# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 1 Introduction  
The Multi-Input Multi-Output (MIMO) technique can boost network throughput, conserve energy, and improve network coverage, which has been supported by various international standards such as 3 rd Generation Partnership Project Long Term Evolution (3 GPP LTE), LTE Advanced (LTE-A), the next or fifth generation (5G) cellular networks and IEEE 802.16e and IEEE 802.16m. However, each wireless device has to be equipped with multiple antennas to exploit the benefits of MIMO. Due to the high hardware complexity and cost, implementation of multiple transmitting antennas sometimes cannot be available, especially in small wireless devices (e.g., sensors). Cooperative MIMO emulates the functionality of multi-antenna systems by grouping wireless devices to operate as virtual multi-antenna nodes [1], which is also called Virtual MIMO (VMIMO). It is desirable for single-antenna devices to take advantage of MIMO gains efficiently, which enables one to make use of all the neighboring terminals and amortize the cost of multiple antennas. There are four transmission modes in VMIMO systems, that is, Single-Input Single-Output (SISO), Single-Input Multi-Output (SIMO), Multi-Input Single-Output (MISO), and Multi-Input Multi-Output (MIMO) [2, 3]. Some typical works take full advantage of these four transmission modes, for example, the Clustering and Cooperative Protocol (CCP) [2] and the Cooperative MIMO(CMIMO) [3]. The MIMO mode of the CMIMO is limited to 2 \(\times\) 2 mode, while that of the CCP is not limited. The authors in [4] have drawn two conclusions: First, the SIMO mode, MISO mode and MIMO mode are more energy-efficient compared with the SISO mode. Second, in many cases, the 2 \(\times\) 2 (MIMO) mode is much more energy-efficient than 1 \(\times\) 1 (SISO) mode, 3 \(\times\) 3 (MIMO) mode and 4 \(\times\) 4 (MIMO) mode. If more nodes cooperate in the VMIMO transmission, it will be very difficult to achieve accurate time synchronization among these cooperative nodes and implement the efficient management of these nodes [5]. Therefore, it is a suitable to limit the number of cooperative nodes to two. In the existing works that fully explore the benefits of VMIMO, there are still some problems. First, a node's transmission capability is not considered in a cluster head selection criteria, which may lead to the node with low transmission capability to be elected as the cluster head. Second, all the cluster members employ the same transmission power when they communicate with their cluster heads, which should be adjusted adaptively according to the distances from them to their cluster heads. Third, the burden of a master cluster head is too heavy since it is responsible for aggregating data sent by other nodes in its cluster and exchanging these data with its slave cluster head besides executing inter-cluster communications and acting as a beacon cluster head. Fourth, a clustering range needs to be set in advance, where the specified value may be inappropriate since it is impossible to know all the nodes' transmission capability in advance. In this paper, we address these problems, and propose an improved clustering scheme for Virtual MIMO-based topology construction (ICV-MIMO), which can determine adaptively not only the inter-cluster transmission modes but also the clustering ranges. Our main contributions are as follows. First, we consider both nodes' Remaining Battery Lifetimes (RBLs) and nodes' approximate maximum transmission range to build the new cluster head selection criterions. Second, we propose an algorithm to optimize a transmission power of each cluster member. Third, we add a data fusion cluster head to amortize the cooperation overhead of a master cluster head, which does not involves more clustering overhead than the CMIMO since the added cluster head selection is integrated into the confirmation process of cluster membership.