# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 4 Performance Evaluation
### Simulation Results and Analysis
This is due to the fact that a FCH shares the majority of the data collection and data aggregation for its MCH. Therefore, the energy consumption is more balanced in the ICV-MIMO scheme than that in any of the three CMIMO schemes. Also, Figure 4 reveals that a smaller clustering range leads to a longer network lifetime among the three CMIMO schemes. This is because there is the smaller load of data collection and data aggregation in the smaller cluster, and thus the total energy consumption for data collection and data aggregation is distributed on the more CHs, which better alleviates the overhead of individual CH. Although a cluster may forward the aggregated data for the more other clusters as the number of clusters increases, there is not any load for any FCH. However, some MCHs need to take the more loads. Usually, a MCH has an advantage over its corresponding FCH in terms of the energy since it is first elected, and also  
Figure 3: Average path hop-count to sink for the four schemes under the different number of nodes. the forwarded data is reduced greatly due to aggregation, so a MCH lifetime will not be affected significantly, which is usually longer than that of its corresponding FCH. Figure 5 shows that the four schemes can ensure network connectivity under the parameters of the first group of simulations. This is because these parameters ensure the clustering ranges of the four schemes are sufficiently small, which does not have impact on network connectivity. For the CMIMO scheme, if the clustering range is set too large, the network connectivity ratio may be less than 100%. The main reasons are as follows. First, the larger clustering range needs the larger average inter-cluster transmission range to ensure inter-cluster connection, that is, the elected MCH communicating with neighboring MCH depends on a greater transmission ability with a larger clustering range, otherwise it disconnects. Second, the CMIMO scheme elects a MCH only according to RBLs of nodes, and thus the elected MCH may have the highest RBL value but the smallest transmission range, which may make a sending source MCH not to find any path to the sink in inter-cluster transmission period. Third, the larger clustering range leads to the higher probability that the nodes with very small transmission ranges cannot communicate with the CHs when they are located in the edge of the cluster in intra-cluster transmission period. Figure 4: Network lifetime for the four schemes under the different number of nodes. Figure 5: Network connectivity ratio for the four schemes under the different number of nodes. Since the clustering range is assigned before the execution of the CMIMO scheme, the above cases may occur due to the lack of network information (e.g., the distribution of nodes' maximum transmission ranges). In the ICV-MIMO scheme, the above cases do not occur since the clustering ranges are determined automatically through the mutual exchange of messages. Figures 6 and 7 illustrate that the ICV-MIMO scheme outperforms the three CMIMO schemes in terms of average path delay while it is not superior to them with respect to average packet delivery ratio. Since the three CMIMO schemes employ the same transmission power in in intra-cluster transmission period, when this transmission power ensures that the bit error rate of any link between any cluster member located at the edge of the cluster and the cluster head is not greater than a predefined value (e.g., \(10^{-5}\)), the bit error rate of any link between any cluster member near the cluster head and the cluster head will be less than this predefined value. Also, for each inter-cluster link, the bit error rate can be ensured to be the same by adjusting inter-cluster transmission power in the four schemes. Therefore, the ICV-MIMO scheme achieves a greater improvement of energy efficiency at the cost of the slight performance degradation in terms of average packet delivery ratio.