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UAV-Enabled Communication Using NOMA

Ali A. Nasir, Hoang D. Tuan, Trung Q. Duong, H. Vincent Poor

arXiv:1806.03604v1cs.IT

TL;DR

The paper studies max-min rate optimization for a single-antenna UAV-BS serving many ground users with NOMA under power, bandwidth, altitude, and beamwidth constraints. It develops path-following algorithms for NOMA, OMA, and DPC formulations despite non-convex optimization variables. Numerically, NOMA outperforms OMA, achieves rates similar to DPC, and benefits from jointly optimizing all parameters.

  • Problem

    Max-min rate optimization remains unsolved for a NOMA-enabled single-antenna UAV-BS when altitude, beamwidth, power, and bandwidth must be jointly optimized.

  • Method

    The paper uses path-following algorithms based on inner convex approximations for NOMA, OMA, and DPC-based max-min rate optimization problems.

  • Results

    NOMA outperforms OMA and achieves rates similar to those attained by DPC.

  • Takeaways & Limitations

    Jointly optimizing power, bandwidth, UAV altitude, and antenna beamwidth produces a clear rate gain over optimizing only a subset of these parameters.

Abstract

from arXiv · show

Unmanned aerial vehicles (UAVs) can be deployed as flying base stations (BSs) to leverage the strength of line-of-sight connections and effectively support the coverage and throughput of wireless communication. This paper considers a multiuser communication system, in which a single-antenna UAV-BS serves a large number of ground users by employing non-orthogonal multiple access (NOMA). The max-min rate optimization problem is formulated under total power, total bandwidth, UAV altitude, and antenna beamwdith constraints. The objective of max-min rate optimization is non-convex in all optimization variables, i.e. UAV altitude, transmit antenna beamwidth, power allocation and bandwidth allocation for multiple users. A path-following algorithm is proposed to solve the formulated problem. Next, orthogonal multiple access (OMA) and dirty paper coding (DPC)-based max-min rate optimization problems are formulated and respective path-following algorithms are developed to solve them. Numerical results show that NOMA outperforms OMA and achieves rates similar to those attained by DPC. In addition, a clear rate gain is observed by jointly optimizing all the parameters rather than optimizing a subset of parameters, which confirms the desirability of their joint optimization.

I. INTRODUCTION

The paper addresses max-min rate optimization for a single-antenna UAV-BS serving many ground users with NOMA, jointly choosing altitude, beamwidth, power, and bandwidth under practical constraints. It develops path-following methods and compares NOMA with OMA and DPC.

  • Motivation: UAVs can act as flying base stations that support wireless coverage and throughput through flexible deployment and line-of-sight communication.The paper motivates UAV deployment for temporary hotspots, relaying, and exceptional traffic or disaster situations.
  • Motivation: A single-antenna UAV is preferred because UAV-enabled downlink communication has poorer scattering than conventional cellular communication.Users served by the UAV share communication bandwidth, creating a multiuser resource-allocation problem.
  • Related work: NOMA serves multiple users on non-orthogonal resources by separating them in the power domain and can improve rates for far users.Near users access information intended for far users, whose received signal power is lower.
  • Research gap: Joint optimization of UAV altitude, antenna beamwidth, power allocation, and bandwidth allocation remains unsolved for the considered NOMA setting.Earlier studies considered subsets of these variables or different objectives, motivating the paper’s broader formulation.
  • Contributions: The paper formulates a constrained max-min rate problem for a single-antenna UAV-BS serving many ground users with NOMA.The constraints cover total power, total bandwidth, UAV altitude, and antenna beamwidth; the objective is non-convex in all optimization variables.
  • Contributions: Inner convex approximations and path-following algorithms address the NOMA problem and corresponding OMA- and DPC-based formulations.Numerical results report that NOMA outperforms OMA, achieves rates similar to DPC, and gains from jointly optimizing all parameters.

II. SYSTEM MODEL AND PROBLEM STATEMENT

The system models a single-antenna UAV serving near and far ground users with NOMA, using shared bandwidth, channel gains based on UAV geometry, and coverage constraints involving altitude and beamwidth.

  • User grouping: A single-antenna UAV serves K ground users, divided into K/2 near users and K/2 far users according to distance from the UAV.Near users are cell-centered, while far users are cell-edge users.
  • NOMA transmission: NOMA pairs each near user with a far user so both users share the same bandwidth resource.The far-user mapping is specified as j(k) = k + K for near-user indices.
  • Coverage constraint: The squared UAV altitude and squared antenna beamwidth must satisfy a coverage condition ensuring all users lie within radius R.The formulation uses these squared variables to handle the non-convex coverage constraint.
  • Channel model: The channel power gain between the UAV and user k is modeled from UAV altitude, horizontal distance, antenna beamwidth, and a reference channel gain.The model assumes free-space path loss with exponent 2 because users are dominated by line-of-sight links.
  • Bandwidth allocation: The total bandwidth B is divided among near users using fractions τ_k, with each paired far user assigned the same bandwidth w_k = τ_kB.The allocation fractions satisfy 0 ≤ τ_k ≤ 1.

A. NOMA Problem Formulation

The NOMA formulation jointly optimizes bandwidth, power, UAV altitude, and antenna beamwidth to maximize the minimum user rate under system constraints. Its non-convex objective and nonlinear coverage constraint are addressed with an inner convex approximation-based path-following algorithm.

  • NOMA lets one user decode another user's message to cancel that user's interference.
  • The achievable rates are defined for near and far users under an additive white Gaussian noise channel.
  • The max-min objective optimizes bandwidth allocation, power allocation, UAV altitude, and antenna beamwidth simultaneously.
  • The formulation constrains bandwidth fractions, total transmit power, UAV altitude, and antenna beamwidth.
  • The problem is non-convex and nonlinear in four variable types, with coverage also depending nonlinearly on beamwidth and altitude.
  • An inner convex approximation-based path-following algorithm is proposed to solve the NOMA optimization problem.

B. DPC Problem Formulation

The DPC formulation considers max-min rate optimization for two users sharing bandwidth. It uses the NOMA rate for one user and the DPC-defined rate for the other within the same joint resource-optimization framework.

  • DPC is treated as practical when two users share the same bandwidth.
  • The near-user rate follows the NOMA formulation, while the far-user rate follows the DPC formulation.
  • The DPC problem jointly optimizes bandwidth, power, UAV altitude, and antenna beamwidth to maximize the minimum user rate.

C. OMA Problem Formulation

Two OMA formulations are considered: one assigns distinct bandwidth to every user, while the other optimizes bandwidth partitions for user pairs. Both jointly optimize bandwidth, power, altitude, and beamwidth.

  • OMA-1: OMA-1 allocates distinct bandwidth to all users and maximizes the minimum rate across them.
  • OMA-1: OMA-1 enforces nonnegative bandwidth fractions whose sum equals one.
  • OMA-1: Under OMA-1, each user's rate is the rate defined by the single-user bandwidth-based formulation.
  • OMA-2: OMA-2 optimizes K/2 bandwidth partitions together with altitude, power, and antenna beamwidth.
  • OMA-2: The OMA-2 objective maximizes the minimum rate among the K/2 user pairs.

III. ALGORITHMS

The formulated OMA, DPC, and NOMA problems are non-convex optimization problems that pose computational challenges. The algorithms section addresses these problems through solution procedures.

  • The problems formulated in Section II are non-convex optimization problems.
  • Their non-convexity creates computational challenges for solving the optimization problems.

A. NOMA Algorithm

The NOMA max-min rate problem is non-concave and non-convex, so the paper uses path-following with concave objective lower bounds and inner convex constraint approximations. Each iteration solves a convex problem, producing feasible improvements that converge to a locally optimal solution.

  • Problem formulation: The NOMA objective is complex and non-concave, while the coverage constraint is also non-convex.
  • Path-following approximation: Path-following constructs a lower-bounding concave objective approximation and an inner convex approximation of the coverage constraint.The inner approximation preserves feasibility because every point feasible for it is feasible for the original constraint.
  • Iterative solution: At iteration κ, the algorithm solves a convex optimization problem to generate the next feasible point over power, bandwidth, altitude, and beamwidth variables.The convex subproblem uses constraints (8b), (8c), (8d), (32), and (33).
  • Algorithm 1: The proposed NOMA algorithm initializes a feasible point, repeatedly solves the convex subproblem, and increments the iteration index.The initial point can use equal power and bandwidth, a feasible beamwidth, and an altitude found from a convex feasibility problem.
  • Convergence: Each iteration improves the feasible objective, and the resulting sequence converges at least to a locally optimal solution of the NOMA problem.The improvement follows because the approximation is a lower bound that matches the original objective at the current point.

IV. SIMULATION RESULTS

The simulations evaluate Algorithms 1–4 in a UAV cell with randomly placed users and specified bandwidth, power, altitude, and beamwidth settings. The experiments use the network topology shown in Fig. 2 and examine algorithm convergence in Fig. 3.

  • The simulations evaluate the proposed Algorithms 1–4 using numerical examples.
  • Network topology: The simulated cell has radius R = 300 meters, K = 20 randomly placed users, and a UAV-BS located at the cell center.Half the users are closer to the UAV-BS and the rest are farther away.
  • Convergence evaluation: Fig. 3 presents convergence results for the NOMA, DPC, OMA-1, and OMA-2 optimization problems.
  • Simulation settings: The default configuration uses B = 15 MHz, P = 2 mW (3 dBm), hmin = 50 meters, hmax = 500 meters, and θmin = 0 to θmax = π/2 rad.

A. Performance of the Proposed Algorithms 1-4

The proposed algorithms optimize max-min rates across bandwidth and noise conditions, with NOMA and DPC outperforming OMA while requiring different iteration counts. Optimized altitude and antenna beamwidth change only slightly as total bandwidth varies.

  • Convergence: NOMA and DPC take around 40 iterations to converge, whereas OMA-1 and OMA-2 require only four iterations.At the fourth iteration, the optimized NOMA and DPC rates are already better than OMA-1.
  • Rate versus bandwidth: NOMA and DPC achieve the same performance while clearly outperforming the OMA counterparts as total available bandwidth increases.The optimized rate increases with total available bandwidth B, and the NOMA–OMA-1 gap widens as B increases.
  • Rate versus noise power density: NOMA and DPC clearly outperform the OMA counterparts as noise power density increases.The optimized max-min rate decreases with increasing noise power density σ2, while the NOMA–OMA-1 gap decreases.
  • Optimized geometry: The optimized UAV altitude and antenna beamwidth show minor changes for different values of total available bandwidth B.The paper describes this as desirable because the UAV is not required to move much when the bandwidth quota changes.

B. Comparison with the Sub-optimal Schemes

The comparisons evaluate fixed-parameter and equal-allocation schemes against algorithms that jointly optimize the system parameters. Joint optimization improves the max-min rate, while equal power allocation can make NOMA perform worse than sub-optimal OMA-1.

  • Joint optimization: 5.77 Mbps is achieved by NOMA and DPC, compared with 5.29 Mbps for OMA-1 and 1.48 Mbps for OMA-2 when all parameters are optimized.The proposed Algorithms 1–4 jointly optimize UAV altitude, antenna beamwidth, power allocation, and bandwidth allocation.
  • Access-scheme comparison: DPC provides similar rate to NOMA, whereas OMA-2 performs quite poorly in the reported comparison.This comparison motivates focusing on NOMA and OMA-1 for the fixed-allocation analysis.
  • Joint optimization: The jointly optimized algorithms clearly outperform schemes with fixed altitude and antenna beamwidth or fixed power and bandwidth allocation.The fixed-parameter comparisons solve only the remaining optimization variables, producing smaller optimized max-min rates than the proposed algorithms.
  • Equal allocation: Sub-optimal NOMA performs worse than sub-optimal OMA-1 under equal power and equal bandwidth allocation.The paper attributes this result to the need for wise power allocation in NOMA; equal power allocation worsens its achievable rate.

V. CONCLUSIONS

The paper formulates joint max-min rate optimization for a UAV-BS serving many users with NOMA, addressing non-convexity across key design variables. Path-following algorithms are developed for NOMA, OMA, and DPC comparisons, with NOMA outperforming OMA and approaching DPC rates.

  • The system uses a single-antenna UAV-BS to serve a large number of users with NOMA.
  • The max-min rate problem is constrained by total power, total bandwidth, UAV altitude, and antenna beamwidth.
  • The objective is non-convex in UAV altitude, antenna beamwidth, power allocation, and bandwidth allocation.
  • Path-following algorithms are developed for the NOMA problem and for corresponding OMA- and DPC-based formulations.
  • NOMA outperforms OMA and achieves rates similar to DPC, while jointly optimizing all parameters produces a clear rate gain over optimizing a subset.
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