IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 2, FEBRUARY 2009 803 Exploiting Close-to-the-Sensor Multipath Reflections Using a Human-Hearing-Inspired Model Satyabrata Sen and Arye Nehorai Abstract—We propose a simple three-dimensional (3-D) direc- tion-finding system that exploits multipath reflections close to the sensors to improve performance by increasing the effective array aperture. Such close-range multipath reflections can originate, for example, from parts of the platform on which the sensor is mounted. Our system is inspired by the human auditory system where multipath reflections from the external ear (pinna) enable 3-D direction finding. To demonstrate the advantage of exploiting multipath reflections, we consider a simple example of a passive system with only one sensor and two nearby reflectors. First, we present a parametric measurement model and then compute the asymptotic Cramér–Rao bound on the 3-D direction estimates for a stochastic source signal of unknown parametrized spectrum. We provide a few numerical examples to illustrate our analytical results. We find that for this example additional reflectors and a wider source spectrum can achieve better direction estimates. Index Terms—Biologically inspired, human hearing analysis, multipath exploitation, 3-D direction finding. I. INTRODUCTION Direction estimation of a target is one of the major problems in radar, sonar, navigation, and robotics. Over the past few decades, a wide variety of techniques have been proposed to solve these prob- lems using sensor arrays. Since the estimation accuracy improves with an increasing number of sensors, many systems use a large number of sensors in different configurations. However, due to a variety of tactical problems, it is not always possible to use a large sensor array. In any practical system there are reflections from parts of the platform or ve- hicle on which the sensor is mounted. For example, in a ground radar, multipath signals occur due to reflections from different body parts of the vehicle. Conventional systems try to suppress these multipath re- flections by treating them as interference. In this correspondence we demonstrate that by exploiting known close-range reflections we can improve the target-direction estimation. A. Motivation Our system is inspired by the human auditory system, which per- forms remarkably well in finding the direction of sound sources in 3-D with just two ears. This performance is possible because of the anatomy of the external ears (pinnae) [1]. When the wavelength is of the same order or shorter than the dimension of the ear, different ridges and notches of the external ear interact significantly with the incident sound, as shown in Fig. 1. Batteau suggested two major ridges in the external ear that act like reflecting surfaces, producing close-range mul- tipath echoes that yield important cues for direction estimation. Manuscript received June 30, 2008; revised September 28, 2008. First pub- lished October 31, 2008; current version published January 30, 2009. This work was supported in part by DARPA by Grant HR0011-07-1-0036, by the Depart- ment of Defense under the Air Force Office of Scientific Research MURI Grant FA9550-05-1-0443, and by the ONR by Grant N000140810849. The associate editor coordinating the review of this manuscript and approving it for publica- tion was Prof. Andreas Jakobsson. The authors are with the Department of Electrical and Systems Engineering Washington University, St. Louis, MO 63130 USA (e-mail: ssen3@ese.wustl. edu; nehorai@ese.wustl.edu). Color versions of one or more of the figures in this correspondence are avail- able online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2008.2008257 Fig. 1. Pinna reflections of sound from different directions of arrival [11]. Over the years, researchers have tried to find experimental evidence that pinna reflections are the major cues for finding elevation angle [2]–[4]. Today, it is well established that, in addition to the pinnae, the human torso, shoulders, and head diffract the incoming sound waves. Collectively, these propagation effects are termed the head-related transfer function (HRTF). Brown and Duda provided some empirical formulae for the multipath delays produced by the pinna [5]. Harris et al. [6] built a VLSI circuitry of 2-D sound localization system inspired by HRTF models. However, they did not include any performance analysis of their system. In [7] we presented statistical performance analysis of the Brown-Duda HRTF model for 3-D direction finding. B. Outline In this correspondence, we model and analyze a 3-D direction- finding system that exploits multipath reflections close to the sensor. To demonstrate our approach, we present a parametric measurement model of a passive system with only one sensor and two nearby reflec- tors in Section II. Our system can be generalized to a more complicated system having multiple reflectors at known positions with respect to the sensor. We analyze the performance of this system for a zero-mean wide-sense stationary Gaussian source signal by computing the asymp- totic frequency domain Cramér–Rao bound (CRB) on the error of the 3-D direction estimate in Section III. We model the spectrum of the source signal in terms of a few unknown parameters. Our numerical examples, presented in Section IV, illustrate the ability of our model to estimate the directional angles and the parameters of the source spec- trum in various scenarios. Section V contains the conclusions and high- lights a few possible directions for future work. II. MEASUREMENT MODEL In this section, we propose a measurement model for exploiting multipath propagation effects due to nearby reflectors. We consider a simple 3-D model as shown in Fig. 2. We choose a Cartesian coordinate system such that the sensor is located at the origin. There are two reflectors close to the sensor: one is parallel to the XY plane at a distance from the sensor, and the other is parallel to the XZ plane at a distance from the sensor. We consider a static far-field point target, located at where and . In reference to a standard spherical coordinate system the elevation angle and the azimuth angle of the target can be expressed as and , respectively, where . From Fig. 2 it is evident that if the reflectors were not present, it would not be possible to estimate the directions of the target. Furthermore, if only the reflector parallel to the XY plane were present then only the elevation angle could be estimated. Here, we want to show that the multipath reflections produced by these two nearby reflectors enable the estimation of both elevation and azimuth angles. We assume that at the operating frequency the reflecting surfaces be- have as smooth flat surfaces, producing only specular reflections. The 1053-587X/$25.00 © 2008 IEEE Authorized licensed use limited to: WASHINGTON UNIVERSITY LIBRARIES. Downloaded on February 17, 2009 at 14:31 from IEEE Xplore. Restrictions apply.