## 3 Transmission Point Selection in Multi-Band Multi-Connectivity Operation
### Sequential Transmission Point Selection Algorithm  
Because a single TP may be selected by multiple users according to Algorithm 1 in Section 3.3, the latency to be selected may increase. It is also due to the fact that the number of connections to be allowed may further degrade the computational complexity. In other words, after TP having the \(c-1\)-th highest value of \(v_{k}\), the TP having the \(c\)-th highest value of \(v_{k}\) is selected among the TPs that were not selected, from the first to \(c-  
computational complexity of sequential TPS in Algorithm 2 is not higher than that of the TPS in Algorithm 1. It is due to the fact that sequential TPS only depends on the number of TPs and the number of users regardless of the allowed number of connections of a user. ```
0:\(\mathcal{K}=\{1,2,\ldots,K\},\mathcal{N}=\{1,2,\ldots,N\},\mathcal{C}(1\leq C\leq N)\)
1: Initialise \(\mathcal{K}_{n}\leftarrow\emptyset,\forall n\in\mathcal{N}\), \(x_{k}^{n}\gets 1,\forall n\in\mathcal{N},\forall k\in\mathcal{K}\)
2:while\(\mathcal{K}\
eq\emptyset\)do
3: Choose any user \(k\in\mathcal{K}\)
4:for\(i\gets 0\) to \(C-1\)do
5:\(\mathcal{N}^{\prime}\leftarrow\mathcal{N}^{\prime}\cup\{i\}\)
6: Set \(\mathcal{K}_{i}\leftarrow\mathcal{K}_{i}\cup\{k\}\)
7:\(i\gets i+1\)
8:endfor
9:\(\mathcal{N}\leftarrow\mathcal{N}\backslash\mathcal{N}^{\prime}\)
10:while\(\mathcal{N}\
eq\emptyset\)do
11: Choose any TP \(j\in\mathcal{N}\)
12: Add \(j\) to \(\mathcal{N}^{\prime}\): \(\mathcal{N}^{\prime}\leftarrow\mathcal{N}^{\prime}\cup\{j\}\)
13: Remove \(j\) from \(\mathcal{N}\): \(\mathcal{N}\leftarrow\mathcal{N}\backslash\{j\}\)
14: Set \(\mathcal{K}_{j}\leftarrow\mathcal{K}_{j}\cup\{k\}\)
15: Find the maximum \(v_{k}^{n}\) in \(\mathcal{N}^{\prime}\) for user \(k\): \[n\leftarrow\operatorname*{argmax}_{n\in\mathcal{N}^{\prime}}v_{k}^{n}\]
16: Set \(x_{k}^{n}\gets 0\)
17: Remove \(n\) from \(\mathcal{N}^{\prime}\): \(\mathcal{N}^{\prime}\leftarrow\mathcal{N}^{\prime}\backslash\{n\}\)
18: Remove \(k\) from \(\mathcal{K}_{n}\)
19:endwhile
20: Remove \(k\) from \(\mathcal{K}\): \(\mathcal{K}\leftarrow\mathcal{K}\backslash\{k\}\)
21:endwhile
22:return\(\mathcal{N}^{\prime},\mathcal{K}_{n},x_{k}^{n},\forall n,k\)
```  
**Algorithm 2** Sequential Transmission Point Selection Algorithm  
The computational complexity of the sequential transmission point selection in Algorithm 2 is \(\mathcal{O}(NK)\), where \(N\) denotes the total number of TPs operating in all frequency bands over the network and \(K\) denotes the number of users in the network. The TPS algorithm selects the \(C\) number of TPs for a user sequentially, by looking up the TPs without considering the other users' value \(v_{j}(j\
eq k)\), i.e., \(\mathcal{O}(C)\). In addition, remaining TPs are determined according to whether they are serving TP or not, by comparing each TP to a TP with a maximum value of \(v_{j}\) in the set of candidate TPs, i.e., \(\mathcal{O}(N-C)\). In other words, the complexity of the transmission point selection only depends on the number of users and the total number of TPs, i.e., \(\mathcal{O}(N)=\mathcal{O}(C)+\mathcal{O}(N-C)\). The sequential TPS algorithm solution, denoted by \(T\), is bounded by  
\[T\leq\frac{1}{N}\sum_{n=1}^{N}\hat{t}_{k}+T^{*}. \tag{17}\]  
Prior to the iteration for the \(l\)-th user, TP \(n\) has the value of \(v_{k}\) between the first to \(C\)-th lowest one. In other words, \(T^{l-1}\) is lower than the mean value of the minimum service time (i.e., \(\hat{t}_{k}\)) for all TPs in the network. Thus, we can obtain \(T^{l-1}\) as follows:  
\[T^{l-1}\leq\frac{1}{N}\sum_{n=1}^{N}\sum_{k\in\mathcal{K}_{l-1}^{l-1}}\hat{t}_ {k}\leq\frac{1}{N}\sum_{n=1}^{N}\sum_{k\in\mathcal{K}_{l-1}^{l-1}}t_{k}=\frac{ 1}{N}\sum_{n=1}^{N}T_{n}^{l-1}, \tag{18}\]where \(\mathcal{K}_{n}^{l-1}\) denotes the set of users who have been allocated to TP \(n\) at the \((l-1)\)-th iteration. Let \(k^{*}\) be the last user who selects the TP \(n^{*}\) at \(l\)-th iteration.