When the sink node collected M rounds predicted value, it can recover the original data. It describes the compression efficiency of the entire network. Although compressive sensing technology can effectively reduce the energy consumption of each node in the network, it is directly related to the measurement value M in compressive sensing.

When the value of M is large, the energy consumption of nodes remains high. To solve this problem, a novel hybrid compressive sensing data aggregating method is proposed, which mainly consists of four parts: network clustering, building the appropriate inter-cluster routing tree, compressive sensing data aggregating in clusters, and cluster head transmitting data to the sink node.

How to construct the routing tree and evolve the process of compressive sensing in clusters is shown below. N nodes randomly distribute in a circular perception area the radius is L ; the sink node is at the center of the sensing area as shown in Fig.

The initial energy and the transmission rate of each sensor node are the same. Nodes can know its own location information using the relative locating technology. Lemma 1: Suppose that nodes in the wireless sensor network are distributed randomly, data aggregating in the cluster uses sparse matrices. If the cluster head is at the center of this cluster, then nodes consume least energy for each measurement value aggregating process.

E d i represents the distance expectations from the i th node to its cluster head. Assuming that the network is divided into N c non-overlapping clusters, that means N c nodes are selected as the cluster heads; the other nodes connect to the cluster head near to them.

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We also assume that the node can adjust their own energy levels based on real transmission distance. Eventually, we use the normalized reconstruction error as the CS signal reconstruction error. Hops are forwarded from current cluster head to other cluster head NoH , i. Lemma 2: Suppose that cluster heads forward measurement values along the inter-cluster multi-hop shortest routing tree, so the energy consumption of inter-cluster will reach to the minimum value.

### 1. Introduction

We propose an iterative algorithm to build distributed inter-cluster routing. Assuming that all cluster heads have the same transmission radius R. Within the communication radius, cluster heads can communicate with each other. All cluster heads broadcast the hops from themselves to the sink node to their neighbors. The NoH of cluster head which contains the sink node in their communication radius is set as 1 at the first time of iterating. At the next iteration, these cluster heads broadcast their NoH to their neighbors and set the NoH of those cluster head nodes without NoH to be 2.

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After a series of iterations, it keeps choosing routing path until no cluster head is left. The algorithm can be abbreviated as the following steps:. Each cluster head determinating its position in the seed vector depends on its position on the backbone tree. Step 2: Start from its position in the seed vector, the i th cluster head node traverses forward N i values depends on the number of its intra-cluster nodes N i. Step 4: CHs forward measurement values to the sink node along the generated forwarding path.

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Analysis of P intra-cluster. Theorem 1 Assuming that wireless sensor network is clustering uniformly, the intra-cluster collect data by using compressive sensing technology, sparse matrix is selected as the measurement matrix, cluster head node is at the center of cluster, and inter-cluster forwards data along the shortest multi-hop routing tree.

Then every time in the data aggregating, the total energy consumption of network is minimum. The aforementioned method is used to construct the inter-cluster multi-hop shortest routing tree between cluster heads and the sink node. Each cluster head can get its own NoH.

In the cluster, data is collected by using compressive sensing technology, then we can get M measurement values of the corresponding cluster head. Cluster heads forward M measurement values to the sink node along the inter-cluster multi-hop shortest routing tree. Based on Theorem 1, the total energy consumption of network during the data acquisition is minimum, so as to achieve the best performance; otherwise, we use machine learning approach to reconstruct signal and then ensure that the total energy consumption is minimum.

Detailed machine learning approach can be found in our relative research works [ 7 , 8 , 9 , 10 , 11 ], because of the length limit of the paper, we ignore the detailed description. The sink node recovers the original data by using corresponding reconstruction algorithm. Because the random space sparse matrix can be dynamically generated by a series of seed vectors, the measurement matrix required for the whole network can be determined by the sink node. On one hand, compared with the Gaussian random matrix, it reduces the number of independent variables; on the other hand, it avoids the problem that nodes cannot save the dynamic measurement matrix while routing path changes in the process of conventional hybrid compressive sensing.

This section provides some simulations and evaluations of this proposed data aggregating method. We compare six schemes: a K-means clustering scheme based on random space sparse measurement matrix, b LEACH clustering scheme based on random space sparse measurement matrix, c K-means clustering scheme based on Gaussian measurement matrix, d LEACH clustering scheme based on Gaussian measurement matrix, e K-means clustering scheme without compressive sensing, and f LEACH clustering scheme without compressive sensing. Comparison of tendency of the network lifecycle changes with the number of nodes.

We also deploy nodes, and L is We use our CS data aggregating method and calculate the energy consumption of the entire network. The sink node is set at the center of sensing field. The algorithm can be described as intra-cluster method based on existing methods and the inter-cluster aggregation based on minimum consumption. The common problem in clustering networks which is the energy balancing during the head selection is well considered by the machine learning process.

The WSNs will inevitably use clustering when the node number is large. It is not a fair comparison between the cluster and non-cluster structure in large-scale networks, so we adopt the overhead of normalized network transmission based on the relative weight. From Fig. A kind of effective data aggregating method based on compressive sensing in WSN is proposed.

The method can effectively reduce the energy consumption of the network. The sink node forwards sparse seed to cluster heads. Within a cluster, the cluster head generates its required measurement matrix according to the received sparse seed and then produces the corresponding measurement values by using random space sparse compressive sensing. Cluster heads forward measurement values to the sink node along the inter-cluster multi-hop routing tree from one cluster to another.

The sink node reconstructs the original signal by using the corresponding compressive sensing reconstruction algorithm. We analyze the energy consumption of the algorithm in the network, the relationship between the size of cluster head and the energy consumption of inter-cluster, and the relationship between the size of cluster head and the energy consumption of network. The experimental results show that this method can effectively reduce the energy consumption of the network. TD , major projects of science and technology for their services in Tianjin No. The work is partially supported by the following funding: training plan of Tianjin University Innovation Team No.

D-gZ designed the algorithm. TZ wrote this paper. JZ did the experimental tests. YD optimized the algorithm and experiments. X-dZ checked the whole paper and figures. All authors read and approved the final manuscript. Ozdemir, K. Agrawal, H. Chen, and P. Xu, J. Heidemann, and D. Shang and J. Candes, J. Romberg, and T. Candes and M. Wakin, M. Duarte, S. Sarvotham, D. Baron, and R. Candes and T. Tropp and A.

Duarte and R. Candes and J. Haupt and R. Leinonen and S.

## Coalition Formation Based Compressive Sensing in Wireless Sensor Networks

IEEE Int. Speech Signal Process. Mahmudimanesh, A. Khelil, and N. Li, X.

## Research – Communications and Wireless Networks Lab (CWNlab)

Tao, and Z. Tao, and G. Sign In. Access provided by: anon Sign Out. On the Implementation of Compressive Sensing on Wireless Sensor Network Abstract: Compressive sensing CS is applied to enable real time data transmission in a wireless sensor network by significantly reduce the local computation and sensor data volume that needs to be transmitted over wireless channels to a remote fusion center.

This is accomplished by i random sub-sampling of data collected at sensor node, ii transmitting only the sign-bit of the data samples over wireless channels. It is shown that this CS-WSN framework is capable of delivering similar performance as conventional local data compression method while greatly reduce the data volume and local computation.