# Preamble Design and Collision Resolution in a Massive Access IoT System
## 3 Preamble Design
### Sub-Preamble Sequence Design  
To address the drawback of the conventional preamble structure that easily leads to RA collision in a massive connective scenario, this paper proposes a new preamble structure with more diversities to reduce the RA collision probability. Specifically, the new preamble is consists of two sub-preambles and an empty sequence, as depicted in Figure 2. The sub-preambles are known as shared sub-preamble and dedicated sub-preamble respectively. The location of the shared sub-preamble is fixed. The location of the dedicated sub-preamble includes two types, which are denoted by \(\mu\in\{1,2\}\), as depicted in Figure 2. In addition, we use subscript \(i\in\{s,d\}\) to represent the variables corresponding to the shared sub-preamble and dedicated sub-preamble respectively. The \(n_{i}\)th sub-preamble sequence with root index \(u_{i}\) and cyclic shift index \(v_{i}\) is generated as follows. \[x_{u_{i},v_{i}}(n_{i})=x_{u_{i}}((n_{i}+C_{v_{i}})\bmod N_{i}),0\leq n_{i}\leq N _{i}-1, \tag{5}\]  
where \(N_{i}\) denotes the length of the \(n_{i}\)th sub-preamble sequence, and \(x_{u_{i}}\) denotes ZC root sequence that is obtained by Equation (2). As a result, the set of available sub-preamble can be obtained as  
\[S_{i}=\{x_{u_{i},v_{0}},x_{u_{i},1},...,x_{u_{i},N_{i}}\},i\in\{s,d\}, \tag{6}\]  
When an IoT device attempts to access to a gNB, it selects the shared sub-preamble and dedicated sub-preamble from the corresponding obtained set to compose a preamble randomly. In other words, each sub-preamble is generated by distinct ZC root sequence. According to the value of \(\mu\), the generated preamble sequence can finally generated by  
\[x_{u_{i},v_{i}}^{u_{d},u_{d}}(n)=\alpha[x_{u_{i},v_{i}}(n_{s}),g_{1}(n_{g_{1}} ),x_{0}(n_{0}),g_{2}(n_{g_{2}}),x_{u_{d},v_{d}}(n_{d})],0\leq n_{i}\leq L_{i}, 0\leq n_{g_{i}}\leq L_{g}, \tag{7}\]  
or  
\[x_{u_{i},v_{i}}^{u_{d},u_{d}}(n)=\alpha[x_{u_{i},v_{i}}(n_{s}),g_{1}(n_{g_{1}} ),x_{u_{i},v_{d}}(n_{d}),g_{2}(n_{g_{2}}),x_{0}(n_{0})],0\leq n_{i}\leq L_{i}, 0\leq n_{g_{i}}\leq L_{g}, \tag{8}\]  
where \(x_{u_{i},v_{i}}(n_{s})\) and \(x_{u_{i},v_{d}}(n_{d})\) represent the shared sub-preamble and dedicated sub-preamble respectively, \(g_{m}(n_{g_{m}})\ m\in\{1,2\}\) denotes Guard Interval (GI), \(x_{0}(n_{0})=0^{1\times L_{0}}\)\((0\leq n_{0}\leq L_{0})\) denotes an empty sequence with length \(L_{0}\). Besides, \(L_{i}\) denotes the length of the sub-preambles, \(L_{g}\) denotes the length of the GI and \(\alpha\) represents the transmission power. The preamble sequence generation scheme is summarized as Algorithm 1. ```
1:\(\mu\), \(\alpha\), \(\beta\), \(\gamma\),


```
0: The sets of available sub-preambles \(S_{s},S_{d}\); location index for the dedicated sub-preamble \(\mu\);
0: A preamble sequence for an RA-attempting device \(x_{u_{1},v_{s}}^{u_{2},v_{d}}(n)\);
1: Randomly select a sub-preamble sequence from \(S_{s}\) as a shared sub-preamble, \(x_{u_{s},v_{s}}(n_{s})\);
2: Randomly select a sub-preamble sequence from \(S_{d}\) as a dedicated sub-preamble, \(x_{u_{d},v_{d}}(n_{d})\);
3: Randomly select a location index for the dedicated sub-preamble, \(\mu\);
4:if\(\mu=1\)then
5: Generating a preamble according to Equation (7);
6:else
7: Generating a preamble according to Equation (8);
8:endif
```
**Algorithm 1** Preamble generation scheme

## 4 Preamble Collision Resolution Scheme

Based on our proposed preamble structure, this section studies how to reduce the preamble collision. The sub-preamble sequence reception scheme is first proposed. Then, we introduce how to capture multiple TA values in a single RA procedure. Thereafter, an integrated preamble collision resolution scheme is studied. ### Sub-Preamble Sequence Reception

After sequence \(y(n)\) is received by the gNB, \(y(n)\) should be sliced into a shared sub-preamble and a dedicated sub-preamble. Since the sub-preamble structure is available to both IoT devices and gNB, the shared sub-preamble is apt to be obtained in the light of its predetermined length and location.