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Joint 3D Trajectory Design and Resource Allocation for Secure Dual-UAV-aided Underlay Systems

This paper proposes a joint optimization framework for 3D UAV trajectories, transmit power, and user scheduling in a secure dual-UAV underlay system to maximize average secrecy spectral efficiency against aerial eavesdroppers by decomposing the non-convex problem into solvable convex subproblems.

Original authors: Hongjiang Lei, Xiaqiu Wu, Ki-Hong Park, Gaojie Chen, Gaofeng Pan

Published 2026-06-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hongjiang Lei, Xiaqiu Wu, Ki-Hong Park, Gaojie Chen, Gaofeng Pan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: A High-Stakes Aerial Heist

Imagine a scenario where a team of ground workers (the Ground Devices) needs to send secret blueprints to a flying drone base station (the Receiver UAV). However, there is a problem: a sneaky, mobile spy drone (the Eavesdropper) is flying around, trying to intercept these blueprints.

To stop the spy, the team deploys a second drone, a Jammer UAV. This drone acts like a "noise machine," blasting static interference to drown out the spy's ability to hear the secret messages, while the main drone tries to get as close as possible to the workers to hear them clearly.

The goal of this research is to figure out the perfect flight plan for both drones, the perfect volume for the noise machine, and the perfect timing for when each worker should speak, so that the secret message gets through loud and clear, but the spy hears nothing but static.

The Setting: The "Underlay" Rule

This isn't just any airspace; it's a crowded one. The drones are flying in a "cognitive radio" zone. Think of this like a shared highway where the drones are allowed to drive, but only if they don't cause a traffic jam for the "Primary Users" (like emergency vehicles or fixed radio towers) already on the road.

The drones must constantly check their "interference temperature." If they get too loud or too close to the emergency vehicles, they have to quiet down or move away. This adds a layer of complexity: they have to be stealthy, fast, and polite all at once.

The Challenge: A Tangled Web

The researchers faced a massive puzzle. They had to decide:

Where to fly: Should the drones go high, low, left, or right? (3D Trajectory)
How loud to shout: How much power should the workers use to talk, and how much static should the jammer blast? (Power Allocation)
Who talks when: Which worker gets to speak in which second? (Scheduling)

The problem is that everything is connected. If the jammer moves, the spy hears differently. If the main drone moves, the signal strength changes. If the workers talk louder, they might annoy the emergency vehicles. It's a "highly coupled" problem, meaning you can't solve one part without messing up the others.

The Solution: Breaking the Puzzle Down

Because the math was too messy to solve all at once, the authors used a strategy called Block Coordinate Descent.

Imagine trying to tune a massive, old-fashioned radio with 100 dials. You can't turn them all at once to get the perfect station. Instead, you:

Freeze 99 dials and turn just one until it sounds best.
Freeze that one, turn the next one until it sounds best.
Repeat the cycle until the music is crystal clear.

The researchers did this with their drones:

Step 1: They fixed the flight paths and power, then figured out the best order for workers to speak.
Step 2: They fixed the schedule and paths, then calculated the best power levels.
Step 3: They fixed the power and schedule, then optimized the horizontal (left/right) flight paths.
Step 4: They fixed everything else and optimized the vertical (up/down) flight paths.

They repeated this cycle over and over. With each pass, the "secrecy" of the system got better, until it reached a point where it couldn't get any better.

The "Secret Sauce": 3D Movement and Probability

Two key findings made their solution special:

The Power of 3D: Many previous studies only looked at drones flying in a flat 2D map (like a video game on a screen). This paper showed that letting the drones fly up and down (3D) is a game-changer.
- Analogy: Imagine trying to whisper to a friend in a crowded room. If you are stuck standing on the floor, you might be blocked by a tall person. But if you can climb a ladder (change altitude), you can see over the crowd and whisper directly to your friend. The 3D movement allowed the drones to find "clear lines of sight" that 2D drones couldn't see.
The "Maybe" Connection: The researchers didn't assume the air was always clear. They used a model that accounts for buildings and obstacles. Sometimes the signal goes straight through (Line-of-Sight), and sometimes it bounces off a building (Non-Line-of-Sight). They calculated the probability of these connections to make sure the flight plan was robust even if the signal got blocked.

The Results: Why It Matters

The computer simulations showed that their method worked much better than older methods.

Compared to fixed paths: Drones that could move freely in 3D and adjust their power got much more data through than drones stuck on a pre-set track.
Compared to flat paths: Drones that could change altitude performed better than those forced to fly at a single height.
The Trade-off: The study found that if the "noise" allowed for the emergency vehicles (the interference threshold) was tighter, the drones had to be more careful, which lowered the secrecy rate. But by optimizing the flight, they could still get good results even with strict rules.

Summary

In short, this paper teaches us how to orchestrate a dance between two drones—one listening, one jamming—to protect secret data from a flying spy. By letting the drones move up, down, and around in 3D space, and by carefully timing who talks and how loud they shout, the system can maximize the amount of secret information delivered while keeping the spy in the dark. The key innovation is solving the complex math by breaking it into small, manageable steps and proving that moving in 3D is far superior to just moving in 2D.

Technical Summary: Joint 3D Trajectory Design and Resource Allocation for Secure Dual-UAV-aided Underlay Systems

Problem Statement
This study addresses the security challenges in Uncrewed Aerial Vehicle (UAV)-assisted data collection systems operating under Cognitive Radio Network (CRN) underlay modes. Specifically, the paper considers a scenario where a legitimate aerial receiver (UAV-U) collects confidential data from multiple fixed Ground Devices (GDs). The system is threatened by a mobile aerial eavesdropper (UAV-E) and constrained by the need to limit interference to a terrestrial Primary User (PU) to a specific Interference Temperature (IT) threshold.

To counter the eavesdropper, a friendly jamming UAV (UAV-J) is deployed to generate artificial noise. The core challenge lies in the joint optimization of four coupled variables: the 3D flight trajectories of both UAVs (U and J), the transmit power of the GDs, the transmit power of the jammer, and the user scheduling of the GDs. The objective is to maximize the Average Secrecy Spectral Efficiency (ASSE) of the system.

The problem is formulated as a non-linear mixed-integer non-convex optimization problem due to several factors:

Channel Uncertainty: The air-to-ground links follow a Probabilistic Line-of-Sight (PLoS) model, where the probability of LoS depends on elevation angles and distance, introducing randomness into the channel state.
Imperfect Information: The location of the aerial eavesdropper is imperfectly known, modeled using a bounded error region.
Coupled Constraints: The optimization variables are tightly coupled through the PLoS model, the IT constraints imposed by the PU, and the physical constraints of UAV propulsion energy and velocity.
Non-Smoothness: The secrecy rate involves a non-smooth operator $[x]^+ = \max(x, 0)$ .

Methodology
To solve the formulated non-convex problem, the authors propose an iterative algorithm based on Block Coordinate Descent (BCD) and Successive Convex Approximation (SCA).

Approximation: The authors first utilize an approximate lower bound on the expected spectral efficiency to streamline the solution. They approximate the secrecy rate by considering the LoS scenario for the legitimate link and removing the non-smooth $[ \cdot ]^+$ operator by setting transmit power to zero when the secrecy rate would be negative.
Decomposition: The original problem is decomposed into four subproblems, which are solved iteratively while fixing the other variables:
- User Scheduling: The binary scheduling variables are relaxed to continuous variables ( $0 \le a_k[n] \le 1$ ) and solved as a linear optimization problem.
- Transmit Power: The power allocation for GDs and the jammer is optimized. Non-convex constraints arising from the secrecy rate expression are handled using a first-order Taylor expansion to create a convex lower bound.
- Horizontal Trajectory: The 2D trajectories of UAVs U and J are optimized. Auxiliary variables and slack variables are introduced to handle the non-convex PLoS probability constraints, interference constraints, and safety distance requirements. SCA is applied to convexify these constraints.
- Vertical Trajectory: The altitude profiles of UAVs U and J are optimized using similar SCA techniques to handle non-convex elevation angle and distance constraints.
Convergence: The algorithm iterates through these subproblems until convergence. Theoretical analysis confirms that the objective value (ASSE) is non-decreasing with each iteration, ensuring convergence to a sub-optimal solution.

Key Contributions

Novel Framework: The paper proposes the first framework to address aerial eavesdropping in a dual-UAV-assisted underlay CRN. Unlike previous works that often assume fixed ground eavesdroppers or single-UAV systems, this work considers a mobile aerial eavesdropper with imperfect location information and a cooperative jammer in a CRN setting.
Comprehensive Modeling: The study incorporates practical factors often overlooked in isolation, including the PLoS channel model (which couples trajectory and distance), the bounded error model for eavesdropper location, and the energy consumption of UAVs for both horizontal and vertical movement.
Algorithmic Solution: The authors develop a rigorous model-driven optimization framework using BCD and SCA. This approach transforms the highly complex, non-convex joint optimization problem into a series of tractable convex subproblems, providing a theoretical benchmark for system performance.
Performance Validation: Through numerical simulations, the study demonstrates that the proposed joint optimization significantly outperforms benchmark schemes (e.g., fixed trajectories, fixed power, or 2D-only trajectory optimization).

Results
Numerical results validate the effectiveness of the proposed approach:

Convergence: The proposed algorithm converges quickly, typically within a few iterations.
3D Trajectory Impact: Jointly optimizing 3D trajectories yields the highest ASSE compared to schemes with fixed trajectories or 2D-only optimization. The results show that the jammer UAV benefits from adjusting its altitude to suppress the eavesdropper while maintaining interference constraints with the PU, while the receiver UAV optimizes its altitude to achieve favorable elevation angles with GDs.
Power Optimization: Optimizing transmit power alongside trajectories provides further gains. Fixed power schemes result in lower performance, particularly in CRN scenarios where power control is critical to meet IT constraints.
Parameter Sensitivity:
- Increasing the propulsion power budget (both horizontal and vertical) improves ASSE by allowing UAVs to access better channel positions.
- A higher IT threshold ( $\Gamma$ ) allows for higher transmit powers and better ASSE, though the system eventually enters a non-cognitive mode where gains plateau.
- Larger estimation errors for the eavesdropper's location ( $r_E$ ) degrade secrecy performance.
- Longer flight durations ( $T$ ) allow for more data collection and improved ASSE.

Significance and Claims
The paper claims that its primary significance lies in bridging the gap between secure UAV communications and cognitive radio networks in the presence of mobile aerial threats. By demonstrating that the complex, coupled optimization problem involving 3D trajectories, power control, and scheduling is solvable via a structured iterative approach, the work provides a foundational benchmark for secure data collection systems.

The authors emphasize that their work offers practical guidance for system design, highlighting that 3D trajectory design is not merely an incremental improvement but a crucial factor in maximizing secrecy performance, especially when dealing with mobile aerial eavesdroppers and spectrum-sharing constraints. The study concludes by noting that future work will extend these findings to multi-antenna systems and integrate beamforming with Integrated Sensing and Communication (ISAC) technologies.