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3D UAV Trajectory and Communication Design for Simultaneous Uplink and Downlink Transmission

Meng Hua, Luxi Yang, Qingqing Wu, A. Lee Swindlehurst

arXiv:2001.00351v2cs.ITeess.SPmath.IT

TL;DR

The paper tackles the open problem of simultaneous uplink and downlink transmission in UAV networks, optimizing their combined throughput. It uses POA for fixed trajectories and iterative SCA for joint 3D trajectory and communication design; the reported results show throughput gains over benchmarks and near-POA performance at lower computational complexity.

  • Problem

    The paper addresses the open problem of integrating simultaneous uplink and downlink in UAV-aided networks and jointly optimizing both networks’ throughput.

    Source: §I · p. 2

  • Method

    The paper applies POA to the fixed-trajectory case and an iterative SCA algorithm to jointly optimize 3D trajectories, scheduling, and transmit power.

    Source: §I · p. 2

  • Results

    The proposed scheme achieves significant system-throughput gains over benchmarks, while SCA attains nearly the same throughput as POA for predetermined trajectories.

    Source: §VI · p. 14

  • Takeaways & Limitations

    For predetermined trajectories, SCA provides nearly POA-level system performance with much lower computational complexity.

    Source: §I · p. 2

Abstract

from arXiv · show

In this paper, we investigate the unmanned aerial vehicle (UAV)-aided simultaneous uplink and downlink transmission networks, where one UAV acting as a disseminator is connected to multiple access points, and the other UAV acting as a base station (BS) collects data from numerous sensor nodes. The goal of this paper is to maximize the sum of the UAV-BS and UAV-AP system throughput by jointly optimizing the 3D UAV trajectory, communication scheduling, and UAV-AP/SN transmit power. We first consider a special case where the UAV-BS and UAV-AP trajectories are pre-determined. Although the resulting problem is an integer and non-convex optimization problem, a globally optimal solution is obtained by applying the polyblock outer approximation (POA) method based on the problem's hidden monotonic structure. Subsequently, for the general case considering the 3D UAV trajectory optimization, an efficient iterative algorithm is proposed to alternately optimize the divided sub-problem based on the successive convex approximation (SCA) technique. Numerical results demonstrate that the proposed design is able to achieve significant system throughput gain over the benchmarks. In addition, the SCA-based method can achieve nearly the same performance as the POA based method with much lower computational complexity.

I. INTRODUCTION

The paper addresses the open problem of integrating simultaneous uplink and downlink in UAV networks, jointly designing trajectories, scheduling, and transmit power to maximize their combined throughput. It develops a globally optimal approach for fixed trajectories and an iterative SCA approach for jointly optimized 3D trajectories.

I. INTRODUCTION

  • The paper integrates UAV-AP downlink dissemination to APs with UAV-BS uplink data collection from sensor nodes, addressing an open simultaneous-transmission problem.The joint objective includes both networks’ throughput and optimizes 3D trajectories, communication scheduling, and UAV-AP/SN transmit power.Source: §I · p. 2
  • For predetermined UAV trajectories, POA finds a globally optimal solution, while SCA achieves nearly the same performance with much lower computational complexity.The fixed-trajectory problem jointly optimizes transmit power and communication scheduling.Source: §I · p. 2
  • For optimized trajectories, a three-layer SCA algorithm alternates among communication scheduling, 3D trajectory design, and transmit-power optimization.Each subproblem fixes the other two design components.Source: §I · p. 2
  • The proposed scheme achieves significantly higher system throughput than other benchmarks.The simulations consider both a single-SN/single-AP scenario and a multiple-SN/multiple-AP scenario.Source: §I · p. 2

II. SYSTEM MODEL

  • The model divides the period into equal time slots and assumes fixed ground-node locations, adjustable UAV headings, and at most one served SN or AP per UAV per slot.The slot duration is chosen so each UAV’s location can be treated as unchanged within a slot.Source: §II · pp. 3–4
  • The system objective is weighted sum throughput across the UAV-BS and UAV-AP networks, subject to scheduling, transmit-power, UAV-mobility, endpoint, and collision-avoidance constraints.The model uses Rician fading for UAV-ground and UAV-UAV links and Rayleigh fading for ground-to-ground links.Source: §II · pp. 3–5

III. GLOBALLY OPTIMAL COMMUNICATION DESIGN

With both UAV trajectories fixed, the communication-design problem remains difficult because transmit power and binary scheduling variables are coupled. The method exposes a monotonic structure, reformulates the problem, and applies POA to obtain a globally optimal solution.

III. GLOBALLY OPTIMAL COMMUNICATION DESIGN

  • For predetermined UAV trajectories, the method seeks a globally optimal solution to the resulting communication-design problem.The paper notes that fixed flight paths occur in applications such as circular cell-edge routes or straight-line routes.Source: §III · p. 5
  • The method handles coupled power and binary scheduling by exploiting hidden monotonicity and converting the problem into an equivalent canonical monotonic optimization formulation.Auxiliary variables represent the UAV-BS and UAV-AP SINRs, yielding an increasing objective over a feasible set.Source: §III · p. 5
  • POA searches the feasible set’s upper boundary through successive polyblocks until it approaches the optimal point.At each iteration, it projects a vertex onto the upper boundary and shrinks the polyblock while retaining the feasible set.Source: §III · pp. 5–6

A. Optimality and Complexity Analysis

The POA optimality argument follows a sequence of projected candidates toward a globally optimal solution. Its computational complexity grows exponentially with the number of variables M.

A. Optimality and Complexity Analysis

  • The projected POA sequence is nonincreasing, and its limit yields a global optimum on the feasible region’s upper boundary.The proof uses a maximizer from the generated “off-springs” subsequence.Source: A. Optimality and Complexity Analysis · p. 6
  • The total number of iterations required for convergence grows exponentially with the number of variables M.The analysis also identifies projection calculations and vertex selection as contributors to Algorithm 1’s computational complexity.Source: A. Optimality and Complexity Analysis · pp. 6–7
  • Despite its global optimality, the POA method has computational complexity that grows exponentially with M.The paper introduces a lower-complexity SCA-based method to address this issue.Source: A. Optimality and Complexity Analysis · p. 7

IV. JOINT 3D TRAJECTORY AND COMMUNICATION DESIGN

The joint 3D trajectory and communication design problem is divided into three subproblems, which are optimized iteratively using SCA.

IV. JOINT 3D TRAJECTORY AND COMMUNICATION DESIGN

  • The method iteratively optimizes communication scheduling, 3D UAV trajectory, and transmit power as separate subproblems.Each subproblem fixes the other design variables.Source: §IV · p. 7
  • The communication-scheduling constraints are relaxed from integer to continuous constraints.The relaxed variables are bounded between 0 and 1, with their sum constrained to at most 1.Source: §IV · p. 7
  • The trajectory and transmit-power subproblems are optimized with communication scheduling and the other design variables fixed, respectively.The decomposition optimizes trajectory with fixed transmit power and scheduling, then power with fixed scheduling and trajectory.Source: §IV · p. 7

A. Communication scheduling optimization with fixed transmit power and trajectory

With transmit power and trajectory fixed, the scheduling subproblem uses SCA to address its non-convex objective and obtain a locally optimal solution through successive updates.

A. Communication scheduling optimization with fixed transmit power and trajectory

  • The communication-scheduling subproblem is formulated for given trajectory Q and transmit power P.Its scheduling variables are updated successively.Source: A. Communication scheduling… · p. 7
  • SCA addresses the scheduling objective’s non-concavity by constructing a convex problem at each iteration.The cited passage describes a first-order approximation in the current feasible point.Source: A. Communication scheduling… · p. 7
  • Successive updates of the scheduling variables yield a locally optimal solution.The convex subproblem provides the next iterate.Source: A. Communication scheduling… · p. 7

B. 3D UAV trajectory optimization with fixed transmit power and communication scheduling

With scheduling and transmit power fixed, the trajectory subproblem is non-convex; slack variables and successive convex approximations produce a convex problem whose repeated solution yields a locally optimal trajectory.

B. 3D UAV trajectory optimization with fixed transmit power and communication scheduling

C. Transmit power optimization with fixed communication scheduling and 3D UAV trajectory

With scheduling and trajectory fixed, the transmit-power subproblem is handled using successive convex approximation. Its convex approximations are solved iteratively to obtain a locally optimal solution.

C. Transmit power optimization with fixed communication scheduling and 3D UAV trajectory

  • For fixed communication scheduling and trajectory, the transmit-power optimization is simplified to a separate subproblem.The optimization is stated for given A and Q.Source: C. Transmit power optimization with… · p. 8
  • The non-convex rate objective is rewritten as a difference of convex functions, then approximated using a first-order Taylor expansion at a feasible point.The approximation is used to form the convex optimization problem in (46).Source: C. Transmit power optimization with… · p. 8
  • Problem (46) is convex, and successively updating its transmit-power solution guarantees a locally optimal solution to problem (39).The power step is one of the updates in the overall BCD algorithm.Source: C. Transmit power optimization with… · p. 9

D. Overall algorithm

The overall algorithm alternates among communication scheduling, UAV trajectory, and transmit-power subproblems using block coordinate descent. Its relaxed objective is non-decreasing across updates, and the algorithm converges to a locally optimal solution before binary scheduling is reconstructed by rounding.

D. Overall algorithm

  • Algorithm 3 alternates among communication scheduling, UAV trajectory, and transmit-power subproblems using block coordinate descent.The three blocks are optimized in turn based on their latest available solutions.Source: D. Overall algorithm · p. 9
  • The relaxed objective is non-decreasing after each update, and Algorithm 3 converges to a locally optimal solution.The objective is bounded by finite flight time and transmit-power budgets; binary scheduling is reconstructed by rounding.Source: D. Overall algorithm · p. 9
  • The algorithm's complexity is analyzed across its linear scheduling subproblem and logarithmic trajectory and transmit-power subproblems.The analysis also accounts for the iterations required by each update and by overall convergence.Source: D. Overall algorithm · pp. 9–10

V. NUMERICAL RESULTS

The numerical evaluation specifies channel, mobility, safety, power, and timing parameters for its simulations.

V. NUMERICAL RESULTS

  • The simulations use 1 MHz bandwidth, −110 dBm noise power, −60 dBm G2G channel gain, and path-loss exponent 3.These are the stated default parameters unless otherwise specified.Source: §V · p. 10
  • UAV altitude is constrained to 100–600 m, horizontal speed to 50 m/s, vertical speed to 30 m/s, and inter-UAV safety distance to 10 m.The values are specified as simulation parameters.Source: §V · p. 10
  • The maximum UAV-AP and sensor-node transmit power is 0.1 W, each time slot lasts 0.5 s, and the penalty factor is 1 × 10^5.The transmit-power value applies to both UAV-AP and SN, respectively.Source: §V · p. 10

A. Single SN and single AP case

In the single-SN/single-AP case, joint 3D trajectory and power optimization outperforms the reported benchmarks. In the multiple-SN/multiple-AP case, it also outperforms benchmarks, while SCA achieves near-POA throughput at much lower computational cost.

A. Single SN and single AP case

B. Multiple SNs and multiple APs case

  • The multiple-node evaluation jointly optimizes trajectory, communication scheduling, and power for four SNs and four APs.The initial UAV trajectories are circles with radii set using the period and maximum horizontal speed.Source: B. Multiple SNs and multiple APs case · p. 11
  • For multiple SNs and APs, SCA yields nearly the same throughput as POA while taking about 3.7 minutes at T = 80s, versus nearly 27 hours for POA.The throughput gap remains small as T increases, and the methods are nearly identical for T ≤ 80s under both tested weighting factors.Source: B. Multiple SNs and multiple APs case · p. 11
  • Algorithm 3 converges in about 6 iterations at T = 40s and 10 iterations at T = 80s.Throughput increases quickly with iteration count in both tested periods.Source: B. Multiple SNs and multiple APs case · p. 11
  • The average-throughput approximation matches simulations for both SN and AP throughput, and lies between the simulated upper and lower bounds.The lower-bound curves fluctuate when the numerator in the logarithm approaches nearly zero.Source: B. Multiple SNs and multiple APs case · p. 12
  • In the multiple-node case, UAVs visit SNs and APs; their paths bend to mitigate cross-network interference, and both descend to reduce path loss.When β1 = 1 and β2 = 1/10, the UAV-BS path between nodes becomes nearly straight because its network has higher priority.Source: B. Multiple SNs and multiple APs case · p. 12
  • At β1 = β2 = 1, UAV speed is nearly maximum or zero; with β2 = 1/10, the UAV-AP flies at maximum horizontal speed for nearly all of T.At β2 = 1/10, the UAV-AP transmits only during t = 28s–35s and t = 48s–55s, staying silent at other times to alleviate interference to the UAV-BS.Source: B. Multiple SNs and multiple APs case · p. 13
  • At T = 120s and β2 = 1, the proposed scheme reaches 1551Mbps, 20%–50% higher than the reported benchmark throughputs.The comparisons are against “3D traj & no power” (1074 Mbps), “2D traj & power” (1245 Mbps), “2D traj & no power” (777 Mbps), and “only power” (1122 Mbps).Source: B. Multiple SNs and multiple APs case · p. 13

VI. CONCLUSION

The paper studies simultaneous uplink and downlink transmission using a UAV-AP to serve APs and a UAV-BS to collect sensor data. Its SCA approach for 3D trajectory and communication design yields significant gains over benchmarks, while nearly matching POA when trajectories are predetermined.

VI. CONCLUSION

  • The study considers one UAV-AP disseminating data to APs and one UAV-BS collecting data from sensor nodes.For predetermined trajectories, the system throughput is maximized using the polyblock outer approximation method.Source: §VI · pp. 13–14
  • Fig. 13 plots system throughput versus period for different benchmarks under different weighting factors.Source: Figure 13 · p. 14
  • SCA achieves nearly the same throughput as POA with predetermined trajectories, while 3D trajectory and transmit-power optimization yields significant gains over benchmarks.The conclusion also identifies managing interference from additional UAV-BSs and UAV-APs as a consideration for extensions to multiple UAVs.Source: §VI · p. 14

APPENDIX A PROOF OF THEOREM 1

Appendix A derives approximation inequalities for Theorem 1 using concavity, convexity, Jensen’s inequality, and a special case. Appendix B proves that optimal scheduling activates at most one SN and one AP per slot, and that problems (17) and (16) are equivalent.

APPENDIX A PROOF OF THEOREM 1

  • Theorem 1’s approximation results follow from concavity and convexity arguments using Jensen’s inequality, including the special case X = 0, Y > 0.The proof defines f1(z) = log2(1 + z) and f2(z) = log2 … and compares bounds for independent positive X and Y.Source: Appendix A · p. 14

APPENDIX B PROOF OF THEOREM 2

  • For problem (17), an optimal solution has at most one active SN and at most one active AP in each time slot.Source: Appendix B · pp. 14–15
  • Problems (17) and (16) are equivalent because each problem’s optimal solution is feasible for the other with the same objective value.Source: Appendix B · p. 15
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