# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 4 Performance Evaluation
### Simulation Results and Analysis  
In the first group of simulations, we study the impact of the number of nodes (that is, it is node density since the simulation field is fixed) on the average transmission power, the average path hop-count, the network lifetime, the network connectivity ratio, the average path delay, and the average packet delivery ratio for the ICV-MIMO and the three CMIMO schemes (denoted as CMIMO-S, CMIMO-M, and CMIMO-L). In the ICV-MIMO, \(\mu\), \(w_{e}\) and \(w_{r}\) take 0.33, 0.5 and 0.5 respectively (i.e., \(\mu\)= 0.33, \(w_{e}\) = 0.5 and \(w_{r}\) = 0.5). For the three CMIMO schemes, the difference is only the value of clustering range, where the clustering ranges of CMIMO-S, CMIMO-M, and CMIMO-L take 60 m, 80 m, and 100 m respectively. Figure 2 shows the impact of the number of nodes on the average transmission power. The results illustrate that, in the three CMIMO schemes, the average transmission power is not affected by the number of nodes. This is because all the cluster members in the same cluster employ the same transmission power corresponding to a given clustering range. In the ICV-MIMO scheme, the average transmission power decreases with the number of nodes. This is due to the fact that, when the more nodes are located in the same cluster, the average distance to the cluster head is shorter due to the more cluster members near the cluster head. The average transmission power of ICV-MIMO is significantly lower than that of CMIMO-L. The main reason is that, on the one hand, the average clustering range of ICV-MIMO is smaller than that of CMIMO-L, on the other hand, in the ICV-MIMO scheme, each cluster member's transmission power can be adjusted, which may be smaller than the transmission power corresponding to a given clustering range. When compared to the CMIMO-S scheme, the advantage of ICV-MIMO is obviously reduced. This is because the average clustering range of ICV-MIMO is larger than that of CMIMO-S. The comparison between ICV-MIMO and CMIMO-M should be fairer since the size of the two scheme's  
Figure 2: Average intra-cluster transmission power for the four schemes under the different number of nodes. clustering ranges is very close, where the ICV-MIMO significantly outperforms the CMIMO-M in the average transmission power, and the superiority of ICV-MIMO over CMIMO-M becomes more apparent when the number of nodes is larger. Figure 3 shows that the variations in the number of nodes in the same simulation area lead to slight fluctuations in the average path hop-count. This is because the previous MCH node may be replaced by the new added node with the best MCH eligibility metric, which owns larger or smaller maximum transmission range with the growing number of nodes, and thus there are the small fluctuations in the inter-cluster topology. Also, Figure 3 reveals that a clustering range has the impact on the number of hops between the sending source CHs and the sink. One can observe that the CMIMO-L has the most path hop-count while the CMIMO-S has the smallest one among the three CMIMO schemes. The primary reason is that a smaller clustering range leads to the more number of clusters in the same network (e.g., CMIMO-S), and the number of neighboring MCHs of any MCH tends to increase under the same maximum transmission range. Therefore, a sending source MCH with more neighboring MCHs is more likely to find a shorter path to the sink. As expected, the ICV-MIMO scheme significantly outperforms the three CMIMO schemes in the average path hop-count. The main reason is that the ICV-MIMO scheme considers nodes' maximum transmission range to elect MCHs, and thus has the advantage of coverage over the three CMIMO schemes. Figure 4 compares the network lifetime under the ICV-MIMO scheme and the three CMIMO schemes using a network lifetime definition: the time until the death of the first MCH. From Figure 4, one can observe that the ICV-MIMO scheme results in a longer network lifetime than the three CMIMO schemes.