# Cluster-Based Transmission Diversity Optimization in Ultra Reliable Low Latency Communication
## 3 System Architecture  
In Figure 2, a cluster-based uplink wireless sensor communication architecture has been considered. In this network, three different types of sensors (General, Audio, and Video sensors) were randomly plotted into different clusters. The clusters are represented as \(Z_{x}=(Z_{1},Z_{2},Z_{3},\ldots,Z_{n})\). The system bandwidth \(B\) is uniformly assigned to the different clusters \(Z_{x}\). Each cluster bandwidth \(B_{z_{x}}\) can be calculated as:  
\[B_{z_{x}}=\frac{B}{Z_{x}} \tag{1}\]  
The system considered a range of frequency for each cluster \(B_{z_{x}}=B_{z_{1}}\), \(B_{z_{2}}\), \(B_{z_{3}}\), \(\ldots\), \(B_{z_{n}}\) and the number of sensor nodes and subcarrier channels are different. There is a dedicated bandwidth assignment for the special sensors (audio and video sensors) as \(B_{d}\). The general sensors transmit their data over randomly selected frequency subcarrier channels from assigned bandwidth \(B_{z_{x}}\). The system considered \(S_{x}\) number of general sensors exist per cluster. If bandwidth \(B_{z_{x}}\) is assigned in each cluster, then each sensor frequency bandwidth \(B_{sx}\) can be evaluated as:  
\[B_{sx}=\frac{B_{z_{x}}}{S_{x}} \tag{2}\]  
with every sub-bandwidth \(B_{z_{x}}\) having a set of a carrier frequency \(f_{set_{x}}\) within their selected cluster bandwidth.  
\[f_{set_{x}}=(f_{a_{x}}f_{a_{x}+1},f_{a_{x}+2},\ldots,f_{b_{x}-2},f_{b_{x}-1},f _{b_{x}}) \tag{3}\]  
In a specific cluster \(a_{x}\) and \(b_{x}\) defines the starting and ending position of subcarrier frequency set. Here, \(x=1\), \(2\), \(3\), \(\ldots\), \(n\) mark cluster number and \(b_{0}=0\). The \(a_{x}\) and \(b_{x}\) must be resided between \(1\) to \(N\) no subcarriers. \(N\) indicates the number of channels and \(T_{g}\) is the total number of general sensors.  
\[\begin{split} b_{x}=b_{x-1}+\frac{N}{T_{g}}\times S_{x}\\ a_{x}=b_{x-1}+1\end{split} \tag{4}\]  
Following Figure 1, each general sensor creates \(d=1\), \(2\), \(3\), \(\ldots\), \(D_{n}\) duplicate packets for higher data accuracy and \(S_{x}\) randomly occupies subcarrier frequency \(f_{c}\) from \(f_{set_{x}}\)  
\[f_{c}\xleftarrow{R}f_{set_{x}} \tag{5}\]The slotted-ALOHA protocol provides the ability to transfer those duplicated packets into different slots. There are \(y\) = 1, 2, 3,..., \(n\times d\) possible packets that can be sent from each \(S_{x}\) using a single slot. For the \(Z_{x}\) number of clusters, the signal \(M_{SG}\) (\(t\)) can be presented as:  
\[M_{SG}(t)=\sum_{y=1}^{n\times d}\hskip-14.226378 pt\sum_{z=1}^{Z_{x}}\hskip-14.226378 ptS _{yz}(t)e^{2\pi if_{y}t} \tag{6}\]  
Here \(S_{yz}\) (\(t\)) is an in-phase quadrature component as well as a complex baseband signal. In each TTI slot, the specialized audio and video sensor choose subcarrier frequency from the dedicated band \(B_{d}\) to have maximum reliability. For a total of AV audio or video frames, the signal \(M_{SS}(t)\) can be expressed [30] as:  
\[M_{SS}(t)=\sum_{k=1}^{AV}\hskip-14.226378 ptS_{z}(t)e^{2\pi if_{d}t} \tag{7}\]  
Without considering the noise interference, the total signal is:  
\[M_{total}(t)=M_{SG}(t)+M_{SS}(t) \tag{8}\]  
Figure 2: System Model.  
At the receiver end, there's the employ of massive MIMO, which provides multiple signals from a different cluster and provides multi-connectivity for different packet duplication conditions.