IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 53, NO. 1, JANUARY 2005 13 Reduced-Rank Adaptive Detection of Distributed Sources Using Subarrays Yuanwei Jin, Member, IEEE, and Benjamin Friedlander, Fellow, IEEE Abstract—We introduce a framework for exploring array detec- tion problems in a reduced-dimensional space. This involves calcu- lating a structured subarray transformation matrix for the detec- tion of a distributed signal using large aperture linear arrays. We study the performance of the adaptive subarray detector and eval- uate its potential improvement in detection performance compared with the full array detector with finite data samples. One would ex- pect that processing on subarrays may result in performance loss in that smaller number of degrees of freedom is utilized. However, it also leads to a better estimation accuracy for the interference and noise covariance matrix with finite data samples, which will yield some gain in performance. By studying the subarray detector for general linear arrays, we identify this gain under various scenarios. We show that when the number of samples is small, the subarray detectors have a significant gain over the full array detector. In ad- dition, the subarray processing can also be successfully applied to the problem of detecting moving sources in an underwater acoustic scenario. We validate our results by computer simulations. Index Terms—Adaptive processing, detection, distributed source, interference cancellation, reduced rank, subarrays. INTRODUCTION,BACKGROUND, AND MOTIVATION T HE problem of detecting underwater acoustic sources using measurements by an array of sensors has been studied extensively in literature. For a large aperture acoustic array, a narrow beam can be formed so as to distinguish two closely spaced emitters. However, the acoustic energy source may be fairly close to the array and may move through several beams during the sonar system’s temporal integration time. The effects of source motion on sonar systems have been studied by several authors (see, for example, [6] and the references therein). One may model the moving transmitter during an integration time as a source with energy scattering in space, which is called a distributed source. The distributed source can be described by a subspace array manifold model [12]. One of the enduring problems associated with the adaptive minimum variance distortionless (MVDR) beamformer (see, e.g., [5] and [10]) lies in the classic dilemma of wanting long observation times for stable covariance matrix estimates yet needing short observation times to track dynamic field behavior. This is especially true for large aperture arrays. This issue has Manuscript received August 23, 2003; revised January 13, 2004. This work was supported by the Office of Naval Research under Grant N00014-01-1-0075. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Jean Pierre Delmas. Y. Jin was with the University of California, Santa Cruz, CA 95060 USA. He is now with Carnegie Mellon University, Pittsburgh, PA 15213 USA (e-mail: ywjin@andrew.cmu.edu). B. Friedlander is with the University of California, Santa Cruz, CA 95060 USA (e-mail: friedlan@cse.ucsc.edu). Digital Object Identifier 10.1109/TSP.2004.838941 been addressed by many authors (see, e.g., [6]) and is one of the research themes of the Acoustic Observatory (AO) Project [1]. There are several ways of dealing with this issue, for in- stance, the diagonal loading method, which is essentially a weighted projection method by adding a constant value to each of the terms along the diagonal of the sample covariance matrix (see, e.g., [6], [13], and the reference therein). Reduced-rank processing is another one of the well known data processing methods (see [4], [11], and the references therein). In this case, the data are mapped into a lower dimensional subspace via a transformation matrix prior to detection. Rank-reduction directly addresses the sample support issue by reducing the number of statistical unknowns associated with the interference. In this paper, we study the problem of detecting distributed sources using subarrays, i.e., a partial collection of sensors of a full array. In this case, the transformation matrix is a structured block diagonal matrix. The motivation for this study lies in the following two observations. First of all, for a general linear array with elements, the beam width is inverse proportional to the array aperture. A subarray with a smaller aperture gives rise to a wider beam which, consequently, is able to cover the distributed source if the subarray beamwidth is chosen to be close to the signal angular spread. Hence, a simple MVDR beamformer can be implemented on each individual subarray. Second, im- plementation of a MVDR beamformer requires of estimating the sample covariance matrix based on data samples. The estimation accuracy is improved for the subarray processing compared with the full array processing based on the same amount of data. This is because we have a smaller amount of unknown parameters to be estimated. This leads to the fol- lowing conjecture: With short data records, statistical stability dominates detector performance, and subarray detection re- quires substantially less SNR than full array processing. With large data records, SNR dominates detection performance, and the subarray detector requires nearly the same SNR as the full array detector. Hence, substantial performance improvements are possible using the subarray detector relative to the full array detector in limited-data situations. It should be noted that the idea of subarray processing has been proposed before and has been studied by several authors, for instance, Cox [8], Morgan [14], Owsley and Swingler [19], and Dhanatawari [9]. Owsley suggested that a narrow band uni- form linear array (ULA) containing elements could be de- composed into, say, nonoverlapped but contiguous subarrays of equal length. Each subarray is operated as a simple delay and sum beamformer and the output from each is treated in exactly the same fashion as the output from a single sensor in a ULA 1053-587X/$20.00 © 2005 IEEE