# Evaluating 60 GHz FWA Deployments for Urban and Rural Environments in Belgium
## 4 Network Planning and Optimisation
### Multi-Objective Methods  
As multiple objectives must be simultaneously satisfied during the simulations, a linear utility function to solve the multi-objective problem is created. It finds the possible solutions with compromises that satisfy the restriction of the network operation. The problem is defined as follows:  
First, each objective variable is described, and then the multi-objective minimisation function is presented. The _user coverage_ variable \(f_{Cov}\) is important, with a weight of 40%. It aims to maximise the number of CPE connected to the core network. Equation (6), describes the user coverage where \(CPE_{ij}\) is a boolean value to identify the connection between \(CPE_{i}\) to \(EN_{j}\), normalised by the total number of CPEs in the area. \[f_{Cov}=1-\left(\sum_{i=0}^{Total_{CPE}}\sum_{j=0}^{Total_{EN}}\frac{CPE_{ij}}{ Total_{CPE}}\right) \tag{6}\]  
The _backhaul utilisation_ variable \(f_{BU}\), has a similar importance to the user coverage since it intends to minimise the mesh network infrastructure, providing the requested user coverage. Equation (7) presents this function where \(EN_{j}\) is a boolean function for an active EN \(j\), normalised by the total number of possible ENs in the network. \[f_{BU}=\sum_{j=0}^{Total_{EN}}\frac{EN_{j}}{Total_{EN}} \tag{7}\]  
The _hop count_ variable \(f_{HC}\) is a crucial function that aims to reduce the delay of the network by reducing the number of hops that a connected CPE needs to reach the PoP. The \(HopCount_{j}\), in Equation (8), represents the total number of hops that the \(EN_{j}\) needs to reach the PoP, normalised by the maximum number of hops \(EN_{j}\) can use to reach the PoP. Figure 6: Ray tracing algorithm example. \[f_{HC}=\sum_{j=0}^{Total_{EN}}\frac{HopCount_{j}}{Max_{hopcount}} \tag{8}\]  
The _path Loss_ variable \(f_{PL}\) aims to minimise the aggregated PL of a specific connection with the final objective of increasing the available supported bit rate of the link. It calculates the path loss \(PL_{ij}\) between the \(CPE_{i}\) and the \(EN_{j}\), and the aggregated path loss of all the \(k\) links associated with that specific path towards the PoP as shown in Equation (9). \[f_{PL}=\sum_{i=0}^{Total_{CPE}}\sum_{j=0}^{Total_{EN}}\left(PL_{ij}+\sum_{k=0}^{ Total_{links}}PL_{jk}\right) \tag{9}\]  
Finally, Equation (10) describes the _power consumption_ variable \(f_{PC}\) that minimises the whole network power consumption by calculating the power used by each active \(EN_{j}\), as shown in [4], normalised by the maximum power consumption of all the available ENs. This final function has the lowest importance, with a weight value of only 5%. \[f_{PC}=\sum_{j=0}^{Total_{EN}}\frac{PowerConsumption_{j}}{Max_{PowerConsumption}} \tag{10}\]  
The multi-objective minimisation function written in canonical from is described in Equation (11), where the objective variables are \(f_{Cow}\), \(f_{BU}\), \(f_{HC}\), \(f_{PL}\) and \(f_{PC}\). \[\min: w_{1}f_{Cow}+w_{2}f_{BU}+w_{3}f_{HC}+w_{4}f_{PL}+w_{5}f_{PC}\] (11) s.t. \[: C_{1}:\forall i,j\in\mathbb{N};0\leq CPE_{ij}\leq 1\] \[C_{2}:\forall i,j\in\mathbb{N};0\leq\sum RB_{ij}\leq EN_{RB}\] \[C_{3}:\forall i,j\in\mathbb{N};\sum EN_{ij}\geq 1,\forall i\
eq j\] \[f_{BU}=\sum_{j=0}^{Total_{EN}}\frac{EN_{j}}{Total_{EN}} \tag{7}\]0 \[f_{BU}=\sum_{j=0}^{Total_{EN}}\frac{EN_{j}}{Total_{EN}} \tag{7}\]1 \[f_{BU}=\sum_{j=0}^{Total_{EN}}\frac{EN_{j}}{Total_{EN}} \tag{7}\]2  
The values of \(w_{1}\) to \(w_{5}\) represent the weights of the independent objective variables. \(w_{1}=w_{2}=40\%\) are the weights for the user coverage and backhaul usage objective functions since they are the most important objectives in this problem. \(w_{3}=10\%\) is the weight of the hop count objective variable. \(w_{4}=w_{5}=5\%\) are the values for the path loss and power consumption variables. The values of \(i,j\) and \(k\), represent the \(i\)th CPE, the \(j\)th EN and \(k\)th PoP nodes, respectively. The multi-objective minimisation function is also subject to several network constraints.