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Joint Optimization of UAV-Carried IRS for Urban Low Altitude mmWave Communications with Deep Reinforcement Learning

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper argues that its EPPO algorithm jointly optimizes UAV trajectory and IRS phase shifts to deliver higher urban mmWave rates and lower UAV energy use than DDPG, TD3, SAC, and PPO in simulation.

desk verdict A plausible DRL package for UAV-mounted IRS, undone by a rate formula missing the squared modulus and a dB/linear path-loss mixup that makes every simulation number uninterpretable. read the letter →

arxiv 2501.02787 v1 pith:7TO3SJX6 submitted 2025-01-06 cs.NI

Wenwen Xie , Geng Sun , Bei Liu , Jiahui Li , Jiacheng Wang , Hongyang Du , Dusit Niyato , Dong In Kim This is my paper · ORCID
classification cs.NI
keywords UAV-carriedIRSjointtrajectoryandphaseshiftoptimizationdeepreinforcementlearningproximalpolicymmWavecommunicationsJain'sfairnessindexRicianfadinglowaltitudeeconomy
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 tries to establish that a UAV carrying an intelligent reflecting surface (IRS) can restore millimeter-wave connectivity in dense urban low-altitude environments where buildings block the direct path between a source user and mobile users. The authors formulate a joint optimization of the UAV trajectory and the IRS phase shifts, with an objective that balances transmission rate, UAV energy consumption, and fairness across users, and they solve it with an enhanced proximal policy optimization (EPPO) algorithm. EPPO combines neural episodic control with state abstraction, a Mogrifier LSTM actor, and a closed-form IRS phase shift computation that removes the phase variables from the action space. The simulation evidence shows EPPO reaching higher cumulative rewards, higher average rates, and lower energy consumption than DDPG, TD3, SAC, and PPO in both single-user and multi-user urban settings.

What carries the argument

The key machinery is the EPPO algorithm, built on three mechanisms: neural episodic control with state abstraction (NECSA), which griddizes the continuous state space and provides intrinsic rewards to speed convergence; a Mogrifier LSTM that augments the actor network to learn long-range dependencies between states and actions; and an IRS phase shift control strategy that evaluates Eq. (15) for each reflecting element, a closed-form phase based only on the geometric angles, reducing the action space from $M_rM_c+3$ to 3. The optimization objective is the fairness rate energy consumption ratio $F_t=(\sum_{i=1}^n \xi R_{i,t})/E_t$, which combines Jain's fairness index, the achievable rate, and the UAV propulsion energy.

What would settle it

Numerically maximize the achievable rate over IRS phase shifts for the full Rician channel model at a fixed UAV location with non-zero $k$ and the Gaussian NLoS terms, then compare that optimum to Eq. (15). If the geometric formula falls short, EPPO's advantage comes from a shortcut the baselines are not given, and the comparison would need to be redone with the same phase law applied to all algorithms.

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Extended reading notes

Core claim

The central claim is that joint optimization of trajectory and phase shifts is tractable in real time with the proposed EPPO algorithm, despite the problem being non-convex and NP-hard in its phase-shift subproblem. EPPO treats the UAV displacement as the only learned action, because the IRS phase shifts are computed in closed form from the azimuth and elevation angles of arrival and departure, shrinking the action space from $M_rM_c+3$ to 3. The reward is a fairness-rate-energy ratio, so the policy is driven to positions that serve all users equitably while keeping propulsion energy low. The paper reports that this design yields higher average data rates and lower cumulative energy consumption than DDPG, TD3, SAC, and PPO in urban simulations, and that the learned trajectories tend to hover at energy-efficient positions.

Load-bearing premise

The closed-form phase shift law assumes that aligning the geometric line-of-sight phases between source, IRS, and user maximizes the data rate, even though the channel model also contains random scattered (non-line-of-sight) components with random phases.

Editorial extensions

If this is right

  • EPPO's phase law makes the IRS beamforming independent of the learning process, so the drone policy only has to learn three continuous actions per time slot regardless of the number of reflecting elements.
  • The fairness-weighted reward means the learned trajectory consciously balances per-user rates, not just the sum rate, in multi-user urban grids.
  • The learned trajectories in simulation converge to low-energy hovering and cruise patterns near the minimum-energy speed, indicating the policy internalizes the propulsion model.
  • Because phase shifts are computed from the current coordinates of source, IRS, and user, the algorithm can react to user mobility at each time slot without re-optimizing beamforming.

Reading between the lines

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

  • A testable extension is to replace the closed-form phase law with a learned phase policy in a fair comparison, keeping all other EPPO components; if the closed-form law is truly optimal under the Rician model, the learned phase policy should converge to the same rates but take longer, and if not, the reported EPPO advantage would shrink.
  • The paper's comparison with DDPG, TD3, and SAC does not give those baselines the same phase-control shortcut; a fairer benchmark would impose the geometric phase law on all algorithms, isolating the contribution of trajectory learning.
  • The phase law itself assumes the LoS geometric phases dominate the channel; under strong NLoS or scattering, an adaptive phase policy that accounts for the random Gaussian components could outperform the closed-form formula, which would weaken the paper's claim that geometric alignment is optimal.
  • The closed-form phase makes the IRS beamforming a deterministic function of geometry, so the UAV trajectory and IRS beamforming are effectively optimized by a single policy; this coupling suggests the method could be extended to multiple IRS elements or inter-cell interference scenarios by augmenting the state space.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper considers a UAV-carried intelligent reflecting surface (IRS) assisting an urban low-altitude mmWave communication link between a source user and mobile users whose direct path is blocked. It formulates a joint optimization problem over the IRS phase shifts and the UAV trajectory, with an objective that combines the sum rate, Jain's fairness index, and UAV propulsion energy consumption. To solve this non-convex, dynamic problem, the authors propose an enhanced PPO algorithm (EPPO) that integrates neural episodic control with state abstraction, a Mogrifier LSTM actor network, and a closed-form IRS phase-shift control strategy said to reduce the action space to the three UAV displacement components. The empirical evaluation compares EPPO with DDPG, TD3, SAC, and PPO in single-user and multi-user simulations and reports higher cumulative rewards, higher average rates, and lower energy consumption for EPPO.

Significance. If the results were valid, the paper would offer a practical DRL pipeline for UAV-carried IRS deployments, with useful engineering heuristics such as the phase-shift control strategy and the episodic control acceleration. The authors also provide a reasonably thorough ablation study (Fig. 6) isolating the contributions of the Mogrifier LSTM, NECSA, and the phase-shift control, and they report a complexity comparison in Table 2. However, the central quantitative claim rests on a rate expression that is missing the squared modulus of the composite channel and that treats dB path loss as a linear gain, so every numerical rate, reward, and energy-efficiency comparison in the paper is uninterpretable as presented. The asserted optimality of the closed-form phase-shift formula is also unproven for the Rician channel with NLoS components, which makes the benchmark comparison potentially unfair regardless of the rate-model error. The significance of the work therefore cannot be assessed until these load-bearing issues are resolved.

major comments (3)
  1. [§3.2, Eq. (5)] The achievable rate expression in Eq. (5) is invalid as written. The standard SNR term is P |g_t^T Θ_t h_{u,t}|^2 / (B σ^2), but the paper uses P g_t^T Θ_t h_{u,t} / (B σ^2) without the squared magnitude. The inner product is a complex quantity; for phase configurations that make it negative real, the log2 argument becomes non-positive and the rate is undefined. Moreover, Eqs. (1)–(2) define the path-loss factors Ψ^SI_t and Ψ^IE_{u,t} in dB (β(D) = 30 dB, exponent n = 2.2), yet these dB values are multiplied directly into the channel vectors as linear gains. At a distance of 100 m, Ψ = 74 dB is treated as a gain of 74 instead of approximately 2×10^{-4} (linear). Either error alone invalidates every simulated rate and reward; together they completely undermine the empirical support for the headline claim in Figs. 5, 6, 8, 11, and 12.
  2. [§4.3.3, Eq. (15)] The IRS phase-shift control strategy is called 'optimal' in the text, but Eq. (15) is asserted rather than derived, and it aligns only the LoS geometric phases. The channel model in Eqs. (1)–(2) explicitly includes Rician NLoS components with independent Gaussian phases, whose contribution is absent from Eq. (15). Without a proof that this closed-form phase vector maximizes the achievable rate (or a statement of the conditions under which it is optimal), the claimed 'optimality' is unsupported. This matters for the evaluation: EPPO uses Eq. (15) to remove the IRS phase shifts from the learned action space, while the benchmark algorithms (DDPG, TD3, SAC, PPO) must learn these phases. If the closed-form phase is only a heuristic, the reward advantage in Figs. 5 and 8 may simply reflect that EPPO is given a better-informed action space, not a superior policy.
  3. [§4.1.3 and §3.4, reward/objective] The optimization objective and the reward function both inherit the invalid rate expression from Eq. (5). In particular, Eq. (10) sets r_t = ξ R_{u,t}/E_t for LoS links and r_t = 0 for NLoS links; since R_{u,t} is not a proper rate, the reward does not correspond to any well-defined communication quantity. Consequently, the cumulative-reward curves, convergence comparisons, and the conclusions about 'higher transmission rates and lower energy consumption' are not grounded in a valid system model. The authors should re-derive the rate with |g_t^T Θ_t h_{u,t}|^2 and consistent linear path-loss gains, then rerun the simulations before the comparative claims can be evaluated.
minor comments (4)
  1. [Global] There are numerous typographical errors that should be corrected: 'alforithm' (§4.2), 'the the' (§4.2), 'Muti-user' (Fig. 8 caption), 'Enhanced PPO' in the title of §4.3, and inconsistent notation between cSU and cUAV in §3.2 and §4.1.1.
  2. [Fig. 6 and Fig. 8 captions] The captions contain font-encoding artifacts that make them unreadable in the provided manuscript; these should be regenerated with the correct text.
  3. [§3.2, Eq. (3)–(4)] The LoS channel expressions omit the normalization by the array size; the authors should clarify whether the steering vectors are normalized, since this affects the scaling in Eq. (5).
  4. [§4.3.3] The paper cites [20] for the phase-shift formula, but [20] considers a different system (IRS-assisted UAV OFDMA) and does not establish optimality for the Rician channel used here; the authors should provide a self-contained derivation or clearly state the heuristic nature of Eq. (15).

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the reward equals the objective by standard RL design, and the only self-citation is a non-load-bearing provenance footnote; Eq. (5) and Eq. (15) issues are correctness/fairness concerns, not circularity.

full rationale

The paper's derivation chain is self-contained. The DRL reward in Eq. (10) is essentially the per-user fairness-rate-energy ratio of Eq. (8), the objective of Eq. (9), plus a boundary penalty, which is the standard RL formulation rather than a fitted input renamed as a prediction; no parameter is fitted to a subset of the simulation data and then used to predict a closely related quantity. The benchmark comparison runs EPPO, PPO, DDPG, TD3, and SAC in the same simulator, so the relative claim is externally falsified within the paper's own environment. The only self-citation is the footnote 'Part of this paper appeared in IEEE ICC 2024 [1]'; it is a provenance disclosure used nowhere in the derivation chain, so it is not load-bearing. The suspicious phase-shift formula (Eq. (15)) is imported from an external citation [20] and may not be optimal under the Rician NLoS channel, and Eq. (5) is invalid as a rate expression because it lacks the squared modulus and applies dB path loss linearly; however, these are correctness and fairness concerns, not circularity, because neither quantity is defined in terms of the simulation result it is used to explain. Score 2 reflects only the minor non-load-bearing self-citation.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central algorithm rests on standard RL hyperparameters chosen by hand, a Rician channel model with a missing Rician factor, an unvalidated energy model from prior work, and a phase-shift formula claimed optimal without derivation. No new physical entities are introduced.

free parameters (5)
  • Discount factor gamma = 0.99
    Hand-chosen in Table 3 for the MDP; not fitted to data but affects learning dynamics.
  • Out-of-bounds penalty p_o = 0.04
    Hand-chosen in Table 3 as a reward penalty; central to shaping behavior but no sensitivity analysis is given.
  • PPO clip ratio epsilon = 0.02
    Hand-chosen in Table 3 for policy update clipping.
  • Number of training episodes N_eps = 3000
    Hand-chosen in Table 3; convergence and final performance depend on this.
  • Rician factor k = not specified
    Appears in channel model Eq. (1)-(2), but no value is listed in Table 3, making the simulation setup incomplete.
assumptions (5)
  • domain assumption The direct SU-user link is completely blocked whenever an obstacle lies between them, so communication is possible only through the UAV-carried IRS with a binary LoS condition.
    Section 3.1; central to the problem setup and the reward in Eq. (10).
  • domain assumption The SU and users are single-antenna and do not use MIMO.
    Section 3.1, stated explicitly, simplifying the channel model; the paper claims extension is easy but does not show it.
  • ad hoc to paper The closed-form phase shift in Eq. (15) is optimal for maximizing the user data rate in the Rician channel.
    Section 4.3.3; the paper does not derive this optimality and ignores NLoS components.
  • domain assumption The rotary-wing UAV propulsion energy model of Eq. (6), taken from reference [27], applies to a UAV carrying an IRS with total mass m.
    Section 3.3; no validation of this model for the specific IRS payload.
  • domain assumption Users are served one at a time in a fixed order under TDMA, and the fairness index is computed on per-time-slot rates.
    Section 3.1 and Section 5.3.3; the interaction of Jain's index with single-user-per-slot service is not analyzed.

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Pith. "Pith review of Joint Optimization of UAV-Carried IRS for Urban Low Altitude mmWave Communications with Deep Reinforcement Learning." pith.science (2026). https://pith.science/paper/7TO3SJX6

@misc{pith2026250102787,
  author       = {Pith},
  title        = {Pith review of: Joint Optimization of UAV-Carried IRS for Urban Low Altitude mmWave Communications with Deep Reinforcement Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7TO3SJX6}},
  note         = {Machine review of arXiv:2501.02787}
}
read the original abstract

Emerging technologies in sixth generation (6G) of wireless communications, such as terahertz communication and ultra-massive multiple-input multiple-output, present promising prospects. Despite the high data rate potential of millimeter wave communications, millimeter wave (mmWave) communications in urban low altitude economy (LAE) environments are constrained by challenges such as signal attenuation and multipath interference. Specially, in urban environments, mmWave communication experiences significant attenuation due to buildings, owing to its short wavelength, which necessitates developing innovative approaches to improve the robustness of such communications in LAE networking. In this paper, we explore the use of an unmanned aerial vehicle (UAV)-carried intelligent reflecting surface (IRS) to support low altitude mmWave communication. Specifically, we consider a typical urban low altitude communication scenario where a UAV-carried IRS establishes a line-of-sight (LoS) channel between the mobile users and a source user (SU) despite the presence of obstacles. Subsequently, we formulate an optimization problem aimed at maximizing the transmission rates and minimizing the energy consumption of the UAV by jointly optimizing phase shifts of the IRS and UAV trajectory. Given the non-convex nature of the problem and its high dynamics, we propose a deep reinforcement learning-based approach incorporating neural episodic control, long short-term memory, and an IRS phase shift control method to enhance the stability and accelerate the convergence. Simulation results show that the proposed algorithm effectively resolves the problem and surpasses other benchmark algorithms in various performances.

Figures

Figures reproduced from arXiv: 2501.02787 by the authors.

Figure 1
Figure 1. UAV-carried IRS-aided mmWave communication system in urban [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The overview of NECSA. • Mogrifier LSTM: Mogrifier LSTM can handle long￾sequence dependencies, enabling the algorithm to learn better. • IRS phase shift control strategy: IRS phase shift con￾trol strategy can reduce the dimension of the action space. They are detailed as follows. 4.3.1 Neural Episodic Control with State Abstraction To speed up the convergence, we first introduce NECSA [42] mechanism into our EPPO al… view at source ↗
Figure 3
Figure 3. Mogrifier LSTM with 5 rounds of updates. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: The framework of the the proposed EPPO. TABLE 2 Complexity Comparison of Different Algorithms. Algorithm Computational complexity Space complexity EPPO O(|θA| + |ϕC | + NepsT|θA| + NepsT NnecV + K(|θA| + |ϕC |)) O(|θA| + |ϕC | + Dr(3|s| + 2|a| + 3)) DDPG O(2|θA| + 2|ϕC…
Figure 5
Figure 5. Figure 5: Training results in the single-user scenario. (a) Cumulative rewards training curve. (b) Average rate training curve. (c) Cumulative energy [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Ablation simulation results in the single-user scenario. (a) Comparison of mogrifier LSTM, LSTM and GRU. (b) Comparison of PPO and [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: 3D trajectories of the UAV for single user. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Muti-user training result. (a) Cumulative reward training curve. (b) Average rate training curve for the first user. (c) Average rate training curve [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Average penalty curve in muti-user scenario. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: 3D trajectories of the UAV under different numbers of users. (a) Trajectory of UAV for 2 users. (b) Trajectory of UAV for 3 users. (c) Trajectory [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: The impacts for different IRS reflection element numbers. (a) [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: The impacts for different user numbers. (a) Average rate curve [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.