# Review and Simulation of Counter-UAS Sensors for Unmanned Traffic Management
## 3 Counter-UAS Sensors Modeling
### Microphone Sensor and RF Sensor  
Microphone sensors and RF sensors are modeled following an azimuth model in which, from the power of the signals sent by the drones, either acoustic or radio frequency, the signal-to-noise ratio at the input of the sensor is calculated, and from the detection, the azimuth and distance to the sensor are obtained. These sensors have a certain sensitivity, and, depending on the signal-to-noise ratio, there will be detection or not. The main characteristics are:  
* Surface propagation losses over land. * Parameters adapted to drone detection (integration times of the order of minutes). * Exploration times on the order of minutes. * Measurement error simulation. * False alarm simulation. The basic parameters defining the model of a sensor are:  
* Sensor position. * Sensor sensitivity. * Distance resolution in kilometers. * Maximum range in meters. * Number of sensors. * Minimum and maximum azimuth in degrees. * Bandwidth. * Receiving beamwidth in degrees. * Direct signal cancellation level. * False alarm probability. The first is to calculate the received signal power of the target echo before the correlator. \[P_{target}=\frac{P_{average}}{D_{C}\cdot Att\cdot L_{p}} \tag{37}\]  
where \(P_{average}\) is the noise power of the drone. \(D_{C}\) is the directivity correction, \(Att\) is the attenuation and \(L_{p}\) is the system power loss. The ratio (\(\frac{S}{N}\)) is calculated at the correlator output. There will be the interference powers of noise and correlator side lobes of different signals, including the target. The \(\frac{S}{N}\) ratio is computed with the following expression:  
\[\left(\frac{S}{N}\right)=\frac{P_{target}}{P_{N\_{clutter}}+P_{N\_signal}+P _{N\_{,}lec}} \tag{38}\]  
In this case, a multisource scenario is assumed, so the directivity correction factor is set at 3 dB. Once the source, the powers and their basic definitions have been characterized, we proceed to obtain the calculation of the effects that produce attenuation. The attenuation in real environments for the propagation of a wave is defined by the following equation:  
\[Att=A_{div}+A_{atm}+A_{gr}+A_{bar}+A_{misc} \tag{39}\]The waves emitted by a drone are those of an omnidirectional source, since it propagates in all possible directions, so the waves emitted are spherical waves whose power level coincides at the same distance from the source. As this distance increases, the wave energy is distributed over a larger and larger area, so that each time this distance is doubled, the power level decreases by a factor of 6 dB theoretically, so the geometric divergence attenuation is:  
\[A_{div}(\mathrm{dB})=20\cdot\log_{10}(R)+11 \tag{40}\]  
where \(R\) is the distance in meters between the drone and the sensor. Atmospheric absorption is the attenuation due to nitrogen, oxygen and carbon dioxide during wave propagation as it travels a specific distance to the receiver. \[A_{atm}(\mathrm{dB})=\alpha\left(\frac{\mathrm{dB}}{\mathrm{km}}\right)\cdot R (\mathrm{km}) \tag{41}\]  
where \(\alpha\left(\frac{\mathrm{dB}}{\mathrm{km}}\right)\) is the atmospheric attenuation coefficient, which depends on the following parameters: the frequency of the wave, the ambient atmospheric temperature, the relative humidity of the air and the ambient pressure. Since there are already estimated tables from which these values can be obtained and for the frequencies of these waves, this coefficient takes values of the order of \(1\times 10^{-3}\) to \(1\times 10^{-2}\). Ground attenuation is mainly due to waves reflected by the ground surface interfering with the propagation of the main wave from the source to the receiver. This attenuation occurs when the source or receiver is close to the ground surface. This model uses an equation that allows for obtaining the ground effect attenuation in a simpler way because its operation is specified only for long distances and with porous or mixed surface. As the source gets closer, this attenuation tends to disappear.