A Wideband, Synthetic Aperture Beamformer for Through-The-Wall Imaging

A coarray-based aperture synthesis scheme using subarrays and post-data acquisition beamforming is presented for through-the-wall wideband microwave imaging applications. Various effects of the presence of the wall, such as refraction, change in speed, and attenuation, are incorporated into the beamformer design. Simulation results verifying the proposed synthetic aperture technique for a TWI system are presented. The effects of incorrect estimates of the parameters of the wall, such as thickness and dielectric constant, on performance are investigated. Comments Copyright 2003 IEEE. Reprinted from IEEE International Symposium on Phased Array Systems and Technology 2003, pages 187-192. Publisher URL: http://ieeexplore.ieee.org/xpl/tocresult.jsp?isNumber=28113&page=2 This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it. This conference paper is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/40 A WIDEBAND, SYNTHETIC APERTURE BEAMFORMER FOR THROUGH-THE-WALL IMAGING’ Fauzia Ahmad’, Moeness G. Amin’, Saleem A. Kassam2, Gordon J. Frazer’ ‘Center for Advanced Communications, ’Moore School of Electrical Engineering, ’ISR Division, DSTO, Villanova University, University of Pennsylvania, Edinburgh, Ausualia Villanova, PA 19085 Philadelphia, PA 19104 E-mail: [email protected] moeness @ece.vill.edu E-mail: [email protected]; E-mail: [email protected] ABSTRACT A coarray-based aperture synthesis scheme using subarrays and post-data acquisition beamforming is presented for through-the-wall wideband microwave imaging applications. Various effects of the presence of the wall, such as refraction, change in speed, and attenuation, are incorporated into the beamformer design. Simulation results verifying the proposed synthetic aperture technique for a TWI system are presented. The effects of incorrect estimates of the parameters of the wall, such as thickness and dielectric constant, on performance are investigated.A coarray-based aperture synthesis scheme using subarrays and post-data acquisition beamforming is presented for through-the-wall wideband microwave imaging applications. Various effects of the presence of the wall, such as refraction, change in speed, and attenuation, are incorporated into the beamformer design. Simulation results verifying the proposed synthetic aperture technique for a TWI system are presented. The effects of incorrect estimates of the parameters of the wall, such as thickness and dielectric constant, on performance are investigated. 1.0 INTRODUCTION “Seeing” through obstacles such as walls, doors, and other visually opaque materials, using microwave signals offers powerful tools for a variety of applications in both military and commercial paradigms. Through-the-wall imaging (TWI) can be used in rescue missions, behind-the-wall target detection, surveillance and reconnaissance. Existing and under development microwave TWI systems have been reviewed by Ferris and Currie 111. Most of these systems can provide a range resolution of a few inches but have poor spatial resolution. In this paper, we use an aperture synthesis scheme based on the coarray formalism for improved spatial resolution. The coarray was originally defined for narrowband far-field active imaging [21, and is represented by a set of pair-wise s u m of the position vectors of the elements in the transmit and receive apertures. The concept of coarrays was also extended to wideband imaging in [3]. The aperture synthesis technique using subarrays, was first proposed in [41 for ultrasound applications. In this scheme, the transmit and receive arrays are divided into subarray pairs, where each subarray consists of a single transmitter and one or more receivers. The subarrays are used independently to form component complex images of the scene by post-data acquisition beamforming [4]. These independent component images are then added coherently to obtain the composite complex amplitude image with the desired spatial resolution. This scheme was later generalized in [51 to incorporate subarrays composed of multiple transmitters using the concept of coarrays. The subarray aperture synthesis scheme was recently extended to wideband microwave imaging, particularly for TWI applications [6,7]. Both these systems divide the transmit and receive arrays into single transmitter/single receiver subarray pairs. Although the work in [7] uses single transmitterkingle receiver pairs, our work in [6] provides a general framework for array synthesis, and permits the realization of desired imaging characteristics by the use of the synthesized aperture. The analysis in [6] did not include a key factor of the problem, namely refraction due to the presence of the wall and the effect of inaccuracies in the wall parameters on TWI. The composition and thickness of the wall, its dielectric constant, and the angle of incidence all affect the characteristics of the signal propagating through the wall [SI. The propagating wave slows down, encounters refraction, and is attenuated as it passes through the wall. In this paper, we present a microwave imaging system based on the concepts of subarrays and coarrays, whose design incorporates these effects. Post-data acquisition processing is used to implement the synthetic aperture beamformer for TWI. In a practical situation, the wall parameters such as its thickness and dielectric constant, are not known apriori. Therefore, reasonable estimates of these parameters have to be used i n beamforming. Any errors in estimating the wall parameters will compromise the beamformer design. An analysis of the effect of erroneous wall parameters on the performance of the beamformer is also provided. * T h i s work was supported by DARPA under Grant No. MDA972-02-1-0022. The content of the information does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred. 0-7803-7827-X/03/$17.00 02003 IEEE. 187 The paper is organized as follows. Section 2 gives an overview of post-data acquisition beamforming in the absence of the wall. In Section 3, we present the design of the synthetic aperture beamformer for TWI. The performance of the proposed system is demonstrated through simulation results. Section 4 deals with the beamformer in the presence of erroneous estimates of wall parameters. Section 5 contains the concluding remarks. 2.0 POST-DATA ACQUISITION BEAMFORMING IN THE ABSENCE OF THE WALL Consider an M-element transmit and an N-element receive line array, both located along the x-axis, which are divided into single transmitterlsingle receiver subarrays. The region to be imaged is located along the positive zaxis, Let the m-th transmitter, placed at location xm, illuminate the scene with a wideband signal s(r). The reflection by any target located in the region being imaged is measured and stored by the n-th receiver located at xrn. For a single point target located at xp=(RpsinBp. R,cosB,), the output of the n-th receiver is given by a(xp)s(trmn ), where a(xp) is the complex reflectivity of the target and rmn is the propagation delay encountered by the signal as it travels from the m-th transmitter to the target at xp, and hack to the n-th receiver, as shown in Fig. 1. This delay is given by (1) where c is the speed of light and d(x,y) denotes the Cartesian distance between locations x and y. This process is repeated with the m-th transmitter, until all the N receivers have been used sequentially. The corresponding N outputs are processed as follows. The region of interest is divided into a finite number of pixels in range and angle. The complex composite signal corresponding to the image of the pixel located at xq, is obtained by applying time delays and weights to the N received signals, and summing them. The resulting output for a single target case is given by rmn = (d(xt, .xp)+d(Xp . x m ) ) l c (2) N n=l zmqW = Z w,a(xp)s(t-r,,, -Fmn) , rmn =(2Rq -d(xtm,xp)-d(xp,x, ,))lc where wm is the weight applied to the output of the n-th receiver, and Fmn is the focusing delay applied to the output of the n-th receiver when the transmitter is at the m-th location. The focusing delay synchronizes the arrivals at different receivers for the same pixel, and thus allows coherent imaging of the scene. The above process is repeated by sequential use of the M transmitters and produces M complex composite signals, z,(r), m=1,2. ... M, corresponding to the image of the pixel at xl. The complex amplitude image value for the pixel located at xq is obtained as I ( x q ) = Z wrmZmq@) (3) I , ; , , where w , ~ is the weight applied to the component signal z,(f) obtained using the m-th transmitter. The process, described by (2)-(3), is performed for all pixels in the region of interest to generate the composite image of the scene. The general case of multiple targets can be obtained by superposition. 3.0 DESIGN OF THE BEAMFORMER IN THE PRESENCE OF THE DIELECTRIC WALL 3.1 Refractions Consider a wall of thickness d, and dielectric constant E. A signal traveling along 0, through a wall-to-air interface will bend away from the normal on transmit (see Fig. 2). The angle of refraction B j r is given by Snell's law as ejr =sin-' (&sin 0,) (4) Due to refraction, a signal traveling to the point x j =(R, s i n B j , R j cosBj) would instead travel to the point Z j = (R j sin g j , R j cos G j ) . In order to develop the relationship between B j and gj , we denote 1 j l as the distance traveled by the signal through the wall along B j , and l j 2 as the distance traveled, after refraction, to gj The parameters d,, E, R,, b'j , and Bjr are all assumed to be known. The parameters 1 j l , 1 j 2 , and Bj are all unknown. FromFig. 2, we obtain Applying the cosine law to the triangle with vertices (0, A, i j ) and solving for 1,2, we get -