# Radio Network Planning towards 5G mmWave Standalone Small-Cell Architectures
## 2 Problem Formulation and Simulation Methodology
### 5G System Module
#### 2.3.1 The Planning Optimization Algorithm  
Our goal herein was to propose a network layout of optimally located microcells that keep the deployment cost to a _minimum_ while at the same time specific coverage and capacity criteria are met. \begin{table}
\begin{tabular}{c c} \hline \hline
**Simulation Parameter** & **Value** \\ \hline Central Frequency & 28 GHz \\ \hline Transmitter EIRP and User Antenna Gain & 60 dBm \\ \hline Sector Antenna Gain (3 GPP pattern for 120\({}^{\circ}\) sector) & 18 dBi \\ \hline Omnidirectional Antenna Gain & 4 dBi \\ \hline Total cable losses & 2 dB \\ \hline Channel Bandwidth & 100 MHz \\ \hline Aggregated Bandwidth (16 Carriers) & 1600 MHz \\ \hline Resource Blocks (RBs) & 132 \\ \hline Minimum Received Power \(P_{rx,~{}min}\) & \(-\)5 dBm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 3: Rate calculations for an LTE-A system with 20 MHz bandwidth and five aggregated component carriers compared to the 5G NR system employed in this work. Since in this analysis we only considered microcells, the deployment cost of each node was the same, \(C\), and hence, the total cost of a network deployment was directly proportional to the number of nodes deployed. Equations (4)-(7) are formulating this optimization problem. \[B_{m}^{OPT}\leftarrow \begin{array}{c}\underset{B^{\prime}m\in\mathbf{B}}{ \operatorname{argmin}}\ \left(\sum_{b\in B_{m}^{\prime}}C_{b}\right)\end{array}  \tag{4}\]  
Subject to:  
\[P_{rx}^{k}\geq P_{rx,min},\ \forall k\in K \tag{5}\]  
\[\sum_{k\in K_{g}}N_{RB,k}\leq RB_{max},\ \forall g\in G, \tag{6}\]  
\[R_{k}\geq R_{CN,min},\ \forall k\in K \tag{7}\]  
where \(B_{m}^{\prime}\) is the set of candidate microsites that are under examination, \(C_{b}\) is the cost of the \(b\) microsite (herein, \(C_{b}=C\)), \(K\) is the fixed set of CNs defined in Section 2.1, \(P_{rx}^{k}\) is the received power of the \(k\) CN, \(G\)' is the set gNBs associated with the \(B_{m}^{\prime}\) sites (as previously mentioned, when sectors are considered, each site comprises three gNBs), \(K_{g}\) is the set of CNs currently served by \(g\) gNB, \(RB_{max}\) is the maximum allowed resource blocks of a gNB, \(R_{k}\) is the rate offered by the system to the \(k\) CN and finally \(R_{CN,min}\) is the capacity requirement. Note that the different candidate solutions that were examined (B) were derived in the context of the Genetic Algorithm (GA) methodology as it is described in the following. The solution to the optimization problem defined earlier was the \(B_{m}^{OPT}\) set of microsites that entails the _minimum total cost_[7] of network deployment while at the same time meets the constraints set by Equations (5)-(7). Herein, the optimization problem was tackled with a multi-objective evolutionary algorithm [10] and specifically with the NSGA-II (Non-sorting Dominated Genetic Algorithm-II). For this, the problem was analyzed and translated into a three-dimensional fitness function, \(F=\{F(1),F(2),F(3)\}\). Each dimension corresponded to an objective that needed to be _minimized_. Equations (8)-(10) define the fitness function to be minimized. \[F(1)=\left|B_{m}^{\prime}\right| \tag{8}\]  
\[F(2)=\left|K^{\prime}\right|\!,\ K^{\prime}=\left\{k\in K\!\left|N_{RB,k} \to 0\right\}\right. \tag{9}\]  
\[F(3)=\sum_{g\in G^{\prime}}\left\{\sum_{k\in K_{g}}N_{RB,k}-RB_{max}\right\} \tag{10}\]  
The first objective, \(F(1)\), corresponds to the weighted network cost, the second, \(F(2)\), is the total number of CNs that do not meet their requirements, either capacity or coverage, while \(F(3)\) is the excess RBs needed at a network level. The NSGA-II algorithm imitates evolutionary mechanisms and employs biological operations found in nature for generating optimal solutions. It starts with a random selection of an initial population (sets of microsites) and by iteratively using operators such as selection, evaluation and crossover or mutation evolves into optimal solutions.