## 2 Materials and Methods
### Empirical Mode Decomposition (EMD)  
In this section, we considered the extraction of some feature vectors from the original signature of the detected target by using the Empirical Mode Decomposition (EMD) technique. We aimed to use the extracted vectors as a stronghold for identifying the detected drone in FS-mode, based on the peculiar signature of a Doppler pattern with V-shape characteristics (towards zero Doppler on the center of baseline) and micro-Doppler surrounding the main Doppler, as proved in [10], thus confirming the possibility of using the DVB-S-based passive FSR system for low-profile target detection. These features may further be used in the identification of this target among other targets in the same bandwidth or surveillance volume, like flying birds (as this constituted our future works). The most robust feature of concern is the micro-motion based on the four-rotor rotating blades which, of course, differs from the micro motions due to flapping birds. This may further classify the target from other similar copter drones or a fixed-wing drone, in addition to a reduction of dimensionality in classification problems [37]. Several methods can be used in extracting the feature of a target; the most common and reliable methods include using STFT, singular value decomposition (SVM) [38; 39], and empirical mode decomposition (EMD) [40], among others. For a target with constant speed, it is assumed that the resultant Doppler frequency shift will also be constant [35]. In reality, a target like a drone does not maintain constant velocity while moving, and neither does the rotating blade. This makes the micro-Doppler analysis become challenging due to the non-linear and non-stationary characteristics of the signal. This non-linear and non-stationary signal make other signal processing techniques like STFT (which assumed linearity and stationary nature) non-optimal; hence, making the empirical mode decomposition (EMD) a good candidate for this analysis of the time-varying Doppler frequency shift. An advantage of EMD was that it does not require pre-defined kernel functions or prior knowledge of the signal behavior. The empirical mode decomposition (EMD) involved a sifting process capability to decompose any given signal into an intrinsic component and derived non-linear functions called Intrinsic Mode Functions (IMF) [41]. This technique was introduced by [PERSON] et al. to analyze a non-linear and non-stationary signal [42]. It is a successive algorithm that enables the primary function, of which can be non-linearly derived from the original signal in an adaptive basis called the IMF. These IMFs are the corresponding frequency components available in the original data, efficiently helping to separate between the Doppler due to radial velocity and the micro-Doppler due to the rotating blade. To achieve an instantaneous frequency component at a time, these conditions must be achieved [40; 41]: i. the differences between the numbers of extremes to that of zero crossing must always be one or equal to zero and ii. the signal envelop's mean value must, at all times, be equal to zero. This mean value is identified by the local minima and maxima of the signal envelope, hence, making the algorithm recursive in nature. To decompose the original signal into intrinsic functions, let \(y_{(n)}\) be the original signal received during the detection. A residue can be initialized as \(r_{0}=y_{(n)}\) for \(i  
where \(Y_{max}\) is upper signal envelope and \(Y_{min}\) is the lower envelope; a new signal, \(Hi(n)\), is obtained by subtracting the mean value from the original signal as  
\[Y(n)-Y_{-}\mu~{}(i)=Hi(n) \tag{3}\]  
If the IMF criteria were met by \(Hi(n)\), then \(Hi(n)=IMF(i)\); otherwise, the sifting process returned to the beginning until all minimum extremes became negative and all maximum extremes returned to positive. A residue was defined by  
\[r(i)~{}=r(i-1)-~{}IMF(i) \tag{4}\]  
such that, once the condition is fulfilled, the sifting process stops; otherwise, the algorithm starts over again.