## 4 Channel Characterization Metrics  
This section describes the different channel characterization metrics taken into consideration in the analysis. Different quality metrics can be used in order to classify frequency channels based on interference level. Regardless of the metric used, the method must classify lowly interfered channels as \"good\" and highly interfered channels as \"bad\". The Received Signal Strength Indicator (RSSI), for instance, measures the RF power level received by an antenna. The channel is characterized by its centre frequency and bandwidth. The higher the RSSI signal, the worse the channel, as it is highly interfered by unwanted coexisting systems. RSSI is usually measured in dBm units, that is, the power ratio (\(P\)) in decibels (dB) referred to one milliwatt (mW):  
\[P(\mathrm{dBm})=10\cdot\log_{10}\frac{P(\mathrm{mW})}{1\;\mathrm{mW}} \tag{1}\]  
The RF power level of a radio signal ranges between 0 dBm and \(-120\) dBm. The closer this value is to \(-120\) dBm, the better, because that means there is little to no interference. Typical lowly interfered environments range between \(-100\) dBm and \(-80\) dBm. Alternatively, frequency channels can be classified using Packet Error Rate (PER), which represents the rate of non-received to sent frames. A channel is classified as bad if its PER exceeds the system defined threshold. Bit Error Rate (BER) can be used in a similar way. In the following sections we will focus on the RSSI as a channel quality indicator, as the measurements and calculations involved with RSSI are less complicated, and RSSI values are easily available from the chipsets. However, the work presented here is equally applicable to other indicators (such as PER) with little or no modification. RSSI values must be measured over a specified observation time for all the available channel frequencies. Figure 2 shows an illustrative example of RSSI signals over an observation time of 1 s for the 16 channels available in an 802.15.4 network. On purpose, some channels are affected only by white noise, while others are interfered to a greater or lesser extent by some coexisting systems. Figure 2: Example of Received Signal Strength Indicator (RSSI) signal over 1 s for an IEEE 802.15.4 network with 16 channels. The RSSI values lie within \(-120\) dBm and 0 dBm. Higher RSSI values indicate channels interfered to a greater extent, while lower RSSI values indicate channels interfered to a lesser extent. From RSSI values, different statistical properties can be obtained for channel characterization [23]. These statistical properties are calculated over a specified observation time for every available frequency channel. * Mean value (mean): A low mean value of the RSSI signal over the observation time indicates low RF power in the channel and, thus, a lowly interfered channel. The lower the mean value, the better the channel. * Standard deviation (std): A high standard deviation indicates a highly interfered channel because of the high variability of the RF power. The lower the standard deviation, the better the channel. * Skewness (skew): The skewness indicates the asymmetry of the RSSI distribution. A symmetric distribution, which means skewness of around zero, is expected when the RSSI signal is only affected by white noise and no interfering radio transmissions. When multiple RSSI peaks occur due to radio transmissions, the distribution of the RSSI signal extends to higher values and, thus, a higher value of skewness is expected. The skewness of a signal, \(x\), is calculated by Equation (2), where \(n\) is the number of RSSI samples, \(mean(x)\) the mean value and \(std(x)\) the standard deviation of \(x\). \[skew(x)=\frac{1}{n}\frac{\sum_{i=1}^{n}(x_{i}-mean(x))^{3}}{std(x)^{3}}\] (2)
* \(x\%\) quantile (quan): The \(x\%\) quantile of a set of samples describes the cut value which divides the statistical distribution so that \(x\%\) of the samples are below the cut value.