IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 52, NO. 6, JUNE 2004 1537 Detection of Distributed Sources Using Sensor Arrays Yuanwei Jin, Member, IEEE, and Benjamin Friedlander, Fellow, IEEE Abstract—In this paper, we consider the problem of detecting a random spatially distributed signal source by an array of sen- sors. We start with an approximate likelihood ratio (LR) detector and analyze its performance. Using the generalized likelihood ratio (GLR) approach, we then derive detectors under several assump- tions on the available statistics. The performance of these detectors is evaluated, and the effect of the angular spread of the source is investigated. The detection performance behaves differently under different scenarios. We notice that the degrees of freedom (DOF) of the distributions of the detection statistics depend on both the signal angular spread and the number of data snapshots. Specifi- cally, at a high SNR level and with small degrees of freedom, an increase of angular spread improves the detection performance. However, with large degrees of freedom, the increase of angular spread reduces detection performance. We provide a detailed dis- cussion of the behavior of detection performance under various conditions. A comparison between the GLR detectors and conven- tional beamformer detectors is made by computer simulations. The results indicate that the GLR detectors perform better as the an- gular spread becomes large than that of the conventional beam- former detectors. Index Terms—Detection, distributed source, generalized likeli- hood ratio (GLR), sensor array. I. INTRODUCTION A LARGE class of modern array processing techniques are designed for point sources, i.e., spatially discrete sources of acoustic or electromagnetic energy. In many practical situ- ations, the transmitter is best modeled as a distributed, rather than a point source. The distributed sources appear to have cer- tain angular spread with a mean direction of arrival (DOA). The point source model is only an approximation of the prac- tical situation when there is a large distance between the source and the receiver array. The principal mechanism for making the source appear to be distributed in space is diffuse (unresolv- able) and specular (resolvable) multipath caused by scattering of the propagating waves. For instance, experimental results ob- tained in urban wireless communications reported significant angular scattering distributions due to local scattering and re- flection from mobile stations [2], [10], [12] and base stations [7], [17]. The characterization of the power azimuth spectrum shows that angular spreads as large as 25 have been observed. The amount of angular spread is highly dependent of the scat- tering around the mobile, the height of the base station, and the distance between the base station and the mobile station. A sec- Manuscript received July 18, 2002; revised August 12, 2003. 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. Alexi Gorokhov. The authors are with the University of California, Santa Cruz, CA 95060 USA (e-mail: yjin@cse.ucsc.edu; friedlan@cse.ucsc.edu). Digital Object Identifier 10.1109/TSP.2004.827196 ondary, but equally important, mechanism is transmitter motion. If the source moves significantly during the observation interval (or coherent integration time), it will appear to be distributed rather than discrete. This is a typical scenario in sonar applica- tion where large number of sensors are used to obtain narrow beams. The moving acoustic sources may travel across several beams during an observation time [6]. Angular spread has a sig- nificant impact on any array processing algorithms [20]. For in- stance, the signal to noise ratio gain (SNRG) of the array re- duces as the angular spread increases [8], causing possible per- formance degradation. In passive array signal processing area, the problems under study concern the extraction of information from measurements using an array of sensors. Given the observations of the sensor outputs, the objective is to estimate the unknown parameters as- sociated with the waveforms corrupted by noise. To this end, we start with a simple and computationally efficient detection scheme. If the “noise only” hypothesis is rejected, other algo- rithms are used to estimate the number of the sources and their unknown parameters, such as range and bearing. Prior work on distributed sources focuses primarily on source localization and DOA estimation (see, e.g., [1], [4], [19], and [23]). Estimation of the number of distributed sources has also been studied in [1]. Subspace detectors have been studied in [18] and [21] for the cases where the signal lies in a deterministic subspace. More recently, the case of detecting Gaussian sig- nals with a low-rank covariance matrix is studied in [15], and matched subspace detectors are developed based on the gener- alized likelihood ratio (GLR) principle. In both cases, the subspace in which the signals lie is assumed to be known; in other words, the dimension and rank of the signal subspace are assumed to be known a priori. However, this assumption does not hold in practical situations. The rank, ori- entation, and strength of the signal subspace vary along with the signal angular spread, DOA, and the energy distribution func- tion. In this case, the unknown parameters may be estimated based on the maximum likelihood principle. In this paper, we develop detectors for distributed sources and study their performance, which is dependent of the angular spread. We first look at the case where all the parameters are known. In this case, the likelihood ratio detector can be approx- imated as a subspace beamformer. The detection performance depends on the distribution of the detection statistics and the sensor SNR. The degrees of freedom (DOF) of the detection statistics are determined by the angular spread and the number of data snapshots. If we fix the number of data snapshots, we show that the increase of angular spread reduces the mean of the detection statistics, which degrades performance, and at the same time reduces its variance, which improves performance. Within a certain range of DOF, detection performance improves 1053-587X/04$20.00 © 2004 IEEE