# Low-Cost Sensor Based on SDR Platforms for TETRA Signals Monitoring
## 2 Material and Methods
### The Procedure of TETRA Signal Channel Power Determination  
Figure 1 shows the processing operations through which the monitoring results of the TETRA signals were obtained. In the case of measurements made in laboratory conditions, TETRA signals are provided by a signal generator, while in the case of measurements in real conditions, they were obtained by means of a receiving antenna scanning the TETRA network emissions.  
The radio interface based on the SDR platform acquires the TETRA signals, transforms them into digital format and records them sequentially. Subsequently, the IQ signal samples obtained at the output of the radio interface are applied to the FFT processor for characterization in the frequency domain. The frequency resolution obtained is given by the ratio between the sampling frequency Fs and the number of points N necessary for the FFT calculation, as shown in Relation (1), based on [27]:  
\[\Delta F=\frac{F_{s}}{N} \tag{1}\]  
If the sampling frequency \(F_{s}\) is 5.12 MHz and the number of points \(N\) is 2048, a resolution of 2.5 kHz is obtained. If we take into account the fact that the bandwidth of the TETRA channel is 25 kHz, it means that 10 points are used for the calculation of the channel power. Through software applications, following the processing of spectral lines resulting from the application of FFT, the TETRA signals can be characterized in detail (for example, the power of each channel can be calculated, etc.).  
The method of the TETRA channel power calculation is presented graphically in Figure 2. At each FFT bin, the details of the TETRA signals will be considered. Starting from the fact that the TETRA spectrum occupies a bandwidth of 5 MHz centered on the frequency of 382.5 MHz in the case of Uplink and on 392.5 MHz in the case of Downlink, a sampling frequency of 5.12 MHz was established for the FFT calculation. In this way, a bandwidth of 0.12 MHz (0.06 MHz left and right, respectively, of the TETRA spectrum) remains outside of the spectrum of interest. The power of a TETRA channel is calculated through the amplitudes of the spectral lines inside the channel. Thus, for this purpose, the mathematical expression presented in [28] will be applied (2):  
\[P_{chi}=10\cdot\lg\left(\frac{B_{ch}}{B_{NIF}}\cdot\frac{1}{N_{i+1}-N_{i}}\cdot \sum_{N_{i}}^{N_{i+1}}10^{\frac{P_{i}}{10}}\right) \tag{2}\]  
where: \(P_{chi}\) represents the power expressed in dBm calculated for channel \(i\) (\(i\) = 0,..., 199); \(B_{ch}\) represents the TETRA channel bandwidth (in this case 25 kHz); \(B_{NIF}\) represents  
Figure 1: Data acquisition and processing steps used to characterize, in detail, the TETRA signals.  
the band of the noise filter used; \(P_{i}\) represents the power in dBm corresponding to each pixel (spectral line); \(N_{i+1}\) and \(N_{i}\) represent the indexes of the measurement points for each TETRA channel.  
In general, the points between which we find the channel \(i\) (\(i\) = 0,..., 199) are determined with the relations of (3):  
\[\left\{\begin{array}{c}N_{i}=i\cdot\frac{0.025}{\Delta F}+\frac{0.06}{\Delta F }+1;\quad i=0,\ldots,199\\ N_{i+1}=(i+1)\cdot\frac{0.025}{\Delta F}+\frac{0.06}{\Delta F}+1;\,i=0,\ldots,1 99\\ \text{Frequency Resolution}=\Delta F[\text{MHz}]=\frac{F_{5}[\text{MHz}]}{N} \end{array}\right. \tag{3}\]  
Therefore, the selection of a TETRA channel is made by identifying the spectral lines corresponding to the channel and the calculation of the channel power takes place further by applying Relation (2).