International Journal of Microwave Science and Technology

Volume 2014, Article ID 601659, 22 pages

http://dx.doi.org/10.1155/2014/601659

## Ultrawideband Noise Radar Imaging of Impenetrable Cylindrical Objects Using Diffraction Tomography

^{1}The Pennsylvania State University, University Park, PA 16802, USA^{2}Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, USA

Received 31 July 2014; Revised 18 November 2014; Accepted 26 November 2014; Published 24 December 2014

Academic Editor: Gian Luigi Gragnani

Copyright © 2014 Hee Jung Shin 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

Ultrawideband (UWB) waveforms achieve excellent spatial resolution for better characterization of targets in tomographic imaging applications compared to narrowband waveforms. In this paper, two-dimensional tomographic images of multiple scattering objects are successfully obtained using the diffraction tomography approach by transmitting multiple independent and identically distributed (iid) UWB random noise waveforms. The feasibility of using a random noise waveform for tomography is investigated by formulating a white Gaussian noise (WGN) model using spectral estimation. The analytical formulation of object image formation using random noise waveforms is established based on the backward scattering, and several numerical diffraction tomography simulations are performed in the spatial frequency domain to validate the analytical results by reconstructing the tomographic images of scattering objects. The final image of the object based on multiple transmitted noise waveforms is reconstructed by averaging individually formed images which compares very well with the image created using the traditional Gaussian pulse. Pixel difference-based measure is used to analyze and estimate the image quality of the final reconstructed tomographic image under various signal-to-noise ratio (SNR) conditions. Also, preliminary experiment setup and measurement results are presented to assess the validation of simulation results.

#### 1. Introduction

Research on the use of random or pseudorandom noise transmit signals in radar has been conducted since the 1950s [1, 2]. Noise radar has been considered a promising technique for the covert identification of target objects due to several advantages, such as excellent electronic countermeasure (ECM), low probability of detection (LPD), low probability of interception (LPI) features, and relatively simple hardware architectures [3–5]. Also, advances in signal and imaging processing techniques in radar systems have progressed so that multidimensional representations of the target object can be obtained [6].

In general, radar imaging tends to be formulated in the time domain to exploit efficient back-projection algorithms, generate accurate shape features of the target object, and provide location data [7]. For multistatic radar systems, the images of a target are reconstructed based on range profiles obtained from the distributed sensor elements. When a transmitter radiates a waveform, spatially distributed receivers collect samples of the scattered field which are related to the electrical parameters of the target object. For the next iteration, a different transmitter is activated, and the scattered field collection process is repeated. Finally, all collected scattered field data are relayed for signal processing and subsequent image formation algorithms.

Tomography-based radar imaging algorithms have been developed based on microwave image reconstruction method [9], characterizing the material property profiles of the target object in the frequency domain and reconstructing specific scattering features inside the interrogation medium by solving the inverse scattering problem. The capability of microwave imaging techniques has been found attractive in malignant breast cancer detection [10–13], civil infrastructure assessment [14–16], and homeland security [17–19] applications due to the advantages of nondestructive diagnosis and evaluation of obscured objects. The quality of the reconstructed image for different values of the electrical contrast for a UWB imaging system was investigated and published for both low-contrast and high-contrast object cases. For low-contrast objects, the obtained target image using a single frequency achieves a good reconstruction of the electrical contrast that is almost equivalent to the one obtained with the entire UWB frequency range. For the high-contrast case, while the formation of a Moiré pattern affects the single frequency reconstruction, this artifact does not appear in the UWB frequency image [20]. Thus, UWB radar tomography is expected to provide advantages over the single or narrow band frequency operation in terms of resolution and accuracy for any target object.

The goal of this paper is to demonstrate successful image reconstruction of the cylindrical conducting objects using the diffraction tomography theorem for bistatic UWB noise radar systems. The paper is organized as follows. First, the paper defines the characteristics of UWB random noise signal and discusses the shortcomings of using such noise signal as a radar transmit waveform in tomographic image reconstruction process in Section 2. The empirical solution to bypass the shortcoming of using UWB random noise waveform is also proposed. The formulations of the image reconstruction of two-dimensional scattering geometry of a bistatic imaging radar system using Fourier diffraction theorem under the assumption of plane wave illumination are presented in Section 3. In Section 4, the numerical simulation results of diffraction tomography using UWB random noise waveforms show that the tomographic image of the target is successfully reconstructed. The image quality measures of the reconstructed images, SNR effects for multiple transmissions of UWB random noise waveforms, and preliminary experimental validation are discussed in Section 5. Conclusions are presented in Section 6.

#### 2. Analysis of White Gaussian Noise Model

The main advantage of transmitting a random noise waveform is to covertly detect and image a target without alerting others about the presence of radar system. Such LPI characteristics of the noise radar are guaranteed because the transmitted random noise waveform is constantly varying and never repeats itself exactly [21]. The random noise waveform can be experimentally generated simply by amplifying the thermal noise generated in resistors or noise diodes while maintaining relatively flat spectral density versus frequency [22]. Hence, relatively simple hardware designs can be achieved for noise radars compared to the conventional radar systems using complicated signal modulation schemes.

For a random noise waveform model, let be a discrete time WSS and ergodic random process and a sequence of iid random variable drawn from a Gaussian distribution, . defined herein is white Gaussian noise; that is, its probability density function follows a Gaussian distribution and its power spectral density is ideally a nonzero constant for all frequencies. However, the finite number of random noise amplitude samples must be chosen for waveform generation for any numerical simulations and practical experiments.

Assume that a sequence of only samples of is selected for generating a white Gaussian noise. In this case, the estimate for the power spectral density, , is given by [23] where is the estimate for the autocorrelation sequence. is defined as the periodogram estimate, and the rigorous analysis of the expected value and variance of the periodogram estimate for any arbitrary is described in [23–25]. The expected value of the periodogram estimate is [23, 24] which suggests that is a biased estimator. However, it is considered to be asymptotically unbiased as approaches infinity. In this case, the expected value of becomes a constant such that

The variance of the periodogram estimate of the white Gaussian noise waveform formed by a sequence of samples is given by [23, 24] which is proportional to the square of the power spectrum density and does not approach zero as increases. In order to decrease the variance of , the periodogram averaging method has been proposed by Bartlett [26]. The average of independent and identically distributed periodograms on samples of size is given by and the expected value of the average with iid periodogram estimate is written as [23] which is considered to be asymptotically unbiased as approaches infinity. Also the variance of the averaged periodogram estimate is given by [23] The variance of the averaged periodogram estimate is inversely proportional to the number of iid periodograms , and consequently the variance approaches zero as approaches infinity. We use (6) and (7) to conclude that the expected value remains unchanged, but only the variance of white Gaussian noise decreases for averaging iid periodogram estimates. Increasing the number of in averaging periodogram estimate truly flattens the spectral density, and the successful tomographic image can be achieved by transmitting multiple random noise waveforms with a large sequence size . For the numerical simulations performed in this paper, a total of 10 iid random noise waveforms are transmitted, and each iid noise waveform is generated with 500 random amplitude samples drawn from . The tomographic image is formed based on the dataset from 41 discrete frequencies chosen uniformly within X-band from 8 GHz to 10 GHz in steps of 50 MHz.

#### 3. Formulation

In this section, the scattering properties for two-dimensional cylindrical impenetrable conducting object in the bistatic scattering arrangement are discussed, and the Fourier diffraction tomography algorithm is applied to reconstruct the image of the object based on the bistatic scattering properties. The Fourier diffraction theorem has been extensively applied in the area of acoustical imaging [27–29]. The goal of diffraction tomography is to reconstruct the properties of a slice of an object from the scattered field. For planar geometry, an object is illuminated with a plane wave, and the scattered fields are calculated or measured over a straight line parallel to the incident plane wave. The mathematical formulation and proof of validity of the Fourier diffraction theorem shown in Figure 1 are not presented in this section since they were already stated and published [30].