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Mobile Edge Computing via a UAV-Mounted Cloudlet: Optimization of Bit Allocation and Path Planning

Seongah Jeong, Osvaldo Simeone, Joonhyuk Kang

arXiv:1609.05362v3cs.NIcs.IT

TL;DR

The paper addresses how a UAV-mounted cloudlet can reduce mobile energy consumption when users offload computation under latency and UAV-energy constraints. It jointly optimizes communication and computation bit allocation with the cloudlet trajectory using successive convex approximation, and reports substantial savings over local execution and partial optimization. The study also shows that the UAV propulsion-energy model affects the resulting trajectory design.

  • Problem

    The paper studies mobile computation offloading through a moving UAV-mounted cloudlet for users with limited local processing capabilities while minimizing total mobile energy under quality-of-service requirements.

  • Method

    The paper jointly optimizes uplink, downlink, and cloudlet-computation bit allocation with the UAV trajectory for orthogonal and NOMA access using successive convex approximation under latency and UAV-energy constraints.

  • Results

    32.7% lower mobile energy is reported for the optimized non-orthogonal-access scheme relative to its non-optimized counterpart, with trajectory optimization contributing 27.4% and bit-allocation optimization 2%.

  • Takeaways & Limitations

    Joint optimization of bit allocation and cloudlet trajectory yields significant mobile-energy savings compared with local execution and partial optimization approaches.

Abstract

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Unmanned Aerial Vehicles (UAVs) have been recently considered as means to provide enhanced coverage or relaying services to mobile users (MUs) in wireless systems with limited or no infrastructure. In this paper, a UAV-based mobile cloud computing system is studied in which a moving UAV is endowed with computing capabilities to offer computation offloading opportunities to MUs with limited local processing capabilities. The system aims at minimizing the total mobile energy consumption while satisfying quality of service requirements of the offloaded mobile application. Offloading is enabled by uplink and downlink communications between the mobile devices and the UAV that take place by means of frequency division duplex (FDD) via orthogonal or non-orthogonal multiple access (NOMA) schemes. The problem of jointly optimizing the bit allocation for uplink and downlink communication as well as for computing at the UAV, along with the cloudlet's trajectory under latency and UAV's energy budget constraints is formulated and addressed by leveraging successive convex approximation (SCA) strategies. Numerical results demonstrate the significant energy savings that can be accrued by means of the proposed joint optimization of bit allocation and cloudlet's trajectory as compared to local mobile execution as well as to partial optimization approaches that design only the bit allocation or the cloudlet's trajectory.

I. INTRODUCTION

The paper studies a UAV-mounted cloudlet that extends mobile cloud computing to infrastructure-limited settings by jointly optimizing offloading, computation, and trajectory decisions. The system supports FDD orthogonal or non-orthogonal access while the UAV follows a discretized, fixed-altitude trajectory under mobility constraints.

  • UAV-mounted cloudlets provide computation offloading opportunities where wireless infrastructure is limited, including rural, disaster-response, emergency-relief, and military settings.
  • C. Main Contributions: The design jointly optimizes uplink, downlink, and computation bit allocation together with the UAV trajectory to minimize total mobile energy consumption.
  • C. Main Contributions: FDD is used with either orthogonal or non-orthogonal access for uplink and downlink transmissions.
  • The offloading procedure comprises uplink application-input transmission, cloudlet execution, and downlink output transmission for each mobile device.
  • A. Set-Up: The UAV flies horizontally at fixed altitude H, with predetermined initial and final locations and maximum speed, while its projected trajectory is discretized across N frames.

B. Energy Consumption Model for Offloading

The offloading energy model accounts for cloudlet computation, mobile and UAV communication, and UAV propulsion under orthogonal and non-orthogonal access. NOMA introduces interference-dependent transmission energy, while propulsion is represented by velocity-only and velocity-and-acceleration models.

  • Computation energy: Cloudlet computation energy depends on processor frequency and the number of input bits executed for each mobile device.
  • Communication energy: Under orthogonal access, uplink and downlink transmission energy is computed for each mobile device within its allocated slot using path loss and transmission-bit quantities.
  • Communication energy: Under NOMA, all mobile devices transmit and receive throughout the frame, so interference from other devices affects each application’s uplink and downlink transmission energy.
  • Flying energy: The UAV propulsion model considers either flying energy dependent only on velocity or a refined model dependent on both velocity and acceleration.

C. Energy Consumption Model for Mobile Execution

The local-execution baseline models each mobile device as processing its entire application locally within the deadline, with CPU frequency selected to meet that deadline and energy computed from processor characteristics.

  • The local-execution reference assumes every mobile device processes its entire application locally within T seconds.
  • Each mobile device’s CPU frequency is chosen to process its I input bits within the deadline.
  • The resulting total mobile energy is obtained from the local-processing model and the effective switched capacitance of each mobile processor.

III. OPTIMAL ENERGY CONSUMPTION FOR ORTHOGONAL ACCESS

For orthogonal access, the paper formulates a joint mobile-energy minimization over communication and computation bit allocation and the cloudlet trajectory, subject to processing, energy-budget, and mobility constraints.

  • Decision variables: The optimization variables include uplink bits, downlink bits, cloudlet-computed bits, cloudlet CPU frequency, and cloudlet position.
  • Computation constraints: The cloudlet CPU frequency must support processing the total bits assigned across all mobile devices within each frame.
  • Objective: The objective jointly optimizes communication and computation bit allocation together with the cloudlet trajectory to minimize total mobile energy consumption.
  • Constraints: The constraints ensure that cloudlet-computed bits do not exceed bits previously received through uplink and enforce the UAV energy budget.

B. Successive Convex Approximation

The paper addresses the non-convex optimization problem using successive convex approximation (SCA), replacing non-convex objectives and constraints with suitable convex approximations. The resulting convex subproblem has a unique solution, and the iterative algorithm converges to stationary solutions under specified step-size conditions.

  • SCA framework: SCA iteratively replaces the non-convex objective function and constraints with suitable convex approximations.The approximated problems can also be solved in a distributed manner using dual decomposition.
  • Objective approximation: Lemma 1 constructs a strongly convex surrogate for products of convex, non-negative functions.A positive constant and positive definite matrix ensure strong convexity.
  • Constraint approximation: Lemma 2 constructs a convex upper bound for non-convex constraints expressed as products of convex, non-negative functions.The constraint approximation is tight at the approximation point and upper bounds the original constraint.
  • Orthogonal-access subproblem: For problem (13), the approximations produce a strongly convex inner approximation with a unique solution ˆz(z(v)).The resulting problem (20) is convex and forms the update subproblem for Algorithm 1.
  • Convergence: Under γ(v) ∈(0, 1], γ(v) →0, and Σ_v γ(v) = ∞, every limit point is stationary, while non-finite termination excludes local minima.The sequence of iterates is bounded.

IV. OPTIMAL ENERGY CONSUMPTION FOR NON-ORTHOGONAL ACCESS

For non-orthogonal access, the paper formulates an energy-minimization problem using the same definitions as before but replaces uplink and downlink energies with their NOMA expressions. It then applies the SCA-based algorithm for the resulting problem.

  • Problem setting: Non-orthogonal access jointly designs bit allocation and the UAV trajectory to minimize total mobile energy consumption.The section specifically addresses the non-orthogonal-access case.
  • Algorithm: Algorithm 1 updates the iterate by solving problem (20), taking a step toward its unique solution, and repeating until stationarity.The update uses z(v + 1) = z(v) + γ(v)(ˆz(z(v)) − z(v)).

A. Problem Formulation

The total mobile energy-minimization problem is formulated by incorporating uplink and downlink communication energies into the existing formulation.

  • The formulation minimizes the total energy consumption of the mobile users (MUs).
  • Uplink and downlink communication energies are substituted into the corresponding terms of the prior formulation.
  • The resulting optimization problem uses the same definitions as the previous section.

B. Successive Convex Approximation

For non-orthogonal access, the paper reformulates the non-convex problem with slack variables and derives convex approximations for its objective and constraints. These approximations yield a strongly convex subproblem with a unique solution used by the SCA algorithm.

  • Problem reformulation: Problem (21) is non-convex because both its objective function (21a) and constraint (21b) are non-convex.Slack variables αk,n ≥0 and βk,n ≥0 are introduced to obtain an equivalent non-convex formulation.
  • Slack-variable formulation: The non-orthogonal-access formulation uses slack-variable vectors α−k,n and β−k,n to redefine uplink and downlink transmission energies.These vectors collect the corresponding variables of users other than k.
  • Convex approximation: SCA convexifies the objective and constraints using Lemma 1 and Lemma 2.The objective contains a product of a non-negative linear function and a non-negative convex function.
  • Inner approximation: For each feasible iterate, the approximations produce a strongly convex inner approximation whose solution ˆz(z(v)) is unique.The convex functions used for the bounds are defined in the appendices.
  • Algorithm: Algorithm 2 solves the convex approximation iteratively and updates z(v) with a step toward ˆz(z(v)).Its convergence follows the same theorem-based SCA argument used in Section III.

V. UAV’S PROPULSION ENERGY CONSUMPTION

The paper refines the UAV propulsion-energy model to depend on both velocity and acceleration, then incorporates this model into trajectory optimization using SCA.

  • The refined propulsion-energy model accounts for both the UAV’s velocity and acceleration vectors, unlike the earlier velocity-only model.The study examines how this modeling choice affects optimal system design.
  • The UAV’s velocity and acceleration are linked to its position through a second-order Taylor approximation model.
  • Orthogonal access: The orthogonal-access formulation adds velocity and acceleration variables, initial and final velocity constraints, and a maximum acceleration constraint.The overall UAV energy constraint uses the refined propulsion model.
  • Successive convex approximation: SCA handles the nonconvex propulsion-energy term by introducing slack variables and constructing a convex upper bound at each iteration.The resulting convex program is embedded in Algorithm 1.
  • Non-orthogonal access: The refined model is also applied to non-orthogonal access by introducing slack variables and solving the resulting convex subproblem through Algorithm 2.

VI. NUMERICAL RESULTS

Numerical experiments show that jointly optimizing UAV trajectory and bit allocation reduces mobile energy consumption, while the energy model and access scheme shape the resulting trajectories and gains.

  • Experimental setup: The experiments compare equal-bit constant-velocity baselines with schemes optimizing bit allocation, UAV trajectory, or both.The simulations evaluate orthogonal and non-orthogonal access under two UAV flying-energy models.
  • Trajectory optimization: The optimized orthogonal-access trajectory keeps the UAV longer near MU 2, which has the largest input workload.Including propulsion energy in Model 2 produces smoother turns than Model 1 to limit acceleration-related energy consumption.
  • Bit allocation: When the UAV is closer to an MU, the algorithm allocates more uplink bits to that MU.Cloudlet computation and downlink allocations are constrained by previously received uplink bits and computed output bits.
  • Bit allocation: Downlink bit allocation is less affected by cloudlet position than uplink allocation because the optimization imposes, rather than minimizes, UAV energy consumption.This behavior is reported for the optimized allocation under Model 2 and similarly under Model 1.
  • Energy comparison: 36.8 J and 29.9 J are the proposed schemes’ average MU energy consumptions at T = 2.7 s for orthogonal and non-orthogonal access, respectively.The corresponding equal-bit, constant-velocity baselines require 43.1 J and 44.3 J, implying 14.5% and 32.7% decreases.
  • Energy comparison: 27.4% of the 32.7% non-orthogonal-access energy decrease comes from trajectory optimization, whereas 2% comes from bit-allocation optimization alone.After optimization, non-orthogonal access is preferred unless the deadline is small; insufficient flight time makes offloading infeasible.

VII. CONCLUDING REMARKS

The paper studies UAV-mounted cloudlets that jointly optimize offloading bit allocation and cloudlet trajectory to reduce mobile energy consumption. Numerical results show significant savings over local execution and partial optimization, while highlighting energy-model accuracy and broader scenario generalization as open issues.

  • The proposed architecture uses a UAV-mounted cloudlet to provide computation offloading opportunities to multiple static mobile devices.
  • The optimization jointly determines uplink, downlink, and computation bit allocation together with the UAV trajectory for orthogonal and non-orthogonal access.
  • Numerical results verify significant mobile energy savings compared with local mobile execution and approaches optimizing only bit allocation or trajectory.
  • Accurate UAV energy-consumption models are important for the optimal system design.
  • Open problems include extending the optimization to multiple moving interfering mobile devices and variable-altitude trajectories.

APPENDIX A DERIVATIONS OF (19)

The appendix constructs convex upper bounds for non-convex communication, computation, and mobility-related energy expressions using successive convex approximation. It also describes propulsion-energy modeling for fixed-wing and rotary-wing UAVs and its frame-level discretization.

  • APPENDIX A DERIVATIONS OF (19): For a feasible point z(v), convex upper bounds are derived for non-convex computing-energy functions using Lemma 2.
  • APPENDIX A DERIVATIONS OF (19): The downlink communication-energy expression is rewritten and replaced by a convex upper bound around z_n(v).
  • APPENDIX A DERIVATIONS OF (19): Analogous convex upper bounds are derived for the non-convex function h^m_N,k,n at a feasible point.
  • APPENDIX A DERIVATIONS OF (19): A convex surrogate function upper-bounds the non-convex energy expression to linearize its concave parts.
  • APPENDIX C DERIVATIONS OF MODEL 2 IN (29): For fixed-wing UAVs, the propulsion-energy model uses aerodynamic parameters including air density, drag coefficient, reference area, Oswald efficiency, and wing aspect ratio.
  • APPENDIX C DERIVATIONS OF MODEL 2 IN (29): For rotary-wing UAVs, propulsion power comprises profile, parasitic, and induced components, while total propulsion energy integrates power over the trajectory.
  • APPENDIX C DERIVATIONS OF MODEL 2 IN (29): Applying a discrete linear state-space approximation yields the rotary-wing propulsion energy consumed in each frame under Model 2.
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