Cooperative Space Time Coding for Semi Distributed Detection in Wireless Sensor Networks

Cooperative Space Time Coding for Semi Distributed Detection in Wireless Sensor Networks

Mohammad A. Al-Jarrah, Nedal K. Al-Ababneh, Mohammad M. Al-Ibrahim, Rami A. Al-Jarrah
DOI: 10.4018/ijwnbt.2012040101
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Parallel distributed detection in wireless sensor networks (WSNs) is considered in this paper. In parallel architecture, sensors process the observations to make local decisions and send them to a central device called fusion center. Parallel architecture is assumed in this paper with cooperative sensors in order to obtain Alamouti space time block codes (STBCs). A similar idea was discussed by Vosoughi and Ahmadi (2009). Although the likelihood ratio provided in that paper is correct, the simulation results don’t make sense. In this paper, we are going to prove that the results provided in (Vosoughi & Ahmadi, 2009) are not correct. Upper bound for the detection performance is also derived. Furthermore, suboptimal fusion rules are derived to support our results. Moreover, correct results are shown in this paper.
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1. Introduction

In general, a WSN consists of a large number of low-cost and low-power sensors, which are deployed in an environment to collect observations and preprocess them to obtain local decisions. WSNs have different architectures depending on the communication between sensors themselves and\or between the sensors and fusion center. WSNs have attracted much of attention and interest recently, and have become an active research area (Hall & Llinas, 2001; Swami, Zhao, Hong & Tong, 2007; Varshney, 1997; J. Chamberland & V. Veeravalli, 2004). WSNs have wide applications in military surveillance, security, monitoring environment, and cognitive radio networks due to their high flexibility, enhanced surveillance coverage, mobility, and cost effectiveness (Swami, et al.; Varshney, 1997).

Tenny and Sandell (1981) formed the Baysian detection problem for multiple sensor system and derived the optimal fusion rules for the individual sensors. This rule is used at local sensors to process their observations. The fusion center rule that combines the local decisions from sensors while minimizing the overall error probability was derived by Chair and Varshney (1986).

Among various types of WSNs, the decentralized parallel WSN attracted many of authors because each sensor node has a limited communication capability that allows it to communicate with other nodes and/or the fusion center via a wireless channel (Thomopoulos, Viswanathan & Bougoulias, 1987; Kam, Zhu & Gray, 1992; Nageswara, 1995; Rago, Willett & Bar-Shalom, 1996; Drakopoulos, & Lee, 1991). In parallel architecture, sensors communicate with the fusion center. For decentralized option, each sensor processes its observations individually to obtain a local decision to be sent to the fusion center. The fusion center processes all received decisions and declare the final decision about the existed hypothesis.

Furthermore, the optimization of decentralized detection problem, which can be realized by a large number of independent identical sensor nodes, was considered by Tsitsiklis (1988). He proved that it is optimal to have all sensors perform an identical likelihood ratio test in the case of two-hypothesis testing problem. Also, he derived the fusion rule where sensors transmit a finite-valued function of their observations to a fusion center.

In addition, some sensing techniques were proposed to enhance the distributed detection system performance, such as; censoring sensors (Rago, Willett & Bar-Shalom, 1996), and consultation schemes (Thomopoulos & Okello, 1992; Al-Ibrahim & Al-Ababneh, 1998). The problem of non-coherent detection for non-orthogonal multi-pulse modulation in the context of the synchronous multiuser Gaussian channel was investigated by Varasani and Russ (1998).

Distributed detection systems are subject to power and bandwidth constraints (Chamberland and Veeravalli, 2004; Jayaweera, 2005; Jayaweera, 2007; Jayaweera, 2007). From one hand, authors in these papers analyzed the band limited distributed detection system assuming non-orthogonal communication links between the sensors and the fusion center via direct sequence code division multiple access (DS-CDMA) technique. On the other hand, optimal power allocation scheme was derived to optimize the total power consumption in the network.

Moreover, the impact of sensor node density on system performance was demonstrated by Chamberland and Veeravalli (2006). They made asymptotic analysis for two cases using the large deviation theorem results: One case is when the signal is deterministic under each hypothesis, and the other one is when the signal is a correlated Gaussian process under each hypothesis. They proposed a framework that offers a guideline to how dense a sensor network should be, how much power each node should use, and how far apart adjacent nodes should be.

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