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Outage Analysis and Bilevel Resource Optimization in RIS-Assisted Clustered UAV-NOMA Networks

Masoud Ghazikor, Ly V. Nguyen, Morteza Hashemi

arXiv:2610.30410v1cs.ITmath.IT

TL;DR

Conventional UAV-NOMA faces scalability challenges as UAV numbers grow, and a unified framework for clustered BS–UAV downlink communications with partitionable RISs has been lacking. The paper develops outage analysis, GRIS clustering, and bilevel joint resource optimization with IOS-I2S. In the evaluated scenario, IOS-I2S improves throughput and reduces network-wide maximum outage versus equal resource allocation, while the conclusion places it between efficiency- and reliability-oriented operating points.

  • Problem

    A unified framework for clustered BS–UAV downlink communications with partitionable RISs is lacking, while conventional NOMA scalability is constrained by SIC complexity and error propagation under imperfect SIC.

    Source: §I · pp. 1–2

  • Method

    The paper develops outage analysis and GRIS clustering, then uses bilevel optimization and IOS-I2S to jointly optimize inter-cluster BS power, intra-cluster NOMA coefficients, and RIS element assignment.

    Source: §I · p. 2

  • Results

    12.3% higher average throughput and 81.0% lower network-wide maximum UAV outage versus equal resource allocation in the evaluated scenario.

    Source: §I · p. 2

  • Takeaways & Limitations

    IOS-I2S provides an intermediate operating point between EOA and ROA while improving efficiency and reliability over NoRIS and ERA.

    Source: §VII · p. 14

Abstract

from arXiv · show

This paper investigates RIS-assisted downlink UAV communications based on NOMA. Since conventional NOMA becomes difficult to scale as the number of UAVs grows, we develop a cluster-based UAV-NOMA framework in which a BS serves multiple UAV groups with the aid of partitionable RISs. Within this framework, we consider direct, RIS-only indirect, and composite links, and develop an analytical model for the received SNR and outage performance under Nakagami-$m$ and double Nakagami-$m$ fading with imperfect SIC. To enable scalable transmission, we introduce a greedy RIS-aware (GRIS) clustering method, which groups UAVs according to spatial and channel-related features. Based on the resulting clusters and RIS assignment, we formulate an efficiency-reliability bilevel optimization problem that jointly optimizes inter-cluster BS power allocation, intra-cluster NOMA power coefficients, and RIS element assignment. Specifically, the outer efficiency problem maximizes the average throughput across clusters, while the inner reliability problem minimizes the worst-UAV outage probability within each cluster. To solve the formulated problem, we propose a two-level iterative framework consisting of an inter-cluster outer-efficiency solver (IOS) and an intra-cluster inner-reliability solver (I2S), where I2S combines a grid-based progressive search (GPS) for NOMA power refinement with reliability-guided RIS element reassignment, and IOS updates the BS power weights. Numerical results demonstrate the effectiveness of GRIS clustering, while pre-optimization analysis reveals efficiency-reliability trade-offs in power allocation. Baseline comparisons illustrate the ability of IOS-I2S to balance efficiency and reliability, while ablation studies highlight the importance of joint optimization.

I. INTRODUCTION

The paper addresses the lack of a unified framework for clustered BS–UAV downlink NOMA with partitionable RISs, developing channel/outage analysis and joint resource optimization under imperfect SIC. It also positions this framework against related RIS-assisted UAV and UAV-NOMA work and describes the clustered system model.

A. RIS-Assisted UAV Communications

  • Prior RIS-assisted UAV studies span diverse UAV roles and objectives, while related work also covers RIS partitioning, clustering, link selection, and joint resource design.Table I summarizes the related work.Source: §I · p. 2, Table I · p. 3

I. INTRODUCTION

  • The paper identifies a gap in unified analysis and optimization for clustered BS–UAV downlink communications with partitionable RISs under imperfect SIC.Its framework jointly optimizes BS power allocation, NOMA power coefficients, and RIS element assignment to balance efficiency and reliability.Source: §I · p. 2
  • IOS-I2S increases average throughput by 12.3% and reduces network-wide maximum UAV outage by 81.0% versus equal resource allocation in the evaluated scenario.Fixing NOMA power coefficients raises maximum outage from 0.0909 to 0.4085 despite optimizing the other resources.Source: §I · p. 2

B. UAV-NOMA Communications

  • The related UAV-NOMA literature uses varied clustering and optimization approaches, while this work combines UAV clustering, downlink NOMA resource allocation, and partitionable RISs in one system model.The cited examples include K-means-based approaches and optimization of placement, power, trajectories, or throughput.Source: B. UAV-NOMA Communications · p. 3

III. SYSTEM MODEL

  • The system serves UAV clusters over orthogonal resource blocks and applies NOMA within each cluster, with a partitionable RIS assigned to each cluster.BS power is split across clusters and then distributed among each cluster’s UAVs using NOMA power coefficients; links may be direct, RIS-only, or composite.Source: §III · p. 4

A. Channel Modeling

The channel model characterizes the RIS-only indirect link using per-element ground-to-RIS and RIS-to-air fading and phase shifts. It accounts for distance-dependent path loss and approximates the resulting channel and SNR distributions.

1) RIS-Only Indirect Link:

  • The RIS-only channel combines ground-to-RIS and RIS-to-air fading across assigned reflecting elements, with a phase shift for each element.The resulting equivalent RIS-only channel gain and maximum instantaneous SNR distribution are characterized using an approximation based on the first Laguerre-series term.Source: 1) RIS-Only Indirect Link · pp. 4–5
  • The RIS phase shifts are selected to maximize received SNR, and the channel model accounts for path loss shared by the assigned elements.The LoS and NLoS path-loss exponents are weighted by the LoS probability.Source: 1) RIS-Only Indirect Link · p. 4
  • The model uses double Nakagami-m fading for each element’s cascaded G2R2A coefficient and assumes the element fading coefficients are independent.The path-loss exponent varies with the LoS probability, which is defined using environmental parameters and transmitter-receiver geometry.Source: 1) RIS-Only Indirect Link · p. 4

2) Direct Link:

The direct G2A link is modeled with Nakagami-m small-scale fading, yielding distributions for its instantaneous SNR. Rayleigh fading is recovered as a special case.

2) Direct Link:

  • The direct G2A channel’s small-scale fading follows a Nakagami-m model, from which the instantaneous SNR PDF and CDF are obtained.Rayleigh fading is recovered when the shape parameter is 1.Source: 2) Direct Link · p. 5

3) Composite Link:

The composite link combines the direct and RIS-only indirect channels, with RIS phase shifts chosen for the composite channel. The analysis approximates its SNR distribution and uses the Q-function in that approximation.

3) Composite Link:

  • The composite channel gain combines the RIS-only indirect and direct channel gains, with the RIS phase shifts set for the composite link.The CDF of its maximum instantaneous SNR is derived using an approximation justified via the central limit theorem.Source: 3) Composite Link · p. 5

B. Effective NOMA Throughput

The section defines ordered-channel NOMA decoding and outage under imperfect SIC, then relates cluster throughput to UAV outage probabilities and assigned resources.

B. Effective NOMA Throughput

  • Under imperfect SIC, UAV m_g retains residual interference from weaker-indexed signals, treats stronger-indexed signals as noise, and must decode all earlier users before its own.Its outage is based on failure to meet any required target rate.Source: B. Effective NOMA Throughput · p. 6
  • Order statistics define the PDF and CDF of the ordered received SNR γ_mg, which is used in the UAV outage analysis.The outage expression is rewritten using the maximum threshold among the decoded signals for non-last users.Source: B. Effective NOMA Throughput · p. 6
  • Cluster throughput R_g depends on BS power weight, NOMA power coefficients, RIS element assignment, and each UAV’s outage probability.The system uses fixed BS transmit power and predetermined UAV target rates in a delay-limited scheme.Source: B. Effective NOMA Throughput · p. 6

IV. UAV CLUSTERING AND RIS ASSIGNMENT

GRIS clustering balances RIS proximity with channel separation, using spatial and direct-channel features to form clusters and assign RISs. These choices target scalable NOMA groups with distinct channel conditions.

IV. UAV CLUSTERING AND RIS ASSIGNMENT

  • GRIS jointly considers UAV–RIS distances and average direct BS–UAV channel gains to construct approximately balanced clusters and refine the partition.The channel criterion promotes larger adjacent gain gaps, reducing sensitivity to small estimation errors that could reverse UAV ordering.Source: §IV · pp. 6–7

A. Cluster-to-RIS Assignment Cost

  • RIS assignment cost is the average 3D distance between UAVs in a cluster and a candidate RIS, with each cluster assigned one RIS and each RIS serving at most one cluster.The minimum-cost assignment is solved with the Hungarian algorithm and recomputed when the partition changes.Source: A. Cluster-to-RIS Assignment Cost · p. 7

B. NOMA Channel Disparity Metric

  • The channel disparity metric is the smallest adjacent ordered direct-channel-gain gap across all clusters; maximizing it prevents well-separated clusters from masking a poorly separated one.Average large-scale direct gains are ordered within each cluster.Source: B. NOMA Channel Disparity Metric · p. 7

C. Normalized Joint Objective

The clustering objective normalizes RIS assignment cost and channel disparity penalties, then GRIS greedily builds and locally refines clusters before assigning RISs. Its candidate moves seek lower objective values while retaining balanced cluster sizes.

C. Normalized Joint Objective

  • The joint objective combines normalized RIS-assignment and channel-disparity penalties, weighted by w_d and w_h, whose sum is one.The metrics use separate RIS-only and channel-only reference clusterings for normalization; normalization does not guarantee penalties in [0, 1].Source: C. Normalized Joint Objective · p. 7

D. Greedy RIS-Aware (GRIS) Clustering

  • Exhaustive clustering becomes computationally prohibitive as UAV numbers grow, so GRIS seeks a high-quality solution through greedy construction, local refinement, and RIS assignment.GRIS minimizes the normalized objective.Source: D. Greedy RIS-Aware (GRIS) Clustering · p. 7

1) Greedy Cluster Construction:

  • Greedy construction seeds one cluster per selected UAV, then assigns each unassigned UAV to a smallest eligible cluster that yields the lowest objective.Candidate destinations must remain below the maximum permitted cluster size, and assignment continues until all UAVs are placed.Source: 1) Greedy Cluster Construction · p. 7

2) Local Refinement and RIS Assignment:

  • Local refinement tests relocations from largest to smallest clusters and pairwise swaps, choosing the move with the largest positive objective improvement.Relocations maintain balance between largest and smallest clusters, while swaps preserve cluster cardinalities; refinement stops when no positive improvement remains.Source: 2) Local Refinement and RIS Assignment · pp. 7–8
  • For each candidate partition, the optimal RIS assignment is obtained by solving the binary assignment problem with the Hungarian algorithm.RIS assignment is recomputed as the partition changes.Source: 2) Local Refinement and RIS Assignment · p. 8

V. PROBLEM FORMULATION AND PROPOSED SOLUTION

The paper formulates a bilevel efficiency–reliability problem and solves it through iterative outer BS-power updates and inner joint NOMA-power and RIS-element optimization. The inner problem is separable across clusters under per-cluster RIS element budgets.

A. Bilevel Efficiency-Reliability Problem Formulation

  • The outer problem maximizes average throughput across clusters by optimizing BS power weights, while the inner problem minimizes the maximum UAV outage within each cluster.The inner variables include NOMA power coefficients and RIS element assignment.Source: A. Bilevel Efficiency-Reliability… · p. 8
  • The NOMA coefficients obey a simplex constraint, imperfect-SIC feasibility is enforced, and each cluster has a limit on assigned RIS elements.The RIS limit is a preassigned element budget for that cluster.Source: A. Bilevel Efficiency-Reliability… · p. 8
  • Per-cluster RIS budgets make the inner reliability problem separable across clusters, allowing the BS to solve clusters in parallel.The resulting optimal NOMA coefficients are used to evaluate cluster throughput and update BS power weights.Source: A. Bilevel Efficiency-Reliability… · p. 8

B. Proposed Bilevel Optimization Framework

  • IOS updates inter-cluster BS power allocation, while I2S jointly optimizes intra-cluster NOMA coefficients and RIS element assignment.The framework iterates between the outer efficiency and inner reliability solvers.Source: B. Proposed Bilevel Optimization… · p. 8
  • GPS refines NOMA power coefficients by searching a grid of candidates around the current coefficients when available, or initializing a candidate set otherwise.The search retains candidates satisfying the stated coefficient-spacing and feasibility conditions.Source: B. Proposed Bilevel Optimization… · p. 9

1) Intra-cluster Inner-reliability Solver (I2S):

I2S refines intra-cluster NOMA power coefficients and RIS element assignments to reduce the worst UAV outage. IOS uses I2S to evaluate candidate BS power weights and updates them to improve average cluster throughput.

1) Intra-cluster Inner-reliability Solver (I2S):

  • I2S alternates NOMA coefficient refinement with reliability-guided RIS reassignment and returns optimized coefficients and element assignments at convergence.Its iterations stop when the NOMA coefficient vector converges.Source: 1) Intra-cluster Inner-reliability… · p. 9
  • I2S selects feasible NOMA power coefficients that minimize the cluster’s maximum UAV outage, then progressively refines the search resolution.GPS searches a global grid initially and local grids around the current coefficients thereafter, retaining candidates that satisfy the simplex and SIC constraints.Source: 1) Intra-cluster Inner-reliability… · p. 9
  • I2S reallocates RIS elements toward the highest-outage UAV, accepting one-element transfers only when they do not worsen the cluster’s maximum outage.It chooses the donor producing the lowest resulting maximum outage and repeats until no non-worsening transfer is available.Source: 1) Intra-cluster Inner-reliability… · p. 9

2) Inter-cluster Outer-efficiency Solver (IOS):

  • For a given BS power weight vector, IOS evaluates average cluster throughput using the intra-cluster solutions returned by I2S.The mapping from BS weights to throughput is implicit through I2S, so IOS treats the outer problem as black-box optimization over the simplex.Source: 2) Inter-cluster Outer-efficiency… · p. 9
  • IOS estimates each cluster’s throughput sensitivity with a feasible finite-difference perturbation, then updates and renormalizes the BS power weights.Clipped exponentiated-gradient updates limit excessively large changes; iterations stop when the throughput change falls below tolerance Δ.Source: 2) Inter-cluster Outer-efficiency… · pp. 9–10

3) Time Complexity of the Proposed Algorithms:

The proposed algorithms combine iterative IOS updates, I2S searches, and GRIS refinement, with complexity depending on cluster sizes, candidate evaluations, and available parallel workers. The numerical evaluation uses a BS-centered cell with 10 UAVs and 3 RISs.

3) Time Complexity of the Proposed Algorithms:

  • I2S complexity depends on GPS search levels and candidate screening, RIS-transfer rounds, cluster size, and parallel donor evaluation.The overall IOS cost is O([1+To(G+1)]⌈G/Wc⌉Ci + ToG^2), in addition to the one-time sequential GRIS cost.Source: 3) Time Complexity of the Proposed… · p. 10
  • GRIS refinement adds a one-time sequential cost of O(M^2(G + Tr)CΨ) to the iterative IOS-I2S complexity.The analysis assumes negligible communication and scheduling overhead and bounds total and feasible GPS candidates at each level.Source: 3) Time Complexity of the Proposed… · p. 10

VI. NUMERICAL RESULTS

  • The simulations deploy 10 UAVs and 3 RISs in a BS-centered cell using Poisson point processes.Key simulation parameters are summarized in Table III.Source: §VI · p. 10, Table III · p. 10

1) Cluster Formation and RIS Assignment:

GRIS balances RIS proximity against channel disparity when forming clusters, and the selected balanced setting is used in the remaining evaluations. The results also examine clustering baselines, cluster-level resource effects, and UAV-level outage trade-offs.

1) Cluster Formation and RIS Assignment:

  • Balanced weights preserve the channel-only disparity of 3.64 dB while reducing RIS assignment cost to 1943.04 m.The RIS-only setting lowers assignment cost to 1529.39 m but has 1.88 dB channel disparity; channel-only clustering has the highest cost, 2120.77 m.Source: 1) Cluster Formation and RIS Assignment · p. 10
  • Varying the GRIS weights produces only three distinct clustering configurations, and the balanced configuration is adopted for the remaining results.Discrete UAV memberships and RIS assignments mean different weight values can yield the same configuration.Source: 2) Impact of wd and wh · pp. 10–11

3) Baseline Comparison:

  • GRIS achieves lower RIS assignment cost and larger minimum channel disparity than balanced random and balanced K-means baseline averages.The baseline results are averaged over 1000 Monte Carlo trials, while GRIS gives identical results across tested random seeds.Source: 3) Baseline Comparison · p. 11, Table IV · p. 11

1) Cluster-Level Performance:

  • At 144 RIS elements, cluster losses reach 0.127 and 0.105 for Clusters 1 and 2, while network-level loss falls from 0.227 to 0.148 as elements increase.Cluster 3 has the largest loss reduction, from 0.362 to 0.196, but retains the highest cluster loss throughout the range.Source: 1) Cluster-Level Performance · p. 11, Figure 5 · p. 11
  • At 20 dBm, Lg is 0.0121, 0.0049, and 0.0007 for Clusters 1, 2, and 3, respectively, as BS transmit power increases.Increasing the power weight ω1 reduces Cluster 1 loss but increases losses for Clusters 2 and 3; network-level loss is lowest at 0.1414 when ω1 = 0.25.Source: 1) Cluster-Level Performance · p. 11, Figure 5 · p. 11

2) UAV-Level Performance:

  • Increasing β1 reduces UAV 1’s outage, while UAV 7’s outage first falls and then rises; maximum outage is minimized near β1 = 0.8588.Cluster 1 loss reaches its minimum of 0.0850 near β1 = 0.8455, showing that efficiency and reliability favor distinct allocations.Source: 2) UAV-Level Performance · p. 11
  • The SIC feasibility limit is ξmax ≈ 0.0111, set by UAV 3; beyond it, residual interference increases UAV 7’s outage.UAV 1’s outage remains unchanged because it performs no SIC.Source: 2) UAV-Level Performance · pp. 11–12
  • The common target rate’s feasibility boundary is 2.369 bpc, set by UAV 1’s decoding constraint; higher targets increase outage near that boundary.UAV 7’s outage rises sharply near the boundary, alongside a rapid increase in cluster loss.Source: Figure 6 · p. 11, 2) UAV-Level Performance · p. 12

C. Performance Evaluation of the Proposed Optimization

IOS-I2S improves throughput and outage relative to NoRIS and equal resource allocation, while occupying an intermediate efficiency-reliability point between EOA and ROA. The reported sensitivity, convergence, and ablation results describe how that operating point is selected and why joint optimization matters.

1) Hyperparameter Sensitivity and Convergence Analysis:

  • Among Pareto-optimal settings, (α, λ) = (0.5, 0.9) yields maximum UAV outage 0.091 and average throughput 6.377 bpc, while (0.5, 0.8) yields 6.469 bpc at outage 0.147.The selected setting maintains outage below 0.1 and converges faster than the closely performing (0.75, 0.9) configuration.Source: 1) Hyperparameter Sensitivity and… · p. 12
  • IOS converges after 14 iterations to BS weights approximately [0.257, 0.239, 0.504], with the largest share allocated to Cluster 3.The weights start equally and shift toward Cluster 3 before their updates diminish.Source: 1) Hyperparameter Sensitivity and… · p. 12
  • I2S coefficient and RIS-assignment updates diminish toward zero; Cluster 2 converges in a few iterations, while Clusters 1 and 3 need more updates.The assignment changes are relatively large initially as RIS elements are redistributed among UAVs.Source: 1) Hyperparameter Sensitivity and… · pp. 12–13
  • For the selected setting, final BS weights are [0.2570, 0.2395, 0.5035], and maximum UAV outage remains below 0.1 in every cluster.The corresponding cluster throughputs are 5.6472, 5.7, and 7.7849 bpc for Clusters 1–3.Source: Table V · p. 13, 1) Hyperparameter Sensitivity and… · p. 13

2) Performance Comparison with Baseline Schemes:

  • 16.1% and 12.3% higher throughput, and 77.4% and 81.0% lower maximum outage, than NoRIS and ERA, respectively; IOS-I2S lies between EOA and ROA.OMA has the lowest maximum outage, 0.0176, but throughput of 1.9960 bpc; EOA reaches 6.5212 bpc, while ROA attains outage 0.0752 at 6.3618 bpc.Source: Table VI · p. 13, 2) Performance Comparison with… · p. 13

3) Decision-Variable Ablation Study:

  • Joint optimization achieves 6.3774 bpc and maximum outage 0.0909; fixing βg raises maximum outage to 0.4085 even when other variables remain optimized.Fixing ω yields throughput 6.1701 bpc and outage 0.1055, while disabling RIS assignment optimization raises outage to 0.1586.Source: Table VII · p. 13, 3) Decision-Variable Ablation Study · p. 13

VII. CONCLUSION

  • The conclusion identifies mobility-aware clustering and learning-based online resource optimization as future extensions for changing UAV positions and dynamic, non-stationary channels.The reported comparisons also state that GRIS improves both clustering metrics over baseline averages and IOS-I2S improves both metrics over NoRIS and ERA.Source: §VII · pp. 13–14
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