# Unsupervised Drones Swarm Characterization Using RF Signals Analysis and Machine Learning Methods

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## Abstract

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## 1. Introduction

- Developing a novel method for unsupervised drone swarm characterization and detection using RF signals and machine-learning algorithms with no a priori knowledge and no labeled data.
- We propose an efficient way to assess the number of drones in a swarm and the risk that comes from automated UAVs beforehand.
- An evaluation of the proposed approach on common datasets published in the literature.
- A comparison of the performance using various features, such as WST and CWT, and different dimension reduction methods.

## 2. Background and Related Work

## 3. Proposed Approach

**Problem statement:**Let us consider that N drones are denoted as ${D}_{1},{D}_{2},\dots ,{D}_{N}$ and communicate using RF packets while assuming that the communication protocol is unknown. Each RF transmitter sends multiple packets p with an unknown dimension $p\in {R}^{{d}_{i}}$ (i.e, with various length). This research proposed an unsupervised method that could match each transmitted packet to the specific drone that sent it, assuming no apriori knowledge about the number of drones, while each drone might send a different number of messages. Let us consider m packets from different drones ${p}_{1},{p}_{2},\dots ,{p}_{m}$ when m depicts the total number of sent messages. We aim to estimate the number of drones (in the swarm), which is equivalent to the number of RF transmitters.

#### 3.1. Datasets

#### 3.1.1. Self-Built Dataset

#### 3.1.2. Common Dataset

#### 3.2. Feature Extraction

**Continuous Wavelet Transform (CWT)**—The CWT originally introduced by P. Goupillaud et al. [42] was used to analyze signals at different scales or resolutions. The wavelet function was scaled and translated in order to analyze the signal at different scales and locations. This allowed the CWT to provide information about the frequency components of the signal at different scales, which could be useful for identifying patterns or features in the signal that might not be apparent at the time domain. The absolute value of the CWT, the so-called scalogram, is expressed by Equation (2). Figure 2 shows the scalogram images of the CWT transform for various RF transmitters.

**Wavelet Scattering Transform (WST)**—Wavelet scattering transform [43] is used to extract discriminant features from the RF-signals. WST refers to an iterative process of applying a set of wavelet transforms and nonlinearities at different scales, making it stable in the case of small deformations and invariant to the input signal translations or rotations. The WST transformation was carried out using (1) convolution, (2) nonlinearity, and (3) averaging. Precisely, the WST coefficients are obtained by applying the convolution operator ∗ between the wavelet modulus and low-pass filter $\varphi $. Assuming that wavelet $\psi \left(t\right)$ is a bandpass filter with a central frequency normalized to one at time index t, the wavelet filter bank ${\psi}_{\lambda}\left(t\right)$ is defined in Equation (3) as follows:

#### 3.3. Dimension Reduction

**t-Distributed Stochastic Neighbor (t-SNE)**—t-SNE is a nonlinear approach for dimension reduction [44] and is used to model pairwise similarities between points in both higher dimensional ${p}_{\left(i\right|j)}$ and lower dimensional spaces ${q}_{\left(i\right|j)}$. Therefore, if two points ${x}_{i}$ and ${x}_{j}$ are close in the input space, then their corresponding points ${y}_{i}$ and ${y}_{j}$ are also close. Equation (4) describes the affinities between points ${x}_{i}$ and ${x}_{j}$ in the input space ${p}_{ij}$.

**Uniform Manifold Approximation (UMAP)**—UMAP uses local manifold approximations and assembles together their local fuzzy-simplicial set representations to form a topological representation of the high-dimensional data. Given some low-dimensional representations of the data, the layout of the data representation in the low-dimensional space is then optimized through the minimization of the cross-entropy between the two topological representations [45]. The cost function for the optimization process, which is carried out by minimizing the fuzzy-set cross-entropy, is depicted by Equation (7) as follows:

**Principal Component Analysis (PCA)**—PCA is used to transform data linearly into a low-dimensional subspace by obtaining the maximized variance of the data. The resulting vectors are an uncorrelated orthogonal basis set, where the principal components are the eigenvectors of the symmetric covariance matrix of the observed data. Using PCA for dimension reduction should retain the extracted principal components corresponding to the m eigenvalues from the total eigenvalues, where ${\gamma}_{k}$ is called the percentage retained in the data representation as described in Equation (8).

**Independent Component Analysis (ICA)**—ICA is a statistical and computational technique that is used to extract features from a set of measurements, such as when the features are maximally independent. The observed variables ${x}_{1}\left(t\right),{x}_{2}\left(t\right),\dots ,{x}_{n}\left(t\right)$ are composed of a linear combination of original and mutually independent sources ${s}_{1}\left(t\right),{s}_{2}\left(t\right),\dots ,{s}_{n}\left(t\right)$ at time point t as defined in Equation (9).

#### 3.4. Clustering

**Mean-Shift**—The mean-shift algorithm is an unsupervised clustering algorithm that seeks to find dense areas of data points in a dataset [48]. An important characteristic of the mean shift is that it does not require prior knowledge of the number of clusters and does not constrain the shape of the clusters. The number of clusters is determined by shifting the data points iteratively toward the mean until convergence is achieved. Given n data points ${x}_{j}(j=1,\dots ,n)$ in the d-dimensional space ${R}^{d}$, the mean shift vector at point x is defined in Equations (11) and (12).

**X-Means**—The X-means algorithm is a k-means extension that can be used to estimate the number of clusters [50]. Cluster centers are split locally during each iteration of the k-means algorithm to obtain better clustering. Splitting decisions are based on the Bayesian Information Criterion (BIC) or Akaike Information Criterion (AIC) as described in Equations (13) and (14).

## 4. Experimental Results

#### 4.1. Various RF Sources (VRF Dataset)

#### 4.1.1. Clustering Accuracy Criteria (CAC)

#### 4.1.2. Estimating the of Number of Clusters

#### 4.2. XBee Dataset

#### 4.3. Matrice Dataset

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Ashush, N.; Greenberg, S.; Manor, E.; Ben-Shimol, Y.
Unsupervised Drones Swarm Characterization Using RF Signals Analysis and Machine Learning Methods. *Sensors* **2023**, *23*, 1589.
https://doi.org/10.3390/s23031589

**AMA Style**

Ashush N, Greenberg S, Manor E, Ben-Shimol Y.
Unsupervised Drones Swarm Characterization Using RF Signals Analysis and Machine Learning Methods. *Sensors*. 2023; 23(3):1589.
https://doi.org/10.3390/s23031589

**Chicago/Turabian Style**

Ashush, Nerya, Shlomo Greenberg, Erez Manor, and Yehuda Ben-Shimol.
2023. "Unsupervised Drones Swarm Characterization Using RF Signals Analysis and Machine Learning Methods" *Sensors* 23, no. 3: 1589.
https://doi.org/10.3390/s23031589