# Power Efficient Random Access for Massive NB-IoT Connectivity
## 5 Performance Evaluations  
In this section we first present the numerical results based on our analysis of power consumption in PE-RAP and compare them to the existing system. Subsequently, we also validate our analysis through simulation results. The power consumed by the device in a CE level depends upon the number of configured repetitions. The network can configure the number of repetitions in a CE level based on channel conditions. Instead of considering only a single value, we perform analysis over a range of repetition values in all the three CE levels. We consider variations in the number of repetitions in CE0 as 2\(\sim\)16, in CE1 as 4\(\sim\)32 and in CE2 as 8\(\sim\)64. The performance parameters are given in Table 3. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline No. of repetition in CE0 (\(R_{0}\)) & 4\(\sim\)16 \\ No. of repetition in CE1 (\(R_{1}\)) & 4\(\sim\)32 \\ No. of repetition in CE2 (\(R_{2}\)) & 8\(\sim\)64 \\ Power Consumption per Repetition CE0 (\(P_{0}\)) & 1 dBm \\ Power Consumption per Repetition CE1 (\(P_{1}\)) & 2 dBm \\ Power Consumption per Repetition CE2 (\(P_{2}\)) & 3 dBm \\ Arrival Rate [a, b] & [3 4] \\ No. of Preambles in CE0 & 12 \\ No. of Preambles in CE1 & 12 \\ No. of Preambles in CE2 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance parameters. In massive connectivity, a large number of devices may simultaneously send transient and rapid session requests in a short time to the network [28]. The classical homogeneous/compound Poisson process is suitable for occasional and steady traffic arrival but can hardly describe the simultaneous burst [32; 33]. It is expected that the 5G network would support over a million devices with frequent bursty traffic arrival. In such scenarios, in each time slot a large number of devices may attempt the transmission of the preambles. As a result, collisions may occur more frequently accumulating into a critical congestion. According to 3 GPP, the Beta distribution emulates the case when umtpeen devices try to synchronously access the network [34] and thus gives a better perception about bursty Machine Type Communications (MTC) traffic. To emulate massive connectivity in NB-IoT we can assume that several devices try to access at time \(t\in(0;T)\) while following a Beta distribution [25], with the probability density function as:  
\[f_{x}(x)=\frac{x^{a-1}(T-x)^{b-1}}{(T)^{a+b-1}B(a,b)} \tag{31}\]  
where, \(a=3\) and \(b=4\)[34]. \(B(a,b)\) represents Beta function \(\int_{0}^{1}x^{a-1}(1-x)^{b-1}dx\). The NPRACH design in NB-IoT manifests 48 subcarriers on an anchor that can be used as a preamble for RAP. Moreover, the basic allocation unit that can be assigned to any CE level comprises of 12 sub-carriers as explained in Section 2. We consider the same number of preambles for CE0 and CE1 valued at 12. We consider CE2 to be configured with the remainder out of 48 preambles. More preambles are considered in CE2 since in legacy network, the devices that fail in CE0 and CE1, ultimately try RAP attempt in CE2. To avoid high collisions in CE2 more preambles are allocated to CE2. The collided devices can jump from lower CE levels to higher level CEs in existing systems while they attempt to successfully transmit their preambles. The devices in PE-RAP can flexibly jump from one level to another based on RSRP measurements. However, the number of reattempts that the device can perform in each CE level is fixed. We consider the device to be able to attempt for the maximum of five times in each CE level after which it is considered as a failure. It is to be noted that each attempt in turn comprises of several repetitions. Each repetition is assumed to consume a unit power in level CE0. In CE1 the power consumption per repetition is doubled, while in CE2 it is considered to be thrice the power consumption in CE0. Here, we have chosen the aforesaid simple setting to represent the comparison of our proposal with the existing one.