## 5 Automatic Signal Recognition
### Validation
#### 5.2.4 Analysis of Practicality  
In general, the experimental validation gives promising results for identifying wideband technologies on narrow-band devices. The detailed study of the confusion matrix exposes some limitations of the sample algorithm, such as the difficulty to cope with the variations of the Wi-Fi signal in the indoor environment. These limitations indicate the importance of sufficient diversities in the training data and eventually the need for more dynamic algorithms. The analysis of the true positive rate with respect to \(N\) and \(T\) unveils the conditions for the features to stay reliable, which is when the average interval of RSSI is kept below 200 us and the observation time is above 50 ms. Recall that the sensor platforms used by [29; 30] allow RSSI to be collected at 11.3 kHz and 31.25 kHz, respectively. The 200 us (\(\frac{1}{200\ us}=5\) kHz) requirement can clearly be supported on these devices. The work in [29] states a minimum observation time of 2.9 ms, which suffices for the purpose of identifying only the ZigBee signal (the minimum packet interval of ZigBee is 2.8 ms). Solutions aiming for classification of multiple technologies generally rely on longer observation periods, ranging from 100 ms [31] to several seconds [30], or multiple days and months if the solution is intended for non-real-time applications [18]. Therefore, the period of 50 ms is considerably shorter than most existing solutions and hence suitable for making real-time decisions in the context of dynamic spectrum sharing.  
Note that we deliberately choose not to involve direct comparison of recognition accuracy, because there is no fair way to compare solutions aiming to distinguish different sets of technologies. Instead, we focus on the system requirements (e.g., ADC sample rate, RSSI update interval), to demonstrate the feasibility of integrating the features of RSSI distribution with existing solutions.  
In addition to system requirements, the complexity and scalability are also important aspects for constrained devices. To ease the complexity analysis, we decouple the sample algorithm into three stages: (i) derive variables directly from the input \(\overline{RSSI}\) such as \(\overrightarrow{H}\), \(\sigma_{\overrightarrow{R}}\); (ii) derive variables from the RSSI histogram \(\overrightarrow{H}\) such as \(\overline{n}\), \(p(\overline{n})\), \(N_{p}\); (iii) make a decision based on the previously-derived variables. For the first stage, the histogram and standard deviation of RSSI can be obtained by simple loops with complexity \(O(sizeof(\overline{RSSI}))\), where the upper bound of the execution time is linear to the input vector size. For the second stage, the iterations required to search and count peaks in \(\overrightarrow{H}\) depend on the number of bins in the histogram, which is an internal setting within the algorithm; hence, the complexity is denoted as \(O(1)\), meaning the worst case execution time of the second stage is independent of the input size. For the third stage, the decision making is purely rule-based conditional statements, and the complexity has clearly no dependency on the input size, thus again \(O(1)\). Regarding scalability, the sample algorithm is not varied upon a change in the network environment. For a larger input vector size, the accuracy of the algorithm is higher, but at the cost of an increased observation period as stated in Section 5.2.3. Hence, the sample algorithm has rather low complexity and high scalability.  
Figure 12: The true positive rate versus the total observation time, for \(N=160\).