# Renyi Entropy-Based Adaptive Integration Method for 5G-Based Passive Radar Drone Detection
## 5 Renyi Entropy for 5G Signal Analysis
### Rationale Behind the Use of the Renyi Entropy for Drone Detection  
Let us consider the passive radar range Equation [44]  
\[R_{e}<\sqrt{\frac{P_{T}G_{T}G_{R}S_{0}\lambda^{2}T_{\rm int}}{(4\pi)^{3}L_{0}D_{0 }kT_{0}}}, \tag{9}\]  
where \(R_{e}=\sqrt{R_{1}R_{2}}\) is the equivalent of the monostatic detection range (\(R_{1}\) is the range from the transmitter to the target and \(R_{2}\) is the range from the target to the receiver), \(P_{T}\) is the transmitter power, \(G_{T}\) and \(G_{R}\) are the transmit and receive antenna gain, respectively, \(S_{0}\) is the target's RCS, \(L_{0}\) stands for the total propagation and system losses, \(D_{0}\) is the detection factor, \(k\) is the Boltzmann constant equal to 1.38 \(\times\) 10\({}^{-23}\) J/K and \(T_{0}\) is the effective noise temperature of the receiver, which depends on its noise figure, according to Equation (10) [23]:  
\[T_{0}=T_{\rm ref}(10^{N_{f}/10}-1), \tag{10}\]  
where \(N_{f}\) stands for noise figure and \(T_{\rm ref}\) is reference temperature, usually assumed to equal 290 K. Most of these parameters are related to a particular system and the passive radar receiver, e.g., wavelength and antenna gains. The most variable parameters that are not related to the equipment belonging to the transmitting station and passive radar are the integration time \(T_{\rm int}\) and the RCS \(S_{0}\). Drones are usually considered as low-RCS targets due to their small size and the material they are made of. Therefore, the detection of such targets requires an extension of the integration time to increase the SNR as much as possible. In 5G networks, a signal duty factor (resource allocation) depends on the data transmitted to terminals. If few data are transferred, only part of the time and frequency resources  
Figure 13: Plot entropy—resource usage. are used. This results in an artificial reduction in the integration time because it may turn out that for the given \(T_{\text{int}}\), the signal was present, for example, 10% of the time. This leads to a decrease in the SNR in the receiver and deterioration of the range resolution. Therefore, autonomous selection of the integration time to optimize the detection probability is essential. Thus, this article uses Renyi entropy to automatically select a signal that allows optimization of the radar equation, i.e., a signal that gives the highest possible effective use of the integration time. Since the Renyi entropy can capture the inner properties of the OFDM signal used in 5G networks, its computation determines the temporal possibility of target detection. Indeed, if the entropy increases, the number of subcarriers (bandwidth) and their duration also increases. Therefore, the effective integration time becomes higher, enabling the detection of a target located far from the passive radar receiver (the right-hand side of (9) grows). In systems characterized by transmitting a signal with variable time and bandwidth, the value of the \(T_{\text{int}}\) parameter differs from the actual integration time. Considering how much of the integration time was effectively taken up by the signal, the actual radar detection range may be much smaller, which results from the theory (9). In order to inspect the signal properties in terms of resolution and coverage, the authors of this article use Renyi entropy, the values of which are related to the time and bandwidth used by the 5G network during data transmission from a non-cooperating base station. This statement can be supported by a simulation analysis, described in Section 6. In a practical application, the proposed technique can be used comprising the following steps:  
1. Calibration (if possible)--record the 5G signal with the maximum allocation of resources. In civilian systems, this is easy to meet and comes down to the load on the network by downloading large amounts of data (e.g., large files) using one or more 5G mobile terminals. As a result, the base station will use the possible resources allowing the maximum entropy value to be assessed.