Orientation Matters: Learning Radiation Patterns of Multi-Rotor UAVs In-Flight to Enhance Communication Availability Modeling

1. Problem Statement

The paper addresses the challenge of modeling Communication Radiation Patterns (RPs) for Uncrewed Aerial Vehicles (UAVs) in real-world, modular scenarios.

• The Core Issue: In modular UAV systems, payloads, sensors, and airframes can change, altering the antenna's radiation pattern. Traditional methods rely on pre-identified theoretical models or laborious laboratory calibration (anechoic chambers), which are impractical for field-deployed, reconfigurable swarms.
• The Gap: Existing robotic communication models often assume idealized, isotropic antennas or fixed patterns. However, the UAV airframe and payload create complex interference, causing direction-dependent signal attenuation (up to -20 dB) that varies with the relative orientation (Azimuth and Inclination) of the communicating UAVs.
• The Goal: Develop a method to rapidly learn and decouple the joint radiation patterns of two heterogeneous UAVs in-flight, without infrastructure, to enable precise autonomous path planning and swarm control.

2. Methodology

A. Joint Calibration Trajectory

To overcome the non-holonomic constraints of standard quadrotors (which cannot arbitrarily rotate in all 6 degrees of freedom while hovering), the authors designed a specific synchronized flight trajectory:

• Setup: Two UAVs start 10 meters apart at an altitude of 20 meters (to minimize ground reflections).
• Motion: Both UAVs fly synchronously around a vertical circle of 10m diameter centered between them.
• Orientation Scanning: After completing each loop, one UAV slightly changes its heading (yaw). By repeating this, the pair samples the full 360° relative orientation space, covering all possible Azimuth ($\alpha$) and Inclination ($\beta$) angles between the two antennas.

B. Mathematical Formulation

The received power ($P_{rx}$) is modeled using the Friis transmission equation:
$$P_{rx} = P_{tx} + G_{tx}(\alpha_{tx}^{rx}, \beta_{tx}^{rx}) + G_{rx}(\alpha_{rx}^{tx}, \beta_{rx}^{tx}) + \text{Path Loss}$$
The core challenge is decoupling the joint gain $G$ into two independent terms: $G_{tx}$ (Transmitter) and $G_{rx}$ (Receiver). The authors treat this as a residual-minimization problem where the goal is to find parameters $\phi$ and $\psi$ that minimize the error between measured and predicted signal strength.

C. Proposed Learning Models

Three linear combination models were compared to represent the radiation pattern $G(\alpha, \beta)$:

1. Spherical Harmonics (SH): Uses orthogonal Legendre polynomials. This is a "dual-domain" approach suitable for spherical data.
2. Basis Grid (BG): A "primary-domain" approach using a grid of inducing samples on the sphere with a Gaussian kernel (similar to Gaussian Processes) to capture local variations.
3. Polynomial (P): An unconstrained polynomial model over azimuth and inclination (noted to be less effective due to ignoring domain periodicity).

Decoupling Strategy: To prevent the mathematical ambiguity where $G = G_1 + \epsilon + G_2 - \epsilon$ (infinite solutions), the authors applied Ridge Regression with a tuned hyperparameter ($\kappa=50$) to regularize the parameters and force a unique solution.

3. Experimental Setup

• Hardware: Two heterogeneous UAVs (DJI F450 and Holybro X500) equipped with off-the-shelf TP-Link Archer T2U Plus Wi-Fi USB modules (2.4 GHz).
• Payloads: One UAV carried a UVDAR payload; the other a LiDAR. Antennas were mounted in different orientations (horizontal vs. vertical).
• Environment: Outdoor, obstacle-free field (rural area) with obstacles >50m away.
• Data: 27,958 RSSI samples collected during the calibration flight, synchronized via NTP (Chrony) to sub-millisecond accuracy.
• Baseline: Compared against Mean (M) and Nearest Neighbor (NN) regressions.

4. Key Results

• Accuracy: The Spherical Harmonics (SH) model with order 14 achieved the best performance, with a Root-Mean-Squared Error (RMSE) of 3.73 dB. The order 28 model achieved 3.39 dB, which is effectively at the level of the inherent measurement noise (local RSSI standard deviation $\approx$ 2.74 dB).
• Decoupling Success: The method successfully separated the joint pattern into distinct patterns for UAV A and UAV B, revealing that the orientation of the UAV relative to the other causes signal gains/losses of up to 10–20 dB.
• Model Comparison:
  • SH: Best balance of accuracy and complexity. Captured fine-grained patterns without overfitting (verified via cross-validation).
  • BG: Performed well but required more tuning; slightly higher error than SH.
  • Polynomial: Performed poorly due to the non-periodic nature of the domain.
  • Baselines: The Mean model had high error (5.43 dB); the NN model (3.43 dB) was accurate but could not decouple the patterns (it learned the joint state, not individual UAV characteristics).
• Overfitting Analysis: High-order models (Order 28) did not show signs of random noise fitting; cross-validation cases produced topologically identical patterns, suggesting the model captured the true underlying physics of the airframe interference.

5. Key Contributions

1. Simultaneous Decoupling: A novel method to learn and decouple the radiation patterns of two heterogeneous UAVs simultaneously from a single joint flight dataset, rather than requiring isolated calibration.
2. In-Flight Calibration Trajectory: A practical, infrastructure-free flight path designed specifically for non-holonomic UAVs to sample the full 3D relative orientation space.
3. Practical Feasibility: Demonstrated that accurate RP modeling (within measurement noise limits) is achievable in real-world outdoor conditions using off-the-shelf hardware, enabling rapid recalibration after payload changes.

6. Significance and Future Work

• Impact: This work enables communication-aware path planning and swarm control in dynamic environments. By knowing the specific radiation pattern of a UAV (which changes with payload), robots can optimize their formation and orientation to maximize link quality and minimize interference.
• Future Directions: The authors suggest extending the work to account for wave polarization, testing different frequencies, optimizing the trajectory as an information-gathering problem, and further analyzing sampling bias and localization sensitivity.

In summary, the paper proves that treating the entire UAV as a complex antenna system and using Spherical Harmonics to model its radiation pattern allows for high-precision, data-driven communication modeling essential for robust autonomous aerial swarms.