Source-linked AI summary
Optimization of UAV Heading for the Ground-to-Air Uplink
Feng Jiang, A. Lee Swindlehurst
TL;DR
The paper asks how UAV motion can improve multi-user ground-to-air uplink performance when ground nodes transmit through a multi-antenna UAV. It analyzes static and mobile-user settings, using beamforming, trajectory or heading optimization, and position prediction. Simulations show benefits from heading adaptation and near-optimal performance from simplified algorithms.
Problem
The paper addresses how to control a UAV's motion to optimize uplink communications performance for multiple ground nodes.
Method
The paper combines beamforming with static trajectory analysis and adaptive mobile-user heading optimization based on predicted terminal positions.
Results
Simulations demonstrate benefits from adapting UAV heading, while simplified algorithms achieve near-optimal performance.
Takeaways & Limitations
UAV heading adaptation can improve uplink communications performance in the studied static and mobile ground-user settings.
Abstract
from arXiv · showhide
In this paper we consider a collection of single-antenna ground nodes communicating with a multi-antenna unmanned aerial vehicle (UAV) over a multiple-access ground-to-air wireless communications link. The UAV uses beamforming to mitigate the inter-user interference and achieve spatial division multiple access (SDMA). First, we consider a simple scenario with two static ground nodes and analytically investigate the effect of the UAV heading on the system sum rate. We then study a more general setting with multiple mobile ground-based terminals, and develop an algorithm for dynamically adjusting the UAV heading in order to maximize a lower bound on the ergodic sum rate of the uplink channel, using a Kalman filter to track the positions of the mobile ground nodes. Fairness among the users can be guaranteed through weighting the bound for each user's ergodic rate with a factor inversely proportional to their average data rate. For the common scenario where a high $K$-factor channel exists between the ground nodes and UAV, we use an asymptotic analysis to find simplified versions of the algorithm for low and high SNR. We present simulation results that demonstrate the benefits of adapting the UAV heading in order to optimize the uplink communications performance. The simulation results also show that the simplified algorithms perform near-optimal performance.
I. INTRODUCTION
The paper optimizes UAV heading for multi-user ground-to-air uplinks with a multi-antenna UAV using beamforming to mitigate co-channel interference. It analyzes static two-user trajectories and develops adaptive heading methods for mobile users, including simplified high-K-factor solutions.
- General approach: The system uses a multi-antenna UAV and single-antenna ground users transmitting simultaneously, with beamforming separating co-channel data streams.The model assumes correlated Rician fading and uses a maximum-SINR beamformer for interference mitigation.
- General approach: The UAV heading affects mutual interference because signal angle of arrival depends on heading and the relative positions of the UAV and ground nodes.The proposed adaptive algorithm adjusts heading to minimize mutual interference and improve uplink performance.
- Static two-user case: For two static ground nodes, a rectangular-path model reduces trajectory optimization to heading optimization, solvable with a simple line search.The analysis also examines how array size influences heading sensitivity.
- Mobile ground network: For mobile ground nodes, the paper derives a lower bound on average achievable sum rate and uses a line-search algorithm to optimize heading at each time step.The UAV predicts future terminal positions with feedback-driven Kalman filtering before selecting its heading.
- Mobile ground network: The study compares TDMA and SDMA and reports a dramatic improvement offered by SDMA in simulations.SDMA allows simultaneous transmissions while the UAV uses beamforming for source separation.
- Asymptotic methods: Under a high K-factor Rician channel, asymptotic low- and high-SNR methods produce performance nearly identical to the optimal algorithm.These asymptotic expressions simplify the heading optimization problem.
C. Organization
The paper organizes its analysis around the signal and channel model, static-user heading optimization, mobile-user prediction and control, asymptotic approximations, and simulations. The model assumes a forward-moving UAV with a multi-antenna ULA and correlated Rician channels.
- Organization: The paper presents the signal and channel model before treating static two-user heading optimization, mobile-network control, asymptotic analysis, and simulations.The simulations evaluate heading control, SDMA versus TDMA, and asymptotic-result validity.
- Signal model: The UAV has M antennas, serves N single-antenna ground nodes, and assumes N ≤ M for the active uplink users.The UAV isolates each node's data by multiplying the received signal by a beamformer.
- Signal model: The UAV maintains constant altitude and velocity while receiving uplink data, and each ground node is assumed to transmit with the same power.The UAV is restricted to non-hovering operation with a required forward velocity.
- Channel model: The channel model combines line-of-sight and correlated Rayleigh components within a correlated Rician fading model.The LOS component depends on signal angle of arrival, while the Rayleigh component uses a receiver-side spatial correlation matrix.
- Channel model: For a ULA, phase delay depends on elevation and azimuth angles, which are computed from UAV heading and UAV-user positions.The paper uses antennas separated by one-half wavelength and permits orientation along the fuselage or wings.
- Channel model: The paper notes that extending the analysis to different array geometries requires new LOS and spatial-correlation expressions.The LOS modification is described as straightforward, whereas deriving the new spatial correlation matrix is more involved.
III. RESULTS FOR THE STATIC TWO-USER CASE
For two static users, the paper studies how rectangular UAV trajectory orientation affects uplink sum rate under geometric and channel conditions. An approximate heading solution achieves near-optimal rates while array size and heading can strongly affect performance.
- Geometric cases: When the UAV flies near the users' midpoint, path loss can lower both users' SINR and the sum rate; separately serving users may then be preferred.The suggested alternative is to circle above each user and alternate between them.
- Trajectory model: The static-user analysis uses a rectangular trajectory parameterized by side lengths and orientation, with dimensions constrained by UAV geometry and user distance.The model assumes the rectangle is small relative to user distance and has a minimum side length accounting for turning radius.
- Approximate optimization: At high SNR and large K-factor, the approximate solution sets Ca = Cmax and Cb = Cmin, leaving heading as the optimization variable.The remaining heading problem can be solved by a simple line search over [0, π/2].
- Simulation results: Increasing the UAV antenna count and choosing the heading appropriately can substantially affect communications performance.The analysis also indicates that a tightly clustered path near the users can make heading effects minimal but may produce highly correlated channels.
IV. HEADING OPTIMIZATION FOR A MOBILE GROUND NETWORK
For multiple mobile ground nodes, the UAV tracks user movement and dynamically selects its heading for future network performance. The framework compares simultaneous SDMA transmission with equal-slot TDMA.
- Mobile network: The mobile-network scenario includes several moving ground nodes whose positions are tracked by the UAV.Both SDMA and TDMA approaches are considered.
- Access schemes: In SDMA, all ground nodes transmit simultaneously and UAV beamforming separates their sources; in TDMA, each user receives an equal transmission slot.The schemes differ in whether users share the channel simultaneously or by time division.
- Position prediction: User position feedback at time step n − 1 is used to predict positions at time n.The predicted positions support the subsequent heading decision.
- Heading control: The adaptive heading is calculated at time step n − 1 so that network performance at time step n is optimized.This creates a one-step-ahead heading-control procedure.
A. Mobility Model and Position Prediction
The UAV predicts mobile ground-node positions with a first-order AR model and Kalman filter, then adjusts its heading by optimizing a rate bound subject to motion and fairness constraints.
- Mobility model: A first-order autoregressive model describes ground-node dynamics, with process and observation noise included in the state-space formulation.The UAV receives noisy position information and uses the model within a standard Kalman-filter implementation.
- Position prediction: The UAV uses current node-location feedback and a Kalman filter to predict each node’s position at the next time step.Prediction uses noisy observations and produces estimated coordinates for heading optimization.
- Heading effects: Heading changes affect received power and line-of-sight angle of arrival, thereby influencing beamformer-based spatial separation of users.The heading changes UAV-user distances and the angle of arrival of the LOS channel component.
- Heading optimization: The UAV maximizes a Jensen-based lower bound on ergodic sum rate by one-dimensional line search over the allowed heading interval.The optimization is a single-variable problem constrained by the maximum heading change per time step.
- Fairness and refinements: Proportional-fair weighting addresses rate imbalance, while periodic weight updates and a center-of-gravity constraint reduce undesirable back-and-forth or excessive UAV motion.The CoG safeguard redirects the UAV toward the user centroid when the calculated heading would exceed dmax; Nw and dmax are selected empirically.
C. TDMA Scenario
The TDMA formulation assigns each node a transmission slot and optimizes the UAV heading using the corresponding rate objective, while asymptotic SDMA methods simplify heading selection under low and high SNR.
- TDMA formulation: In TDMA, each node transmits in its own time slot, and maximum-ratio combining determines the user SNR.The resulting mean SNR supports the TDMA heading-optimization formulation.
- TDMA implementation: The TDMA objective can replace the SDMA objective in the adaptive heading algorithm to implement TDMA heading control.The optimization is incorporated into the algorithm’s heading-selection step.
- Asymptotic simplification: Under high K-factor channels, asymptotic analysis removes the rate-bound calculation and yields simpler heading-control algorithms.The paper derives low-SNR and high-SNR alternatives for the max-sum-rate SDMA case, with proportional-fair and TDMA extensions described as straightforward.
- Low- and high-SNR cases: At low SNR, the optimal heading has a closed-form solution, whereas at high SNR, maximizing sum rate reduces to minimizing summed inter-user channel correlations over finite candidate headings.The high-SNR criterion can be evaluated without the general line search.
- Performance: The asymptotic algorithms achieve performance essentially identical to the general line-search algorithm.Each approximation is slightly better in its corresponding SNR regime, but the difference is small.
A. Asymptotic Analysis for Low SNR Case
For high K-factor channels at low SNR, the paper approximates the heading-dependent rate as a sinusoidal function and obtains a closed-form heading update.
- Low-SNR approximation: The low-SNR SINR approximation assumes a large Rician K-factor and treats angle-insensitive terms as minor or locally constant.The approximations rely on small heading changes and limited UAV movement relative to user distance.
- Heading-dependent model: Using predicted user positions and the UAV’s prior position, the analysis expresses channel-related quantities as functions of the candidate heading.Intermediate coefficients capture the heading dependence through cosine and sine terms.
- Rate structure: The average sum rate is approximated by a sinusoidal function of the UAV heading.The expression follows from substituting the approximated channel terms into the rate objective.
- Closed-form solution: The resulting low-SNR heading problem has a closed-form approximation, eliminating the need for a line search.This is the simplified optimization used by the adaptive heading algorithm in the low-SNR regime.
B. Asymptotic Analysis for High SNR Case
For high K-factor channels at high SNR, the paper simplifies heading selection by minimizing inter-user channel correlations, then evaluates the resulting algorithms through mobility and rate simulations.
- Correlation criterion: Under these approximations, the UAV seeks headings that minimize correlations between mean channel vectors of different users.The resulting criterion is consistent with minimizing inter-user channel correlation.
- High-SNR assumptions: The high-SNR derivation neglects Rayleigh contributions and distance changes that are small over one time step, focusing on angle-dependent mean-channel terms.It also assumes an approximately diagonal mean-channel Gram matrix.
- Candidate headings: Because the correlation criterion is piecewise concave, its minimum can be found by evaluating boundary and zero-point candidates.The analysis uses a piecewise quadratic approximation to locate the relevant zero points.
- Asymptotic solution: The asymptotic high-SNR solution is expressed as a finite candidate-heading rule derived from the correlation criterion.The paper gives the final asymptotic solution after identifying the relevant zero locations.
- Mobility results: In simulations, the UAV tracks moving users, uses loop maneuvers to maintain communications geometry, and follows different spatial patterns under max-sum-rate and proportional-fair objectives.The max-sum-rate UAV tracks the densest user region, whereas the proportional-fair UAV visits users in turn and incurs only slight sum-rate degradation.
- Turning-rate effect: Increasing the maximum turning rate improves performance by reducing loop distance and time spent with the array poorly aligned to users’ arrival angles.The simulations average ergodic rates over independent channel realizations.
- SDMA performance: SDMA achieves approximately a factor-of-3.3 rate gain over TDMA and reaches a sum rate about 15% below the no-interference benchmark.These results indicate effective interference suppression by the multi-antenna UAV receiver.
- Approximation performance: The low- and high-SNR approximations perform essentially identically to the line-search algorithm across all evaluated SNR values.Each approximation is slightly better in its own SNR regime, but the performance difference is small.
VII. CONCLUSION
The paper studies UAV heading and trajectory optimization for multi-user uplink communications, covering static and mobile ground users. It proposes adaptive and approximate algorithms, with simulations indicating effective heading selection and near-optimal simplified solutions.
- The paper investigates positioning and trajectory optimization for a multiple-antenna UAV serving multiple ground-based users.
- For two static users, an approximate trajectory method reduces the problem to a simple line search.
- For mobile users, an adaptive heading algorithm predicts terminal positions and uses UAV beamforming to maximize SINR at each time step.
- The optimization considers either maximizing a lower bound on average uplink sum rate or guaranteeing proportional fairness among users.
- Simulations indicate that the algorithms automatically generate suitable UAV headings, while SDMA improves uplink performance over TDMA.
- Closed-form low- and high-SNR heading approximations replace line search while retaining near-optimal performance in their respective scenarios.
APPENDIX A
The appendix derives an approximate two-user heading optimization under assumptions that simplify the UAV trajectory and channel model. The resulting interpretation links the optimal trajectory to minimizing average channel correlation between users.
- The optimal trajectory minimizes the average correlation between the two users' channels.
- The expected trajectory-averaged data rate is identical for both users, allowing the analysis to focus on one user's SINR.
- For large K, the Rayleigh component is ignored and the SINR is expressed as a function of position along the trajectory.
- Jensen's inequality provides an upper bound on average sum rate, and the analysis assumes maximizing this bound approximately optimizes the average rate.
- The approximation replaces the original trajectory problem by assuming the UAV remains effectively fixed at the midpoint between two ground users.
- Under this assumption, only the UAV heading changes the uplink rate, while the elevation angles remain constant.
2. Note that since
This derivation transforms the heading objective into a one-variable optimization by exploiting the relationship between the UAV's headings and the users' angular geometry. It then partitions the domain according to the ordering of two auxiliary quantities.
- When the second user’s azimuth differs by π, the sine terms are negatives of one another, simplifying the objective.
- The UAV uses heading δ along one trajectory segment and heading δ + π along the other.
- Substitution into the objective yields an optimization problem over a single variable.
- The auxiliary ratio R is bounded by 1 ≤ R ≤ Rc, allowing the objective to be rewritten in terms of s1 and s2.
- The domain is divided into S1 and S2 according to whether s2 < s1 or s2 ≥ s1, producing two subproblems.
- The minimum over the first subproblem is shown to determine the equivalent formulation, and equation (15) follows from the resulting relation.