# Rapid Estimation of TVWS: A Probabilistic Approach Based on Sensed Signal Parameters
## 2 Spectrum Sensing Overview
### Sensed Signals  
Let us consider that the composite signal \(Xo(p)\) is the combination of the noise \(W(p)\) and the _PU_ signals. To obtain accurate information regarding \(W(p)\), two devices sensed simultaneously the TV-UHF spectrum, as seen in Figure 2; signal \(Xo(p)\) was collected through the Winegard antenna [16] and processed with one RFE [7]. At the same time, another RFE device with similar characteristics and a 50 \(\Omega\) matched impedance replacing the antenna was used to sense the noise of the system [6]. As a result, both signals \(Xo(p)\) and \(W(p)\) were collected by the MSSS and processed as separated signals. Additionally, we saved the geographical coordinates to geolocate the readings. The MSSS scans at the 198-MHz bandwidths of the 500 MHz to 698 MHz TV-UHF spectrum had a separation of 1.76 MHz at a given time instance. This means that 112 samples were collected per RFE at each time instance. Along with the two RFE devices, we used a GPS device. Hence, a single reading consisted of a 112 signal power samples in dBm, 112 noise power samples in dBm, and 1 location-time stamp sample. The RFE devices took readings every 0.340 s, which implies that, for 1 minute period, we had \((112+112+1)\)\(\times\)\((60/0.34)\) = 39,705.88 data samples.  
Our MSSS was composed of two RFE devices [7], from which signals were collected in parallel, compared, and processed to identify their characteristics. The used RF Explorer was a portable spectrum analyzer designed for the specific needs of digital radio frequency communication. The workflow was supported by the RF Explorer, including detection of expected transmission and power, automatically resolving Resolution Bandwidth (RBW), and sweep time and spectrum data calculations. It included functions such as real-time processing for adjusted signals, 3D spectrogram waterfall, Comma-Separated Values (CSV) export, and high-quality graphics, and it could work with Windows on a PC. This is a low-cost, open hardware-software, and portable device, the main characteristics of which are shown in Table 1.  
An example reading is represented in Figure 3, where panel (a) shows the noise signal \(W(p)\) and panel (b) represents the composite signal \(X_{o}(p)\). Red peaks observed in panel (b) are the energy of the PU, which means that those channels were used by the incumbents. On the other hand, channels where the only signal sensed was the noise level was considered as unused channels or TVWS [17]. The energy detected in the TV-UHF channels is illustrated in Figure 3c. Readings collected in ten points are overlapped, allowing us to observe those channels with a higher probability of being used by a PU along the TV-UHF spectrum in the sensed area. In this case, the most used channels along the sensed geographical area were 21, 22, 26, 31, 32, 38, 41, 43, 44, 45, 49, and 50.  
\begin{table}
\begin{tabular}{c c c} \hline
**Ord** & **Characteristic** & **Values** \\ \hline
1 & Frequency Range & 240 MHz to 960 MHz \\
2 & Span & 0.112 MHz to 300 MHz \\
3 & Frequency Resolution & 1 kHz \\
4 & Average Noise Level & \(-115\) dBm \\
5 & Amplitude Resolution & 0.5 dBm \\
6 & Automatic RBW & 2.6 kHz to 600 kHz \\ \hline \end{tabular}
\end{table}
Table 1: RFE technical characteristics.  
Figure 2: TV-UHF spectrum samples were collected by using two Radio Frequency Explorer (RFE) devices in parallel, one to characterize the noise signal \(W(p)\) and another to collect the composite signal \(X_{o}(p)\), together with a GPS receptor antenna to geolocate the readings. Each reading consisted of 112 samples for the composite signal and 112 samples for noise. The separation between two samples was 1.76 MHz, and all 112 samples covered 198 MHz, which is the TV-UHF bandwidth.