# User-BS Selection Strategy Optimization with RSSI-Based Reliability in 5G Wireless Networks
## 4 Wireless BS Selection-Strategy Optimization Based on Identified Distribution
### Constrained Optimization  
The receiving sensitivity constraint condition is relatively simple with Formula (17). For input location \(x_{l}\) and calculated distance \(d_{i}\) to each BS \(i\), it can be judged whether \(x_{i}input\) is within the signal effective range \(C_{i}\) given by BS \(i\) or outside. Let those \(s_{i}\) corresponding to outside BSs be 0, which is not considered; only those BSs within the effective range of SEN distance are calculated step by step according to the above DP method.  
According to Formula (11), the BS capacity constraint actually considers that the number of users connected to a certain one BS cannot exceed the limit, which can be transformed into the following form:  
\[\iint s_{i}(x_{l})Mf(x)dx=\mathbb{E}[ms_{i}(x_{l})], \tag{31}\]  
where \(m\) represents the user density at position \(x\), whose density function is \(Mf(x)\).  
Corresponding to input position \(x\), the BS capacity constraint condition needs to ensure \(\mathbb{P}[ms_{i}(x)<N_{BS}(i)]>1-\alpha\). We have:  
\[\begin{split}\mathbb{P}[ms_{i}(x_{l})<N_{BS}(i)]&>1 -\alpha\\ \mathbb{P}[m<\frac{N_{BS}(i)}{s_{i}(x_{l})}]&>1- \alpha\\ \frac{N_{BS}(i)}{s_{i}(x_{l})}&>\lambda_{1-\alpha}\\ s_{i}(x_{l})&<\frac{N_{BS}(i)}{\lambda_{1-\alpha}}, \end{split} \tag{32}\]  
\(\lambda\) represents the confidence region of \(m\)'s distribution under \(\alpha\), which can be obtained from the distribution table when the distribution is identified.  
Adding the BS capacity constraint to the DP method, we can obtain:  
\[F_{k+1}(I)= \min_{s\in\mathcal{S}}\sum_{i=1}^{k+1}s_{i}(x_{l})\cdot R_{BS}(i) \log_{10}d_{i}(x_{l}), \tag{33}\] \[s.t.\;s_{C_{i}}<\frac{N_{BS}(C_{i})}{\lambda_{1-\alpha}}\;for\;i=1,\ldots,k+1\] \[= \min_{s_{k+1}}[F_{k}(I-s_{k+1}(x_{l}))\] \[+s_{k+1}(x_{l})R_{BS}(k+1)\log_{10}d_{k+1}(x_{l})],\] \[s.t.\;s_{C_{k+1}}<\frac{N_{BS}(C_{k+1})}{\lambda_{1-\alpha}}.\]  
According to the above analysis, the process of solving wireless BS selection-strategy optimization on the basis of identified distribution can be obtained as shown in Algorithm 1.  
```
0:\(x\): user's location; BS: BS information, including locations, reliability, and connection limit numbers; \(D\): maximal signal connection distance;
0:\(s\): BS-user connection strategy;
1: initialize: Set \(s=0\);
2: Step 1: Calculate distance \(d_{i}\) from \(x\) to each BS \(i\), and find BS set \(K_{C}\) within the signal effective range of the user SEN on the basis of (17); let \(k=N(K_{C})\).
3: Step 2: Calculate the BS capacity constraint at position x according to (32).
4: Step 3: Use the DP method (16) to calculate the optimal user selection strategy \(s\) under the condition of meeting the connection restriction.
5: return\(s\)
```  
**Algorithm 1**Wireless BS selection-strategy optimization based on identified distribution.  
First, the distance from \(x\) to each BS is calculated, and the nodes within the effective range of the signal are selected according to Formula (16). Then, the DP recursive formula in (33) is combined to optimize the user-BS selection strategy.