Elsevier

Physical Communication

Volume 13, Part C, December 2014, Pages 244-252
Physical Communication

Full length article
Radar sensor network for target detection using Chernoff information and relative entropy

https://doi.org/10.1016/j.phycom.2014.01.003Get rights and content

Abstract

In this paper, we propose to apply information theory to Ultra wide band (UWB) radar sensor network (RSN) to detect target in foliage environment. Information theoretic algorithms such as Maximum entropy method (MEM) and mutual information are proven methods, that can be applied to data collected by various sensors. However, the complexity of the environment poses uncertainty in fusion center. Chernoff information provides the best error exponent of detection in Bayesian environment. In this paper, we consider the target detection as binary hypothesis testing and use Chernoff information as sensor selection criterion, which significantly reduces the processing load. Another strong information theoretic algorithm, method of types, is applicable to our MEM based target detection algorithm as entropy is dependent on the empirical distribution only. Method of types analyzes the probability of a sequence based on empirical distribution. Based on this, we can find the bound on probability of detection. We also propose to use Relative entropy based processing in the fusion center based on method of types and Chernoff Stein Lemma. We study the required quantization level and number of nodes in gaining the best error exponent. The performance of the algorithms were evaluated, based on real world data.

Introduction

Time varying and rich scattering complex environment of forest makes target detection through foliage an ongoing challenge. In Radar Sensor Network (RSN), multiple distributed radar sensors survey a large area and observe targets from different angles. We can formulate the target detection as a binary hypothesis testing. To apply the Bayesian detection, accurate statistical information is necessary for this decision making problem. However, in many situations of practical interest we do not know the statistics of the probability of the target present or it might be very small. Also the distribution of foliage clutter is important. But it was shown that the foliage clutter behaves dynamically and it is impulsive in nature  [1]. The challenges that are unique for this study are:

  • Foliage clutter is dynamic and impulsive.

  • The prior statistical information about the target presence is unknown.

  • UWB signal shape changes many times during radar viewing. So conventional matched filters or correlators are unsuitable for target detection  [2].

To deal with these problems we performed the data analysis and introduced information based target detection. Radars used in our experiments were mono-static and acted independently. From the experimental data collected by Air Force, it has been found that echoes with target has more random phenomena than the region without target, [3]. This finding leads us to use Maximum entropy Method (MEM) and mutual information as the target detection tool  [4]. In this paper, we explain the reason of using relative entropy based preprocessing in fusion center. This can be explained based on method of types and Chernoff Stein Lemma. Method of types is a strong procedure that analyzes the sequences that have the same empirical distribution. This is applicable for our MEM based target detection algorithm, as entropy is dependent on the empirical distribution only. Based on this, we can find the bound on probability of detection. Also, the error probability associated with the detection is crucial in understanding the performance of the detection. Chernoff information gives the best error exponent in hypothesis testing, thus can be used as a sensor selection scheme in fusion center.

The potential of the method of types and Chernoff information is widely explored recently. A wide variety of information theoretic problems and communication problems deals with this new concept. Type based decentralized detection in wireless sensor network was investigated in  [5]. A method of types approach was used for the acknowledgment reduction technique in multi-cast networking  [6]. Chernoff information was used in optimization of sensor network in distributed detection  [7]. Error exponents in target class detection was investigated in  [8]. They were used in UWB  [9] and also used in analysis of energy detectors of cognitive radio  [10].

The rest of the paper is organized as follows: In Section  2, we describe the system model and block diagram. In Section  3, we explain the theory behind the method of types and Chernoff Information that are used in preprocessing and in sensor selection scheme. In Section  4, we present the simulation results. We conclude this paper and propose some future research in Section  5.

Section snippets

System model

RSN and rake structure that we employ in our work has nine different radars, each collected 35 readings as shown in Fig. 1. These radars are mono-static and independent. Since two radars will not experience deep fading at the same time, RSN provides better signal quality when they are spaced sufficiently far apart. Also the collections of the reading from different positions of the radar were not taken at the same time. This guarantees the time as well as spatial diversity in the proposed RSN.

Method of types

Method of types is a powerful procedure in which we consider the sequences that has the same empirical distribution  [11]. With this restriction, we can derive strong bounds on the number of sequences with a particular empirical distribution and the probability of each sequence in this set. It is then possible to derive strong error bounds in target detection problem, when Target detection is done using information theoretic method like entropy and mutual information, which depends only on

Simulation results

Our work is based on the sense-through-foliage data from Air Force Research Lab  [13]. The target is a trihedral reflector with a slant length of 1.5 as shown in Fig. 4. This kind of reflector is used to represent metallic military equipment under foliage cover. The target was located 300 feet away from the lift where the entire measurement equipment was located. Each sample is spaced at 50 ps interval, and 16,000 samples were collected for total time duration of 0.8 ms at a rate of

Conclusion

In this paper, we propose a new scheme for target detection through foliage. To enhance the performance of the poor signal we apply information theory to radar sensor network. Chernoff information gives best error exponent in hypothesis testing. In this study we proposed to use Chernoff information as sensor selection scheme, which significantly reduces the processing and improved the performance as well. We also proposed to use relative entropy or KL distance for processing in the fusion

Acknowledgments

The authors would like to thank Dr. Sherwood W. Samn in Air Force Research Laboratory for providing the sense-through-foliage data. This work was supported in part by US Office of Naval Research under Grants N00014-13-1-0043, N00014-11-1-0071, N00014-11-1-0865, and US National Science Foundation under Grants CNS-1247848, CNS-1116749, CNS-0964713.

Ishrat Maherin is a current Ph.D. student in the Department of Electrical Engineering at University of Texas at Arlington. Her research interests include wireless communications, cognitive radio, information theory, UWB Radar Sensor Network, Target Detection and wireless sensor networks.

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Ishrat Maherin is a current Ph.D. student in the Department of Electrical Engineering at University of Texas at Arlington. Her research interests include wireless communications, cognitive radio, information theory, UWB Radar Sensor Network, Target Detection and wireless sensor networks.

Qilian Liang is a professor in the Department of Electrical Engineering at University of Texas at Arlington, where he has been since August 2002. Prior to this he was a Member of Technical Staff in Hughes Network Systems Inc. at San Diego, California. Dr. Liang received his B.S. degree from Wuhan University, China in 1993, M.S. Degree from Beijing University of Posts and Telecommunications in 1996, and Ph.D. degree from University of Southern California (USC) in May 2000, all in Electrical Engineering. His research interests include wireless sensor networks, wireless communications, information theory, fuzzy logic and sensor fusion, etc. Dr. Liang has published more than 200 journal and conference papers, 6 book chapters and has 6 US patents pending. He received 2002 IEEE transactions on Fuzzy Systems Outstanding Paper Award, 2003 US Office of Naval Research (ONR) Young Investigator Award, 2005 UTA college of Engineering Outstanding Young Faculty Award, 2007, 2009, 2010 US Air force Summer Faculty Fellowship program Award and 2012 UTA College of Engineering Excellence in Research Award.

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