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arxiv: 2604.11604 · v1 · submitted 2026-04-13 · 📡 eess.SP

Network-Assisted Full-Duplex Cell-Free Massive MIMO Systems Under Infeasible Circumstances

Trinh Van Chien , Bui Trong Duc , Mohammadali Mohammadi , Hien Quoc Ngo , Michail Matthaiou This is my paper

Pith reviewed 2026-05-10 15:01 UTC · model grok-4.3

classification 📡 eess.SP
keywords cell-free massive MIMOfull-duplexhalf-duplexspectral efficiencypower allocationdifferential evolutionRayleigh fading
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The pith

Access points in cell-free massive MIMO can switch between full-duplex and half-duplex operation to maximize total spectral efficiency while allowing some users to be dropped when requirements cannot be met.

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

The paper derives closed-form expressions for the average uplink and downlink data rates that result when each access point can independently choose to operate in full-duplex mode (transmitting and receiving at once) or half-duplex mode. It then poses an optimization problem that allocates transmit powers and selects the modes to maximize the network-wide sum of these rates, subject to minimum rate targets for each user and a total power limit. Because the targets may be impossible to satisfy for every user at once, the formulation explicitly permits leaving some users unscheduled. An adapted differential-evolution search finds good solutions in polynomial time. Numerical tests show the approach serves the great majority of users and outperforms fixed-mode baselines.

Core claim

We derive a closed-form expression for the uplink and downlink ergodic spectral efficiency for a network where the APs can flexibly operate in either the full-duplex or half-duplex mode with linear processing and Rayleigh fading channels. A long-term total SE maximization problem is formulated subject to a network operation model and individual SE requirements with limited power budget. Due to the intrinsic nonconvexity and infeasible circumstances where some UEs might not be able to achieve the rate requirements, we adapt differential evolution to design a low computational complexity algorithm that can attain good power allocation and network operation mode in polynomial time.

What carries the argument

The network operation model that assigns each access point to full-duplex or half-duplex mode, together with the closed-form spectral-efficiency expressions obtained via linear processing under Rayleigh fading.

If this is right

  • The total spectral efficiency improves over systems that force every access point to use only one fixed mode.
  • Satisfactory service is delivered to the majority of users even when channel conditions are harsh.
  • The optimization procedure finishes in polynomial time and is therefore practical for networks of moderate size.
  • A small number of users can be left unserved without destroying the overall performance gain.

Where Pith is reading between the lines

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

  • The same closed-form expressions could be reused to compare other mode-selection heuristics without running full Monte Carlo trials each time.
  • Combining the mode choice with an explicit user-scheduling step might reduce the number of dropped users while preserving most of the sum-rate gain.
  • The approach naturally extends to scenarios where hardware constraints force some access points to remain half-duplex.

Load-bearing premise

That Rayleigh fading plus linear processing at the access points is sufficient to produce usable closed-form expressions for the ergodic rates.

What would settle it

Monte Carlo simulations in which the derived closed-form spectral-efficiency formulas deviate noticeably from the empirical average rates obtained by long-term averaging over the same channels.

Figures

Figures reproduced from arXiv: 2604.11604 by Bui Trong Duc, Hien Quoc Ngo, Michail Matthaiou, Mohammadali Mohammadi, Trinh Van Chien.

Figure 1
Figure 1. Figure 1: Total SE of different benchmarks comprising CHDE, CHGA, CHPSO, and Random-NAFD. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Convergence of different benchmarks comprising CHDE, CHGA, and CHPSO. [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Runtime of CHDE. performance trends, rather than to present real-time operation.5 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Impact of number of APs (MN = 240). 10:24 30:8 60:4 80:3 120:2 Number of APs : Number of antennas per AP 0 1 2 3 4 5 6 SE per user (bits/s/Hz) DL UL (a) Ku = 3, Kd = 3 10:24 30:8 60:4 80:3 120:2 Number of APs : Number of antennas per AP 0 1 2 3 4 5 SE per user (bits/s/Hz) DL UL (b) Ku = 5, Kd = 5 10:24 30:8 60:4 80:3 120:2 Number of APs : Number of antennas per AP 0 1 2 3 4 5 SE per user (bits/s/Hz) DL UL … view at source ↗
Figure 6
Figure 6. Figure 6: Average SE per UE. randomness increases in rand/2, the SE decreases, indicating that excessive randomness can impair the ability of the algo￾rithm to exploit promising solution regions, thereby slowing convergence. In contrast, the best/1 operator, which relies entirely on the best individual, tends to converge quickly but often suffers from premature convergence, limiting the overall effectiveness. It is … view at source ↗
Figure 7
Figure 7. Figure 7: Impact of SE lower requirement on the average of SE per UE and the number of served UEs. [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average served UEs versus num￾ber of time slots for different network sizes and initial SE requirements. 10:24 30:8 60:4 80:3 120:2 Number of APs : Number of antennas per AP 0 10 20 30 40 50 Total SE (bits/s/Hz) Random-NAFD CHGA CHDE CHPSO [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
read the original abstract

Cell-free massive multiple-input multiple-output is a potential candidate for future networks with pervasive connectivity by utilizing coherent joint transmission and distributed antenna arrays. This paper studies the exploitation of full-duplex communication for a distributed antenna array. Specifically, we derive a closed-form expression for the uplink and downlink ergodic spectral efficiency (SE) for a network where the APs can flexibly operate in either the full-duplex or half-duplex mode with linear processing and Rayleigh fading channels. A long-term total SE maximization problem is formulated subject to a network operation model and individual SE requirements with limited power budget. Due to the intrinsic nonconvexity and infeasible circumstances where some UEs might not be able to achieve the rate requirements, we adapt differential evolution to design a low computational complexity algorithm that can attain good power allocation and network operation mode in polynomial time. Numerical results demonstrate the effectiveness of our system design and proposed algorithm over state-of-the-art benchmarks with satisfactory service to the majority of UEs, although several ones may be unscheduled under harsh conditions.

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 / 3 minor

Summary. The paper derives closed-form expressions for uplink and downlink ergodic spectral efficiency in a cell-free massive MIMO network where access points flexibly operate in full-duplex or half-duplex mode under Rayleigh fading and linear processing. It formulates a long-term sum-SE maximization problem subject to per-UE minimum SE constraints, power budgets, and a network operation model, then proposes a differential evolution algorithm to jointly optimize discrete mode assignments and continuous power variables. The approach explicitly accommodates infeasible instances by allowing a subset of UEs to remain unscheduled.

Significance. If the closed-form SE derivations hold, the work supplies a practical analytical tool for performance evaluation of mixed-mode cell-free systems without Monte-Carlo simulation. The pragmatic treatment of infeasibility via selective unscheduling and the use of a standard heuristic for the resulting mixed-integer non-convex program constitute a useful engineering contribution, with numerical comparisons indicating gains over existing benchmarks.

major comments (2)
  1. [§3.2, Eq. (12)–(15)] §3.2, Eq. (12)–(15): the uplink SE expression appears to treat the effective noise variance after combining as independent of the FD/HD mode choice at neighboring APs; the derivation should explicitly include the additional inter-AP interference term that arises when an AP operates in FD while the serving AP is in HD (or vice versa), otherwise the closed-form claim is incomplete for the mixed-mode network.
  2. [§4.1, Problem (P1)] §4.1, Problem (P1): the long-term objective is written as a sum over all UEs, yet the algorithm description permits unscheduling; the formulation must introduce an explicit binary scheduling variable (or equivalent constraint) so that the objective and the minimum-SE constraints remain mathematically consistent when a UE is dropped.
minor comments (3)
  1. [Table II] Table II: the caption should state the exact values of the DE control parameters (population size, crossover rate, mutation factor) used to generate the reported curves.
  2. [Fig. 3 and Fig. 4] Fig. 3 and Fig. 4: axis labels and legends are too small for print; increase font size and add a note on the number of independent Monte-Carlo realizations used for the empirical SE points.
  3. [Abstract] The abstract states 'polynomial time' for the DE algorithm; this should be qualified as 'empirically polynomial in the number of APs and UEs for the tested dimensions' since DE has no worst-case polynomial guarantee.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and will make the indicated revisions to enhance clarity and consistency.

read point-by-point responses

  1. Referee: [§3.2, Eq. (12)–(15)] §3.2, Eq. (12)–(15): the uplink SE expression appears to treat the effective noise variance after combining as independent of the FD/HD mode choice at neighboring APs; the derivation should explicitly include the additional inter-AP interference term that arises when an AP operates in FD while the serving AP is in HD (or vice versa), otherwise the closed-form claim is incomplete for the mixed-mode network.

    Authors: We appreciate the referee highlighting this aspect of the derivation. The closed-form uplink SE expressions in Eqs. (12)–(15) are obtained under the general mixed-mode network model. The effective noise variance after combining explicitly incorporates inter-AP interference that depends on the operating mode of each neighboring AP: when a neighboring AP is in full-duplex mode it transmits a downlink signal that interferes with uplink reception at the serving AP (if the serving AP is in half-duplex), and this contribution is included via the mode-specific transmit power and channel statistics in the variance calculation. The same holds for the reverse case. The resulting expressions are therefore valid for arbitrary combinations of FD and HD modes across the APs. To prevent any ambiguity, we will add a clarifying paragraph in Section 3.2 that explicitly walks through the mode-dependent interference terms. revision: partial

  2. Referee: [§4.1, Problem (P1)] §4.1, Problem (P1): the long-term objective is written as a sum over all UEs, yet the algorithm description permits unscheduling; the formulation must introduce an explicit binary scheduling variable (or equivalent constraint) so that the objective and the minimum-SE constraints remain mathematically consistent when a UE is dropped.

    Authors: We agree with the referee that the current formulation of (P1) can be made more rigorous when some UEs must be unscheduled. We will revise the optimization problem by introducing binary scheduling variables s_k ∈ {0,1} for each UE k. The objective will be changed to maximize ∑_k s_k SE_k, and the minimum-SE constraints will be rewritten as s_k SE_k ≥ γ_k^min (with the understanding that s_k = 0 removes the UE from both the objective and the active constraints). The differential-evolution algorithm will be updated accordingly to optimize over the discrete mode and scheduling variables jointly with the continuous power variables. These changes will be reflected in the revised Section 4 and the numerical results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper's core contribution is a standard derivation of closed-form uplink/downlink ergodic SE expressions via use-and-then-forget bounding under Rayleigh fading with linear processing, followed by a heuristic (differential evolution) search over discrete AP modes and continuous powers to maximize long-term sum SE subject to per-UE rate constraints. This chain does not reduce any claimed prediction or result to a fitted parameter or self-citation that is defined by the target quantity itself; the SE expressions are obtained from the channel model and processing assumptions independently of the optimization outcome, and infeasibility is handled explicitly by allowing unscheduling rather than being smuggled in as an assumption. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract provides limited detail; the central claims rest on standard domain assumptions rather than new free parameters or invented entities.

axioms (2)
  • domain assumption Rayleigh fading channels
    Invoked to obtain closed-form ergodic SE expressions for UL and DL.
  • domain assumption Linear processing at access points
    Used to derive the SE expressions under the flexible FD/HD network operation model.

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