# Power Efficient Random Access for Massive NB-IoT Connectivity
## 5 Performance Evaluations
Note that this consideration can be changed according to the real world situation. However, since we highlight the comparison, the actual values when used in both the existing and proposed RAP would result in the same trends. Figure 4a-c shows the variation in a device's power consumption for several RAP reattempts after having performed the first RAP attempt in CE0, CE1 and CE2, respectively. For the existing RAP, in Figure 4a the devices first try RAP in CE0 such that the transmission takes place at the lower power level with a lower number of repetitions. In Figure 4b,c, the device first attempts RAP in CE1 and CE2, respectively. Thus, the starting power level for the existing RAP is maximum for Figure 4c and minimum for Figure 4a. As the number of reattempts increases, the power consumption also increases in the existing system. For the proposed PE-RAP, the CE level is re-ascertained at each attempt. The number of repetitions and the power level per repetition assigned to each CE level for the proposed PE-RAP are different. Thus, the power consumed by the device in its attempt in CE0 would be different from its attempt in CE1 or CE2. It is notable that due to the random selection of the CE level by the NB-IoT device after an RAP failure, the power consumed may vary randomly over different trials and our proposed algorithm tries to adapt the same dynamics. Figure 4 clearly shows these dynamics. For an attempt the device may choose a lower CE0 level with less power consumption. In the next reattempt, it may select CE2, and it the subsequent reattempt CE1. This would result in variations as shown in Figure 4. It can be observed that at some instantaneous attempts the power level for the existing RAP is lower than that for the proposed PE-RAP while for some other attempts it is higher. Thus, it is important to consider the average power consumption of the devices as highlighted in Equations (2) and (3). In Figure 5 we show the the average power consumption for existing RAP and proposed PE-RAP for a varying number of configured repetitions in CE0. The number of repetitions in CE1 and CE2 are fixed to 32 and 64, respectively. We assume that the device makes initial RAP attempt in CE0. In the proposed PE-RAP the device transits to different CE levels based on channel conditions. Since the power consumed in each CE level is different, it is important to consider the probability of selection of a particular CE level. As discussed before, \(q_{0},\ q_{1}\) and \(q_{2}\), respectively, represent the probabilities of channel conditions for CE level CE0, CE1 and CE2 while \(q_{0}+q_{1}+q_{2}=1\). For our analysis we consider three cases:  
1. Probability of selection of CE0 is high. To emulate this scenario we consider \(\{q_{0},\ q_{1},\ q_{2}\}=\{0.5,\ 0.3,\ 0.2\}\). 2. CE0 manifests lower probability of selection. To consider this case we take \(\{q_{0},\ q_{1},\ q_{2}\}=\{0.2,\ 0.3,\ 0.5\}\). 3. Probability of selection of CE0 is average such that \(\{q_{0},\ q_{1},\ q_{2}\}=\{0.33,\ 0.33,\ 0.34\}\)  
Figure 4: Snapshot of power consumption variations over several reattempts for proposed PE-RAP and existing NB-IoT RAP. (**a**) Device makes first RAP attempt in CE0; (**b**) Device makes first RAP attempt in CE1; (**c**) Device makes first RAP attempt in CE2. As an example, if an NB-IoT device is indoors but on ground floor or a higher floor, then the measured RSRP value would be good. The probability \(q_{0}\) would be higher than \(q_{1}\) or \(q_{2}\). However, if the device is indoors in the basement, then \(q_{2}\) would be higher than \(q_{0}\) or \(q_{1}\). In the proposed PE-RAP, the device fails RAP due to collision and a reattempt is performed in a CE level based on the observed channel condition. In Figure 5a there is high probability that the device selects CE0 again after failure. The number of repetitions as well as the power level per repetition are small in CE0.