# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 4 Performance Evaluation
### Simulation Metrics and Deployment Settings  
Our metrics are as follows: (a) the average transmission power for the cluster members in all the clusters of the network. The metric is computed by \(p_{av}=\frac{1}{|N|}\sum_{i\in N}p_{i}^{t}\), where \(N\) and \(\left\lvert N\right\rvert\) are the _set_ of the cluster members in all the clusters and the number of these cluster members respectively, and \(p^{t}_{i}\) is the transmission power from any cluster member \(i\) to its FCH. (b) The average inter-cluster path hop-count for all the paths from the MCHs/SCHs to the sink. The metric is obtained by \(h_{av}=\frac{1}{|M|}\sum_{i\in M}h_{x}\), where \(M\) and \(\left\lvert M\right\rvert\) are the cluster _set_ and the number of clusters in the network respectively, and \(h_{x}\) is the inter-cluster path hop-count for the path from the MCH/SCH (in the cluster \(x\)) to the sink. In the ICV-MIMO scheme, each cluster member first transmits its data to the FCH, and then the FCH broadcasts the aggregated data to the MCH/SCH. Next, the inter-cluster transmission begins. In the three CMIMO schemes, each cluster member first transmits its data to the MCH, and the data aggregated in the MCH is then sent to the SCH, which is followed by the inter-cluster transmission. Therefore, in the four schemes, the average path hop-count for all the paths from the cluster members to the sink is obtained by \(h_{av}+2\). (c) The network lifetime. After the virtual MIMO-based topology is constructed, each cluster member is allowed to send a data packet in a round (i.e., a fixed time). A FCH aggregates all the data packets from the cluster members in its cluster into one data packet, and then sends it to the MCH/SCH in its cluster. The MCH/SCH will forward it to the sink (in the manner of one-hop or multi-hop) through inter-cluster communications. In our simulation, the network lifetime is defined as the first death of MCHs in the network since the death of any MCH destroys the network topology. If a FCH or SCH first dies, the MCH in its cluster takes over its job, and thus the cluster structure has not been destroyed. When the first death of MCHs occurs, the number of sending rounds denotes the lifetime of the network. (d) The network connectivity ratio. The metric is the ratio of the number of nodes connected to virtual MIMO-based topology to the number of total nodes. (e) The average path delay for all the paths from the cluster members to the sink. The metric is computed by the formula \(t_{av}=\frac{1}{|N|}\sum_{i\in N}t_{i}\), where \(t_{i}\) is the end-to-end delay of the path from the cluster member \(i\) to the sink. (f) The average packet delivery ratio for all the paths from the cluster members to the sink. The metric is obtained by the formula \(d_{av}=\frac{1}{|N|}\sum_{i\in N}d_{i}\), where \(d_{i}\) is the packet delivery ratio of the path from the cluster member \(i\) to the sink, which is defined as the ratio of the number of delivereddata packet to the destination from the cluster member \(i\) and the number of data packet sent by the same source to the same destination. The wireless sensor nodes are randomly deployed in a square of length 1000 m. The sink is located to the right of the square, at a horizontal distance of 500 m and a vertical distance of 0 m from the center of the field. Without impacting all comparison objects based on the same assumptions, the parameter values used in our simulation are listed in Table 2, where we determine the ranges for these parameters based on the ranges of related simulation parameters in [1; 2; 3; 8; 27; 28; 29]. The simulation experiments are carried out by using OMNeT++ 4.1 network simulator [33]. In the simulation settings, each node (e.g., node \(i\)) employs \(f\left(\gamma_{i,j}\right)=\left(1-e^{-0.5\gamma_{i,j}}\right)^{M}\) in [34] to estimate