# Transmission Delay-Based Uplink Multi-User Scheduling in IEEE 802.11 ax Networks +
## 4 Transmission Delay-Based Station Clustering  
### Clustering-Based Channel Use Improvement  
Stations may perform frame aggregation for uplink multi-user transmissions. The channel will be underutilized if transmission delays of the scheduled stations are different from each other because of various amounts of backlogged data or transmission rates. In the proposed scheduling method, stations with similar transmission delays are clustered together [21]. In order to acquire the CSI, the channel sounding process is performed in advance. After channel sounding, the SINR information for each uplink station is given as (1), and the uplink transmission rate of each station is given as \(R_{s_{i}}(\gamma_{a_{S},s_{i}})\). Note that \(R_{s_{i}}(\gamma_{a_{S},s_{i}})\) can be decided following the link adaptation strategy in the network. Let \(\mathcal{Q}_{s_{i}}\) denote the size of uplink data in which station \(s_{i}\in\mathcal{S}\) attempts to transmit to the AP. The \(\mathcal{Q}_{s_{i}}\) can be an aggregated payload for uplink transmissions, i.e., aggregated MAC protocol data unit pre-end-of-frame padding. Stations in the network have different data transmission rates and queue sizes for uplink data transmissions. If there are stations that have no data in their queue, they are excluded from the uplink scheduling. For the stations requiring uplink data transmissions, the transmission delay of station \(s_{i}\) can be simply calculated as follows:  
\[d_{s_{i}}=Q_{s_{i}}/R_{s_{i}}(\gamma_{a_{S},s_{i}}). \tag{2}\]  
Note that each station may have different transmission delays \(d_{s_{i}}\), \(s_{i}\in\mathcal{S}\). The proposed method creates station clusters based on the transmission delay \(d_{s_{i}}\) of each station so that stations with similar transmission delays are configured to transmit uplink data simultaneously. Let \(\mathcal{C}^{UL}=\{\mathcal{C}^{UL}_{l},\mathcal{C}^{UL}_{l},\mathcal{C}^{UL}_ {l},\cdots\}\) be the set of station clusters, where \(\mathcal{C}^{UL}_{l}=\{\{s_{i}\}|s_{i}\in\mathcal{S}\}\) and \(\mathcal{C}^{UL}_{l}\cap\mathcal{C}^{UL}_{m}=\emptyset\), for \(\mathcal{C}^{UL}_{l},\mathcal{C}^{UL}_{m}\subset\mathcal{C}^{UL}\). We define the function representing the difference in transmission delays between any two stations in the same cluster by \(\tau(d_{s_{i}},d_{s_{j}})=|d_{s_{i}}-d_{s_{j}}|\), \(s_{i}\
eq s_{j}\in\mathcal{C}^{UL}_{l}\) for \(\mathcal{C}^{UL}_{l}\subset\mathcal{C}^{UL}\). In the proposed method, clusters are configured to minimize the maximum difference in the transmission delay of clusters, and the station clustering problem is formulated as follows:  
\[\begin{split}&\min_{d_{s_{i}},d_{s_{j}}\in\mathcal{C}^{UL}_{l}, \mathcal{C}^{UL}_{l}\subset\mathcal{C}^{UL}}\ \ \tau(d_{s_{i}},d_{s_{j}})\\ &\text{subject to }\ \ 1\leq|\mathcal{C}^{UL}_{l}|\leq B_{a_{S}},\ \mathcal{C}^{UL}_{l}\subset\mathcal{C}^{UL}\\ &\ s_{i}\in\mathcal{C}^{UL},\forall s_{i}\in\mathcal{S}.\end{split} \tag{3}\]  
Note that if there are available frequency bands owing to a small number of stations participating in uplink multi-user transmissions, i.e., \(|\mathcal{C}^{UL}_{l}|<B_{a_{S}}\), the available frequency resources can also be utilized by downlink transmissions or channel sounding for newly joining stations. Hence, in this paper, we focus on the uplink multi-user transmissions,and the proposed method tries to fully utilize available bandwidths by employing the maximum number of stations for uplink multi-user transmissions. If we assume that the stations are clustered to maximize the cluster size and the maximum number of stations is scheduled to transmit uplink data simultaneously, i.e., \(|C_{l}^{UL}|=B_{ag}\), the problem in (3) can be easily solved following a greedy approach. For example, stations are sorted based on transmission delays, then stations are sequentially grouped into the same cluster until the number of stations in the cluster reaches the maximum capacity of simultaneous uplink transmissions \(B_{ag}\). After, for the remaining stations, the same procedure can be repeated.