# A Cluster-Based Dual-Adaptive Topology Control Approach in Wireless Sensor Networks
## 2 Related Work  
The authors in [6; 7] employed virtual antenna arrays to obtain diversity and coding gains, where several single-antenna nodes cooperate on information transmission (or reception) to achieve energy-efficient communications. Then, several Virtual MIMO (VMIMO) systems that exploit the diversity gain using the Distributed Space-Time Block Code (DSTBC) for WSNs were proposed. For example, the authors in [8] studied a cooperative MIMO scheme for single-hop transmissions; the author in [9] proposed a cooperative MIMO scheme for delay and channel estimation; the author in [10] analyzed the energy efficiency and training overhead of cooperative MIMO; the authors in [11] considered the incorporation of data aggregation into cooperative MIMO; the authors in [12] investigated a VMIMO for multi-hop transmissions. Differing from the above VMIMO schemes, the author in [13] exploited the multiplexing gain of VMIMO to reduce the cooperation overhead and the circuit energy consumption, which was realized by using the Vertical-Bell Laboratories Layered Space-Time (VBLAST) technique; the authors in [14] optimized MIMO's operation under power and delay constraints by using VBLAST for spatial multiplexing. In addition, some literatures studied the VMIMO configuration for decision fusion. For example, in [15], the array-processing techniques over VMIMO channels were applied to distributed energy detection for decision fusion in WSNs, while a performance analysis of the maximum ratio combining decision fusion rule over MIMO channels was presented in [16]. Also, some other literatures employed a massive MIMO (where antenna arrays are placed at base stations) to improve both spectrum utilization and energy efficiency. For example, the work in [17] studies channel-aware decision fusion over a VMIMO channel, while the literature [18] focused on a massive MIMO-based decentralized estimation within the massive MIMO framework. In all the above-mentioned works, multi-hop communications and clustering for early data aggregation were not taken into consideration, which limits the scalability of these schemes in large WSNs. That is, the data cannot be aggregated in cluster head since planar network architecture is adopted, which is hardly applied to large WSNs. Some works addressed these problems. For example, the authors in [19] proposed the MIMO-LEACH scheme, which extended the LEACH [20] scheme to build a cluster-based cooperative MIMO scheme for multi-hop communications in WSNs. The Basic-CMIMO [21] and the Clustering and Cooperative Protocol (CCP) are the DSTBC-based CMIMO schemes for clustered WSNs. The number of cooperative nodes in each cluster of the Basic-CMIMO is limited to two, whereas the CCP optimizes the number of cooperative nodes in each cluster and selects cooperative nodes so as to minimize the energy imbalance (i.e., the cooperative nodes are selected in such a way that the variance of residual energy is minimized). However, the CCP requires solving the problem of optimal cooperative node selection, which leads to a combinatorial problem of high computational complexity. Thus, to maintain a reasonable computational overhead, the CMIMO limited its treatment to two cluster heads per cluster. Moreover, to minimize the energy consumption, the transmission mode and power of the CMIMO can be different for different hops in inter-cluster communications. The Cluster Head Rotation Cooperative MIMO (CHR-CMIMO) scheme [22] introduced cluster-head rotation, where cluster members rotate to be cluster heads by inner-cluster selection. However, this scheme leads to frequent changes of inter-cluster communication distances. The Group Collaboration MIMO (GCMIMO) [23] proposed the concept of Cooperative Group (CG), where each CG composed by two source nodes sends the source data directly through virtual MIMO link without forwarding data to the cluster head.