Serial distributed detection for wireless sensor networks with sensor failure
 Junhai Luo^{1}Email author and
 Zuoting Liu^{1}
https://doi.org/10.1186/s1363801709116
© The Author(s) 2017
Received: 20 January 2016
Accepted: 30 June 2017
Published: 14 July 2017
Abstract
We study serial distributed detection and fusion over noisy channels in wireless sensor networks (WSNs) with bathtubshaped failure (BSF) rate of the sensors in this paper. In the previous work, we applied BSF rate to parallel topology and derived the Extension Loglikelihood Ration Test (ELRT) rule. Although ELRT is superior to traditional fusion rule without considering failed sensors, the detection performance decreases noticeably in the presence of a large number of failed sensors. In this paper, we construct a serial topology based on the target radiation energy attenuation model, apply BSF rate to serial topology, and derive the corresponding fusion rule. Unlike the parallel fusion, where the local sensors send their decisions to the Global Fusion Center (GFC) in the region of interest (ROI) directly, sensors in the serial topology transmit local decisions through multihop, shortrange communications. At the same time, we extend ELRT to noisy channels. Finally, simulation results prove the effectiveness of the proposed fusion rules.
Keywords
Serial distributed detection bathtubshaped failure rate failed sensors1 Introduction
WSNs have attracted many researchers in various disciplines due to their flexibility, robustness, mobility, and costeffectiveness. A major application of WSNs is target detection. WSN typically consists of a vast number of small, inexpensive, and lowpowered sensors, which are deployed in the ROI to obtain and preprocess the received observation. The GFC is making a final decision about whether the target is present or not. There are two popular detection methods: centralized detection and distributed detection. In the centralized detection, the local sensor sends the received observation to the GFC directly without any processing. In the distributed detection, each sensor quantifies its observation into a local decision (“0” or “1”) and sends it to the GFC. Although centralized detection achieves the highest performance, it is at the cost of more bandwidth and communication energy to obtain realtime results. Thus, the distributed detection is often preferable in these situations.
Distributed target detection has been extensively studied in many kinds of literature. In [1, 2], each sensor made a local decision by conducting likelihood ratio test and sent the local decision to the GFC to perform global loglikelihood ratio test, and then the GFC made a final decision. In [3], a uniformly most powerful (UMP) detector based on likelihood ratio test was developed, and an elegant test for target presence or absence was also derived. Typically, the performance of local sensors is hard to calculate. Therefore, in [4], a suboptimal fusion rule requiring less prior information was proposed, which we refer to as the counting rule (CR). CR employed the total number of decisions transmitted from local sensors for hypothesis testing at the GFC. In [5], CR was extended to the case where the total number of sensors was uncertain. Authors in [6–9] took into account imperfect communication channels between the sensors and the GFC, such as additive white Gaussian noise (AWGN) channels and fading channels. In [6], noisy communication links were considered and a Bayesian framework for distributed detection was presented, where noisy links were modeled as binary symmetric channels (BSC). In [7], distributed detection fusion in hierarchical WSNs was investigated in the presence of fading and noise, two fusion rules were derived accordingly, one utilized the complete fading channel state information (CSI), the other utilized the channel envelope statistics (CS). For resourceconstrained sensor networks, a fusion rule using CSI was more preferable. Typically, local sensors communicated with the GFC directly. In [10], authors considered the case where local decisions need to be relayed through the multihop transmission to reach the GFC and also took fading into account. In [11], based on various decisions from local sensors, a decision rule was derived in the case of unknown probability distributions. In [12, 13], decision fusion rules with unknown detection probability were investigated. Clusteringbased decision fusion algorithms and fusion rules for distributed target detection in WSNs were studied in [14–16].
The structure of the WSNs can be classified into three categories: parallel topology, serial topology, and tree topology. Most researchers focus on parallel distributed detection. However, sensors are usually powered by a battery, so the energy and the communication range are limited. When sensors are far away from the GFC, the power consumption increases dramatically and the lifetime of the WSN has shortened accordingly. In [17, 18], serial distributed detection was investigated, where local decisions are transmitted to the GFC through shortrange and multihop communication. The channel between two adjacent sensors was modeled as BSC. However, authors in [17] assumed the received energy emitted by the target at the local sensors was a deterministic value. In this case, the detection performances of the local sensors were similar.
The most common practice of traditional fusion rules, such as CR and ChairVarshney fusion rules, is to employ all sensors in the ROI to derive a final decision. However, the signal emitted by the target often decays as the distance from the target increases. Sensors far away from the target make little contribution to the final decision at the GFC or are more likely to make a false judgment in the presence of background noise. In this paper, we simply employ sensors around the target to make the final decision.
We propose a new serial topology reconstruction method, where decisions are transmitted from sensors with lower credibility to sensors with higher credibility. Assuming the transmission channels were ideal, we applied a BSF rate of the sensor into the parallel structure and proposed ELRT in [19]. In this paper, we solve the problem when there are failed sensors in the serial structure and propose the corresponding fusion rule over noisy channels which we call serial rule (SR). In order to demonstrate the more stable detection performance of the serial structure, we also extend ELRT to noisy channels and derive the corresponding fusion rule in the same scenario which we call parallel rule (PR).
The remainder of this paper is organized as follows. In Section 2, the BSF rate of the sensor is described. In Section 3, a sensor deployment model is described. In Section 4, a detection system model is described. In Section 5, the fusion rules of the serial and parallel structure are derived. In Section 5, the performance of the proposed fusion rules is provided through simulation. In Section 6, conclusions are drawn.
2 BSF rate
where a and b are related with life data of the products and h _{0} is a worthy constant adding to the failure rate function.

Normal sensors, sensors that can detect and transmit decision reliably

Partially disable sensors, sensors that are still operable, but have poor detection capability

Inoperable sensors, sensors which no longer function at all

Failed sensors, the group of sensors consisting of the combination of the partially disable and the inoperable sensors
where ceil(·) denotes the ceiling function.
where s is the number of the partially disable sensors at time t, it is easy to note that p _{ i } is constant at time t and Pr(R _{ i }=1)=1−p _{ i }. We use p which denotes Pr(R _{ i }=0) in the latter sections.
3 Sensor deployment model
where P _{0} is the signal power from the target at a reference distance D _{0} and D _{ i } represents the Euclidean distance between the target and sensor s _{ i }. The signal attenuation exponent γ ranges from 2 to 3.
The radiation energy of the target can be assumed as a series of concentric circles centered at the target. In this paper, we set the interval between two adjacent circles identical. Sensors lying in the same circular ring possess similar signaltonoise ratio (SNR) and decision credibility, and the circular ring interval is 10. Due to the fast attenuation of the target radiation energy, we consider the circular area of the radius of 40 centered at the target in this paper. Firstly, sensors in the same circular ring form a serial fragment, then all fragments form the whole serial topology from the outside to the inside. We can see that decisions are transmitted from sensors with lower credibility to sensors with higher credibility in this serial structure, so the final decision at the last sensor of the serial structure possesses the highest credibility.
4 System model description
H _{0} and H _{1} denote the absence and the presence of the target to be detected respectively. M ^{′} is the number of sensors in the serial topology at time t. y _{ i } is the signal received by sensor s _{ i }, and n _{ i } is the noise observed by sensor s _{ i }. In this paper, we assume that noises at the local sensors are independent identically distributed (i.i.d.) and follow the standard Gaussian distribution, i.e, n _{ i }∼N(0,1).
In Fig. 4, v _{ i } denotes the decision made by sensor s _{ i }, and u _{ i } denotes the bit received by sensor s _{ i+1} which may differ from v _{ i }. Sensor s _{1} to \({s_{M^{\prime }}}\) cooperatively determine whether the target is present or not in the ROI. Sensor \({s_{M^{\prime }}}\) is the fusion center (FC) of the serial structure at time t. Because we apply BSF to the serial structure, \({s_{M^{\prime }}}\) may be a partially disable sensor. If \({s_{M^{\prime }}}\) is a partially disable sensor, the final decision is not reliable. In this paper, we let sensor \({s_{M^{\prime }}}\) transmits its observation to the GFC, then the GFC replaces sensor \({s_{M^{\prime }}}\) and serves as the FC of the serial structure. In this way, the M ^{′}th sensor of the serial structure in Fig. 4 is actually the GFC at time t.
5 SR and PR
5.1 SR
5.2 PR
6 Performance analysis
We use the Matlab simulator to evaluate the performance of the proposed fusion rules in this paper, and 10^{4} Monte Carlo runs are used in each simulation. The objective is to demonstrate that serial structure has more stable detection performance than the parallel structure in the presence of a vast number of failed sensors. In [19], we studied the parallel distributed detection applying BSF rate of the sensor over ideal channels and proposed ELRT rule. Simulations demonstrated that ELRT outperformed ChairVarshney rule in the presence of failed sensors. In this paper, we apply BSF to the serial structure over noisy channels and also extend ELRT to noisy channels, because sensors far away from the target make little contributions to the final decision at the GFC and are more likely to make wrong decisions in the presence of background noise. Thus, we consider sensors within the circular area centered at the target in this paper, the deployment in the presence of failed sensors is presented in Fig. 2. The fusion rules of the serial and parallel are given in the previous sections.
7 Conclusions
This paper investigates distributed decision fusion of serial structure in the presence of failed sensors over noisy channels. Previous literature focus on serial structure usually assumes the signal received by the local sensor is identical. While in this paper we construct a serial topology based on isotropic attenuation power model, the local decision in this topology is transmitted from sensors with lower credibility to sensors with higher credibility. We also derive the corresponding fusion rule. For comparison, we extend ELRT to noisy channels in the same scenario. Simulations show that serial is more robust than parallel in the presence of a large number of failed sensor over noisy channels. The deployment we considered in this paper is relatively ideal, we will study different deployment in the future.
Declarations
Acknowledgements
This work was supported in part by the Overseas Academic Training Funds, University of Electronic Science and Technology of China (OATF, UESTC) (Grant No. 201506075013), and the Program for Science and Technology Support in Sichuan Province (Grant nos. 2014GZ0100 and 2016GZ0088).
Authors’ contributions
JL conceived of and designed the research. JL and ZL performed the experiments and analyzed the result. JL and ZL wrote the paper. Both authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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