Adaptive Cell Range Expansion in Multi-Band UAV Communication Networks

Ian P. Roberts; Xinsong Feng

REVIEW 3 major objections 4 minor 15 references

Adaptive Cell Range Expansion in Multi-Band UAV Communication Networks

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A closed-form bias factor computed from network statistics can offload users to mmWave UAVs, improving coverage and data rates in multi-band UAV networks.

desk verdict The closed-form bias and antenna-gain approximation are genuinely new, but the coverage/SE analysis conditions on the wrong distance distribution, so the central analytical claims don't describe the proposed policy. read the letter →

arxiv 2411.18123 v1 pith:LKWPEIZF submitted 2024-11-27 cs.IT eess.SPmath.IT

Xinsong Feng , Ian P. Roberts This is my paper · ORCID

classification cs.ITeess.SPmath.IT MSC 60D0560G5594A05

keywords UAVnetworksmillimeter-wavecellrangeexpansionstochasticgeometrycoverageprobabilityspectralefficiencyPoissonpointprocessbiaseduserassociation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that user association in a two-band UAV network can be made both simple and adaptive by biasing users toward millimeter-wave UAVs with a bias factor $\beta$ computed in closed form from network statistics. The authors model low-frequency and mmWave UAVs as independent Poisson point processes and introduce a refined distribution for the antenna gain that an interfering mmWave UAV presents toward a non-serving user. Under the proposed association rule $\beta S_m > S_{\mathrm{lf}}$, they derive the association probability, coverage probability, and average spectral efficiency as explicit stochastic-geometry expressions. The payoff, if correct, is that an operator can compute the bias from density, height, transmit-power, and path-loss parameters alone, and reap higher coverage and per-user rates than conventional maximum-average-power association without real-time tuning.

What carries the argument

The central object is the closed-form bias factor $\beta = \frac{\zeta\beta_0}{1+(\beta_0-1)\exp(\alpha(1-\tau))}$, a logistic function of the expected spectral-efficiency ratio $\tau$ between the mmWave and low-frequency tiers, standardized by $\zeta$, the ratio of average received powers. It appears in the association rule $\beta S_m > S_{\mathrm{lf}}$. Alongside it, the key mechanism is a two-state model for the antenna gain of interfering mmWave UAVs: gain $G_M$ with probability $p_\theta p_\phi$ and $G_S$ otherwise, where the main-lobe elevation probability $p_\phi$ is approximated from the serving-distance distribution of the nearest mmWave UAV, Eq. (11). This gain law feeds the Laplace transforms of per-tier interference, which are integrated against the serving-distance densities to produce the association probability, coverage probability, and spectral efficiency.

What would settle it

Recompute the coverage probability and spectral efficiency while explicitly conditioning the mmWave serving-distance distribution on the association event $\beta S_m > S_{\mathrm{lf}}$ (so the serving distance is drawn from the biased-offloaded set of users), and compare the results with the paper's Eq. (20) and spectral-efficiency expressions; a material difference would show that the unconditional nearest-UAV distance used for $P_{Cm}$ does not represent users actually served under the bias rule.

Watch

Extended reading notes

Core claim

The paper's central claim is that the usual maximum-average-power association rule is suboptimal in multi-band UAV networks, and that a rule of the form 'associate with the mmWave UAV if $\beta S_m > S_{\mathrm{lf}}$'--with $\beta$ given by a closed-form sigmoid of the expected spectral-efficiency ratio between bands--captures most of the available gain. When the mmWave tier offers higher expected spectral efficiency ($\tau > 1$), the bias favors mmWave UAVs to exploit lower interference and wider bandwidth; when the low-frequency tier is better, the bias shifts the other way, with saturation built in to avoid overloading either tier. The paper further claims that its new statistical model of mmWave antenna gain, which derives the main-lobe elevation probability from the nearest-UAV distance distribution, yields accurate interference Laplace transforms and therefore accurate coverage and spectral-efficiency predictions. Simulations are presented as evidence that the analytical curves track the simulated ones and that the proposed scheme raises coverage probability at a 0 dB SINR threshold from about 65% to nearly 90%, with larger per-user data rates as the mmWave density increases.

Load-bearing premise

The load-bearing premise is that a user's probability of being assigned to the mmWave tier and the signal quality that user then experiences from that tier can be analyzed as independent, even though both depend on the same nearest-mmWave-UAV distance and the same bias rule; if that independence fails, the reported coverage and spectral-efficiency numbers are not the true quantities under the proposed policy.

Editorial extensions

If this is right

Under the proposed policy, an operator can set the cell-range-expansion parameter from network statistics alone (UAV densities, height, transmit powers, path-loss exponents, and expected spectral-efficiency ratio), with no real-time channel measurements or hand tuning.
If the simulations are representative, switching from maximum-average-power association to the proposed bias rule raises coverage probability at a 0 dB SINR threshold from roughly 65% to nearly 90%.
The bias saturates through its sigmoid form, so mmWave UAVs are favored only up to a maximum bias $\beta_0$ and low-frequency UAVs are protected by a lower bound near $\beta=0.5$, which should prevent either tier from being overloaded.
The derived analytical expressions for coverage and spectral efficiency make the scheme directly comparable across deployment parameters such as the mmWave-to-low-frequency density ratio and the number of mmWave antennas, without rerunning network simulations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the same construction--a logistic bias built from an expected spectral-efficiency ratio and standardized by path loss--could be transferred to terrestrial heterogeneous networks or to UAV networks with more than two bands, since the argument does not rely on anything specific to airborne nodes beyond the distance distributions.
Editorial inference: the analyzed gains likely overstate what a real deployment would achieve if the association-SINR independence in Eq. (20) is violated, because users offloaded to mmWave by the bias tend to be farther from their serving mmWave UAV than the unconditional nearest-UAV distance assumes.
Editorial inference: the antenna-gain approximation for interfering mmWave UAVs could be checked against a ray-tracing or 3GPP-style channel model; a significant discrepancy in the elevation main-lobe probability would change the interference Laplace transform and therefore the predicted benefit of the bias.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this paper has two real ideas—a closed-form bias factor based on a spectral-efficiency ratio, and a new approximation for interfering mmWave antenna gain—but the analytical coverage and spectral-efficiency expressions have a load-bearing flaw. They average SINR over the unconditional serving-distance distribution, while the association policy depends on that same distance. The stress-test note is correct.

The bias formula in (14) is clever and practical: it depends only on network statistics, no real-time tuning, and saturates to avoid overloading. The antenna-gain derivation in Section III-B is inventive and arguably better than the uniform beam model in [6]. The simulations look plausible and show coverage gains over MAP.

The problem: Eq. (20) writes total coverage as Alf*PClf + Am*PCm, and PCm in (28) integrates over f_Rm(r) from Eq. (3), the unconditional nearest-mmWave distance. But association under (12) uses the event beta S_m > S_lf, which depends on the same r_m. Users that actually connect to mmWave tend to have shorter serving distances and longer low-frequency distances. Averaging over the unconditional distance overestimates their SINR. The same mis-conditioning affects PClf. So the derived coverage and SE are not the quantities the proposed policy produces. This isn't a small approximation; it changes the numbers.

There's also a minor internal inconsistency: the text says tau=1 gives beta=1, but (14) gives beta=zeta at tau=1, and zeta is generally not 1. And the simulations only compare against MAP, not prior CRE methods like [10]-[12], so the practical claim of being better than existing CRE isn't tested.

If the authors fix the conditioning—properly deriving the serving distance distribution under the biased association rule—the paper could be solid. The idea is good, the execution in the analysis section is currently not. I'd send it to referee, because the novel pieces deserve scrutiny, but I'd expect major revision. As is, I would not rely on the analytical results.

Referee Report

3 major / 4 minor

Summary. The paper studies downlink coverage and rate in a two-tier UAV network in which low-frequency and mmWave UAVs form two independent homogeneous Poisson point processes. It proposes a cell-range-expansion association rule that biases users toward mmWave UAVs with a closed-form bias factor β depending on an expected-spectral-efficiency ratio τ, derives association probabilities, coverage probabilities, and spectral efficiency via stochastic geometry, and introduces an analytical model for the antenna gain of interfering mmWave UAVs. Simulation results are used to claim that the proposed scheme improves coverage and per-user data rates relative to conventional maximum-average-power association.

Significance. If the analysis were correct, the closed-form bias factor would be practically appealing because it depends only on network statistics and system parameters, and the antenna-gain derivation would be a useful modeling contribution. The simulation comparisons also suggest a qualitatively promising offloading idea. However, the current analytical framework does not actually characterize the proposed association policy: the coverage and spectral-efficiency expressions ignore the dependence between the association event and the serving distance. Because this issue is load-bearing for every quantitative claim in the paper, the present version cannot be accepted; the core ideas are, in my view, salvageable with a re-derived conditional analysis, so I recommend major revision rather than rejection.

major comments (3)

[Section III-D, Eq. (20)] The factorization PC(γ) = PClf(γ)·Alf + PCm(γ)·Am is not valid for the association rule in Eq. (12). Because the event {user is served by mmWave} is {βS_m(r_m) > S_lf(r_lf)}, the set of users served by each band is selected based on r_m and r_lf. Equations (24) and (28) nevertheless integrate the SINR condition over the unconditional nearest-UAV densities f_Rlf and f_Rm from Eq. (3). For mmWave-served users the correct serving-distance density is f_Rm(r)(1 − F_Rlf(η^{1/α_lf} r^{α_m/α_lf}))/Am, with Am from Eq. (19), and an analogous conditional density is needed for low-frequency-served users. Since the conditioning event favors smaller r_m and larger r_lf, the unconditional averages overestimate PCm and SEm and distort PClf and SElf. This error propagates into the spectral-efficiency ratio τ in Eq. (13), the bias factor β in Eq. (14), and the claimed agreement between analysis and simulation in Figs. 3a–3c.
[Section III-E and Eq. (13)-(14)] The spectral-efficiency ratio τ is defined in Eq. (13) using SElf and SEm from Eqs. (33) and (36), but those quantities are computed with the unconditional serving-distance distributions. Under the proposed policy, the users actually served by mmWave UAVs have a stochastically smaller serving distance than the unconditional nearest-mmWave distance, and users served by low-frequency UAVs have a stochastically smaller low-frequency serving distance. Therefore τ does not represent the ratio of per-user spectral efficiencies under the policy, and the beta-based adaptation in Eq. (14) is not the claimed equalizing bias. The authors need to re-derive SElf and SEm using the conditional serving-distance densities and recompute τ, β, and the resulting curves in Fig. 3 before the adaptive-CRE claim can be considered established.
[Section III-B, Eqs. (9)-(11)] The derivation of pϕ uses f_Rm, the density of the distance from a typical user to its nearest mmWave UAV, as the density of the distance r from an interfering UAV to the user it serves. These are different objects in a PPP model with a separate user point process: the former is a nearest-neighbor distance from a fixed point, while the latter is a Palm/Voronoi quantity that also depends on the user process and on the association rule. The authors should justify this replacement or re-derive the UAV-to-served-user distance distribution; this point is load-bearing because the gain distribution G_x enters the mmWave interference Laplace transform in Eq. (38) and hence all mmWave coverage and spectral-efficiency results.

minor comments (4)

[Section III-C, text after Eq. (14)] The statement 'When τ = 1, then β = 1' is inconsistent with Eq. (14) unless ζ = 1; in general Eq. (14) gives β = ζ at τ = 1. Please clarify whether the standardization term ζ is intended to be part of the effective bias or a separate normalization.
[Section III-C, text after Eq. (14)] The claim that β is lower-bounded by about 0.5 as τ → 0 is not supported by the simulation parameters (β0 = 5, α = 5), which give β → ζ·β0/(1+(β0−1)e^α) ≈ 0.0084ζ. Please state the parameters for which the stated lower bound holds.
[Section III-D, Eq. (21)] There is a missing closing parenthesis in 'E[P(SINRlf > γ)' ; it should read E[P(SINRlf > γ)].
[Section IV, Fig. 3c caption] The word 'numer' should be 'number'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the bias factor is a closed-form function of network statistics and the reported curves are checked against independent simulation.

full rationale

The paper does not fit any parameter to the coverage or SE curves it reports. The adaptive bias factor β in Eq. (14) is a closed-form sigmoid of the model-derived SE ratio τ (Eq. (13)) and the standardization term ζ (Eq. (15)); both are computed from system parameters and PPP distance distributions, not calibrated to simulation targets. No constants are extracted from the coverage/SE data, and no claim is validated solely by a self-citation: the antenna model is attributed to external works [6], [14], [15], and there are no references to the present authors' prior results. The central claims are empirically checkable because Fig. 3 compares the analytical expressions against Monte Carlo simulation that implements the actual biased association policy, so agreement with analysis is an external check rather than a construction. The concern that Eq. (20) uses unconditional nearest-UAV distance distributions f_Rm and f_Rlf in PCm and PClf, ignoring conditioning on the association event in Eq. (12), is a modeling approximation or potential accuracy issue, not a circular reduction: the derivation does not define the predicted coverage in terms of itself, and the simulation provides an independent evaluation. The statement that τ=1 gives β=1 is imprecise because Eq. (14) gives β=ζ at τ=1, but this is a minor presentation issue and is not load-bearing for the claimed improvement. Overall, no load-bearing step reduces to its own input by construction.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

No physically new entities are introduced; the key modeling objects are the bias factor beta and the random antenna gain G_x, which are analytical constructs rather than new physical postulates. The main burden rests on the independence and nearest-UAV assumptions in Eqs. (3) and (20), listed as axioms.

free parameters (2)

beta_0 (maximum bias factor) = 5
Hand-selected saturation level in the sigmoid bias function in Eq. (14) and used in simulations in Section IV; not fitted to data, but the scheme's behavior depends on it.
alpha (bias growth rate) = 5
Hand-selected slope of the sigmoid in Eq. (14); simulation parameter that controls how aggressively beta responds to deviations of tau from 1.

assumptions (6)

domain assumption UAV locations in each band form independent homogeneous PPPs at a common height h.
Sec. II. This provides f_Rt in Eq. (3) and the PPP probability generating functional used in Eqs. (37)-(38).
ad hoc to paper Users associate within each band with the highest average received signal strength, which is treated as equivalent to the nearest UAV in that band.
Sec. II and Eq. (3). The equivalence to nearest ignores that mmWave received power includes random beam-alignment gain, and the CRE policy can attach a user to a non-nearest mmWave UAV.
ad hoc to paper The total coverage probability factors as PClf*Alf + PCm*Am, meaning association events and SINR coverage are independent.
Sec. III-D, Eq. (20). No conditioning on the association event is applied when averaging over serving distance, despite association depending on r_m.
domain assumption Narrow beamwidth and moderate mmWave density keep the elevation beam edges inside [0, pi/2] with high probability.
Sec. III-B before Eq. (5). Used to derive p_phi in Eq. (11); can fail for low-altitude, wide-beam, or very dense deployments.
domain assumption The sectorized UPA antenna gain model from [14], with main-lobe gain G_M and side-lobe gain G_S, accurately represents mmWave beamforming.
Sec. II; imported from prior literature. The analysis depends on the two-state gain distribution in Eq. (4).
domain assumption Rayleigh fading for the low-frequency band and Nakagami-m fading for the mmWave band, with independent fading across links.
Sec. II. Used for the exponential and Gamma fading assumptions in the coverage and spectral efficiency integrals.

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Cite this review

Pith. "Pith review of Adaptive Cell Range Expansion in Multi-Band UAV Communication Networks." pith.science (2026). https://pith.science/paper/LKWPEIZF

@misc{pith2026241118123,
  author       = {Pith},
  title        = {Pith review of: Adaptive Cell Range Expansion in Multi-Band UAV Communication Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LKWPEIZF}},
  note         = {Machine review of arXiv:2411.18123}
}

read the original abstract

This paper leverages stochastic geometry to model, analyze, and optimize multi-band unmanned aerial vehicle (UAV) communication networks operating across low-frequency and millimeter-wave (mmWave) bands. We introduce a novel approach to modeling mmWave antenna gain in such networks, which allows us to better capture and account for interference in our analysis and optimization. We then propose a simple yet effective user-UAV association policy, which strategically biases users towards mmWave UAVs to take advantage of lower interference and wider bandwidths compared to low-frequency UAVs. Under this scheme, we analytically derive the corresponding association probability, coverage probability, and spectral efficiency. We conclude by assessing our proposed association policy through simulation and analysis, demonstrating its effectiveness based on coverage probability and per-user data rates, as well as the alignment between analytical and simulation results.

Figures

Figures reproduced from arXiv: 2411.18123 by the authors.

**Figure 1.** UAVs at height h, users on the ground. Users associate with either low-frequency or mmWave UAVs, with interference from non-serving UAVs. TABLE I UNIFORM PLANAR ANTENNA ARRAY PARAMETERS [14] Number of antennas N Half-power beamwidth ∆θ = ∆ϕ p 3/N Main-lobe gain GM N Side-lobe gain GS √ N− √ 3 2π Nsin √ 3 2 √ N √ N− √ 3 2π sin √ 3 2 √ N (e.g., 30 GHz). We assume all UAVs hover at a height of h meters, with the … view at source ↗

**Figure 2.** An example bias function with β0 = 5, α = 1, and ζ = 1. network statistics and system parameters. We first introduce the SE ratio τ as τ = E[log2 (1 + SINRm)] E[log2 (1 + SINRlf)] , (13) where SINRlf and SINRm are given in (1) and (2), respectively. Then, we define our proposed bias factor β as β = ζ · β0 1 + (β0 − 1) exp(α(1 − τ )), (14) where the standardization term ζ is given by ζ = PlfKlfE [PITH_FULL_IMAGE:fi… view at source ↗

**Figure 3.** Comparison of coverage probability, per-user data rate, and spectral efficiency in multi-band UAV networks under our proposed CRE scheme. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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M. R. Akdeniz, Y . Liu, M. K. Samimi, S. Sun, S. Rangan, T. S. Rappaport, and E. Erkip, “Millimeter wave channel modeling and cellular capacity evaluation,”IEEE J. Sel. Areas Commun., vol. 32, no. 6, pp. 1164–1179, Jun. 2014

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J. Chakareski, S. Naqvi, N. Mastronarde, J. Xu, F. Afghah, and A. Razi, “An energy efficient framework for UA V-assisted millimeter wave 5G heterogeneous cellular networks,” IEEE Trans. Green Commun. Netw. , vol. 3, no. 1, pp. 37–44, Mar. 2019

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J. G. Andrews, F. Baccelli, and R. K. Ganti, “A tractable approach to coverage and rate in cellular networks,” IEEE Trans. Commun., vol. 59, no. 11, pp. 3122–3134, Oct. 2011

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Coverage analysis of mmWave and THz-enabled aerial and terrestrial heterogeneous networks,

A. A. Raja, H. Pervaiz, S. A. Hassan, S. Garg, M. S. Hossain, and Md. Jalil Piran, “Coverage analysis of mmWave and THz-enabled aerial and terrestrial heterogeneous networks,” IEEE Trans. Intell. Transp. Syst., vol. 23, no. 11, pp. 22 478–22 491, Nov. 2022

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