# Preamble Design and Collision Resolution in a Massive Access IoT System
## 3 Preamble Design
### Sub-Preamble Sequence Design
The resource efficiency is defined as follows

\[\eta\triangleq\frac{n_{success}}{n_{PUSCH}}, \tag{22}\]

where \(n_{success}\) denotes the number of PUSCH resources which are allocated to collision-free devices. As shown in Figure 8, the resource efficiency under the proposed scheme is higher than that under other schemes, especially when the amount of RA-attempting devices on the same PRACH is large. When \(n_{k}>20\), the resource efficiency under the proposed scheme and that under PACR scheme both decrease with \(n_{k}\). This is because the PUSCH resources are not enough to be allocated to the collision-free devices when \(n_{k}>n_{PUSCH}\). However, the proposed scheme can still guarantee a high resource efficiency even though \(n_{k}\) is large. Figure 7: Comparison of RA success probability (\(n_{PUSCH}=100\)). ### Analysis of TA Capturing Performance

In this subsection, the performance of TA capturing is evaluated in terms of TA capturing accuracy. Specifically, TA capturing accuracy is defined as

\[\varepsilon_{TA}=N_{captured}/N_{penmble}, \tag{23}\]

where \(N_{captured}\) denotes the number of TA values which is captured correctly, and \(N_{penmble}\) denotes the number of received preambles on the same PRACH resource. Compared with the conventional preamble, the sub-preamble is shorter. As a result, sub-preamble structure may degrade the performance of TA capturing. For the sake of performance analysis of the proposed multiple TA value capturing scheme, we focus on the collision of the shared sub-preambles. Assume that \(M\) preambles from \(M\) different devices are received on the same PRACH where the shared sub-preambles are set to the same index. Besides, the dedicated sub-preamble indexes and location indexes are randomly selected. The number of the available dedicated sub-preambles is set to 60, the number of available locations is set to 2. As depicted in Figure 9, the number of preambles sent on the same PRACH is set to \(M=\{2,4,6,8,10\}\). It is observed that better TA capturing performance can be guaranteed when less devices transmit identical preamble on the same PRACH. For the case of \(M=2\), the proposed scheme can guarantee over 80% accuracy even though the SNR is low (i.e., \(-10\) dB). Similar accuracy can be obtained when SNR reaches 6 dB for the case of \(M=10\) where interference is severe. Please note that the probability that 10 devices select the same shared sub-preamble is quite low. According to Equation (12), the probability is only 2.59% when 1000 devices request RAs with 60 available preambles. Figure 8: Comparison of PUSCH resource efficiency (\(n_{PUSCH}=20\)). ## 7 Conclusions

In this work, a preamble collision resolution scheme was proposed for the IoT systems. The number of collision-free devices on the same PRACH was expanded by the proposed sub-preamble sequence structure. To obtain multiple TA values of the RA-attempting devices, a multiple TA capturing scheme was also proposed. Simulation results verified that the proposed RA scheme performed well in preamble collision probability, RA success probability, resource efficiency and TA capturing. In particular, the proposed scheme improved the RA success probability with ignorable degradation in preamble detection performance. Hence, the proposed scheme has a great potential for supporting massive access in the future IoT systems. In addition to the preamble design, preamble repetition is also an important way to improve the random access performance. Hence, our future work will focus on the preamble repetition mechanism design for a massive IoT system. **Author Contributions:** This work was a collaborative development by all authors. [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] proposed the idea, were involved in the theoretical performance analysis, designed and optimized the algorithm, and wrote the paper. All authors have read and agreed to the published version of the manuscript.