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Joint Altitude, Beamwidth, Location and Bandwidth Optimization for UAV-Enabled Communications

Zhaohui Yang, Cunhua Pan, Mohammad Shikh-Bahaei, Wei Xu, Ming Chen, Maged Elkashlan, Arumugam Nallanathan

arXiv:1806.02221v1cs.ITmath.IT

TL;DR

The paper addresses minimizing uplink sum power for UAV-assisted communications while meeting ground terminals' minimum-rate demands. It jointly optimizes UAV altitude, beamwidth, location, and terminal bandwidth through iterative subproblem optimization; numerical results report lower sum power than restricted alternatives, especially at high minimum-rate demands.

  • Problem

    The paper studies how to minimize uplink sum power in UAV-enabled communications while satisfying ground terminals' minimum-rate demands.

    Source: §I · p. 1

  • Method

    The algorithm iteratively optimizes UAV altitude and beamwidth, location, and ground-terminal bandwidth, globally optimizing each subproblem with the other variables fixed.

    Source: §I · p. 1, §III · p. 2

  • Results

    The proposed algorithm outperforms fixed-location, fixed-altitude-and-beamwidth, and fixed-bandwidth methods in sum power, especially at high minimum-rate demands.

    Source: §I · p. 1, §IV · p. 4

  • Takeaways & Limitations

    The numerical results indicate that jointly optimizing altitude, beamwidth, location, and bandwidth can improve uplink sum-power performance.

    Source: §I · p. 1, §V · p. 4

Abstract

from arXiv · show

This letter investigates an uplink power control problem for unmanned aerial vehicles (UAVs) assisted wireless communications. We jointly optimize the UAV's flying altitude, antenna beamwidth, UAV's location and ground terminals' allocated bandwidth and transmit power to minimize the sum uplink power subject to the minimal rate demand. An iterative algorithm is proposed with low complexity to obtain a suboptimal solution. Numerical results show that the proposed algorithm can achieve good performance in terms of uplink sum power saving.

I. INTRODUCTION

The paper targets uplink sum-power minimization in UAV-assisted communications. It jointly optimizes UAV and bandwidth choices, addressing limitations in prior beamwidth work that assumed equal bandwidth allocation.

I. INTRODUCTION

  • UAV-enabled communications can provide connectivity in areas without infrastructure coverage and higher capacity on line-of-sight links with ground terminals.The introduction attributes growing attention to UAV maneuverability and increasing affordability.Source: §I · p. 1
  • Prior work jointly optimized beamwidth and altitude but used equal bandwidth allocation, although proper bandwidth allocation can further enhance system performance.Earlier studies also considered UAV altitude, location, trajectory, and user-UAV association.Source: §I · p. 1
  • The proposed approach jointly optimizes UAV altitude, beamwidth, location, and bandwidth to minimize uplink sum power.The algorithm solves three subproblems iteratively, with each subproblem optimized for fixed values of the other variables.Source: §I · p. 1
  • Numerical results show lower sum power than fixed-location, fixed-altitude-and-beamwidth, and fixed-bandwidth methods, especially at high minimum-rate demands.The fixed-beamwidth or fixed-bandwidth comparisons address restrictions in prior approaches.Source: §I · p. 1

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model considers ground terminals transmitting to a flying UAV base station. The problem minimizes their total transmit power while meeting minimum-rate requirements and system constraints.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • One UAV serves K ground terminals, whose horizontal locations are x_k, while the UAV has horizontal location y and altitude H.Ground-terminal altitude is assumed to be zero relative to the UAV.Source: §II · p. 1
  • The UAV carries an adjustable directional antenna whose azimuth and elevation half-power beamwidths are equal, both denoted 2Θ ∈ (0, π); each ground terminal uses an omnidirectional antenna with unit gain.Source: §II · p. 1
  • The uplink model uses a predominantly line-of-sight channel, with pathloss exponent α≥2, to determine each covered terminal's achievable rate.The rate depends on allocated bandwidth and transmit power; the noise power is proportional to bandwidth.Source: §II · p. 1
  • The optimization minimizes all ground terminals' uplink sum power subject to each terminal meeting its minimum rate demand.For sum-power minimization, each terminal transmits at the minimum rate required.Source: §II · p. 2
  • Feasibility constrains total allocated bandwidth, terminal transmit powers, UAV altitude, and antenna half-beamwidth; every terminal must lie within UAV coverage.The altitude and beamwidth bounds reflect obstacle heights, authority regulations, and practical antenna tuning.Source: §II · p. 2

III. PROPOSED ALGORITHM

The proposed algorithm addresses the nonconvex sum-power problem through iterative optimization of UAV altitude and beamwidth, location, and bandwidth.

III. PROPOSED ALGORITHM

  • The problem is nonconvex because of its objective function and constraints, making a globally optimal solution generally difficult to obtain.The algorithm is designed as a low-complexity approach to the problem.Source: §III · p. 2
  • The algorithm iteratively optimizes UAV altitude and beamwidth, location, and bandwidth in sequence.The three steps optimize (H, Θ), y, and w, respectively.Source: §III · p. 2
  • With the other variables fixed at each step, each subproblem can be globally optimized.Source: §III · p. 2

A. Optimal Altitude and Beamwidth

The altitude-and-beamwidth step reduces the joint search by exploiting the objective's dependence on altitude and the structure of the beamwidth constraints. For pathloss exponent α=2, the optimal beamwidth can be found by bisection.

A. Optimal Altitude and Beamwidth

  • The objective increases with altitude when beamwidth is fixed, so the altitude solution is characterized using the maximum squared horizontal distance D_max.The analysis considers separate cases for the optimal altitude.Source: A. Optimal Altitude and Beamwidth · p. 2
  • For general pathloss exponent, the optimal beamwidth can be obtained by one-dimensional exhaustive search over its feasible interval.For α=2, a bisection method obtains the optimal beamwidth.Source: A. Optimal Altitude and Beamwidth · p. 2
  • For individual terminal power constraints, the beamwidth-related function is either increasing or first decreases and then increases, enabling equivalent constraint handling.In the latter case, the turning point is obtained by bisection.Source: A. Optimal Altitude and Beamwidth · p. 3
  • The beamwidth objective is handled by checking its monotonicity over the feasible interval and selecting an endpoint or interior minimum accordingly.The subproblem is feasible only when the lower feasible bound does not exceed the upper bound.Source: A. Optimal Altitude and Beamwidth · p. 3

B. Optimal Location Planning

With altitude, beamwidth, and bandwidth fixed, the location-planning subproblem is convex and can be solved by an interior-point method.

B. Optimal Location Planning

C. Optimal Bandwidth Allocation

For fixed UAV location, altitude, and beamwidth, bandwidth allocation is formulated as a convex problem and its optimum is found using a scalar bisection search.

C. Optimal Bandwidth Allocation

  • With optimized altitude, beamwidth, and location, the bandwidth-allocation problem is convex because each u_k(x) is convex.The passage also states that u_k(x) is monotonically decreasing, which helps transform the rate constraints.Source: C. Optimal Bandwidth Allocation · p. 3
  • The section derives the bandwidth-allocation conditions using a Lagrangian and KKT conditions for the convex problem.Source: C. Optimal Bandwidth Allocation · p. 3
  • The optimal bandwidth vector is obtained from (25) after finding the unique λ that satisfies the total-bandwidth constraint by bisection.The function determining total bandwidth is strictly decreasing in λ, with limits +∞ as λ approaches 0 and 0 as λ approaches +∞.Source: C. Optimal Bandwidth Allocation · pp. 3–4

D. Iterative Algorithm and Complexity Analysis

Algorithm 1 alternates among optimizing altitude and beamwidth, location, and bandwidth until the objective converges; its complexity depends on beamwidth search and a bisection step.

D. Iterative Algorithm and Complexity Analysis

IV. NUMERICAL RESULTS

The proposed algorithm uses joint optimization to outperform methods fixing location, altitude and beamwidth, or bandwidth, especially at high rate demand; its power is slightly above the exhaustive method. The results also show a nonmonotonic sum-power response to beamwidth.

IV. NUMERICAL RESULTS

  • The simulation uses 20 uniformly distributed ground terminals in a 300 m-radius circle, equal rate demand, and 10 MHz system bandwidth.Each terminal's maximum transmit power is 20 dBm; the tested altitude range is 50–500 m.Source: §IV · p. 4
  • For each minimal rate demand, sum power first decreases and then increases as Θ increases.This is reported with equal bandwidth allocation and the UAV at the circle's center.Source: §IV · p. 4
  • The proposed algorithm achieves lower sum power than FL, FAB, and FB, especially at high minimal-rate demand, while Exhaustive is slightly lower.The authors say this indicates the proposed algorithm approaches the globally optimal solution; Exhaustive runs Algorithm 1 from 1000 initial points.Source: §IV · p. 4

V. CONCLUSION

The conclusion reports improved uplink sum-power performance from the proposed algorithm and describes the sum-power trend with beamwidth as first decreasing and then decreasing.

V. CONCLUSION

  • The proposed algorithm improves uplink sum-power performance.Source: §V · p. 4
  • The conclusion describes uplink sum power as first decreasing and then decreasing with beamwidth.Source: §V · p. 4
  • The paper investigates sum-power minimization in uplink UAV-enabled communications.Source: §V · p. 4

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