# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 3 The Improved Clustering Scheme
### Design Issues of the ICV-MIMO Scheme
When compared with the cluster member association in [3], the Algorithm 4 in this paper increases a FCH selection. However, this election process is integrated into the membership determining process, so it does not increase the running cost. Differing from the CMIMO scheme in [3], in this paper, a power adjustment process has to be executed after a cluster formation. Therefore, we increase the Algorithms 5 and 6. Table 1 presents a comparison of the communication and computational complexities of the ICV-MIMO scheme and the CMIMO scheme. Since \(N_{deg}\) is the number of neighbors at the node's clustering range, it is less than \(N_{nei}\). Therefore, the CMIMO scheme slightly outperforms the ICV-MIMO scheme in terms of both the message overhead and the time complexity. In spite of this, their complexity is still in the same order of magnitude. Then, we discuss the synchronization of the ICV-MIMO scheme. The MCH of the source cluster accesses the medium using CSMA/CA and sends an RTS packet. Upon receiving the RTS, the MCH of the receiving cluster responds with a CTS packet that serves as a synchronization signal for the MCH and SCH in the source cluster, so that they transmit their data simultaneously to achieve MIMO diversity gain. In addition, a FCH also acts as a beacon cluster head to send a synchronization signal, so that its corresponding MCH and SCH start sending the data simultaneously to the CHs of a receiving cluster. Next, we discuss the reclustering issue of the ICV-MIMO scheme. In most cases, a FCH may be the one that deplete its battery first (before MCHs, SCHs and non-CH nodes) because of its great responsibility in aggregating data, sending it to its MCH/SCH. Therefore, the reclustering request to be sent by any FCH is a viable option. The key idea for reclustering is that when the RBL of any FCH falls below a specific threshold (e.g., 10% of its initial value), this FCH sends a reclustering message to its MCH, and this MCH forwards it to its neighboring MCHs at its maximum power level. This message will be heard by the requesting MCH's non-CH nodes, its SCH and FCH, and its neighboring MCHs. Reclustering messages are similar to the hello messages used in the neighborhood discovery process in the cluster-formation phase. Neighboring MCHs that hear a reclustering message relinquish their cluster head role and invoke a neighborhood discovery process. In fact, if the MCHs do not die, the cluster structure is not destroyed. Even if any FCH dies, the corresponding MCH can take over its work. This can effectively extend the heavy reclustering intervals and thus reduce the cost of reclustering. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scheme** & **Message Overhead** & **Time Overhead** \\ \hline ICV-MIMO & \(O(N_{nei})\) & \(max[O(T_{t})\), \(O(N_{nei}\cdot T_{r})]\) \\ CMIMO & \(O(N_{deg})\) & \(max[O(T_{t})\), \(O(N_{deg}\cdot T_{r})]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The overhead comparison between the clustering schemes. Finally, it is worth noting that, the ICV-MIMO scheme only considers large scale fading (i.e., path loss), but ignores small scale fading (e.g., Rayleigh fading). The main reasons are as follows. First, none of very accurate values of maximum transmission ranges is required in our scheme because these values are only regarded as a factor for cluster head election. Therefore, it is enough for us to obtain these values from the same radio propagation formula. And if we take into account small scale fading, our scheme will be more complex and cumbersome. Second, an exact transmission range is hardly obtained at the cost of scheme complexity in the power adjustment process of intra-cluster communications when we consider both large and small scale fading. For a simplified scheme, we only consider a path loss model in our scheme. However, by increasing or decreasing a small real number \(\varepsilon\), a rough power obtained from the path loss model turns to an actual required power, as described in Section 3.3.