**1. Introduction**

12 Will-be-set-by-IN-TECH

[3] Federal Communication Commission (2002). Revision of Part 15 of the communication's rules regarding ultra wideband transmission systems. First report and order, ET Docket

[4] Tai, C. T. & Collin, R. E. (2000). Radiation of a Hertzian Dipole Immersed in a Dissipative Medium, *IEEE Transactions on antennas and propagations*, Vol. 48, No. 10, pp. 1501-1506 [5] Gabriel, C. & Gabriel, S. et al. (2012). An Internet Resource for the Calculation of the Dielectric Properties of Body Tissues, Italian National Research Council website,

[7] Grimm, M. & Manteuffel, D. (2010). Electromagnetic Wave Propagation on Human Trunk Models excited by Half-Wavelength Dipoles, *Antennas and Propagation Conference*

[8] Norton, K. A. (1937). The Propagation of Radio Waves over the Surface of the Earth and in the Upper Atmosphere, *Proceedings of the Institute of Radio Engineers*, , Vol. 24, No. 10,

[9] Norton, K. A. (1941). The Calculation of Ground-Wave Field Intensity over a Finitely Conducting Spherical Earth, *Proceedings of the Institute of Radio Engineers*, Vol. 29, No. 12,

[10] Friis, H. (1946). A Note on a Simple Transmission Formula, *Proceedings of the IRE*, Vol.

[11] Grimm, M. & Manteuffel, D. (2012). Evaluation of the Norton Equations for the Development of Body-Centric Propagation Models, *European Conference on Antennas and*

[12] IT'IS Foundation (2012). Whole-Body Human Models, Enhanced Anatomical Models,

[13] Wait, J.R. (1996). *Electromagnetic Waves in Stratified Media*, IEEE Press, ISBN

Available from: http://niremf.ifac.cnr.it/docs/DIELECTRIC/home.html

[6] IMST (2012). EMPIRE XCcelTM, URL: http://www.empire.de

*(LAPC)*, pp. 493-496, ISBN 978-1-4244-7304-5

98-153, FCC 02-48

pp. 1367-1387

pp. 623-639

34, pp. 254-256

0-7803-1124-8

*Propagations (EUCAP)*

URL: http://www.itis.ethz.ch

In this chapter, we analyze the problem of power allocation for a distributed wireless sensor network with sensor nodes based entirely on ultra-wide bandwidth (UWB) technology. The network is used to perform object detection as well as object classification, where the absence, the presence, or the type of an object is observed by the sensors independently. UWB signals can be used for data communication between the sensor nodes as well as for radar applications. The approach of misemploying the communication sensors as radar sensors, such that the data transmission is misused as a radar beam in order to detect or to classify a target object, helps in realizing an energy-efficient radar system with compact and cheap sensor nodes. A further advantage of such radar systems is the fulfillment of major requirements of wireless sensor networks. This exploitation presupposes that the integration of sensing functionality into usual UWB sensors is implementable easily without the usage of any additional hardware units. Since the compact and low complexity UWB sensors are limited in power and communication capabilities, the detection and classification performance of a single sensor is restricted compared to that of a common complex radar system. To obtain an appropriate overall system performance, we consider the case of distributed detection and classification, where the local observations of the sensors are fused into a reliable global decision. Due to noisy communication channels and differences in distances between the object and the sensor nodes, both, the observations and their transmissions are unequally interfered. One simple way to suppress noise interference is to increase the power of each sensor node. But if the total power of the entire network is limited, then power allocation procedures are needed in order to increase the overall detection and classification probabilities. In general, it is challenging to evaluate the detection and the classification probabilities analytically, if possible at all. This particularly holds for the detection probability under a Neyman-Pearson-hypotheses-test criterion as well as for the classification probability under a Bayesian-hypotheses-test criterion [5]. This limits the usability of these criterions for analytical optimization of power allocation. Bounds, such as the Bhattacharyya bound [8], are also difficult to use for optimizing multidimensional

©2013 Alirezaei et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ©2013 Alirezaei et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 2 Will-be-set-by-IN-TECH 166 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications Power Allocation Procedure for Wireless Sensor Networks with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities <sup>3</sup>

problems. Therefore, we employ an information theoretic approaches [3], which help to solve the power allocation problem with a lower mathematical complexity. This approach yields a simple however suboptimal analytical solution for the power allocation problem. Furthermore, the proposed technique enables the consideration of object detection and classification at the same time. This is a further advantage of this method, which enables the usage of the same allocation algorithm in both cases. Hence a sensor network, which is used to classify target objects, can also be used to detect the absence or the presence of a target object with equal system settings. Therefore we only describe the case of object classification, which also includes the case of object detection, in the following sections.

*Hk*

observations factorizes according to

target object and their radiated powers *P<sup>R</sup>*

corresponding distance *d<sup>C</sup>*

*dR <sup>N</sup>*, *<sup>P</sup><sup>R</sup> N*

**Figure 1.** System model of the distributed wireless sensor network.

*<sup>f</sup> <sup>R</sup>*(*<sup>X</sup>* <sup>|</sup> *Hk*) :<sup>=</sup>

*N* ∏*n*=1 *f R*

are not identically distributed because the sensor nodes have different distances *d<sup>R</sup>*

where *X* denotes the sequence of random variables *X*1,..., *XN*. In general, the observations

ratio (SNR) varies between the sensor nodes. Due to the distributed nature of the problem, the *n*th sensor *Sn* performs independent measurements and processes its respective observation *Xn* by generating a local decision *Un* :<sup>=</sup> *<sup>θ</sup>n*(*Xn*)∀*<sup>n</sup>* <sup>∈</sup> <sup>F</sup>*N*, which depends only on its own observation and not on the observations of other sensor nodes. After deciding locally, each sensor transmits its decision to a fusion center located at a remote location. The communication between the sensor node and the fusion center is determined by the

*<sup>n</sup>* as well as by the transmission power *P<sup>C</sup>*

node. We refer to this communication channel, between the sensor nodes and the fusion center, as the *second* communication link and denote all dedicated parameters by the superscript *C*. Furthermore, we assume that both communication channels are non-fading channels and that all data transmissions are affected only by additive white Gaussian noise (AWGN). We disregard time delays within all transmissions and assume synchronized data communication. We use two distinct pulse-shift patterns for each sensor node in order to distinguish its first and second communication link from the communication links of other sensor nodes as described in [13]. Each pattern has to be suitably chosen in order to suppress inter-user interference at each receiver. Hence the *N* received signals at the fusion center are uncorrelated and are assumed to be conditionally independent for each of the underlying hypotheses. These received random signals correspond to the local decisions *U*1,..., *UN* and

*dR* <sup>2</sup> , *<sup>P</sup><sup>R</sup>* 2

*dR* <sup>1</sup> , *<sup>P</sup><sup>R</sup>* 1

Target

Object

Sensor Nodes

AWGN AWGN

*S*1 Channel Channel

*SN*

At any instance of time, a network of *<sup>N</sup>* <sup>∈</sup> <sup>N</sup> independent and spatially distributed sensors, as shown in Figure 1, obtains random observations *<sup>X</sup>*1,..., *XN* <sup>∈</sup> <sup>R</sup>. In the case of energy classification, *Xn* models the received signal at the receiver of the *n*th sensor. If a target object is present, then the received energy is a part of the radiated energy of the same sensor, which is reflected from the object's surface and is weighted by its reflection coefficient. We refer to this communication channel, between the sensors and the target object, as the *first* communication link and denote all dedicated parameters by the superscript *R*. The random observations *X*1,..., *XN* are assumed to be conditionally independent for each of the underlying hypotheses, i.e., the joint conditional probability density function of all the

*S*2

*dC <sup>N</sup>*, *<sup>P</sup><sup>C</sup> N*

*<sup>n</sup>* (*Xn* <sup>|</sup> *Hk*), <sup>∀</sup>*<sup>k</sup>* <sup>∈</sup> <sup>F</sup>*K*, (1)

*<sup>n</sup>* are also different. Therefore, the signal-to-noise

*<sup>n</sup>* from the

*<sup>n</sup>* of the same sensor

*dC* <sup>2</sup> , *<sup>P</sup><sup>C</sup>* 2

*dC* <sup>1</sup> , *<sup>P</sup><sup>C</sup>* 1

with Integrated Ultra-Wide Bandwidth Communications and Radar Capabilities

Center

Fusion

Power Allocation Procedure for Wireless Sensor Networks

167

The origin of research on distributed detection has been the attempt to fuse signals of different radar devices [10]. Currently, distributed detection is usually discussed in the context of wireless sensor networks, where the sensor unit of the nodes might be based on radar technology [7, 9, 14]. Other applications for UWB radar systems, which require or benefit from the detection and classification capabilities, are for example localization and tracking [6] or through-wall surveillance [4]. The physical layer design for an integrated UWB radar network that utilizes OFDM technology was analyzed in [11]. In [2] the case of object detection is considered, where for the problem of power allocation an approach based on the maximization of the Kullback-Leibler distance is used. In a recent publication [1] another approach is discussed, where the bit-error probability of data communication is used in order to allocate the transmission power and to increase the overall detection probability.

This chapter is divided into the following three sections except the introduction. First, the system model of the wireless network including sensor nodes and the fusion center is described. Here, all system parameters and assumptions with detailed mathematical formulations are introduced. Furthermore, the global classification rule in the fusion center as well as the local decision rules in the nodes are motivated. In the second section, we present a novel approach for power allocation in order to increase the overall classification probability, following which, the solution of this optimization approach is briefly discussed. The last section shows some results and demonstrates the feasibility of object classification by using the proposed power allocation method in UWB signaling systems. This chapter concludes with an interpretation of the achieved system performance.
