# CeRA-eSP: Code-Expanded Random Access to Enhance Success Probability of Massive MTC
## 5 Performance Evaluation  
### Simulation Environment  
We developed a simulator in Python 3.7 to measure the performance of the proposed CeRA-eSP scheme. Table 1 lists the system parameters used in the simulations. We implemented an mMTC scenario with \(N=100,000\) devices in single-cell access during 4000 RAO. In the case of the CeRA method, an experiment was performed in an environment with a codeword length \(L_{c}=2\) and a situation in which devices were connected for a total of 2000 virtual frames. Each experiment was performed 100 times, and the average value of the experimental results was used as the measurement value. We compared the performance of the proposed CeRA-eSP scheme with legacy schemes such as baseline, access class barring, back-off, and legacy CeRA. The operation summary of each random access method is described below and Figure 6 illustrates the comparison of the four different random access schemes. * Baseline: This refers to the existing RA method in which each device transmits a random preamble sequence from a set of 54 contention-based preambles. Because congestion control is not considered, activated devices transmit a preamble on every RA occasion. Moreover, because the number of total preamble sequences is less than the number of available PUSCH resources, a successful preamble transmission means that PUSCH resource allocation is also successful. * Access class barring and back-off (ACB and BO): This refers to the proposed ACB and BO technique for solving the high access intensity problem in the mMTC scenario [11; 12; 13]. Activated devices select an arbitrary value between zero and one. When the value is less than the access barring rate, the device is barred for a certain duration. In terms of the preamble transmission, the devices transmit a random preamble sequence among 54 contention-based preambles, similar to the baseline scheme. When a preamble collision occurs, the device waits for the random back-off time between zero and the given back-off time duration and then retransmits the preamble sequence again. Because the number of preamble sequences in the ACB and BO scheme is less than the number of available PUSCH resources, the restriction of PUSCH resources is not considered in the baseline. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline Traffic distribution model & Beta distribution(\(\alpha=3\), \(\beta=4\)) \\ Time duration & 10 (s) \\ PRACH configuration & 6 [21] \\ Total random access occasion & 4000 (n) \\ Preamble codeword length (\(L_{c}\)) & 2 \\ Available preamble sequence (M) & 54 (n) \\ Available PUSCH resources (\(N_{ST}\)) & 144 (n) [26] \\ Maximum number of \(N_{fp}\) & 27 (n) \\ Minimum number of \(N_{fp}\) & 2 (n) \\ Waiting window time (\(W\)) & 10 (ms) \\ Delay constraint & 10 (s) \\ Maximum number of preamble retransmission & 10 (n) \\ Back off time & 20 (ms) \\ Barring rate & 0.3 \\ Mean barring time & 1 (s) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. Legacy CeRA: This refers to an existing CeRA transmission scheme in which PUSCH resource constraints are not considered. Because the codeword length of the target system is 2, devices select one of the \(54^{2}=2916\) preamble codewords in the preamble transmission step. Because congestion control is not considered, activated devices transmit preamble codewords in every RA cycle. CeRA utilizes two consecutive RAOs as one RA cycle; thus, the number of RA cycles considered in the simulation is 2000. If the number of PUSCH resources is less than the number of deduced preamble codewords, the BS drops the extra preamble codewords. * The proposed CeRA-eSP: In the same way as legacy CeRA, one of the preamble codewords is randomly selected to perform the preamble transmission. The main difference between the proposed CeRA-eSP method and the legacy CeRA method is that a different scale of preamble codeword sets can be selected according to the access intensity.