# Towards an Efficient Method for Large-Scale Wi-SUN-Enabled AMI Network Planning
## 4 Proposed Method
### AIDA Method
#### 4.4.5 Step 5--SM Clustering  
This step refers to grouping SMs to a particular candidate position. In this process, LRP values calculated in the previous step are evaluated, as are the maximum accepted connections of the CPs (the maximum amount of SMs that can be connected to a CP). A connection can be established if the minimum LRP (\(l_{min}\)) is computed for an \(SM\Leftrightarrow CP\) link.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Description** \\ \hline \(\mathcal{V}=\{v_{1},\ldots,v_{u}\}\) & Set of smart meters, \(v_{i}\) \\ \hline \(\mathcal{C}=\{c_{1},\ldots,c_{z}\}\) & Set of CPs, \(c_{j}\), where \(c_{j}=<c_{j}^{t},c_{j}^{t}>\) \\ \hline \(c_{j}^{n}\) & Number of SMs connected to \(c_{j}\) \\ \hline \(c_{j}^{r}\) & Communication range of \(c_{j}\) \\ \hline \(\mathcal{L}\) & Set of LRP values, \(l_{v_{i},c_{j}}\), for links \(v_{i}\leftrightarrow c_{j}\) \\ \hline \(\mathcal{V}_{con}\) & Set of SMs connected to CPs, \(<v_{i},c_{j},v_{v_{i},c_{j}}^{max}>\) \\ \hline \(\mathcal{M}\), \(\mathcal{N}\) & Subsets of \(\mathcal{L}\) \\ \hline \(\mathcal{Q}\) & Subset of \(\mathcal{C}\) \\ \hline \(l_{min}\) & Minimum LRP value to establish a connection \\ \hline \(n_{max}\) & Maximum number of SMs per CP device \\ \hline \(dist(v_{i},c_{j})\) & Distance between SM \(v_{i}\) and CP \(c_{j}\) \\ \hline \(c_{s}\) & CP selected to connect an SM \(v_{i}\) \\ \hline \(n_{v}\) & Counter of \(v_{i}\) in the range of a CP \(c_{j}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Input and output parameters of the algorithms.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Description** \\ \hline Wi-SUN operating frequency & 920 MHz \\ \hline Smart meter transmission power (\(P_{tx}\)) & 26 dBm \\ \hline Smart meter antenna gain (\(G_{tx}\)) & 2 dBi \\ \hline Smart meter antenna height & 1.5 m \\ \hline Gateway/router antenna gain (\(G_{rx}\)) & 6.25 dBi \\ \hline Gateway/router antenna height & 7 m \\ \hline Gateway/router communication range & 3000 m \\ \hline Gateway/router maximum connections (\(n_{max}\)) & 2000 \\ \hline Minimum distance between Poles and DA Poles & 1000 m \\ \hline Minimum LRP to establish a connection (\(l_{min}\)) & \(-95\) dBm \\ \hline Stopping criteria & \(p_{u}^{max}=2\%\) \\ \hline Maximum number of hops (\(h_{max}\)) & 7 \\ \hline High-quality (HQ) link criteria & LRP \(\geq-95\) dBm \\ \hline Medium-quality (MQ) link criteria & \(-105\leq\) LRP \(<-95\) dBm \\ \hline Low-quality (LQ) link criteria & LRP \(<-105\) dBm \\ \hline \hline \end{tabular}
\end{table}
Table 3: Equipment and method parameters.  
Two heuristic approaches are evaluated for clustering: bottom-up and top-down. At each iteration of AIDA, both approaches are executed, and the one that results in the smallest number of CPs will be taken as the basis for defining the list of SMs and poles for the next iteration. Both approaches aimed to reach the objectives expressed by the objective functions (1), (2), (4) and (5).  
The clustering approaches are described as follows (see Table 2 for their input and output parameters):  
* Bottom-Up Approach (BU): In this approach (Algorithm 1), an exhaustive search strategy is used to evaluate the LRP values calculated for the link between each smart meter and the CPs in their range. An \(SM\Leftrightarrow CP\) connection is established with the position with the highest LRP value. This aims to maximize the LRP value between the smart meter and the router/gateway to which it will be connected.
* Top-Down Approach (TD): In this approach (Algorithm 2), a greedy search strategy is used to connect the maximum number of SMs to each CP, presenting \(LRP\geq l_{min}\), prioritizing the connection to the SMs with higher values of received power. This aims to maximize the use of the CP, connecting to it as many meters as possible, limited to \(n_{max}\) (see Table 2).