# Renyi Entropy-Based Adaptive Integration Method for 5G-Based Passive Radar Drone Detection
## 2 5G Passive Radar Principles  
Passive bistatic radar (PBR) or Passive Coherent Location (PCL), unlike active radar, does not have its own source of illumination. It relies on the usage of a non-cooperating transmitter of opportunity. Typically, the transmitter is in a different location to the receiver, which leads to bistatic geometry, depicted in Figure 1. The passive radar receives an electromagnetic wave directly from the transmitter (\(x_{r}\)--reference signal) and an echo reflected from the target (\(x_{s}\)--surveillance signal). Therefore, it requires at least two receiving channels working coherently. Directional antennas or antenna arrays are usually used for those channels in order to employ beamforming techniques. The signals are coherently received and digitized, yielding \(x_{\text{ref}}\)--from the reference channel, and \(x_{\text{sur}}\)--from the surveillance channel. The aim of passive bistatic radar is to determine the bistatic range and bistatic velocity of a target [23]. The bistatic range \(R_{b}\) is defined as the difference of the indirect path (with reflection of the target) and direct path of the wave:  
\[R_{b}=R_{1}+R_{2}-L, \tag{1}\]  
where \(R_{1}\) is the range from the transmitter to the target, \(R_{2}\) is the range from the target to the receiver, and \(L\) is the baseline length (see Figure 1). The bistatic velocity \(V_{b}\) is obtained from the measured Doppler shift between \(x_{\text{ref}}\) and \(x_{\text{sur}}\) and is defined as  
\[V_{b}=-\lambda f_{d}, \tag{2}\]  
where \(\lambda\) is the wavelength of the signal and \(f_{d}\) is the measured Doppler shift. Once the signals are received and digitized, they are then digitally processed. A typical PCL processing scheme is depicted in Figure 2.  
Here, the authors intentionally omitted the step that is usually the first one in the processing pipeline, namely digital beamforming (DBF) [24]. The main rationale behind DBF is to provide a highly selective reference beam (so that echoes from observed targets are not present inside). This provides a larger radar surveillance area. In addition, using DBF, the direction in which a target is located relative to the radar can be estimated. This is additional information that can be used to improve the quality of target tracking or target localization. However, since the authors used a simplified demonstrator with only two antennas during the presented experiments, the DBF technique was abandoned and not included in Figure 2.  
Figure 1: Typical PCL geometry. Figure 2: PCL radar processing scheme. Passive radars operate with very low energy of echoes coming from targets. To observe echoes from targets, it is necessary to remove all unwanted components present in the surveillance signal \(x_{\text{sur}}\). These components result from the leakage of the transmitted signal, and are called direct-path interference (DPI); they can also come from echoes from stationary or slowly moving targets. Adaptive filters or the CLEAN method are used to remove them [25; 26]. To obtain the bistatic range and velocity of the target, the cross-ambiguity function (CAF) is computed with the following formula [23]:  
\[\chi(R_{b},V_{b})=\int_{-T_{\text{int}}/2}^{T_{\text{int}}/2}x_{\text{sur}}(t) x_{\text{ref}}^{\circ}\bigg{(}t-\frac{R_{b}}{c}\bigg{)}e^{-2\pi\frac{V_{b}}{ \Delta t}t}\,\text{d}t, \tag{3}\]  
where \(T_{\text{int}}\) is the integration time. For the purpose of carrying out target detection, a thresholding of the CAF against its noise estimate is performed [23]. This assumes a certain minimum signal-to-noise ratio (SNR) for which false and true detections are fixed (with given values of the probability of false alarm \(P_{\text{fa}}\) and probability of detection \(P_{d}\), respectively). The simplest estimator of the noise level is a constant value estimator, such as the mean or median of the CAF values. However, the noise distribution cannot always be modeled in this way, and more sophisticated adaptive methods are needed, such as the constant false alarm rate (CFAR) processor [27].