In this study, we present a novel decision-making framework for defending critical assets against coordinated UAV drone swarm attacks. Our approach integrates a Graph Attention Network (GAT) with Long Short-Term Memory (LSTM) networks to model the spatial interactions and temporal evolution of incoming UAV drone groups, enabling dynamic and refined threat assessment. We further develop an area‑kill weapon employment strategy optimization model tailored for ultra‑wideband high‑power microwave (HPM) systems. Extensive simulations demonstrate that our method significantly improves threat discrimination among homogeneous UAV drones and enhances overall defense efficiency.
1. Introduction
The rapid proliferation of UAV drone technology has enabled the formation of large, coordinated swarms that pose a severe challenge to traditional air defense systems. Unlike conventional aircraft, UAV drone swarms rely on dense communication networks and cooperative behaviors to saturate defenses. Conventional point‑kill weapons suffer from low engagement efficiency and high ammunition cost when facing dozens or hundreds of low‑cost UAV drones. Ultra‑wideband high‑power microwave (HPM) weapons offer a promising area‑kill capability, as they can instantaneously disable multiple UAV drones within a wide angular beam. However, the operational use of HPM weapons requires intelligent antenna pointing and sequential scanning decisions to maximize the cumulative neutralization of high‑threat UAV drones over time.
Existing threat assessment methods primarily rely on static features such as speed, distance, time‑to‑go, and heading. For homogeneous UAV drone swarms, these features are nearly identical across individuals, resulting in poor threat discrimination. Moreover, they ignore the interaction topology and temporal evolution of the swarm. To address these gaps, we propose a spatio‑temporal threat evaluation model that combines GAT and LSTM. The GAT captures the communication‑based interaction graph among UAV drones at each observation time slice, while the LSTM models the sequential evolution of the embedded features. The resulting dynamic threat indicator (thri(t)) provides fine‑grained differentiation among swarm members, enabling optimized HPM weapon allocation.
Furthermore, we formulate a novel angle‑pre‑coverage weapon scheduling model. Instead of assuming one‑to‑one target engagement, this model seeks, for each decision epoch, the optimal rotation angle Δγ(t) of the HPM antenna such that the total threat weight of UAV drones that fall within the beam in the near future is maximized. Our contributions are three‑fold:
- We develop a graph‑based representation of UAV drone swarms using link capacity thresholds and eigenvector centrality.
- We design a GAT‑LSTM architecture for dynamic threat assessment that achieves superior discrimination among homogeneous UAV drones.
- We propose an angle‑pre‑coverage optimization model for HPM weapons and evaluate it under seven meta‑heuristic solvers.
2. Related Work
Counter‑UAV drone operations are typically divided into four phases: long‑range detection, medium‑range jamming, short‑range engagement, and terminal protection. Table 1 summarizes the stages and typical measures.
| Phase | Typical Measures | Expected Effect |
|---|---|---|
| Long‑range detection | Radar, RF, acoustic, infrared sensing | Identify swarm position and intent |
| Medium‑range jamming | Link disruption, spoofing, sensor blinding | Degrade or paralyze UAV drone capabilities |
| Short‑range engagement | HPM, laser, fragmentation munitions | Dense area neutralization |
| Terminal protection | Net barriers, decoys, smoke screens | Reduce reconnaissance and targeting |
Threat assessment for UAV drone swarms has been tackled via three main approaches: (1) extension of single‑target methods using machine learning classifiers; (2) pre‑clustering of tracks followed by group‑level evaluation; (3) graph neural network (GNN) based modeling of swarm interactions. The first two approaches struggle with intra‑cluster differentiation and fail to exploit dynamic interaction cues. The third approach, especially GAT and spectral methods, shows promise in identifying key nodes, but most existing work treats the evaluation as static or short‑term. Our work extends the temporal dimension via LSTM to capture the entire inbound timeline.
For weapon allocation, recent studies have employed Hungarian algorithm, multi‑agent reinforcement learning, or convolutional neural networks for interceptor assignment. However, these approaches are primarily designed for point‑kill weapons and do not account for the area‑kill characteristic of HPM systems. Our angle‑pre‑coverage model fills this gap by directly optimizing the scanning path of a wide‑beam weapon.
3. Graph Network Modeling of UAV Drone Swarm Ingress
3.1 Graph Elements
At each time instant t, we construct an ingress graph Gt = {St, Et, Pt}, where St = {s1t, s2t, …} is the node set representing individual UAV drones, Et is the edge set indicating communication links, and Pt is the weight matrix. Communication feasibility is determined by a threshold capthres on the link capacity. The link capacity between nodes i and j is computed using the Shannon‑Hartley formula:
$$linkCap_{ij}^{t} = B \cdot \log_2\left(1 + \frac{1}{N_0} \cdot \frac{P_0}{(u_{ij}^{t})^{\alpha}}\right)$$
where B is bandwidth, N0 noise power, P0 transmission power, uijt Euclidean distance between two UAV drones, and α path‑loss exponent (typically 2–4). The edge weight is defined as:
$$p_{ij}^{t} = \begin{cases}
0, & \text{if } linkCap_{ij}^{t} < cap_{\text{thres}} \\
linkCap_{ij}^{t}, & \text{otherwise}
\end{cases}$$
3.2 Node Features
For each UAV drone i, we extract features from radar measurements: velocity vector **v**i = (vXi, vYi, vZi), position vector **l**i = (lXi, lYi, lZi). Derived threat‑relevant quantities include distance di, time‑to‑go tsi, and lateral range slpi:
$$d_i = \sqrt{(l_{Xi})^2 + (l_{Yi})^2 + (l_{Zi})^2}$$
$$ts_i = -\frac{\mathbf{l}_i \cdot \mathbf{v}_i}{\lVert \mathbf{v}_i \rVert^2}$$
$$slp_i = \frac{\lVert \mathbf{l}_i \times \mathbf{v}_i \rVert}{\lVert \mathbf{v}_i \rVert}$$
Additionally, we encode UAV drone type (reconnaissance:1, jammer:3, strike:5) and jamming capability (strong:8, medium:6, weak:4, none:2). The eigenvector centrality (ECit) is used to quantify topological importance:
$$EC_i^{t} = \sum_{j=1}^{N} p_{ij}^{t}$$
A baseline static threat weight rwi is computed as the sum of normalized features (each mapped to [1,2]):
$$rw_i = -d_i – slp_i – ts_i + c_i + a_i + EC_i^t$$
$$Weight_i = \frac{rw_i}{\sum_{i=1}^{N} rw_i}$$
This static weight serves as a baseline and is also used in the final dynamic fusion.
4. GAT‑LSTM Based Dynamic Threat Assessment
4.1 Graph Attention Network for Spatial Hiding
For each time slice, we apply a GAT autoencoder to learn node embeddings from the graph features. The input feature matrix X(0) ∈ ℝN×F and edge index ε are fed into a two‑layer GAT. At layer l, we perform a linear transformation:
$$\mathbf{X}_{in}^{l} = \mathbf{H}^{(l-1)} \mathbf{W}^{(l)} \in \mathbb{R}^{N \times F_l}, \quad \mathbf{H}^{(0)} = \mathbf{X}^{(0)}$$
Attention coefficients between node i and neighbor j are computed using a single‑layer feedforward network:
$$e_{ij}^{l} = \text{LeakyReLU}\left( (\mathbf{a}^l)^T \left[ \mathbf{X}_{in}^{l}(i) \,\|\, \mathbf{X}_{in}^{l}(j) \right] \right)$$
$$\alpha_{ij}^{l} = \frac{\exp(e_{ij}^{l})}{\sum_{k \in \mathcal{N}_i} \exp(e_{ik}^{l})}$$
The hidden representation is updated by aggregating neighbor features:
$$\mathbf{H}^{(l+1)}(i) = \sigma\left( \sum_{j \in \mathcal{N}_i} \alpha_{ij}^{l} \mathbf{X}_{in}^{l}(j) \right)$$
Multi‑head attention (8 heads) is used to stabilize learning, and the final embedding is obtained by averaging over heads:
$$\mathbf{H}^{(l+1)} = \sigma\left( \frac{1}{M} \sum_{m=1}^{M} \mathbf{H}_m^{l} \right)$$
The reconstructed features are obtained via a linear decoder:
$$\mathbf{X}^{recon} = \mathbf{H}^{(L)} \mathbf{W}’$$
The autoencoder is trained to minimize the mean squared error between input and reconstruction:
$$\mathcal{L}_{MSE} = \frac{1}{N \times F} \sum_{i=1}^{N} \sum_{f=1}^{F} \left( \mathbf{X}^{recon} – \mathbf{X}^{(0)} \right)^2$$
4.2 Temporal Modeling with LSTM
For each UAV drone i, we collect the sequence of GAT embeddings over time, concatenated with the original static features: Vi(T) = {HL(t) ‖ X(0)(t), t ∈ T}. The LSTM processes this sequence with input, forget, output gates, and a cell state. The LSTM update equations are:
$$\mathbf{in}(t) = \sigma(\mathbf{W}_{in} \mathbf{V}^L(t) + \mathbf{U}_{in} \mathbf{h}_{t-1} + \mathbf{b}_{in})$$
$$\mathbf{fg}(t) = \sigma(\mathbf{W}_{fg} \mathbf{V}^L(t) + \mathbf{U}_{fg} \mathbf{h}_{t-1} + \mathbf{b}_{fg})$$
$$\tilde{\mathbf{z}}(t) = \tanh(\mathbf{W}_c \mathbf{V}^L(t) + \mathbf{U}_c \mathbf{h}_{t-1} + \mathbf{b}_c)$$
$$\mathbf{z}(t) = \mathbf{fg}(t) \odot \mathbf{z}(t-1) + \mathbf{in}(t) \odot \tilde{\mathbf{z}}(t)$$
$$\mathbf{ou}(t) = \sigma(\mathbf{W}_{ou} \mathbf{V}^L(t) + \mathbf{U}_{ou} \mathbf{h}_{t-1} + \mathbf{b}_{ou})$$
$$\mathbf{h}_t = \mathbf{ou}(t) \odot \tanh(\mathbf{z}(t))$$
4.3 Threat Indicator Calculation
The LSTM output ou(t+1) is fused with the static weight Weighti(t) using a mixing parameter μ ∈ [0,1]:
$$thr_i(t) = \left[ \mu,\; (1-\mu) \right] \begin{bmatrix} Weight_i(t) \\ ou(t+1) \end{bmatrix}$$
Here μ controls the balance between current observation and historical temporal information. A higher μ gives more emphasis to the instantaneous static weight, while a lower μ trusts the LSTM’s learned temporal pattern. In our experiments, we set μ = 0.5 as a default.
5. Weapon Employment Strategy Optimization via Angle Pre‑Coverage
5.1 Problem Formulation
Let the HPM weapon have a beamwidth β and current pointing direction γ(t). The weapon can rotate by Δγ(t) (positive for clockwise, negative for counter‑clockwise) at each decision step. The rotation takes time Δt = |Δγ(t)| / v, where v is the scan rate. At a future time tLh = t + Δt, the beam covers the angular sector [γ(t)+Δγ(t) – β/2, γ(t)+Δγ(t) + β/2]. The objective is to maximize the total instantaneous threat of all UAV drones that will fall within the beam at that future moment:
$$\max_{\Delta\gamma(t)} \sum_{j: \theta_j(t_{Lh}) \in [\gamma(t)+\Delta\gamma(t) \pm \beta/2]} thr_j(t_{Lh})$$
We schedule over a finite horizon (e.g., up to the maximum time‑to‑go among UAV drones). This is a sequential decision problem. For computational tractability, we treat each time step independently using a one‑step lookahead (greedy) or multi‑step horizon (lookahead_steps = 5 in our experiments).
5.2 Performance Metrics
We evaluate a strategy using three metrics. Let Ncover be the number of UAV drones detected (i.e., covered by the beam at some decision step), and tCoveri the time when UAV drone i is first covered. Define:
$$dRate = \frac{N_{cover}}{N}$$
$$dCover = \frac{\sum_{i=1}^{N_{cover}} thr_i(t_{Cover_i})}{\sum_{t} \sum_{i=1}^{N} thr_i(t)}$$
$$dTime = \frac{\sum_{i=1}^{N_{cover}} t_{Cover_i}}{N_{cover}}$$
dRate is the detection rate, dCover is the weighted coverage ratio (higher means more high‑threat UAV drones are covered), and dTime is the average time to first coverage (lower is better).
6. Experimental Validation
6.1 Simulation Setup
We simulate a triangular formation of 40 UAV drones inbound toward a defended asset. The swarm uses a coupled oscillator model to maintain relative positions while ensuring no collisions. The time‑to‑go spread among UAV drones is less than 10 seconds. Example trajectories are shown in earlier figure (without numbered reference). The hyperparameters of the GAT‑LSTM model are listed in Table 2.
| Parameter | Value |
|---|---|
| GAT layers | 2 |
| Hidden dimension | 16 |
| Attention heads | 8 |
| LSTM units | 32 |
| Optimizer | Adam |
| Dropout | 0.6 |
| Activation | ReLU |
| Epochs | 100 |
| Batch size | 16 |
| Learning rate | 0.001 |
| Lookahead steps | 5 |
| Population size (for meta‑heuristics) | 30 |
6.2 Model Convergence and Prediction Accuracy
The GAT‑LSTM model converged within 100 epochs with a stable loss. The prediction performance on threat indicators is illustrated by the R² value of 0.8824, indicating that the model explains 88.24% of the variance. For low‑threat values (Weight < 0.6), predictions closely match ground truth; for high‑threat values (Weight > 0.8), predictions show slight dispersion but maintain the overall trend.
6.3 Comparison of Optimizers on Weapon Scheduling
We compare seven optimization algorithms on the angle‑pre‑coverage model: Greedy, Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO), Differential Evolution (DE), Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). The results are summarized in Table 3 and Table 4.
| Method | Static Baseline | GAT‑LSTM Dynamic |
|---|---|---|
| Greedy | 1.0 (12/12) | 1.0 (12/12) |
| ACO | 1.0 | 1.0 |
| PSO | 1.0 | 1.0 |
| DE | 1.0 | 1.0 |
| GA | 1.0 | 1.0 |
| SA | 1.0 | 1.0 |
| TS | 1.0 | 1.0 |
| Method | Static dCover | Dynamic dCover | Static dTime (s) | Dynamic dTime (s) |
|---|---|---|---|---|
| Greedy | 0.62 | 0.68 | 2.3 | 2.4 |
| ACO | 0.60 | 0.72 | 2.6 | 2.1 |
| PSO | 0.61 | 0.70 | 2.4 | 2.5 |
| DE | 0.63 | 0.74 | 2.5 | 2.0 |
| GA | 0.61 | 0.73 | 2.7 | 2.2 |
| SA | 0.60 | 0.69 | 2.8 | 2.3 |
| TS | 0.61 | 0.70 | 2.5 | 2.6 |
All methods achieve a detection rate of 1.0 (all 12 UAV drones are eventually covered). However, the weighted coverage dCover is consistently higher (≥0.68) for the GAT‑LSTM dynamic threat than for the static baseline (≤0.63). The improvement is most pronounced for DE (0.74 vs 0.63) and ACO (0.72 vs 0.60). In terms of average coverage time, dynamic assessment yields shorter times for ACO, DE, GA, and SA, but marginally longer for Greedy, PSO, and TS. This is because the higher threat discrimination provided by GAT‑LSTM creates a more rugged fitness landscape; population‑based algorithms (DE, GA, ACO) exploit this to converge faster, while gradient‑free single‑trajectory methods (Greedy, TS) may be trapped in local optima.
6.4 Discussion
The experimental results confirm that our GAT‑LSTM dynamic threat assessment significantly improves the ability to differentiate among homogeneous UAV drones, leading to better prioritization in HPM weapon scheduling. The angle‑pre‑coverage optimization framework effectively translates this improved threat information into operational decisions. We recommend the use of differential evolution or ant colony optimization for solving the weapon scheduling problem when a high weighted coverage is the primary objective, while greedy can serve as a fast baseline.
7. Conclusion
In this work, we have presented a comprehensive framework for counter‑UAV drone swarm defense decision making. By discretizing the ingress timeline and combining graph attention networks with LSTM, we capture both the spatial interaction structure and the temporal evolution of UAV drone swarms. This yields dynamic threat indicators that significantly outperform static methods in distinguishing critical UAV drones. Furthermore, our angle‑pre‑coverage weapon strategy optimization model, tailored for area‑kill HPM systems, provides a principled way to generate sequential scanning decisions. The performance evaluation across multiple meta‑heuristic solvers demonstrates the practical efficacy of our approach.
Future work will extend the experimental validation to more diverse swarm motion models (e.g., Vicsek, Couzin), incorporate multi‑weapon coordination, and investigate online learning under uncertain sensing conditions.