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ISAC from the Sky: UAV Trajectory Design for Joint Communication and Target Localization

Xiaoye Jing, Fan Liu, Christos Masouros, Yong Zeng

arXiv:2207.02904v1eess.SYcs.IT

TL;DR

The paper studies how a moving UAV can jointly support downlink communication and target localization while accounting for shared-resource trade-offs and limited flight energy. It designs weighted UAV trajectories, progressively refines unknown target locations through multiple stages, and solves the resulting non-convex problem iteratively; the trade-off design yields about an order-of-magnitude lower target estimation error than communication-only design with a slight communication-performance decrease.

  • Problem

    The paper asks how to jointly improve communication and target localization with a moving UAV while accounting for shared resources and the UAV’s limited battery capacity.

  • Method

    It formulates a weighted trajectory optimization, uses a multi-stage design for an initially unknown target, and applies an iterative algorithm to obtain a locally optimal solution.

  • Results

    About an order of magnitude better target estimation error is achieved than with a communication-only approach, with a slight decrease in communication performance.

  • Takeaways & Limitations

    Tuning the weighting factor and accounting for UAV energy capacity provide flexible control of the communication–sensing performance trade-off.

Abstract

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Unmanned aerial vehicles (UAVs) as aerial base stations (BSs) are able to provide not only the communication service to ground users, but also the sensing functionality to localize targets of interests. In this paper, we consider an airborne integrated sensing and communications (ISAC) system where a UAV, which acts both as a communication BS and a mono-static radar, flies over a given area to transmit downlink signal to a ground communication user. In the meantime, the same transmitted signal is also exploited for mono-static radar sensing. We aim to optimize the UAV trajectory, such that the performance for both communication and sensing (C$\&$S) is explicitly considered. In particular, we first formulate the trajectory design problem into a weighted optimization problem, where a flexible performance trade-off between C$\&$S is achieved. As a step forward, a multi-stage trajectory design approach is proposed to improve the target estimation accuracy. While the resultant optimization problem is difficult to solve directly, we develop an iterative algorithm to obtain a locally optimal solution. Finally, numerical results show that the target estimation error obtained by the trade-off approach is about an order of magnitude better than a communication-only approach with a slight decrease on communication performance.

I. INTRODUCTION

The paper motivates moving-UAV ISAC as a way to jointly design communication and sensing while managing their inherent resource trade-offs and limited UAV energy. It formulates weighted trajectory optimization, uses multi-stage localization when the target is initially unknown, and shares one signal for both functions.

  • ISAC jointly uses wireless hardware and signals for communication and sensing, aiming to reduce hardware cost and improve spectral efficiency.
  • Moving UAVs add positioning and trajectory degrees of freedom that can improve communication and sensing by bringing the UAV closer to users and targets.
  • The paper jointly minimizes target-localization CRB and maximizes downlink communication rate under a UAV battery-energy constraint.
  • The system uses one pre-designed ISAC signal for continuous downlink communication and mono-static sensing, with sensing measurements fused from multiple hovering points.
  • A weighting factor adjusts the trajectory design priority between communication and sensing, whose shared resources create fundamental performance trade-offs.
  • Because the target location is initially unknown, the proposed multi-stage approach progressively improves target estimates and the resulting UAV trajectory.

B. Communication Model

The communication and sensing models characterize downlink rate and target-localization accuracy from UAV geometry, signal quality, and echo measurements. Sensing performance is evaluated through the CRB of the target coordinates, while communication uses average downlink rate.

  • The communication model uses line-of-sight propagation and free-space path loss, with channel quality determined mainly by UAV-receiver distance.
  • The communication metric is the average downlink communication rate, with nearly unchanged rate approximated along each waypoint-to-waypoint line segment.
  • The sensing model estimates target distance from two-way echo delay measurements collected at the UAV’s hovering points.At least Ktot = 3 hovering points are needed to determine the target’s two-dimensional coordinates.
  • Echo-distance measurements are modeled with zero-mean Gaussian noise whose variance is inversely proportional to the received ISAC-echo SNR.
  • The sensing metric is the sum CRBxt,yt of the CRBs for xt and yt, providing a lower bound for the sum of achievable coordinate-estimation MSEs.
  • The coordinate FIM is obtained by first constructing the distance-parameter FIM from echo measurements and then applying a Jacobian-based chain rule.

A. Problem Formulation

The problem formulation jointly optimizes UAV trajectory variables for communication and sensing under flight-speed, area, and onboard-energy constraints. A weighting factor controls the trade-off between average communication rate and target-localization CRB.

  • The UAV energy model includes propulsion energy while ignoring ISAC transmission energy because transmission consumption is typically orders of magnitude smaller.
  • The propulsion power model depends on UAV velocity and parameters describing blade profile, induced power, rotor speed, fuselage drag, air density, rotor solidity, and disc area.
  • The trajectory design determines UAV waypoints, hovering points, and flying velocities to maximize average communication rate while minimizing target-localization CRB.
  • The weighting factor η ranges from 0 to 1, with higher values assigning higher priority to sensing in the communication-sensing trade-off.
  • The formulation constrains the UAV to remain within the given area and limits total trajectory energy consumption to its onboard battery capacity.

B. ISAC Protocol

The multi-stage protocol designs UAV trajectories using an estimated target location because the ground-truth location is initially unknown. Each stage combines communication and sensing, updates the estimate from echoes, and continues subject to available energy.

  • B. ISAC Protocol: The sensing CRB depends on hovering-point locations and the target location, but the true target location is initially unknown.The protocol therefore evaluates the CRB using an estimated target location.
  • B. ISAC Protocol: The multi-stage approach splits trajectory design into stages to progressively improve target estimates and trajectory accuracy.It addresses the gap between the CRB evaluated at the true location and at an estimated location.
  • B. ISAC Protocol: The number of stages depends on total energy; intermediate stages use predetermined waypoint and hovering-point counts, while the final stage uses the remaining energy.The process continues until energy runs out, with K1 + K2 + ... + KM = Ktot and N1 + N2 + ... + NM = Ntot.
  • B. ISAC Protocol: Each completed stage uses received target echoes to obtain an updated target-location estimate for the next stage.The first stage begins from the initial UAV location and collects K1 echoes while following its designed path.
  • B. ISAC Protocol: In stage m, communication and sensing metrics are calculated using all previous stages plus the current stage’s trajectory.The UAV starts each stage from the final waypoint of the preceding stage.

IV. PROPOSED ALGORITHM FOR SOLVING P2 (m)

The proposed algorithm addresses the non-convex stagewise trajectory problem by convexifying constraints and approximating the objective iteratively. It searches descent directions with stepsizes to obtain a locally optimal feasible solution.

  • IV. PROPOSED ALGORITHM FOR SOLVING P2 (m): P2 (m) is difficult to solve globally because its objective function and constraints are non-convex.The algorithm therefore seeks a locally optimal solution.
  • IV. PROPOSED ALGORITHM FOR SOLVING P2 (m): Auxiliary variables reformulate non-convex constraints, including the relation involving [δm (i)]2 and ξm (i).At the optimum, the reformulated inequality holds with equality.
  • IV. PROPOSED ALGORITHM FOR SOLVING P2 (m): Successive convex approximation replaces non-convex constraint terms with first-order Taylor lower bounds.The resulting lower-bounded constraints preserve feasibility for the original problem when satisfied.
  • IV. PROPOSED ALGORITHM FOR SOLVING P2 (m): The remaining non-convex objective is approximated by a first-order Taylor expansion around the previous SCA iterate.The method then solves a reformulated problem at each iteration.
  • IV. PROPOSED ALGORITHM FOR SOLVING P2 (m): The algorithm selects stepsizes along the computed descent directions while maintaining feasibility of the optimization variables.The feasibility guarantee is established in Appendix A.

B. Estimation Approach for Target Location

Target coordinates are estimated by maximum likelihood from the accumulated sensing measurements. The proposed multi-stage procedure alternates trajectory design, hovering-based measurements, and coordinate updates until the UAV’s energy is nearly exhausted.

  • B. Estimation Approach for Target Location: The target-coordinate estimate is obtained using maximum likelihood estimation from the measurement vector accumulated across stages.At the end of stage m, the vector contains K1 + ... + Km measurement elements.
  • B. Estimation Approach for Target Location: The MLE is defined as the target-coordinate value that maximizes the likelihood function.Its stationarity condition is obtained by setting the derivative to zero.
  • B. Estimation Approach for Target Location: Algorithm 1 repeats stage trajectory design, hovering measurements, MLE-based target estimation, and energy updates.The final stage uses the maximum achievable waypoint and hovering-point counts supported by the remaining energy.
  • B. Estimation Approach for Target Location: Because the MLE has no closed-form expression, the method uses a numerical grid search.The MSE is evaluated through Monte Carlo simulation.

C. Initialization of the Iterative Algorithm

The iterative algorithm is initialized with a naive trajectory constructed from straight-line motion. Its waypoints connect the stage start toward a midpoint associated with the communication user and target-estimation geometry.

  • C. Initialization of the Iterative Algorithm: Each stage’s iterative optimization requires initial waypoint inputs, with the preceding stage’s final waypoint providing the next stage’s starting reference.The initial inputs are calculated from the last waypoint of the previous stage.
  • C. Initialization of the Iterative Algorithm: The initial trajectory uses a straight line and a fixed flying speed Vstr to provide a relatively fair starting point for communication and sensing.Its direction runs from the start point toward the designated midpoint.
  • C. Initialization of the Iterative Algorithm: The midpoint of the line connecting the relevant stage endpoints is used as the target point for constructing the initial path.This naive path supplies the initial inputs for the iterative algorithm.
  • C. Initialization of the Iterative Algorithm: Figure 3 depicts the designed trajectory used to calculate the algorithm’s initial inputs.The path is a straight-line initialization rather than the final optimized trajectory.

V. SIMULATION RESULTS

Simulations evaluate convergence, sensing accuracy, and C&S performance under varying measurement noise and energy budgets. The proposed iterative and multi-stage approaches are assessed using Monte Carlo estimation and benchmark comparisons.

  • The MSE of the MLE is evaluated using Monte Carlo simulations with 100 runs.
  • Convergence behaviour: The iterative algorithm reaches within 1% of its final value in 5 iterations during the first stage.
  • Sensing performance: When a = 50 rather than a = 10, the target estimation error increases because the measurement noise has larger variance.
  • Sensing performance: As Etot increases, both the target-coordinate MSE and CRB decrease.

A. The C&S Performance of the Proposed ISAC Approaches and Benchmarks with UAV Energy Constraints

The proposed trajectory design is compared with communication-only and straight-path benchmarks under different UAV energy constraints. Greater energy improves sensing and communication, while the trade-off design substantially improves localization accuracy at some communication cost.

  • Benchmark comparison: The proposed approach achieves target estimation error about one order of magnitude better than communication-only and more than two orders better than straight.
  • Benchmark comparison: The trade-off design incurs communication-performance loss compared with the communication-only approach.
  • Energy constraints: Increasing Etot improves sensing performance and increases the average communication rate.
  • Energy constraints: Larger Etot lets the UAV fly farther, obtain more observation measurements, and improve sensing performance.
  • Trajectory paths: The trade-off trajectory flies closer to the target, while increasing Etot also reduces the average distance to the communication user.

B. The Trade-off between C&S

Tuning the weighting factor η exposes a smooth communication–sensing trade-off over most of the range. Even a small sensing weight can greatly improve sensing with only a slight communication decrease relative to communication-only design.

  • There is a trade-off between average communication rate and estimation error, especially when Etot is small.
  • The C&S performance changes smoothly from η = 0.25 to η = 1 but sharply from η = 0 to η = 0.25.
  • Including sensing with a small weight produces a large sensing enhancement and only a slight communication-performance decrease relative to communication-only design.
  • A larger η makes the trajectory more suitable for sensing by bringing the UAV closer to the target and diversifying hovering-point viewing angles.

C. Behaviour of the Multi-stage Trajectory Design Approach

The multi-stage approach evaluates C&S performance under a fixed waypoint budget while progressively updating the target estimate. Multiple stages improve sensing accuracy but reduce communication performance, with the outcome depending on the balance between stages and observations.

  • Multi-stage setup: The evaluation fixes the total UAV waypoints at Ntot = 80 to fairly compare multi-stage and one-time trajectory designs.For Nstg = 25, the design uses M = 4 stages.
  • Sensing performance: Multiple stages enhance sensing performance by progressively refining the target-location estimate.Updated target estimates make subsequent trajectory designs more suitable for sensing.
  • Communication performance: Communication performance decreases as the multi-stage approach prioritizes trajectories based on increasingly accurate target estimates.
  • Stage-count trade-off: The stage-count trade-off depends on whether additional target-estimate updates outweigh having more observations within each stage.Larger Nstg reduces estimation error in some cases, while smaller Nstg provides more opportunities to update the estimate.
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