# Enhanced Matching Game for Decoupled Uplink Downlink Context-Aware Handover
## 4 Proposed Model
### Decoupled Uplink-Downlink Handover Algorithm  
To resolve these challenges, we defined two principal stages. At the beginning, we radically change the issue from a many-to-many case to a many-to-one case by assigning BSs with each other in order to maximize the benefit of UE in terms of QoS. However, as described in Algorithm 1, we assume that all the UEs are first associated with the great BS primarily based on the SINR. At that point, with the target of maintaining a good UE QoS, when the mobile UE (denoted by k) experiences a degradation of the required QoS, it outlines the desired matching list considering Equation (8). The \(UE_{k}\) makes a ranking list based on \(\succ_{k}\) of the accessible BSs and applies to the most favored one of them. As a result, if the actual BS service (denoted via m) for \(UE_{k}\) is no longer its most desired one compared to BS services (denoted via i), it makes a matching suggestion \(\mu_{mi}^{k}\) to an agent \(BS_{i}\). Therefore, in our proposed Algorithm 1, we consider a matching suggestion \(\mu_{mi}^{k}\) as a handover request. Once a matching suggestion is received, the concerned agent \(BS_{i}\) updates its utility. Specifically, \(BS_{i}\) accepts the suggestion only if it is strictly beneficial. Each \(BS_{i}\) in agent \(BS_{i}\) ranks the candidates based on the actual matching \(\mu\), then verifies if the \(\mu_{ml}^{k}\) is strictly beneficial for both \(BS_{i}\) to get computed in the set of UEs asking for association (denoted via \(N^{req}\)). In other words, the agent \(BS_{i}\) will not accept hosting \(UE_{k}\) if and only if both BSs from agent \(BS_{i}\) benefit from this association. The UE that was dismissed in the previous stage would follow to their next favored BS, then the BSs adjust their rejected list accordingly. However, if the \(\mu_{ml}^{k}\) is beneficial for both agents \(BS_{l}\), then we update the set of UEs sending requests to \(BS_{l}\), the BSs adjust their waiting list accordingly, and will update the new matching solution (denoted via \(\mu^{\prime}\) ), adding the link (k,i) to \(\mu^{\prime}\). Nevertheless, given our considered externalities in every progression \(\mu^{\prime}\), the utilities would be refreshed in view of the actual matching. Accordingly, an iterative approach will be embraced. The \(BS_{l}\) evaluates its utility for the new matching solution \(\mu^{\prime}\); in that way, it will take into consideration all UEs asking for a handover at the same time as \(UE_{k}\). Therefore, for all \(BS_{i}\) in agent \(BS_{i}\) will keep dismissing the worst case from its \(N^{req}\) until it gets a beneficial utility. The final resulted \(N^{req}\) will be associated with the agent \(BS_{i}\). The procedure keeps running until achieving a beneficial matching based on \(\succ_{l}\), described as follows. **Definition 2**. : _Given a pair of UEs \(k,j\in N\) and BSs \(m,i\in M\), a matching \(\mu\) with \((m,k),(i,j)\in\mu\) is stable if no stable handover-matching \(\mu_{m,i}^{k}=\mu\setminus(m,k)\bigcup(i,k)\) exists, such that:_  
* \(\forall x\in\{k,j,m,i\},U_{x}(\mu_{m,i}^{k})\geq U_{x}(\mu)\)__
* \(\exists x\in\{k,j,m,i\},U_{x}(\mu_{m,i}^{k})\geq U_{x}(\mu)\)__  
The UE and BS stable matching \(\mu\) with \((m,k)\in\mu\) is achieved if no \(BS_{i}\) or \(UE_{j}\), where \(BS_{i}\) lean toward \(UE_{j}\) to \(UE_{k}\) or \(UE_{k}\) lean towards \(BS_{i}\) to \(BS_{m}\), exists. In other words, while considering the externalizations in a UE and BS matching, dismissing-matching should happen only in the event that it is entirely disadvantageous for the included BS to get balanced matching. ```
Initializing--each UE is initially associated with a BS \(i\) based on downlink max-SINR association.