# Preamble Design and Collision Resolution in a Massive Access IoT System
## 3 Preamble Design
### Sub-Preamble Sequence Design

Table 1: Simulation parameters. the preamble detection performance. Hence, it is applicable to the IoT scenario where massive devices may request random access at the same time. ### Comparison of Collision Probability

Figure 5 depicts the relationship between the RA collision probability and the number of RA-attempting devices on a PRACH. In our simulations, the performance of the proposed RA scheme is compared with the conventional RA scheme, E_PACD scheme [14], and PACR scheme [15]. Firstly, the analytical results under the proposed RA scheme and that under the conventional scheme are both close to the simulation results, which verifies the accuracy of our analysis approach. It is also observed that the collision probability of the conventional RA scheme and that of E_PACD scheme are identical, since their collision probabilities only depend on the number of available preambles. Differently, the collision probability of PACR scheme depends on both the number of TA values \(N_{TA}\) and the number of available preambles that can be allocated to the devices. Additionally, greater \(N_{TA}\) means the gNB can detect more preambles on a PRACH, which can reduce the collision probability. However, \(N_{TA}\) depends on the length of zero correlation zone of the detected preambles. Hence, \(N_{TA}\) is finite. On the other hand, the RA collision probability of the proposed scheme depends on the size of sub-preamble sequence sets and the number of available locations of a dedicated sub-preamble. From Figure 5, we also observe that: (1) With the increase of the amount of RA-attempting devices, the collision probability of each scheme increases; (2) When the amount of RA-attempting devices is the same, the proposed scheme guarantees a lower RA collision probability than the other schemes, which means it is more suitable for massive connective scenarios. Figure 4: Comparison of the average preamble detection probabilities. ### Comparison of RA Success Probability

In this subsection, the RA success probability varying with the number of RA-attempting devices on a PRACH is analyzed. In our simulation experiment, we set \(n_{p}=n_{p,s}=60\). Figures 6 and 7 depict the simulation results with configuration \(n_{PUSCH}=20\) and \(n_{PUSCH}=100\) respectively. Figure 5: Comparison of collision probability. Figure 6: Comparison of RA success probability (\(n_{PUSCH}=20\)). Similar to Figure 5, the analytical results under the proposed and conventional schemes are both close to the simulation results, which validates the effectiveness of our theoretical analysis. As observed in Figure 6, the RA success probability under the proposed scheme is approximately 100%, when \(n_{k}<20\). This is because the RA collision probability of the proposed scheme is close to zero. Therefore, all PUSCH resources can be allocated to the collision-free devices. When \(n_{k}>20\), the RA success probabilities under the proposed scheme, the conventional scheme, PACR and E_PACR scheme all decrease rapidly, since the number of available PUSCH resources is insufficient. In this case, PUSCH resources shortage is the main influence on RA success probability. Besides, the RA success probability under the proposed scheme performs better than the other schemes. It is observed that the RA success probability under PACR scheme can be convergent to the proposed scheme only if \(N_{TA}=\infty^{+}\) that is impractical in a real-world system. In Figure 7, \(n_{PUSCH}\) is extended to 100. It is found that with the increase of \(n_{PUSCH}\), the proposed scheme can guarantee a high RA success probability even though the number of RA-attempting devices on a PRACH beyond 100. Hence, it is verified that the proposed scheme can guarantee a higher RA success probability as long as the PUSCH resource is enough. ### Comparison of Resource Efficiency

In this subsection, the resource efficiency is analyzed under different schemes.