## 4 Performance of SERENA and TDMA/CA
### Necessity of Using Exclusively Links of Good Quality  
We first show the necessity of using exclusively links of good quality, both in the association protocol and in the routing protocol. We consider a configuration with 49 nodes and a density of 8. In this configuration, any node received with a power higher than the receiver sensitivity is considered as a one-hop neighbor from the routing point of view and can be used in the association process. We apply SERENA general coloring. Nodes with the same color transmit simultaneously.  
_By definition, a color conflict occurs between two nodes having the same color when these nodes prevent each other or some neighbor destination to receive correctly the intended message because of a collision._  
\begin{table}
\begin{tabular}{c c c} \hline  & Simulation parameter & Value \\ \hline Configuration & Number of nodes & 25–100 \\  & Density & 8–10–12 \\ \hline PHY & Bandwidth & 250 kbps \\  & Transmission range & 11.5 m \\  & Reception threshold & –92 dBm \\  & Sensitivity threshold & –95 dBm \\  & Capture threshold & 5 dBm \\ \hline \end{tabular}
\end{table}
Table 6: Simulation parameters.  
Contrary to what coloring algorithms generally suppose, conflicts still occur for any number of hops considered for color reuse. This is due to interferences received from nodes that could not be detected as neighbors (having a received signal power \(<-92\ dBm\)).  
For instance, let us consider Figure 6(a) that uses the same notation as Figure 3. Node 2 is one-hop neighbor of nodes 0 and 4. Nodes 3 and 13 have the same color and transmit simultaneously. A collision occurs on node 2 between the acknowledgements sent by node 0 to node 3 and by node 4 to node 13. This does not matter since node 2 is not the destination and any destination correctly receives its frame. This is no longer the case with the next example. Nodes 6 and 27 have the same color and transmit data to their one-hop neighbor, nodes1 and 26 respectively. Node 1 that acknowledges node 6, prevents node 26, a two-hop node, to receive correctly from node 27. This is due to the fact that the link between nodes 26 and 27 is of poor quality (-92 dBm) and the signal from node 1 is received by node 26 at -96 dBm.  
More generally, such conflicts can occur with any slot assignment algorithm providing bandwidth spatial reuse based on node neighborhood and using links of bad quality. The explanation comes from the violation of assumption \(A1\) required by such algorithm and among them SERENA. Indeed, node 1, a two-hop neighbor of node 26, prevents the correct reception from a one-hop neighbor. That is why we recommend the following rule:  
_Rule R3: Only links of good quality, where each link node receives the other with a power higher than or equal to the receiver sensitivity plus the capture threshold, are used for routing and association._  
Notice that SERENA considers as one-hop node any node received with a power higher than or equal to the receiver sensitivity, whereas only nodes with a power higher than or equal to the receiver sensitivity plus the capture threshold are used as parent in the association process and as next hop in the routing protocol. When this rule is met, we get a colored configuration without conflict. This has been checked with all the simulations we did. From now on, \(Rule~{}R3\) is assumed to be met, whatever the application considered.