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Intelligent Reflecting Surface Enhanced Multi-UAV NOMA Networks

Xidong Mu, Yuanwei Liu, Li Guo, Jiaru Lin, H. Vincent Poor

arXiv:2101.09145v2cs.ITeess.SP

TL;DR

The paper addresses interference and resource-allocation challenges in multi-UAV NOMA networks assisted by IRSs. It jointly optimizes UAV placement and power, IRS reflections, and decoding orders using a BCD-based iterative method. The proposed NOMA-IRS scheme achieves higher sum rate than OMA-IRS and NOMA without IRS, while IRS assistance enhances served-user channels and mitigates inter-UAV interference.

  • Problem

    Multi-UAV IRS-NOMA design requires jointly handling coupled placement, power, reflection, and decoding-order variables in a mixed-integer non-convex optimization problem.

  • Method

    The paper proposes a multi-UAV IRS-NOMA framework and solves its joint design using a BCD-based algorithm that alternates among three subproblems with penalty and successive convex approximation methods.

  • Results

    The proposed NOMA-IRS scheme achieves higher sum rate than OMA-IRS and NOMA without IRS, while IRS enhances served-user channels and mitigates inter-UAV interference.

  • Takeaways & Limitations

    Optimizing UAV placement makes NOMA's sum-rate gain more distinct by enabling flexible decoding-order design.

  • Takeaways & Limitations

    Additional interference-cancellation methods are required for large UAV transmit power, motivating future investigation.

Abstract

from arXiv · show

Intelligent reflecting surface (IRS) enhanced multi-unmanned aerial vehicle (UAV) non-orthogonal multiple access (NOMA) networks are investigated. A new transmission framework is proposed, where multiple UAV-mounted base stations employ NOMA to serve multiple groups of ground users with the aid of an IRS. The three-dimensional (3D) placement and transmit power of UAVs, the reflection matrix of the IRS, and the NOMA decoding orders among users are jointly optimized for maximization of the sum rate of considered networks. To tackle the formulated mixed-integer non-convex optimization problem with coupled variables, a block coordinate descent (BCD)-based iterative algorithm is developed. Specifically, the original problem is decomposed into three subproblems, which are alternatingly solved by exploiting the penalty method and the successive convex approximation technique. The proposed BCD-based algorithm is demonstrated to be able to obtain a stationary point of the original problem with polynomial time complexity. Numerical results show that: 1) the proposed NOMA-IRS scheme for multi-UAV networks achieves a higher sum rate compared to the benchmark schemes, i.e., orthogonal multiple access (OMA)-IRS and NOMA without IRS; 2) the use of IRS is capable of providing performance gain for multi-UAV networks by both enhancing channel qualities of UAVs to their served users and mitigating the inter-UAV interference; and 3) optimizing the UAV placement can make the sum rate gain brought by NOMA more distinct due to the flexible decoding order design.

I. INTRODUCTION

UAV-enabled communications offer controllable aerial deployment and high-capacity access, but multiple UAVs create severe line-of-sight interference. IRS and NOMA are presented as complementary tools for improving channels, suppressing interference, and serving many users.

  • UAV communications: UAVs can act as aerial base stations and exploit controllable mobility to improve ground-user channel conditions.They may fly closer to intended users while supporting applications such as disaster recovery and temporary hotspot offloading.
  • Challenges: Multiple UAV-mounted base stations face severe interference from line-of-sight air-to-ground channels.The challenge becomes especially pronounced when several UAVs transmit concurrently.
  • IRS assistance: IRSs use reconfigurable passive reflecting elements to combine desired signals coherently or suppress interference destructively.Their reflection coefficients can be adjusted through amplitudes and phase shifts, and they can be deployed on existing structures.
  • NOMA access: NOMA lets multiple users share time/frequency resources through superposition coding, SIC, and power-domain separation.It is motivated by spectral-efficiency and massive-connectivity advantages for UAV-enabled beyond-5G networks.
  • Smart NOMA: Jointly changing UAV and IRS channels enables flexible NOMA decoding orders instead of relying only on conventional channel-condition-based ordering.This motivates a smart NOMA operation in which mobility and IRS reflection adjustments enhance or degrade user channels.

B. Motivation and Contributions

The paper addresses the coupled design challenges of IRS-enhanced multi-UAV NOMA networks by proposing a joint optimization framework and an iterative solution method. Numerical results report improved sum rate, channel quality, interference management, and NOMA gains relative to benchmark schemes.

  • Motivation: Existing IRS-UAV studies largely consider single-UAV or single-user settings, leaving IRS-enhanced multi-UAV NOMA performance insufficiently investigated.The paper identifies this as an open area and frames multi-UAV, multi-user operation as the target setting.
  • Challenges: Multi-UAV NOMA design jointly couples UAV placement, IRS reflection coefficients, transmit power, and channel-condition-based decoding orders.UAV placement must balance desired signal strength and inter-UAV interference, while IRS coefficients are shared across multiple users.
  • Contributions: The proposed framework uses NOMA at each UAV-mounted base station and an IRS to enhance intended-user transmission while mitigating interference to unintended users.The associated objective jointly optimizes UAV 3D placement and transmit power, the IRS reflection matrix, and NOMA decoding orders for sum-rate maximization.
  • Solution Method: A BCD-based iterative algorithm alternates among three decomposed subproblems using penalty methods and successive convex approximation.The subproblems cover UAV placement and decoding-order design, IRS reflection design, and UAV transmit-power optimization.
  • Solution Method: The algorithm converges to a stationary point of the original problem with polynomial time complexity.This establishes a tractable solution guarantee for the formulated coupled optimization problem.
  • Results: Numerical results show higher sum rates than benchmark schemes, while IRS deployment improves served-user channels and mitigates interference to unserved users.Optimizing UAV placement further enlarges users’ channel differences and enhances NOMA’s gain over OMA through flexible decoding-order design.

A. Channel Model

The channel model combines UAV–user, UAV–IRS, and IRS–user links with LoS, Rician, and random NLoS components, then models IRS-assisted NOMA transmission and SIC. Users share spectrum, while UAV placement, IRS phase shifts, decoding order, and power allocation shape received rates.

  • A. Channel Model: The model represents channels using deterministic LoS and random Rayleigh-distributed NLoS components, with Rician models for UAV–user and IRS–user links.The UAV–IRS channel is assumed to be LoS.
  • A. Channel Model: The IRS uses a uniform linear array, with steering responses determined by carrier wavelength, element spacing, and angles of departure and arrival.The formulation assumes an integer number of IRS elements and continuous phase shifts.
  • A. Channel Model: The effective channel power gain combines the UAV–user, IRS–user, and UAV–IRS links through the IRS reflection matrix.The model includes path-loss exponents, Rician factors, and a reference-distance path loss.
  • B. NOMA Transmission: Multiple UAVs share one frequency band and use NOMA to serve ground users, whose signals are transmitted with allocated powers under per-UAV power constraints.The received signal includes additive white Gaussian noise, and SIC removes intra-group interference.
  • B. NOMA Transmission: NOMA decoding orders are represented by binary variables, with stronger-channel users decoding weaker-user signals before decoding their own.The formulation permits Mk! decoding-order combinations per group and allocates higher power to weaker-channel users.
  • B. NOMA Transmission: Successive interference cancellation produces each user’s SINR, which determines its communication rate through Rk,i = log2(1 + γk,i).The ordering and power constraints support non-trivial rates for weaker users and improved fairness.

III. PROBLEM FORMULATION

The section formulates an expected-rate maximization problem under random channel gains and decoding orders. It uses an analytical approximation based on channel-power statistics and user–UAV distances, relying on statistical rather than instantaneous CSI.

  • III. PROBLEM FORMULATION: The optimization objective is to maximize the sum rate of all users in the considered networks.The section first introduces the performance metric before stating the joint optimization problem.
  • A. Performance Metrics: The user rate Rk,i and expected achievable rate E{Rk,i} are random because the channel contains random NLoS components.The expected rate is used because the underlying channel-rate distribution is difficult to obtain in closed form.
  • A. Performance Metrics: The expected rate is approximated using a theorem for independent positive random variables and a lemma for expected effective channel power gain.The resulting expression is reported in equation (15).
  • A. Performance Metrics: The approximation is reported to achieve high accuracy in UAV-assisted communications.The proof references an appendix, while the accuracy statement supports using the approximation for subsequent design.
  • A. Performance Metrics: The approximated rate depends on deterministic LoS components, large-scale path losses, and the IRS reflection matrix.This dependence makes the metric suitable for optimizing IRS-assisted network design variables.
  • A. Performance Metrics: The formulation uses statistical CSI rather than instantaneous CSI because acquiring instantaneous CSI is challenging for nearly passive IRSs.The paper assumes perfect statistical CSI can be obtained through recently proposed estimation methods.
  • A. Performance Metrics: The decoding orders among users are also random and are approximated using distances between users and their paired UAVs.The approximation relies on direct UAV–user links dominating effective channel gains because UAV–IRS–user links experience substantial path loss.
  • A. Performance Metrics: The distance-based decoding-order approximation is supported by direct-link fading being on a different magnitude scale from distance-dependent average path loss.A shorter distance to the paired UAV generally corresponds to a higher effective channel power gain.

B. Joint Optimization Problem Formulation

The paper formulates joint optimization of UAV placement, transmit power, IRS reflection, and NOMA decoding orders to maximize network sum rate. The resulting mixed-integer non-convex problem is addressed by a BCD-based iterative procedure using penalty methods and SCA.

  • B. Joint Optimization Problem Formulation: The objective jointly optimizes UAV 3D placement, transmit power, IRS reflection matrix, and intra-group NOMA decoding orders for maximum sum rate.The optimization is posed as an offline design under known ground-user locations and statistical CSI.
  • B. Joint Optimization Problem Formulation: Constraints impose UAV height and separation limits, transmit-power bounds, IRS phase-shift restrictions, and decoding-order consistency.The decoding constraints assign the nearer user as stronger and prevent both paired users from receiving the same strength designation.
  • B. Joint Optimization Problem Formulation: The formulation is difficult because variables are highly coupled, the objective is neither concave nor convex, and binary decoding-order variables create integer constraints.Consequently, finding a globally optimal solution is difficult.
  • IV. BCD-BASED ITERATIVE ALGORITHM: BCD divides the variables into three blocks and alternately optimizes UAV placement and decoding orders, transmit power, and IRS reflection while fixing the other blocks.The power block uses SCA, while the placement and decoding-order block is also treated iteratively.
  • IV. BCD-BASED ITERATIVE ALGORITHM: Auxiliary variables, continuous relaxations, and penalty terms transform binary and non-convex constraints into tractable subproblems.The penalty formulation becomes equivalent to the binary-constrained problem as the penalty coefficient increases, while SCA supplies iterative suboptimal solutions.
  • IV. BCD-BASED ITERATIVE ALGORITHM: SCA replaces non-convex objective and constraint components with first-order approximations and convex lower bounds.The resulting convex subproblem can be solved using existing convex optimization solvers such as CVX.
  • IV. BCD-BASED ITERATIVE ALGORITHM: The proposed algorithm has a non-decreasing objective across iterations and is guaranteed to converge to a stationary point of the original problem.The computational complexity is polynomial, while an inner algorithm is guaranteed to converge to a locally optimal solution.

V. NUMERICAL RESULTS

The numerical evaluation uses a two-UAV, two-group network with three users per group and fixed simulation parameters. Results are generated from one random user-distribution realization.

  • V. NUMERICAL RESULTS: The simulated network contains two user groups served by K = 2 UAVs, with 3 users per group distributed across adjacent 250×250 m2 areas.The reported results use one random realization of the user distribution.
  • V. NUMERICAL RESULTS: UAV heights are constrained to Zmin = 60 meter and Zmax = 100 meter, with equal maximum transmit power across UAVs.The accuracy threshold is εmax = 0.1 and the corresponding placement step is δ = 5 meter.
  • V. NUMERICAL RESULTS: The initialization uses e N = 10 initial-point sets, uniformly random horizontal UAV locations, midpoint heights, distance-based decoding orders, and random IRS phases.Each UAV initially uses maximum transmit power equally allocated among served users.

A. Convergence of BCD-based Algorithms

The convergence study evaluates the BCD-based algorithm under three combinations of IRS size and UAV transmit power. The algorithm converges in all three cases, with larger IRS size requiring additional iterations.

  • A. Convergence of BCD-based Algorithms: The study compares M = 20, Pmax = 20 dBm; M = 60, Pmax = 20 dBm; and M = 60, Pmax = 30 dBm.These cases vary the number of IRS sub-surfaces and maximum UAV transmit power.
  • A. Convergence of BCD-based Algorithms: The proposed BCD-based algorithm converges as the number of iterations increases in all three cases.The figure reports convergence for different simulation parameters.
  • A. Convergence of BCD-based Algorithms: Around 5 extra iterations are required in Cases 2 and 3, where M = 60, because larger M increases Algorithm 2’s computational complexity.The additional iterations occur in both higher-IRS-size cases.

B. Benchmark Schemes

The evaluation compares the proposed scheme with OMA and interference-free benchmarks. These benchmarks remove selected interference, decoding-order, or power-design components to isolate performance differences.

  • B. Benchmark Schemes: The OMA benchmark shares one frequency band among UAVs and serves users in equal-size orthogonal time slots.Each UAV uses transmit power satisfying 0 ≤ pk ≤ Pmax.
  • B. Benchmark Schemes: The interference-free benchmark assigns UAVs orthogonal frequency bands and equal-size orthogonal time slots, eliminating inter-UAV interference.All UAVs use maximum transmit power in this benchmark.
  • B. Benchmark Schemes: The proposed algorithm is reused for the benchmarks with scheme-specific terms removed from the optimization problems.OMA omits intra-group interference and decoding-order design, while the interference-free case omits interference, decoding-order, and UAV-power design.

C. Optimal UAV Placement for Different Schemes

The optimized UAV placements differ across NOMA, OMA, and IF because placement affects both served-user signal strength and inter-group interference. NOMA and OMA place UAVs near selected served users, whereas IF favors symmetric placement to enhance all served users.

  • Comparison: The figure compares the optimal placements of the two UAVs obtained for the different transmission schemes.The proposed BCD-based algorithm supplies these placements under Pmax = 20 dBm and M = 40.
  • NOMA and OMA: NOMA and OMA place the two UAVs near users (1, 1) and (2, 3), respectively, with both UAVs flying at z_k = Zmin.These placements balance served-user signal strength against interference to unserved users.
  • NOMA and OMA: For NOMA and OMA, UAV locations affect both desired received signal strengths and inter-group interference to unserved users.Consequently, the UAVs remain near some served users while staying relatively far from other unserved users.
  • IF: IF places the two UAVs symmetrically among served users and uses the minimum flying height Zmin.Because IF does not need to control inter-group interference, its placement prioritizes received signal strengths for all served users.

D. Effect of Deploying the IRS

The IRS changes channel qualities differently across transmission schemes by enhancing desired links and, for non-orthogonal schemes, reducing interference links. These channel effects help explain the scheme-dependent UAV placements and sum-rate behavior.

  • NOMA and interference effects: The IRS enhances channel gains from UAVs to served users while degrading gains from UAVs to unserved users, thereby reducing interference.For user (1, 3), the desired gain with UAV 1 increases by more than 10%, while the interference gain with UAV 2 decreases by more than 40%.
  • User-dependent channel effects: The IRS effect is especially pronounced for users (1, 3) and (2, 1), which are closest to the IRS.Their proximity allows them to benefit substantially from the IRS-enhanced channel qualities.
  • NOMA and interference effects: For NOMA, mitigating inter-group interference is an effective way to increase sum rate because rates are dominated by users with good channel conditions.Users (1, 1) and (2, 3) are closest to the UAVs in the NOMA placement.
  • OMA: For OMA, the IRS produces the same double effect at each user, with the strongest improvement at user (1, 3).The figure evaluates channel-quality variation under the optimized UAV placements with Pmax = 20 dBm and M = 40.
  • IF: For IF, the IRS only enhances desired channel gains because completely orthogonal transmission eliminates interference.The strongest channel-gain improvements occur for users (1, 3) and (2, 1), which are near the IRS.

E. Sum Rate versus M and Pmax

The experiments examine how IRS size, UAV placement, and transmit power affect sum rate across NOMA, OMA, and IF. NOMA benefits most from IRS and placement optimization at limited transmit power, while IF becomes superior at sufficiently large transmit power.

  • Sum rate versus M: Sum rates for all IRS-assisted schemes increase with the number of IRS sub-surfaces M, whereas schemes without IRS remain unchanged.Larger IRSs provide higher reflecting-array gains.
  • Sum rate versus M: The proposed NOMA scheme achieves the best sum-rate performance among the three transmission schemes.NOMA serves all users simultaneously in every resource block, while UAV placement and IRS reflection provide additional degrees of freedom for decoding-order design and interference mitigation.
  • Sum rate versus M: The IRS gain is more pronounced for NOMA than for the other transmission schemes.This supports the promise of the IRS-enhanced multi-UAV NOMA framework.
  • Placement optimization: Optimizing UAV placement substantially improves NOMA sum rate even without IRS and makes NOMA's gain over OMA more distinct.Placement enlarges user-channel disparity and enables flexible NOMA decoding-order design; for OMA, placement optimization is more effective than IRS reflection optimization.
  • Sum rate versus Pmax: As maximum transmit power increases, NOMA and OMA become interference-limited and their sum rates approach finite upper bounds.Inter-group interference causes this saturation at high transmit power.
  • Sum rate versus Pmax: IF outperforms NOMA and OMA above a certain transmit-power level, while NOMA is preferable at limited transmit power.The results therefore identify different preferred schemes across transmit-power regimes.
  • Conclusions: The study jointly optimizes UAV 3D placement, transmit power, IRS reflection, and NOMA decoding orders using a BCD-based algorithm for the mixed-integer non-convex problem.The algorithm iteratively finds a suboptimal solution, and the reported results show gains from UAV placement, IRS deployment, and NOMA.
  • Conclusions: The paper considers one IRS and indicates that additional interference-cancellation methods are required for large UAV transmit power.Deploying multiple distributed cooperative IRSs is identified as future work.

APPENDIX A: PROOF OF LEMMA 1

Appendix A proves Lemma 1 by decomposing the relevant expectation and using zero-mean independence before substituting the resulting terms into the target expression.

  • Proof: The proof decomposes E and derives the needed terms before arriving at equation (14).The derivation uses the zero means and mutual independence of ȟ^H and ř^H.
  • Proof: Substituting the results from (54a)–(54c) into (53) completes the proof of Lemma 1.The appendix explicitly identifies this substitution as the final proof step.
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