# Efficient User-Serving Scheme in the User-Centric Cell-Free Massive MIMO System
## 4 Proposed Scheme and Power Control
### Proposed User Serving Scheme  
To solve the above problems, the following new scheme is proposed. The newly proposed scheme works when unserved users exist, and this scheme can serve users within the area, while solving the limitations in (a) and (b).  
Algorithm 1 describes an efficient user service scheme that can serve the unserved users when a large number of users exist within the area. First, the limitation (a) can be solved through STEP 1. It is confirmed that the case in which the previously served users are dropped in order to serve unserved users is prevented. Once the set \(\mathcal{P}\) is selected through STEP 1, the set \(\mathcal{S}\) is defined as the set of users served by the set \(\mathcal{P}\). In STEP 2 and STEP 3, the indices and gain are extracted. The limitation in (b) can be solved by first performing disconnection of the lower-level APs connected to the user supported by the most APs. In STEP 4, the priority is given in order of receiving service from the largest number of APs among users in set \(\mathcal{S}\). Through this, it is possible not to damage the gain of existing users served by a relatively small number of APs as much as possible. In STEP 5, the index of the APs that serve the gains less than the median of the total gain is extracted for each user in the set \(\mathcal{S}\) according to the priority given in STEP 4. Finally, in STEP 6, a connection with user \(i\) is made according to the priority given in STEP 5, and the signal-to-interference-plus-noise-ratio (SINR) accumulation for user \(i\) is performed. If the cumulative sum of the SINR for user \(i\) is larger than or equal to the threshold value \(\xi\), STEP 6 stops, and the search for other unserved users is performed again.  
In the following Section 5, the performance for the newly proposed scheme is applied and is compared with previous scheme. Comparisons with three cases are performed to confirm that the proposed scheme works well in the user-centric cell-free massive MIMO model.  
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Input : Channel Matrix : \(\mathbf{H}\), Subset of AP for user \(k\) : \(\mathcal{M}_{k}\), Channel Estimation : \(\gamma\),  Connection Matrix : \(\boldsymbol{\alpha}\), Threshold : \(\xi\) for\(\mathbf{i}=1\to K\) if\(\mathcal{M}_{i}=\varnothing\) STEP 1 : Select \(\mathcal{P}\) candidate APs with high channel gain \(\gamma\) from user \(i\). (If there is a user served only by a specific AP among users served by the APs in \(\mathcal{P}\), the corresponding AP is excluded from group \(\mathcal{P}\).) STEP 2 : Define the set of users served by \(\mathcal{P}\) as \(\mathcal{S}\). STEP 3 : Extract the index set and channel gain of users in \(\mathcal{S}\). STEP 4 : Prioritize and list them in the order in which they are served by the largest number of APs among users in \(\mathcal{S}\). STEP 5 : Extract APs that provide the gains below the median in descending order for each user value from among the gains listed in descending order for each user. STEP 6 : Connect the user \(i\) with the AP sets extracted in STEP 5 and execute the SINR cumulative sum (\(\delta\)). while\(\xi>\delta\)  The APs of the set extracted in STEP 5 are sequentially connected to the user \(i\). end while endif endfor
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**Algorithm 1** Proposed Unserved user Serving Scheme