Wireless Communications and Mobile Computing

Volume 2018, Article ID 5131949, 12 pages

https://doi.org/10.1155/2018/5131949

## CS-PLM: Compressive Sensing Data Gathering Algorithm Based on Packet Loss Matching in Sensor Networks

^{1}School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China^{2}Department of Computer Science and Technology, Xi’an Jiaotong University, Xi’an, China^{3}Department of Mathematics and Computer Science, Northeastern State University, USA

Correspondence should be addressed to Rong Tao; moc.361@654321_gnoroat

Received 9 April 2018; Accepted 4 July 2018; Published 5 August 2018

Academic Editor: Dajana Cassioli

Copyright © 2018 Zeyu Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The data transmission process in Wireless Sensor Networks (WSNs) often experiences errors and packet losses due to the environmental interference. In order to address this problem, we propose a Compressive Sensing data gathering algorithm based on Packet Loss Matching (CS-PLM). It is proven that, under tree routing, the packet loss on communication links would severely undermine the data reconstruction accuracy in Compressive Sensing (CS) based data gathering process. It is further pointed out that the packet loss in CS based data gathering exhibits the correlation effect. Meanwhile, we design a sparse observation matrix based on packet loss matching and verify that the designed matrix satisfies the Restricted Isometry Property (RIP) with a probability arbitrarily close to 1. Therefore, reliable transmission of the compressed data can be guaranteed by adopting the multipath backup routing among CS nodes. It is shown in the simulation results that, with a 60% packet loss ratio of the link, the CS-PLM algorithm can still ensure the effective reconstruction of the data gathered by the CS algorithm and the relative reconstruction error is lower than 5%. Therefore, it is verified that the proposed algorithm could effectively alleviate the sensitivity to packet losses for the CS based data gathering algorithm on unreliable links.

#### 1. Introduction

The nodes in the wireless sensor networks (WSNs) are usually densely deployed and a lot of redundancy exists in the data gathered, which leads to the waste of the energy of the nodes. The compressive sensing (CS) algorithm is a new technique which could largely reduce the sampling frequency and execute the sampling process in parallel with the compression process. As a result, this technique has drawn much attention by researchers.

In order to balance and reduce the energy consumption of the nodes as well as prolong the network lifetime, researchers have proposed data gathering algorithms based on compressed sensing. At present, most of these algorithms are focused on how to effectively reduce network energy consumption and extend the network lifetime [1–3]. For example, it was proposed in paper [4] to employ sparse measurement matrices to reduce the communication cost of each measurement. The spatial and temporal correlation of the sensing data was exploited in [5] to improve the compression ratio and further reduce the number of measurements. A multilevel hierarchical clustering topology was employed in [6] to gather the data in the network as well as reduce the number of sent and received packets at each layer of nodes. As a result, the total number of transmitted packets is reduced in the entire network. It was pointed out in [7] that the block diagonal measurement matrix could guarantee the reconstruction accuracy with a smaller number of measurements and a longer network lifetime. In recent years, with the progress in the theory of CS, researchers have started to investigate CS based data gathering algorithms for practical applications. The fact was considered in [8] that the data sparsity in realistic data sets would vary with time and space. Therefore, it was proposed to employ the autoregressive AR model to predict data changes and adaptively adjust the number of measurements to achieve the optimal reconstruction performance. It was pointed out in [9] that the environmental noise of the wireless links imposes prominent influences on the transmission of the undersampled CS data in the network. An approximate gradient descending algorithm was therefore proposed to reconstruct the compressed data under the influence of noise. For the TF-packet loss problem of wireless links in practical application scenarios, there are relatively few works studying CS based data gathering algorithms. Due to the dynamic and asymmetry of wireless links, channel interference, improper antenna direction and height, etc., unreliable links are often the key issue faced by data gathering algorithms in practical sensor networks [10].

For the CS based data gathering problem on unreliable links, we propose a compressive sensing data gathering algorithm based on packet loss matching (CS-PLM). In this algorithm, the nodes in the network are divided into two types, i.e., the traditional forwarding (TF) nodes and the compressive sensing (CS) nodes. The packet loss of TF nodes does not exhibit the correlation while the lost packets of CS nodes are strongly correlated. In the process of the Compressive Sensing data gathering, a packet loss will lead to the loss of the data gathered from multiple nodes; the packet loss correlation effect is caused by the superimposed transmission of the collected data from each node of the multihop link in the CS compression sampling process. The closer the packet loss node is to Sink, the greater the effect of packet loss is. In particular, if the packet of the next-hop neighbor node of Sink is lost, the correlation effect will result in the loss of data collected by some nodes of the whole network. While TF nodes only relay data in the traditional way of data gathering, packet loss has no correlation. As a result, we design a sparse measurement matrix based on the packet loss matching to recover the gathered data if packet losses occur at TF nodes. Therefore, the recovery problem for lost packets is transformed into the sparse matching sampling process in CS. However, for the lost packets at CS nodes, we design the multipath backup transmission scheme to guarantee the reliable data transmission and avoid the correlation effect for packet loss. Therefore, the impacts of unreliable links are alleviated for the CS based data gathering process and the reconstruction accuracy is guaranteed.

The main contributions of this paper are as follows.

①By analyzing the routing with tree structure, it is pointed out that the packet loss would seriously undermine the reconstruction accuracy of the CS based data gathering process and the packet loss in the CS based data gathering process exhibits the correlation effect.

②We design a SPLM measurement matrix and further prove that this matrix satisfies the Restricted Isometry Property (RIP) with a probability arbitrarily close to 1.

③We propose a multipath backup routing transmission scheme based on Hybrid CS to guarantee the reliable handover of the CS projection data.

#### 2. Related Works

Due to its feature of simple encoding and complex decoding, compressed sensing theory has been widely applied to the area of data collection in WSNs. At present, the research of CS based data collection algorithms in wireless sensor networks mainly focuses on how to use CS technology to reduce the network energy consumption of the data gathering process in WSNs. Most of these works assume that the network link is an ideal link where the impact of packet loss on the CS based data gathering process is ignored. The number of transmitted data packets was presented in paper [11] under the tree topology with and without CS based data gathering algorithm. Furthermore, a hybrid CS based data gathering method was proposed which combines the conventional relay based data gathering method with the CS based data gathering method. It was shown that the network energy consumption could be further reduced by less transmitted data packets in the proposed protocol.

The application of CS was investigated in [2, 12] under the clustering routing structure. Since single-hop transmission is employed in the clustering topology, the packet loss on the links does not exhibit the correlation. As a result, the CS based data gathering algorithm is insensitive to the packet loss on the links. A CS based data gathering algorithm was proposed in [13] for unreliable links under the cluster topology where the column vectors of the measurement matrix are adjusted according to the packet loss nodes in the cluster. Therefore, the influence of packet loss on CS based data reconstruction can be alleviated. The tree-like multihop network routing topology is often used for large-scale WSNs. The CS based data gathering algorithm with multihop routing is studied in paper [14, 15], where the unreliability of the wireless link was ignored while special attention was paid to the optimal matching between the measurement matrix in CS and the structure of the tree-like routing topology. However, the transmission of CS data packets under the multihop routing requires the weighted superposition of the data from multiple nodes. Multiple original data can be lost once one packet loss occurs. Therefore, the transmission of CS data packets is highly sensitive to the packet loss under the multiple-hop routing.

It was shown via simulations in [16–18] that the data reconstruction accuracy under the tree topology can be seriously affected by the packet losses on the link and the Sparsest Random Scheduling (SRS) was further proposed for CS based data gathering in lossy WSNs. In this protocol, a sparsest measurement matrix is constructed according to the reception condition at the Sink end, which is further employed to reconstruct the original sensing data for all the nodes in the network and alleviate the influence of packet losses on CS data reconstruction [19–22]. However, this algorithm is only limited to the application scenarios where the spatial correlation of the sensing data in the network is relatively strong.

There are other data gathering methods in conventional WSNs such as ARQ, multipath transmission, network coding, etc. However, there are relatively few works studying the reliable CS based data gathering algorithm in WSNs. Furthermore, the CS based data gathering algorithm is much more sensitive to packet losses than conventional methods. Therefore, the study of CS based data gathering algorithm on unreliable links is quite meaningful to the application of CS theory in practical scenarios.

In wireless sensor network, serious packet loss will undermine the communication performance, service quality, and application effect of sensor network. In recent years, the research premise of the CS based data gathering theory is the ideal link, and, because of the dynamic characteristics of the wireless link, channel interference and asymmetry of conflict, the wrong direction, and height of antenna, the unreliable link issues are commonly encountered in practical applications. There are many methods to ensure the reliable transmission of links in the traditional data gathering methods of wireless sensor networks, but to the best of our knowledge, there is little work for reliable sensor network data gathering method based on compression perception. In addition, the sensitivity of the CS data gathering method to link packet loss is much higher than that of traditional data gathering, so the research on compressed sensing data gathering algorithm under unreliable link is of great significance to the application of compressed sensing technology in real sensor network.

#### 3. Network Model and Problem Description

The CS is a new technique which samples the sparse signal with a frequency below the Nyquist sampling frequency and achieves the projective transformation of the target signal from a high-dimension space to a low-dimension one. The accurate reconstruction of the compressed signal is achieved via the optimal reconstruction algorithm which is widely studied and applied in many areas due to its excellent compression performance.

Assume that nodes are randomly deployed in the WSN and the gathered data is denoted as . Assuming that is sparse with respect to base and the measurement matrix is , The received vector can be expressed as *. *The Sink node can reconstruct the original data with certain accuracy by solving the optimization problem in the following:

where is the sensing matrix and is the norm of the sensing data vector which is defined as

In the data gathering process of WSNs, each round of CS based data gathering is performed with times of independent measurements, which is expressed as follows:

Assume that ordinary sensor nodes and one immobile Sink node are deployed in the WSN. All the sensor nodes are uniformly and randomly deployed with fixed locations in a monitoring area of size* a*×*a*. The Sink node is at the center of the monitoring area while the sensor nodes periodically gather and transmit the sensing data to the Sink node. Furthermore, the transmission power of the sensor nodes can be adjusted dynamically and adaptively. The Sink node is assumed with strong computation capability so that it can periodically gather and reconstruct the sensing data and acquire the location information for all the nodes in the network. The Minimum Spanning Tree (MST) routing is established by all the nodes in the network to perform data gathering, i.e., a connected undirected graph is constructed where is the set of sensor nodes, is the set of links in the MST, and (*q*) indicates that the link is connected with probability . If we set* p*=1-*q*, then p indicates the packet loss ratio of the link. In addition, the CS technique is employed for data gathering in the WSN, which exhibits the following features: ① Discrete Fourier Transform (DFT) is employed for the sparse transformation base of the sensing data vector. The sparse transformation and the orthogonal sparse base are presented in (5) and (6), respectively. When measurements are received at the Sink end, we employ the Orthogonal Matching Pursuit (OMP) algorithm to reconstruct the original sensing data. ② The relative error* η* is adopted in (7) as the metric to indicate the CS based reconstruction accuracy and a lower

*means more accurate reconstruction. If the relative error is higher than 5%, the reconstruction is considered as a failure.*

*η*The CS based data gathering process on unreliable links under the tree-like topology is illustrated in Figure 1.