## 4 Characterization of Real-Life Signals
### Feature Space Design
#### 4.3.2 Features from RSSI Time Series  
As seen in Table 1, Wi-Fi's distinctive feature is the visible noise peak \(p(\overline{n})\), which is a common feature of non-streaming technologies. Therefore, how can we distinguish multiple non-streaming technologies with narrowband RSSI? We aim to answer this question with a case study of Bluetooth and Wi-Fi. First, IQ samples are collected at 25 MHz for 1 s when 10 pairs of Bluetooth piconets are activated in a testbed environment. Note that piconet refers to a group of connected Bluetooth devices, which has a specific frequency hopping sequence determined by the'master' device. More experiment details are described in [37]. Figure 9a displays 50 ms of the recorded signal in the form of a spectrogram. As expected, the Bluetooth signal is spread randomly over multiple channels, and there is also variation in packet duration and signal strength. The latter is due to the fact that the Bluetooth piconets are placed at different distances from the sample collector. The variation in packet duration is according to the Bluetooth standard [38]. Bluetooth piconet may hop to a new channel every 625 \(\upmu\)s, which is the base of the transmission slot. A Bluetooth data packet may last 1, 3 or 5 slots, depending on the payload length (note that \(N\times 625\)\(\upmu\)s is the maximum duration of an N-slot packet, not the exact time). In addition, various control packets are sent for link management purposes, among which a short probing packet (approximately 126 \(\upmu\)s long, referred to as the POLL packet) is always sent from the master to the slave to initiate data transfer, as indicated in the Figure 9.  
Next, the 25 MHz-wide IQ samples are down sampled to 1 MHz to derive RSSI with Equation (1) when \(N=20\). The down sampling is combined with proper filtering, so that only signals in the middle channel (indicated by the red rectangle in Figure 9a) remain. The RSSI vector of the first 50 ms is plotted in Figure 9b, and the normalized histogram of the RSSI vector is shown in Figure 9c. As expected, the histogram of 1-MHz RSSI from the Bluetooth signal also contains a high \(p(\overline{n})\) like Wi-Fi. The histogram appears to have a more uniform distribution in the interval of \([-60,\,-20]\) dB than Wi-Fi, because in this particular setup, the Bluetooth network has more transmitters spread over a larger area than Wi-Fi. Clearly, the observation is subject to the measurement setup; hence, it should not be generalized to distinguish Wi-Fi and Bluetooth. The histogram of Bluetooth RSSI confirms that simply using the features of the RSSI distribution is insufficient to categorize non-streaming technologies, thus the need for other features. Intuitively, by setting an energy threshold \(\lambda\) and counting the number of consecutive RSSI above the threshold, one can obtain the duration of a packet in the air as follows:  
\[T_{P_{i}}=N_{i}\times T_{RSSI},N_{i}\in\text{Z}.\]  
where \(N_{i}\) is the number of RSSI corresponding to the \(i\)-th packet and \(T_{RSSI}\) denotes the averaging interval of a single RSSI, in this case \(T_{RSSI}=20\)\(\upmu\)s. \(N_{i}\) is identified based on the following condition \(y_{ij}>\lambda\) and \(j=1,2,...,N_{i}\), where \(y_{i,j}\) denotes an RSSI with index \(j\) in the frame of the \(i\)-th packet. Figure 9: Characteristics of the Bluetooth signal: (**a**) the 25 MHz-wide spectrogram of the Bluetooth signal; the 1-MHz signals on the middle channel are extracted to obtain the RSSI, as shown in (**b**); (**c**) the normalized histogram of the narrowband RSSI. When this process is iterated through the entire RSSI trace, we obtain a vector \(\overrightarrow{T_{P}}\) containing the duration of all packets in the trace.