# Power Efficient Random Access for Massive NB-IoT Connectivity
## 3 Collision--CE Level Based RAP (PE-RAP)
The device competes for preambles with other newly arrived devices as well as the backlogged devices from the previous RAP attempts (highlighted in Step 6). For new arrival we consider Beta distribution. The simultaneous access by massive number of NB-IoT devices would result in congestion. * Massive Connectivity and Collisions To improve the access quality-of-service in machine type traffic, the access class barring (ACB) scheme is widely adopted [29]. In steps 7 to 11, the devices perform an ACB check. Two or more  
Figure 3: (**a**) Existing RAP in NB-IoT; (**b**) Proposed PE-RAP Mechanism. NB-IoT devices that pass the ACB check can send a random access attempt of RAP by selecting the same preamble. If the preamble is the same, it would result in collision. * Collision Probability and Access Attempt Failure According to 3 GPP, the choice of the number of repetitions in each CE level is targeted to achieve 99% detection probability of the preamble [14; 30]. The CE level is re-ascertained at each reattempt in PE-RAP. This ensures that the correct number of repetitions is selected such that the impediments due to poor channel become negligible. In other words we can say that the chances of RAP failure due to collision are much higher than due to preamble not being detected in poor channel conditions. Thus, in the PE-RAP algorithm it is assumed that the reattempt can occur only after the collision. We evaluate the collision probability \(\mathbb{P}_{r}(C)\) (step 13). The collision probability is calculated in the subsequent subsection and is used to obtain the average power consumed by the device unconditioned to the number of attempts (step 24). Step 15 shows that the device goes back to step 4 for CE level re-selection if the collision occurs. * Number of attempts and average power evaluations In a massively connected environment, the RAP may fail often due to collision events. After the collision the device should perform an RAP reattempt and each reattempt is accomplished by several repetitions. To evaluate the average power consumption PE-RAP, we count the number of attempts that the devices make in each of the CE levels (Step 11 for CE0). The devices that are successful are removed from the system (step 17). Finally, from steps 23 and 24 we can obtain the average power in PE-RAP over n trials and unconditioned to n, respectively. * Power Ramping As clear from the algorithm, power ramping is not applied. If the device after collision selects the same or a lower CE level, then power ramping would cause unnecessary wastage in low power NB-IoT devices. Thus, In PE-RAP, the device has the option to reattempt RAP in the same CE level at the same power. It can also transit back from the higher CE level to a lower CE level if the channel improves in the subsequent attempt. Since lower CE levels are configured for transmission at lower power levels, the power saving is substantial. Moreover, if the channel deteriorates while an RAP attempt is made, the device has the feasibility of selection of higher CE levels for its reattempt. In case of a reattempt at the higher CE level, the preamble transmission is performed at higher power. Thus, power ramping becomes implicit and is not explicitly included in the algorithm. The aim of PE-RAP is to highlight the power consumption of NB-IoT devices due to (i) repetitions per transmission and (ii) massive connectivity on the random access procedure. In the next subsection we evaluate the average power consumption of NB-IoT devices over different repetitions and channel probabilities. In PE-RAP, a reattempt can occur only after the device fails an RAP attempt due to collision. Thus, we base our analysis on collision probability and the probability of the device belonging to a particular CE level. The list of parameters used in the analysis is delineated in Table 2.