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arxiv: 1907.11264 · v1 · pith:JL5D6URGnew · submitted 2019-07-25 · 💻 cs.NI · math.ST· stat.AP· stat.TH

Delay Analysis in Full-Duplex Heterogeneous Cellular Networks

Leila Marandi , Mansour Naslcheraghi , Seyed Ali Ghorashi , Mohammad Shikh-Bahaei This is my paper

Pith reviewed 2026-05-24 15:39 UTC · model grok-4.3

classification 💻 cs.NI math.STstat.APstat.TH
keywords full-duplexheterogeneous networkslocal delaystochastic geometryenergy efficiencyself-interference cancellationdownlinkcellular networks
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The pith

Distance-based duplex switching enables tractable local delay and energy efficiency analysis in full-duplex HetNets via stochastic geometry despite imperfect self-interference cancellation.

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

The paper establishes that users in heterogeneous cellular networks can be assigned full-duplex or half-duplex operation according to their distance from the serving base station, yielding closed-form expressions for downlink local delay, defined as the average number of time slots until successful transmission. This modeling choice matters because it lets the analysis account for residual self-interference in practical full-duplex systems while still using stochastic geometry tools that average over random base-station and user locations. The same framework is then used to compare energy efficiency between the two duplex modes when local delay is taken into account. Extensive Monte Carlo simulations are presented to check how the derived expressions behave across changes in network density, threshold distance, and cancellation quality.

Core claim

By conditioning duplex mode on a distance threshold from the serving base station, the authors derive the local delay for the downlink in a two-tier heterogeneous network under a Poisson point process model, incorporating the effects of imperfect self-interference cancellation in full-duplex links and the absence of such cancellation in half-duplex links, then extend the same conditioning to obtain energy-efficiency expressions that incorporate the local-delay cost for both modes.

What carries the argument

Distance-threshold duplex-mode selection applied inside a stochastic-geometry model of heterogeneous cellular networks to compute local delay.

If this is right

  • Local delay can be expressed in closed form for both half-duplex and full-duplex operation once the distance threshold is fixed.
  • Energy efficiency for each mode follows directly once local delay is known, allowing direct numerical comparison.
  • Performance trends versus network density, path-loss exponent, and residual self-interference power become visible from the derived formulas.
  • The model supplies a concrete way to trade spectral-efficiency gains of full-duplex against the extra delay caused by residual interference.

Where Pith is reading between the lines

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

  • The same threshold logic could be applied to uplink traffic or to multi-antenna base stations without changing the underlying stochastic-geometry machinery.
  • Dynamic adjustment of the threshold according to instantaneous load or measured cancellation quality would be a natural next modeling step.
  • The framework highlights a concrete design knob (the distance threshold) that network operators could tune to meet target delay or energy budgets.

Load-bearing premise

There exists a fixed distance threshold that keeps both the local-delay probability and the resulting energy-efficiency expressions analytically tractable when imperfect self-interference cancellation is present.

What would settle it

Monte Carlo simulations of the same two-tier network with the proposed distance-based switching rule produce local-delay curves that deviate substantially from the paper's closed-form expressions over a range of base-station densities and cancellation levels.

Figures

Figures reproduced from arXiv: 1907.11264 by Leila Marandi, Mansour Naslcheraghi, Mohammad Shikh-Bahaei, Seyed Ali Ghorashi.

Figure 1
Figure 1. Figure 1: An illustration of three-tier HetNet with hybrid HD/FD duplexing modes along with the desired and interfering signals. TABLE I: SUMMARY OF NOTATION Notation Description Φk, Φu Point Process of BSs in tier k/ Point Process of users Φja, ΦFD ja , ΦHD ja Point Process of active FD BSs/ Point Process of active HD BSs in tier j λk, λu Density of BSs in tier k/ density of users pk, pu Transmit power of BSs in ti… view at source ↗
Figure 3
Figure 3. Figure 3: Local Delay for a typical user FD and HD in the hybrid network and EE in three-tier hybrid systems versus SIR threshold τ for different values of silent probability, where α1 = α2 = αu = 3.5, λu = 50  users km2  , λ3 = 4λ2 = 8λ1  BSs km2  . (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Local Delay for a typical user FD and HD in the hybrid network and EE versus SIR threshold τ for different values of λ2 λ1 , where α1 = α2 = αu = 3.5, χ1 = χ2 = 0.5 and λu = 50  users km2  . (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 2
Figure 2. Figure 2: Local Delay for a typical user FD and HD in the hybrid network and EE versus SIR threshold τ for different values of silent probability, where α1 = α2 = αu = 3.5, λu = 10λ2 = 50λ1  users/BSs km2  . V. CONCLUSION We analyzed the local delay of K-tier HetNet with hybrid HD/FD communications. By using tools from the stochastic geometry, we derived the local delay expression for both HD and FD modes. Analyti… view at source ↗
Figure 6
Figure 6. Figure 6: Local Delay for a typical user FD in the hybrid network versus SIR threshold τ for different values of β, where α1 = α2 = αu = 3.5, χ1 = χ2 = 0.5, λu = 10λ2 = 50λ1  users/BSs km2  [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Local Delay in two tiers versus SIR threshold τ for different silent probabilities, where α1 = α2 = αu = 3.5, λu = 10λ2 = 50λ1  users/BSs km2  . to be symmetric. FD communications with asymmetric data and a dissimilar channel is another worthwhile open problem to pursue. APPENDIX A. Proof for Lemma 1 The event of rk ≤ ϑk for FD users, the association proba￾bility with the kth tier can be given as A FD k … view at source ↗
read the original abstract

Heterogeneous networks (HetNets) as a combination of macro cells and small cells are used to increase the cellular network's capacity, and present a perfect solution for high-speed communications. Increasing area spectrum efficiency and capacity of HetNets largely depends on the high speed of backhaul links. One effective way which is currently utilized in HetNets is the use of full-duplex (FD) technology that potentially doubles the spectral efficiency without the need for additional spectrum. On the other hand, one of the most critical network design requirements is delay, which is a key representation of the quality of service (QoS) in modern cellular networks. In this paper, by utilizing tools from the stochastic geometry, we analyze the local delay for downlink (DL) channel, which is typically defined as the mean number of required time slots for a successful communication. Given imperfect self-interference (SI) cancellation in practical FD communications, we utilize duplex mode (half-duplex (HD) or FD) for each user based on the distance from its serving base station (BS). Further, we aim to investigate the energy efficiency (EE) for both duplexing modes, i.e., HD and FD, by considering local delay. We conduct extensive simulations to validate system performance in terms of local delay versus different system key parameters.

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 manuscript analyzes local delay in the downlink of full-duplex heterogeneous cellular networks via stochastic geometry. It selects HD or FD mode per user according to distance from the serving BS to accommodate imperfect self-interference cancellation, derives local-delay expressions, and evaluates energy efficiency for both modes while incorporating local delay; extensive simulations are used for validation.

Significance. If the distance-threshold mode selection preserves analytical tractability of the local-delay expressions under a PPP HetNet with residual SI, the work supplies useful design insights on delay-EE trade-offs in FD HetNets. Credit is due for employing standard stochastic-geometry tools and for providing simulation validation. The significance is reduced by the absence of explicit statements on whether the resulting coverage-probability integrals remain closed-form.

major comments (1)
  1. [Abstract] Abstract (and the modeling choice described therein): the distance-threshold rule for assigning HD/FD modes is load-bearing for the central claim of tractable local-delay expressions. Conditioning the serving link on distance to the nearest BS and then re-labeling interfering BSs according to the same threshold generally violates the independence and displacement properties required for a closed-form Laplace transform of aggregate interference under a PPP; the manuscript must show in which section the coverage probability or local-delay integral is obtained and whether further approximations beyond Rayleigh fading and power-law path loss are introduced.
minor comments (1)
  1. The abstract supplies no error bars on the simulation results, no explicit values for path-loss exponents or fading distributions, and no statement on whether the distance threshold is optimized, fixed, or fitted.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments. We address the major comment below, clarifying the derivation approach and tractability without misrepresenting the analysis.

read point-by-point responses

  1. Referee: [Abstract] Abstract (and the modeling choice described therein): the distance-threshold rule for assigning HD/FD modes is load-bearing for the central claim of tractable local-delay expressions. Conditioning the serving link on distance to the nearest BS and then re-labeling interfering BSs according to the same threshold generally violates the independence and displacement properties required for a closed-form Laplace transform of aggregate interference under a PPP; the manuscript must show in which section the coverage probability or local-delay integral is obtained and whether further approximations beyond Rayleigh fading and power-law path loss are introduced.

    Authors: The local delay expressions are derived in Section III (Theorems 1 and 2). We condition on the serving distance r to fix the mode for the typical link. For the interference, the PGFL of the PPP is applied with independent thinning: each interfering BS selects its mode independently according to the distribution of its own serving distance (derived from the PPP association), yielding an exact integral form for coverage probability under Rayleigh fading and power-law path loss. No additional approximations are introduced. The resulting expressions involve single-fold integrals that are numerically computable but not closed-form without integration; we will revise the abstract and Section I to explicitly state the section and the integral nature of the results. revision: partial

Circularity Check

0 steps flagged

No circularity: standard SG derivation with independent modeling choice

full rationale

The paper applies standard stochastic geometry (PPP HetNet, Laplace transforms of interference, local delay as 1/P(success)) to derive expressions for DL local delay under distance-based HD/FD mode selection and imperfect SI. The distance threshold is introduced as an explicit modeling assumption to keep analysis tractable; it does not redefine any target metric in terms of itself, nor does any reported prediction reduce to a fitted parameter or self-citation chain. No load-bearing uniqueness theorems or ansatzes are imported from the authors' prior work. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard domain assumptions from stochastic geometry wireless literature (Poisson point process for base stations, Rayleigh fading, path-loss exponent) plus the modeling choice of a distance threshold for duplex mode; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Base station locations follow a homogeneous Poisson point process
    Invoked when applying stochastic geometry tools to derive local delay expressions
  • domain assumption Imperfect self-interference cancellation can be captured by a residual interference term whose statistics allow closed-form success probability
    Stated when the paper conditions the duplex-mode choice on distance

pith-pipeline@v0.9.0 · 5781 in / 1422 out tokens · 22868 ms · 2026-05-24T15:39:07.443734+00:00 · methodology

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Reference graph

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