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Optimization of Wireless Relaying With Flexible UAV-Borne Reflecting Surfaces
Taniya Shafique, Hina Tabassum, Ekram Hossain
TL;DR
The paper develops a theoretical framework for analyzing and optimizing integrated UAV-IRS relaying across UAV-only, IRS-only, and integrated modes. It derives performance expressions, formulates fractional-programming optimizations for altitude and IRS-element count, and provides a mode-selection criterion. Numerical results validate the expressions and algorithms, while showing that the integrated mode outperforms the separate modes for outage and ergodic capacity.
Problem
Integrated UAV-IRS performance characterization and optimization had not been investigated, despite the need to jointly exploit flexible UAV deployment and IRS-assisted relaying.
Method
The paper derives exact and approximate outage, capacity, and energy-efficiency expressions for three transmission modes and solves altitude and IRS-element optimization problems using fractional programming.
Results
The integrated mode outperforms IRS-only and UAV-only modes for all N in terms of outage and ergodic capacity.
Takeaways & Limitations
An analytic criterion supports transmission-mode selection, while optimal height and IRS-element count depend on the operating mode and propagation conditions.
Abstract
from arXiv · showhide
This paper presents a theoretical framework to analyze the performance of integrated unmanned aerial vehicle (UAV)-intelligent reflecting surface (IRS) relaying system in which IRS provides an additional degree of freedom combined with the flexible deployment of full-duplex UAV to enhance communication between ground nodes. Our framework considers three different transmission modes: {\bf (i)} UAV-only mode, {\bf (ii)} IRS-only mode, and {\bf (iii)} integrated UAV-IRS mode to achieve spectral and energy-efficient relaying. For the proposed modes, we provide exact and approximate expressions for the end-to-end outage probability, ergodic capacity, and energy efficiency (EE) in closed-form. We use the derived expressions to optimize key system parameters such as the UAV altitude and the number of elements on the IRS considering different modes. We formulate the problems in the form of fractional programming (e.g. single ratio, sum of multiple ratios or maximization-minimization of ratios) and devise optimal algorithms using quadratic transformations. Furthermore, we derive an analytic criterion to optimally select different transmission modes to maximize ergodic capacity and EE for a given number of IRS elements. Numerical results validate the derived expressions with Monte-Carlo simulations and the proposed optimization algorithms with the solutions obtained through exhaustive search. Insights are drawn related to the different communication modes, optimal number of IRS elements, and optimal UAV height.
I. INTRODUCTION
The paper addresses the previously uninvestigated characterization and optimization of integrated UAV-IRS systems. It develops a framework spanning performance analysis, parameter optimization, and transmission-mode selection.
- Integrated UAV-IRS characterization and optimization had not been investigated in prior work.
- The paper optimizes IRS-element count and UAV altitude to maximize spectral and energy efficiency.
- The framework characterizes outage probability, ergodic capacity, and energy efficiency for integrated UAV-IRS systems.
- It formulates IRS-only and UAV-only design tasks as fractional optimization problems, including energy-efficiency maximization and power minimization under rate constraints.
- An analytic criterion selects UAV-only or IRS-only transmission to maximize capacity and energy efficiency for a given IRS-element count.
- Numerical results report that IRS-only operation is more energy efficient than UAV-only operation at lower altitudes, with low to moderate active-element counts and larger UAV-source or UAV-destination distances.
II. SYSTEM MODEL AND ASSUMPTIONS
The system places an IRS-equipped UAV between ground source and destination nodes without a direct source-destination link. It models altitude-dependent aerial channels and compares UAV-only, IRS-only, and integrated transmission modes.
- A UAV carrying an IRS assists communication between ground source S and destination D, with no direct S-D link.
- The UAV can be positioned at any altitude h within [hmin, hmax], whose limits are determined by aviation authorities.
- LoS probability and path-loss exponent depend on elevation angle and environment parameters for the UAV-ground links.
- All modes use the same bandwidth, while UAV operation uses in-band full-duplex transmission and is limited by self-interference.
- UAV-only uses the UAV relay, IRS-only uses the IRS relay, and integrated mode combines both received signals through selection combining.
- The receiver buffers IRS observations arriving one time slot before UAV observations, while the IRS uses a uniform linear array and controller.
1) UAV-only Mode:
The UAV-only mode relays decoded data from the source to the destination through a full-duplex UAV, with end-to-end performance determined by the two aerial links and residual self-interference.
- Channel model: The source-to-UAV and UAV-to-destination links use Rician fading with channel power modeled by non-central chi-square variables.The link SNRs depend on path loss, transmit powers, noise, residual self-interference, and the corresponding channel gains.
- Receiver operation: Selection combining chooses the branch with the highest SNR and avoids co-phasing multiple branches.This gives the receiver low overhead, simple implementation, and a tractable analysis.
- Signal model: The full-duplex UAV decodes the source signal before relaying it to the destination.The source transmits BPSK to the UAV, which forwards the decoded signal to D.
- End-to-end model: The UAV-only end-to-end SNR is modeled from the source-to-UAV and UAV-to-destination transmissions under residual self-interference.The UAV absorbs incoming IRS signals in this mode, so the IRS remains non-active.
- IRS assumptions: The IRS geometry is represented by element-wise channels and phase shifts, while the IRS can also operate with minimal reflection delay and zero self-interference.For compact UAV-mounted surfaces, source and destination distances to each element are approximated by their distances to the UAV.
E. Energy Consumption Model
The model accounts for UAV, IRS, transmission, and terrestrial circuit power consumption, then uses these components to characterize outage probability, capacity, and energy efficiency across the three relaying modes.
- Power components: Total system power includes UAV hovering and transmission, IRS hardware, source and destination transmission, and ground-base-station circuit consumption.The mode-specific totals are PUAV = pu + pd + C, PIRS = pu + pIRS + C, and PINT = pu + pd + pIRS + C.
- UAV consumption: UAV power is the sum of circuit, IRS, and hovering power: puav = pc + pIRS + ph.The hovering model uses UAV and rotor parameters, while the UAV communication time is tied to hovering time.
- IRS consumption: IRS power is passive transmission-wise but increases with the number of elements and phase resolution.Its hardware consumption is pIRS = NPr(b); the cited examples give Pr(6) = 78 mW and Pr(∞) = 45 dBm.
- Outage analysis: UAV-only outage is the probability that the minimum of the two hop SNRs falls below Γ0.It is expressed through the two link CDFs as OUAV = 1 − (1 − Fγu(Γ0))(1 − Fγd(Γ0)).
- IRS-only analysis: For IRS-only relaying, the product of independent non-identical Rician amplitudes is modeled by a double-Rician distribution and approximated using a Gaussian limit for large N.Simulations show convergence to a non-central chi-square variable for N ≥20.
C. Outage Probability of Integrated UAV-IRS Mode of Relaying
The paper derives tractable capacity and energy-efficiency characterizations for UAV-only, IRS-only, and integrated UAV-IRS relaying, using exact expressions and approximations validated against simulations.
- Integrated mode: The integrated UAV-IRS receiver uses selection combining to select among transmission modes, with outage derived from the UAV-only and IRS-only outcomes.The integrated mode provides an additional operating choice but increases resource consumption because both UAV and IRS transmissions are active.
- Capacity and energy efficiency: Energy efficiency is defined as each mode’s ergodic capacity divided by its corresponding power consumption.The paper derives exact end-to-end energy-efficiency expressions for the considered modes.
- UAV-only characterization: The UAV-only capacity and energy-efficiency expressions are obtained using Jensen’s inequality and approximations involving the minimum of the two hop SNRs.The resulting expressions are stated in Proposition 2 and their bounds are validated using simulations.
- Validation: The derived approximations and bounds are compared with exact analyses and Monte-Carlo simulations across the three relaying modes.The cited validation passages include the UAV-only bounds and comparisons for capacity and energy efficiency.
- IRS-only and integrated characterization: The IRS-only capacity and energy-efficiency expressions use Jensen’s inequality and the moments of the non-central chi-square representation.The integrated-mode approximation similarly combines the IRS end-to-end channel with the two UAV link channels under selection combining.
V. OPTIMIZATION OF UAV-IRS RELAYING
The optimization section targets energy efficiency and power consumption under rate constraints, jointly considering UAV-only and IRS-only relaying design variables.
- Optimization objectives: The optimization problems maximize network energy efficiency and minimize network power consumption subject to rate constraints.Both UAV-only and IRS-only relaying modes are considered.
- Design variables: For IRS-only relaying, the optimized variables are the number of active IRS elements and the UAV-mounted IRS height.For UAV-only relaying, the optimization instead targets the corresponding UAV design parameters.
A. IRS-only Mode: Optimizing the Number of IRS Elements
The IRS-only mode optimizes the number of IRS elements through fractional-programming formulations, using quadratic transforms and iterative algorithms with global-optimality guarantees for key subproblems.
- Problem formulation: The IRS-only energy-efficiency maximization is formulated as a fractional program in λ, which is directly proportional to the number of IRS elements N.The feasible range is bounded by practical minimum and maximum IRS sizes.
- Optimization method: Quadratic transformation converts the concave-over-convex formulation into a convex form by introducing an auxiliary variable y.The algorithm alternately optimizes λ and y.
- Optimization method: The iterative algorithm is guaranteed to converge to the global optimal solution for the single-ratio objective in P1.A related multiple-ratio problem is also solved using quadratic transformation and an algorithm with proved convergence.
- Solution: The optimal IRS size N⋆ is obtained from the optimized λ⋆ through the relation N⋆ = λ⋆ − λ′.The algorithm updates λ using a convex optimization tool for fixed auxiliary variables.
- Validation: Approximation-induced mismatch in the optimal solutions is negligibly small and is mainly due to arctan and Taylor approximations.The comparison with exact solutions is validated in Fig. 5.
C. UAV-only Mode: Height Optimization
The UAV-only mode optimizes UAV height using transformed fractional and max-min formulations, with convex subproblems under specific concavity conditions and negligible approximation mismatch.
- Problem formulation: Height optimization is based on an approximation for the UAV-only mode, where the channel-related terms depend on the UAV height h.The resulting objective is non-convex and is transformed before optimization.
- Concavity condition: Under a specific condition, the transformed objective has a concave-convex form in h, guaranteeing an optimal solution for the corresponding problem.The numerator O_i(h) is concave under the stated condition, while R_i(h) is convex.
- Optimization method: Quadratic transformation introduces auxiliary variables and recasts the max-min problem as maximizing z subject to constraints involving O_i(h).Because O_i(h) can be negative, the formulation is shifted to make it positive inside the square-root constraint.
- Algorithm: The resulting optimization is solved iteratively by updating h and z with fixed auxiliary variables using a convex optimization tool.Algorithm 3 performs the updates for the UAV-only mode.
- Validation: The transformation into the final convex formulation does not impact the optimality of the solution.Approximate formulations show only a slight mismatch with exhaustive-search solutions.
D. Mode Selection to Maximize Energy Efficiency
Mode selection compares UAV-only, IRS-only, and integrated UAV-IRS operation using SNR- or power-based criteria, then pairs the selected mode with its optimized height and IRS size.
- Selection framework: The framework derives mode-selection probabilities from instantaneous fading channels and develops a criterion for selecting the number of active IRS elements.The criterion is used with optimized heights to maximize overall integrated-system energy efficiency.
- SNR-based selection: The IRS-only mode is enabled when the number of IRS elements exceeds the threshold N_th.The threshold criterion is based on average SNR at an arbitrary height.
- Performance comparison: The selected mode and corresponding optimal height are chosen by comparing the optimized terms for UAV-only and IRS-only operation.The analysis provides outage, capacity, power-consumption, and energy-efficiency comparisons across the modes.
- Power-based selection: For power-consumption-based selection, the integrated UAV-IRS mode is never selected because its power consumption exceeds that of the UAV-only and IRS-only modes.IRS-only is selected when N ≤ p_d/P_r(b), and UAV-only otherwise.
- SNR-based selection: For SNR-based selection, the integrated UAV-IRS mode is selected because it chooses the maximum SNR of the IRS-only and UAV-only modes.This differs from energy-efficiency selection, where the integrated mode is not selected because its denominator includes higher power consumption.
VI. NUMERICAL RESULTS AND DISCUSSION
Numerical results examine outage, capacity, power consumption, and energy efficiency across transmission modes while optimizing IRS size and UAV height. The results show mode performance depends on IRS elements, bit-resolution power, LoS probability, distances, and altitude.
- Outage and capacity: As N increases, IRS-only and integrated UAV-IRS modes reduce outage probability and increase capacity through enhanced IRS transmission links.
- Outage and capacity: The integrated UAV-IRS mode outperforms IRS-only and UAV-only modes for all N in outage probability and ergodic capacity.
- Outage and capacity: Lower LoS probability worsens all schemes and requires more IRS elements to reduce outage and maximize transmission capacity.
- Power and energy efficiency: IRS-only power consumption increases with N, with a steeper slope as per-element power Pr(b) increases, while UAV-only consumption is independent of N.
- Power and energy efficiency: Energy efficiency first increases with N and then decreases when power consumption becomes dominant; higher Pr(b) therefore favors fewer IRS elements.
- IRS-size optimization: Optimal IRS size increases with source–UAV distance, while optimal energy efficiency decreases; proposed solutions match exhaustive-search optima.
- Height and mode selection: For weak LoS, UAV-only outperforms IRS-only, whereas strong LoS favors IRS-only across a wide altitude range; integrated mode performs better than both in weak LoS.
- Height and mode selection: When source–UAV distance is below 1200 m, UAV-only is optimal; near the destination, IRS-only becomes optimal and the selected height switches accordingly.
VII. CONCLUSION
The paper analyzes an integrated UAV-IRS relaying system in three transmission modes and evaluates outage probability, ergodic capacity, and energy efficiency. It optimizes IRS size and UAV height and derives criteria for mode and height selection.
- The study characterizes outage probability, ergodic capacity, and energy efficiency for IRS-only, UAV-only, and integrated UAV-IRS relaying modes.
- For IRS-only mode, the paper optimizes IRS element count and UAV height, while UAV-only optimization focuses on UAV height.
- Optimal height varies with the selected transmission mode.
- An analytical criterion is provided for optimal height and mode selection in terms of Ri(h).
APPENDIX A: RATIO OF CONCAVITY-CONVEXITY OF (44)
The appendix analyzes the curvature of the ratio used in height optimization. Under stated distance and parameter conditions, it establishes concavity of the negative outage term and convexity of Ri(h).
- The analysis treats separate cases ẑi > h and h > ẑi by substituting the corresponding form of max(ẑi,h).
- Under the stated parameter-order assumption, Ri(h) is convex.
- A horizontal source–UAV distance of at least 10 m is used as a condition supporting concavity of the numerator −Oi(h).