.02648 · v1 · pith:RO7GKLPEnew · submitted 2019-07-03 · 💻 cs.IT · eess.SP· math.IT

What is the Benefit of Code-domain NOMA in Massive MIMO?

Mai T. P. Le , Luca Sanguinetti , Emil Bj\"ornson , Maria-Gabriella Di Benedetto This is my paper

Pith reviewed 2026-05-25 09:51 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords Massive MIMONOMAcode-domain NOMAspectral efficiencyfavorable propagationplanar antenna arraysuser clustering
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The pith

Code-domain NOMA increases spectral efficiency in Massive MIMO when user equipments are spatially close.

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

This paper examines whether code-domain non-orthogonal multiple access can improve Massive MIMO performance in the standard regime where the number of users K is less than the number of base station antennas M. It focuses on cases of poor favorable propagation that arise when user equipments are located close together. Numerical results indicate that planar antenna arrays can achieve higher spectral efficiency by applying NOMA in these practical clustered-user scenarios.

Core claim

While NOMA has been shown to help overloaded Massive MIMO systems where K exceeds M, code-domain NOMA can also raise spectral efficiency in the classical K less than M regime when favorable propagation is degraded by spatially close UEs, as demonstrated by simulations using planar arrays.

What carries the argument

Code-domain NOMA combined with Massive MIMO precoding to manage interference arising from poor favorable propagation conditions.

If this is right

  • Massive MIMO systems can achieve better spectral efficiency by incorporating code-domain NOMA when users cluster spatially.
  • Planar antenna arrays receive particular performance gains from NOMA in scenarios with close user equipments.
  • The benefits appear without requiring an increase in the number of base station antennas.

Where Pith is reading between the lines

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

  • The gains may appear in other array geometries if similar spatial clustering occurs.
  • System designers could consider NOMA as an option alongside antenna count increases in dense user settings.
  • The results point toward potential advantages in indoor or urban deployments where users naturally group together.

Load-bearing premise

The chosen simulation parameters and channel models accurately represent real-world conditions with spatially close UEs that produce poor favorable propagation.

What would settle it

A field measurement in an environment with spatially close users that shows no spectral efficiency gain from adding code-domain NOMA to Massive MIMO.

Figures

Figures reproduced from arXiv: 1907.02648 by Emil Bj\"ornson, Luca Sanguinetti, Mai T. P. Le, Maria-Gabriella Di Benedetto.

Figure 2
Figure 2. Figure 2: Behaviour of the variance defined in (16) for the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: Average sum SE for a single-cell two-user setup with [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Average sum SE for the multi-cell K-users setup with ∆ = 2◦ vs. K with mMIMO and mMIMO-NOMA for N ∈ {2, 4, 8}. The 2D and 3D models are both considered. favorable propagation conditions between the UEs. We stress that there are important use cases where this scenario may occur, for example, in stadiums, train stations, public events, and so forth. With NOMA, each cluster is divided into K/N (which is assum… view at source ↗
read the original abstract

In overloaded Massive MIMO systems, wherein the number K of user equipments (UEs) exceeds the number of base station antennas M, it has recently been shown that non-orthogonal multiple access (NOMA) can increase performance. This paper aims at identifying cases of the classical operating regime K < M, where code-domain NOMA can also improve the spectral efficiency of Massive MIMO. Particular attention is given to use cases in which poor favorable propagation conditions are experienced. Numerical results show that Massive MIMO with planar antenna arrays can benefit from NOMA in practical scenarios where the UEs are spatially close to each other.

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 / 1 minor

Summary. The paper investigates whether code-domain NOMA can improve spectral efficiency in Massive MIMO systems in the classical regime K < M, with particular focus on poor favorable propagation conditions arising when UEs are spatially close. It concludes, based on numerical simulations with planar antenna arrays, that NOMA provides benefits in such practical scenarios.

Significance. If the numerical findings are robust, the work would be significant for identifying new operating regimes where NOMA augments Massive MIMO beyond overloaded cases, particularly for correlated users. The reliance on numerical experiments to demonstrate the effect under poor FP is a clear strength of the approach.

major comments (1)
  1. [Numerical Results] Numerical Results section: the headline claim that NOMA improves SE for planar arrays when UEs are spatially close rests on the implicit assumption that the chosen spatial correlation, path-loss, and antenna response models faithfully reproduce the eigenvalue spread of the Gram matrix that occurs with physically close UEs. No sensitivity analysis or comparison against alternative correlation models is provided, so it is unclear whether the reported NOMA gain is general or an artifact of the specific modeling choices.
minor comments (1)
  1. [Abstract] Abstract: the range of K/M ratios and the precise definition of 'spatially close' used in the simulations could be stated more explicitly.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: Numerical Results section: the headline claim that NOMA improves SE for planar arrays when UEs are spatially close rests on the implicit assumption that the chosen spatial correlation, path-loss, and antenna response models faithfully reproduce the eigenvalue spread of the Gram matrix that occurs with physically close UEs. No sensitivity analysis or comparison against alternative correlation models is provided, so it is unclear whether the reported NOMA gain is general or an artifact of the specific modeling choices.

    Authors: We agree that additional justification and sensitivity checks would strengthen the presentation. The models in the paper follow standard choices in the Massive MIMO literature (exponential spatial correlation with coefficient 0.9 to induce poor favorable propagation for nearby UEs, 3GPP urban micro path-loss, and the standard uniform planar array response vector). These are selected precisely because they produce the high channel correlation (and thus large eigenvalue spread of the Gram matrix) that occurs when UEs are physically close. In the revised version we will add a dedicated paragraph in the Numerical Results section that (i) recalls why these parameters reproduce the target eigenvalue spread and (ii) reports a brief sensitivity study varying the correlation coefficient over [0.7,0.95] together with a comparison against the one-ring scattering model. The NOMA gain remains visible across this range, supporting the claim that the benefit is not an artifact of one particular parameterization. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on independent numerical simulations

full rationale

The paper presents no derivation chain or first-principles result that reduces to its own inputs. Its central claim is supported solely by Monte Carlo simulations of achievable spectral efficiency under standard channel models (correlated Rayleigh fading, planar arrays, path-loss). No parameters are fitted to a subset of data and then relabeled as predictions, no self-citations supply load-bearing uniqueness theorems, and no ansatz is smuggled in. The simulation setup is externally falsifiable and does not contain the target NOMA gain by construction, satisfying the criteria for a self-contained, non-circular analysis.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim depends on standard assumptions in MIMO and NOMA literature regarding channel models and the ability to perform joint processing.

free parameters (1)
  • UE spatial distribution and channel correlation parameters
    The benefit is shown for specific UE placements that induce poor favorable propagation, which are chosen in the simulations.
axioms (1)
  • domain assumption The system model allows superposition of NOMA codes on top of massive MIMO precoding without significant interference issues
    This is the basis for investigating the combination.

pith-pipeline@v0.9.0 · 5639 in / 1201 out tokens · 69254 ms · 2026-05-25T09:51:53.680456+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages

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