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REVIEW 3 major objections 3 minor 13 references

Reconfigurable Intelligent Surface Assisted UAV Communication: Joint Trajectory Design and Passive Beamforming

T0 review · 3 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Jointly optimizing a UAV's flight path and a reconfigurable surface's reflecting phases markedly raises the average achievable rate in blocked urban links.

desk verdict A competent but incremental RIS-UAV combination; the SCA monotonicity claim doesn't hold as written because the slack variables are never reset. read the letter →

arxiv 1908.04082 v3 pith:X3B7ND4V submitted 2019-08-12 cs.IT math.IT

Sixian Li , Bin Duo , Xiaojun Yuan , Ying-Chang Liang , Marco Di Renzo This is my paper · ORCID
classification cs.ITmath.IT
keywords reconfigurableintelligentsurfaceUAVcommunicationtrajectorydesignpassivebeamformingsuccessiveconvexapproximationphasealignmentaverageachievablerateRicianfading
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 studies a wireless downlink in which a drone serving a ground user has its direct line of sight blocked, and a wall-mounted reconfigurable intelligent surface (RIS) reflects the drone's signal to the user. Its claim is that maximizing the user's average data rate requires the drone's flight path and the RIS's reflecting phases to be designed together. For any fixed path, the paper gives a closed-form phase setting that makes all reflected paths add coherently at the user, and it then solves the remaining path-planning problem by successive convex approximation. Numerical results show this joint design achieves a considerably higher average rate than optimizing either the path or the phases alone.

What carries the argument

The load-bearing object is the phase-alignment identity (11): choosing each RIS phase as $\theta_i[n]=\arg(\tilde h)+\omega_i+\frac{2\pi}{\lambda}d(i-1)\varphi_{UR}[n]$ makes every reflected path arrive at the user with the same phase, so the SNR becomes a squared sum of magnitudes instead of a random phasor sum. This converts the non-convex joint problem into an optimization over two distances, $d_{UG}[n]$ and $d_{UR}[n]$. The second piece is Lemma 1, which asserts that $f(x,y)=\log_2(1+K_1 x^{-\kappa}+K_2 y^{-2}+K_3 x^{-\kappa/2}y^{-1})$ is convex for $x,y>0$; that property justifies using first-order Taylor expansions as global underestimators inside the successive-convex-approximation loop. With slack variables $u[n]$, $v[n]$ bounding the distances, the trajectory subproblem is convex and can be solved by standard tools.

What would settle it

Compute the Hessian determinant of $f(x,y)=\log_2(1+K_1 x^{-\kappa}+K_2 y^{-2}+K_3 x^{-\kappa/2}y^{-1})$ at a grid of positive $x,y$ using the paper's parameter values; a single negative determinant disproves Lemma 1 and would invalidate the SCA lower bound. A second test is to run the joint algorithm with imperfect channel estimates (e.g., 10-20% phase error at the RIS) and compare against trajectory-only optimization: if the rate gap shrinks sharply, the reported benefit depends on perfect phase alignment rather than on joint optimization alone.

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Extended reading notes

Core claim

The central claim is that a UAV serving a ground user through a building-mounted RIS should not simply hover above the user; it should fly an arc that balances the direct UAV-user link against the UAV-RIS-user reflected link, with the RIS phases set to align the two signal components at the receiver. For a fixed trajectory, phase alignment across all reflecting elements---equation (11), $\theta_i[n]=\arg(\tilde{h})+\omega_i+\frac{2\pi}{\lambda}d(i-1)\varphi_{UR}[n]$---maximizes the received signal power and collapses the joint design into a trajectory-only problem. The trajectory problem is then solved with slack variables and successive convex approximation, using the lemma that the rate expression is convex in the two distances $d_{UG}$ and $d_{UR}$. In the paper's simulations the joint algorithm beats benchmarks that optimize only one side of the problem, and the optimized trajectory is an arc whose hovering point sits away from directly above the user.

Load-bearing premise

The algorithm's monotone improvement rests on Lemma 1's claim that the per-slot rate expression is bowl-shaped in the two distances, so each successive-approximation step is a valid lower bound; if that convexity fails, the trajectory update may not improve the rate and the reported joint gain is not guaranteed.

Editorial extensions

If this is right

  • A UAV serving a ground user in a blocked environment should fly an arc that balances the direct and reflected links; hovering directly above the user is suboptimal when a RIS is available.
  • System designers should treat UAV path planning and RIS configuration as one coupled problem; optimizing either alone leaves a measurable rate gain on the table.
  • Because the phases are closed-form once the path is known, the RIS update is computationally cheap and can be applied in real time as the UAV moves.
  • The trajectory subproblem is a disciplined convex program, so standard solvers can find each update, with monotone improvement and $O(K_{\mathrm{ite}}N^{3.5})$ complexity.
  • The result supports deploying RISs as a low-power way to restore connectivity in UAV-to-ground links when the line of sight is blocked, without adding transmit power.

Reading between the lines

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

  • Beyond the paper: the phase-alignment identity is structural and should carry over to rectangular RIS arrays or multi-antenna UAVs, since it only needs the product form of the reflected channel.
  • Beyond the paper: a direct sensitivity test would add channel-estimation noise to the phases in (11); the paper assumes perfect CSI, so the real-world gap between joint and one-sided design may narrow when alignment errors grow.
  • Beyond the paper: the convexity lemma, if valid for all positive parameters, is a reusable tool for other RIS-UAV rate maximizations and could save repeated convergence proofs.
  • Beyond the paper: the simulations suggest a design heuristic---move the hover point toward the RIS as the direct link weakens and toward the user as the reflected link weakens---that could be tested as a low-complexity substitute for full optimization.
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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 / 3 minor

Summary. The paper studies a downlink in which a UAV communicates with a ground user through a blocked direct link and a RIS-reflected link. The authors formulate the joint optimization of the UAV trajectory and the RIS phase shifts to maximize the average achievable rate, derive a closed-form phase-alignment solution in Eq. (11), and then optimize the trajectory via successive convex approximation (SCA) with slack variables, leading to problems (14) and (18). The numerical section (Figs. 2-3) compares the joint design with benchmarks that optimize only one of the two design aspects. The paper is a letter, and its claimed contribution is the joint design plus the closed-form phase solution, with an SCA trajectory solver and an accompanying convergence statement.

Significance. If the claims hold, the paper establishes a useful design principle: in a RIS-assisted UAV link, the UAV trajectory should balance the direct and reflected link distances instead of simply hovering over the user. The closed-form phase-shift solution (11) is a clean and valuable result, and the decomposition into passive beamforming and trajectory optimization is a standard and appropriate structure. The simulation comparison against three benchmarks is a reasonable way to demonstrate the benefit of joint optimization. The paper would be stronger if it shipped machine-checked proofs or code, but that is not claimed. The central idea is defensible, yet two load-bearing algorithmic guarantees are currently not substantiated: the monotone convergence of the SCA loop and the convexity lemma that underpins the minorization step. The numerical evidence also lacks statistical reporting. These gaps are repairable within the scope of the manuscript.

major comments (3)
  1. [Section III-C, Algorithm 1, problem (18)] The claim that the average achievable rate is non-decreasing over iterations is not supported. The first-order Taylor expansion in (15) is a global underestimator of R_slack(u[n],v[n]) only if Lemma 1 holds, and constraints (18b)-(18c) do ensure that any feasible (q,u,v) has u[n]>=d_UG(q[n]) and v[n]>=d_UR(q[n]). However, the standard SCA monotonicity argument also requires the surrogate to be tight at the previous iterate, i.e., the linearization point should satisfy u_{k-1}=d_UG(q_{k-1}) and v_{k-1}=d_UR(q_{k-1}). In Algorithm 1 the slack variables are not reset to the actual distances after the trajectory update, so u_k from (18) equals (d_UG(q_k)^2+u_{k-1}^2)/(2u_{k-1}), which is strictly larger than d_UG(q_k) whenever u_{k-1} differs from d_UG(q_k), and similarly for v. Consequently the surrogate value at the previous point is strictly below the true rate, and the chain F(q_k) >= R_slack(u_k,v_k) >= L_k(u_k,v_k) >= L_k(u_{k-1},v_{k-1}) = R_slack(u_{k-1},v_{k-1}) <= F(q_{k-1}) does not imply F(q_k) >= F(q_{k-1}). A concrete single-slot instance with d_1(q)=sqrt(1+(q-2)^2), d_2(q)=sqrt(1+(q-8)^2), A=B=1, gamma0=1, q0=5.5 and u0=v0=100 gives a true rate that strictly decreases after one iteration (from log2(1.4175) about 0.503 to log2(1.4) about 0.485). The algorithm should be modified to reset u_k and v_k to the exact distances d_UG(q_k), d_UR(q_k) after each trajectory update, and the monotonicity proof should be restated under that rule.
  2. [Appendix, Lemma 1] The convexity proof is incomplete. In the main text the positive definiteness of the Hessian is asserted without demonstration; the supplementary material expands eta^2 f_xx f_yy into a long list of positive monomials and then concludes that the negative terms in (28) are dominated by the positive terms in (29) on the basis of a blue-part comparison, but no explicit algebraic inequality among the monomial coefficients is actually provided. Since Lemma 1 is the foundation for the global underestimator property (15) and hence for the validity of the SCA step (18), this is a load-bearing gap. The authors should either supply a complete factorized proof of the Hessian determinant inequality or verify the lemma rigorously for the parameter ranges used in the simulations (e.g., kappa=3.5). If Lemma 1 were false in some region, the first-order Taylor expression could overestimate R_slack, and the minorization argument would collapse.
  3. [Section IV, Figs. 2-3] The numerical results do not specify the number of channel realizations over which the average rate is computed, nor do they provide error bars or confidence intervals. Because h_tilde in (2) and h_NLoS in (4) are random, the achievable rate is a random variable; without Monte Carlo averaging, the reported 'considerable improvement' of JT&PB over the benchmarks could be within statistical fluctuation. The authors should state the number of random realizations used and, ideally, show confidence intervals or multiple realization curves to support the magnitude of the claimed gain.
minor comments (3)
  1. [Algorithm 1, initialization] The initialization of u0 and v0 is not specified in Algorithm 1. This matters because the SCA tightness issue in the first major comment is aggravated when the initial slack values are loose; the authors should explicitly set u0[n]=d_UG(q0[n]) and v0[n]=d_UR(q0[n]).
  2. [Throughout] There are several typos and formatting issues: 'matirx' in Section II-B, 'repate' in Algorithm 1, 'Sine' in the supplementary proof (should be 'Since'), and the figure label 'versus T' should be 'versus T' consistently formatted.
  3. [Section III-C, complexity] The complexity statement O(Kite N^3.5) is given without derivation or reference; please clarify whether it is per-iteration complexity or total complexity, and state the complexity of solving the convex problem (18) with a standard solver.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the rate improvement is obtained from a direct co-phasing phase solution and an independent SCA trajectory update, with no fitted parameter renamed as a prediction.

full rationale

The paper's central derivation is self-contained against the stated system model. The passive-beamforming update in (11) is a direct phase-alignment construction: for any given trajectory, the RIS phases are set to cancel the path-phase differences and align with arg(h̃), so the resulting objective (13) is obtained by an explicit maximization of the received signal amplitude, not by any quantity fitted from the final rate. The trajectory subproblem introduces slack variables u[n] ≥ d_UG[n], v[n] ≥ d_UR[n], and uses a first-order Taylor expansion of the convexified rate term to build the convex surrogate (18). The coefficients A0[n], B0[n], C0[n] are evaluated at the previous iterate from the model parameters (A, B, γ0, κ) and are not calibrated to match the simulation output. The performance comparison uses independent heuristic benchmarks (HT/PB, HT/NPB, T/NPB), so the claimed considerable improvement is not forced by construction. The only fragile step is the assertion, following reference [3], that the average rate is non-decreasing over iterations. That assertion depends on the surrogate (18) being a valid global underestimator at the current iterate, which is questionable because the slack variables are not reset to the true distances. However, this is a correctness or convergence-argument concern, not a circularity defect: no equation in the paper reduces to its own input, no parameter is fitted and then renamed as a prediction, and the cited monotonicity result is not a self-citation chain. Accordingly, the circularity score is 0.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central optimization relies on standard wireless channel modeling assumptions (fixed altitude, LoS U-R, Rayleigh U-G, Rician R-G, perfect CSI) and on the unverified convexity lemma used to justify the SCA surrogate problem; there are no fitted free parameters and no invented entities. The simulation parameters are system parameters, not fitted values.

assumptions (4)
  • domain assumption U-R link is LoS with free-space path loss exponent 2, U-G link is Rayleigh fading, R-G link is Rician with known K factor (Eqs. 2-4).
    These are standard models but untested for real RIS-UAV deployments; the algorithm's performance depends on them.
  • domain assumption Perfect CSI of all links is available at the controller (stated after Eq. 5).
    Channel estimation for RIS-assisted channels is cited to [12], [13], but no estimation error model is included.
  • ad hoc to paper Lemma 1: the slack-variable rate function is jointly convex for all positive x,y.
    This convexity is essential for the SCA underestimator property; the appendix proof is a sketch with asserted inequalities rather than a verifiable derivation.
  • domain assumption Monotone convergence of alternating optimization follows from [3].
    The non-decreasing property of the average rate over iterations is cited to [3], not proven for this problem; it requires the surrogate to be a global lower bound.

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Cite this review

Pith. "Pith review of Reconfigurable Intelligent Surface Assisted UAV Communication: Joint Trajectory Design and Passive Beamforming." pith.science (2026). https://pith.science/paper/X3B7ND4V

@misc{pith2026190804082,
  author       = {Pith},
  title        = {Pith review of: Reconfigurable Intelligent Surface Assisted UAV Communication: Joint Trajectory Design and Passive Beamforming},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X3B7ND4V}},
  note         = {Machine review of arXiv:1908.04082}
}
read the original abstract

Thanks to the line-of-sight (LoS) transmission and flexibility, unmanned aerial vehicles (UAVs) effectively improve the throughput of wireless networks. Nevertheless, the LoS links are prone to severe deterioration by complex propagation environments, especially in urban areas. Reconfigurable intelligent surfaces (RISs), as a promising technique, can significantly improve the propagation environment and enhance communication quality by intelligently reflecting the received signals. Motivated by this, the joint UAV trajectory and RIS's passive beamforming design for a novel RIS-assisted UAV communication system is investigated to maximize the average achievable rate in this letter. To tackle the formulated non-convex problem, we divide it into two subproblems, namely, passive beamforming and trajectory optimization. We first derive a closed-form phase-shift solution for any given UAV trajectory to achieve the phase alignment of the received signals from different transmission paths. Then, with the optimal phase-shift solution, we obtain a suboptimal trajectory solution by using the successive convex approximation (SCA) method. Numerical results demonstrate that the proposed algorithm can considerably improve the average achievable rate of the system.

Figures

Figures reproduced from arXiv: 1908.04082 by the authors.

Figure 1
Figure 1. A RIS-assisted UAV communication system. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. UAV trajectories by different algorithms when [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Average achievable rate performance by different al [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Reference graph

Works this paper leans on

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