# Multi-Parametric Analysis of Reliability and Energy Consumption in IoT: A Deep Learning Approach
## 3 System Model
### The Data
Key Observations  
The relationship between \(PDR\) and \(EC\) is shown in Figure 2. Being a ratio, \(PDR\) ranges between 0 and 1 with median (0.97) close to 1. Both \(PDR\) and \(EC\) appear to lie in close proximity but for the lower quarter of \(PDR\) values. A zoomed inner frame in Figure 2 reflects this relationship for the bottom half of \(PDR\) values. It is evident that there is a rapid hike in \(EC\) as \(PDR\) falls below 0.3. This tremendous variation in \(EC\) values can be explained in two ways. First, as losses (radio) increase, energy consumed to transmit for the lost frame gets wasted and thus induces a rise in \(EC/bit\). Second, although the total number of packets transmitted is 300, depending on the maximum value of \(MT\) (which can be either 1, 3, or 5), the actual number of attempts can be as high as 1500. This phenomenon leads to an enormous positive skew with a very high standard deviation of 7.31 compared to both mean (1.30) and median (0.27) for \(EC\) values. Considering the forward error correction limit of \(10^{-3}\) on bit error rate, which is expected to be far less in modern wireless communication systems, a \(PDR\) of less than 25% itself remains under question for performance characterization. In order to further understand the parameters working behind the scenes, Figure 3a shows a 3D plot of \(EC\) in relation to \(TP\) and \(DT\). It is evident that \(EC\) is extremely high when the \(TP\) level is at a minimum (i.e., 3). This is due to the fact that the \(TP\) level is not adequate for successful transmission and, as a result, frames suffer radio losses. This results in increased \(EC\) for successfully transmitted data bits. However, the values for \(EC\) keep decreasing as the \(DT\) decreases. To understand more, Figure 3b shows both \(EC\) and \(PDR\) in relation to \(TP\). It is again clear from the plot that, for a \(TP\) level of 3, and low \(PDR\), there is a visible hike in \(EC\). Despite this large deviation, in order to consider the entire amount of data, better prepare it for learning, and expect a practical prediction accuracy, these statistics encourage us to split the \(EC\) data based on \(PDR\) values. Median based z-score measure is used to decide the split because \(PDR\) has a negative skew with median (0.97) being higher than mean (0.87). The formula used to split \(EC\) data is:  
\[z_{score}=PDR_{med}\pm 3\times PDR_{std}. \tag{4}\]  
This results in 0.25 as a value for \(z_{score}\), where \(PDR_{med}\) is 0.97 and \(PDR_{std}\) is 0.24, and, based on this value, the data is split into two parts for prediction of EC; first, where \(PDR>=0.25\) and the second where \(PDR<0.25\). The first part consists of 95.1% data (referred to as \(EC_{\text{dense}}\)) ranging between 0.136 and 1.155 with both mean (0.279) and median (0.267) closely located and a small standard deviation of 0.087. This reflects an acceptable distribution for \(EC_{\text{dense}}\) improving the chances of good prediction accuracy. The data in the second split (referred to as \(EC_{\text{sparse}}\)) comprises only 4.9% of the total data spread over the range of 0.161 and 159.453 and are seen as outliers. Mean (26.085) and standard deviation (26.06) are close enough for \(EC_{\text{sparse}}\) data. However, the median (4.166) is still relatively low, thus indicating dispersion of data. As a result, before proceeding to deep learning, the data have three target variables to predict: \(PDR\), \(EC_{\text{dense}}\), and \(EC_{\text{sparse}}\).