IN THE FIELD of array signal processing, a class of

Transcription

1 960 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 4, APRIL 1997 Distributed Source Modeling Direction-of-Arrival Estimation Techniques Yong Up Lee, Jinho Choi, Member, IEEE, Iickho Song, Senior Member, IEEE, Seong Ro Lee Abstract In direction-of-arrival (DOA) estimation, the direction of a signal is usually assumed to be a point. If the direction of a signal is distributed due to some environmental phenomenon, however, DOA estimation methods based on the point source assumption may result in poor performance. In this paper, we consider DOA estimation when the signal sources are distributed. Parametric nonparametric models are proposed, estimation methods are considered under these models. In addition, the asymptotic distribution of estimation errors is obtained to show the models statistical properties. I. INTRODUCTION IN THE FIELD of array signal processing, a class of direction-of-arrival (DOA) estimation methods has been developed based upon the eigenstructure of the array output covariance matrix (e.g., [11], [12]). One well-known DOA estimation method (the multiple signal classification (MUSIC) method) is proposed in [12], its variations can also be found in the literature (e.g., [3], [8]). In [2], [4], [7], [14], the statistical properties of MUSIC are analyzed. Other estimation methods utilize the maximum likelihood (ML) estimate of the covariance matrix (e.g., [13]). These MLbased DOA estimation methods can be categorized as either conditional or unconditional, depending on assumptions associated with the signal amplitudes. The DOA estimation methods mentioned above are based on the assumption that the signal sources are point sources, i.e., if the DOA of a source is, then there is no other source at for a sufficiently small value of Under this assumption, the DOA estimation method utilizes a statistic constructed from a weighted sum of sensor outputs, the sensor outputs are modeled by plane waves emanating from a small number of discrete far-field point sources with an additive spatially temporally uncorrelated Gaussian noise vector. In real surroundings, the signals received at an array include not only a direct path signal (which can be regarded as a point source) but also angularly spread signals that are coherent, phase-delayed, amplitude-weighted replicas of the direct path signal: The signals observed from an array can then be regarded as a superposition of plane waves originating from Manuscript received May 3, 1994; revised August 18, This work was supported by the Korea Science Engineering Foundation under Grants The associate editor coordinating the review of this paper approving it for publication was Dr. Monique Fargues. Y. U. Lee is with the Wireless Communication search Team, Telecommunication R/D Center, Samsung Electronics Co. Ltd., Seoul, Korea. J. Choi is with the R/D Center, DACOM Co., Daejeon, Korea. I. Song S. R. Lee are with the Department of Electrical Engineering, Korea Advanced Institute of Science Technology (KAIST), Daejeon, Korea. Publisher Item Identifier S X(97) a continuum of directions. (Typical examples [1], [11] are the angularly spread effects created from the local scattering on the lower layers in a multibeam echo sounder spurious phenomenon due to clutter in radar. In [15], a more detailed discussion can be found.) In such cases, the signal source direction is spread around, which is the signal s direct path, with angularly spread signals existing in some interval on a single frequency for some nonnegligible value of [8], [9]. We call such a signal source a distributed source. When the signal source direction is distributed, i.e., angularly spread, the beamformer output is not correctly modeled by a noisy weighted sum of spatially sampled plane wave signals. Thus, application of point source DOA estimation methods is not guaranteed to work for distributed sources. It has been shown (e.g., [9], [15]) that if a source spread in frequency is incorrectly modeled as a single frequency source, estimation performance is degraded. When point sources are partially (or fully) correlated, spatial smoothing DOA estimation methods under the point source assumption can be applied [11], [13]. This application, however, requires spatial smoothing information, e.g., a spatial smoothing of covariance matrix or reflection coefficients. In this paper, we remove this requirement. In this paper, the distributed sources are considered starting from the most general class classified into the parametric nonparametric sources based on the distributed source shape. Then, the two source models estimation problems for the models are studied. It is shown that existing DOA estimation procedures can be extended to the case of distributed sources. cently, estimation for one type of distributed source (which corresponds to the parametric sources in this paper) has been considered. Although both this paper [15] address the problem of parametric source estimation, this paper distinctively differs from [15] in the following aspects. In [15], signals from different sources are spatially uncorrelated with each other, signals within a source may or may not be correlated (coherent or incoherent). In this paper, on the other h, signals from different sources may or may not be spatially correlated, signals within a source are correlated. Thus, the mathematical expressions of the array output covariance matrix include those of [15] as special cases when the number of sources is greater than one. In addition, in [15], which is a more complete description for a source, is done (coherent or incoherent), as in this paper, more attention is given to the relation among sources. We would also like to X/97$ IEEE

2 LEE et al.: DISTRIBUTED SOURCE MODELING AND DIRECTION-OF-ARRIVAL ESTIMATION TECHNIQUES 961 mention that the spatial auto-correlation function of sources is assumed to be known in [15], as the distributed source shape (intensity) is assumed to be known in this paper. A point source with DOA envelope can be represented as II. DISTRIBUTED SOURCE MODELS Consider plane wave sources impinging on the array sensor from (azimuth) directions respectively. For convenience, we restrict our attention to linear arrays (which results in ambiguity in elevation) thus consider only azimuth. We would like to mention, however, that with small notational modifications, many of the results can be easily extended to nonlinear arrays. Assume that the directions of plane wave sources are modeled by points in angle (i.e., point sources), the plane wave sources are narrowb with carrier frequency, the outputs of the array sensor are frequency-shifted to baseb signals. Under the point source assumption, the output of an array with sensor elements can be represented in the form is the scaled envelope. Then, the complex representation of the plane wave propagating across the array sensor is is a function of the envelope DOA Generalizing the function, or equivalently, generalizing the DOA of a point source into a number of unknown parameters (e.g., the mean anglespread extent), the distributed source can be expressed as (1) vector of the array output, th point source, steering vector, DOA of the th point source. The steering vector is specified by the distance from the origin to the th sensor the propagation velocity of medium. It is assumed that the zero-mean white complex normal noise vector is stationary with covariance matrix ( is the known variance), Here, denotes the space of complex-valued vectors. If we define is a function of the envelope unknown parameters. Denoting the distributed source density by, we have since is periodic in Here, the coefficients are assumed to be stationary zeromean complex normal rom processes with covariance This assumption can be justified in the generalization of the point source since the point source in (1) is generally assumed to be a zero-mean complex normal rom process. Under this formulation, the covariance function of the distributed source can be obtained as (3) (1) can be rewritten as is sta- the zero-mean complex normal vector tionary with covariance matrix (2) the output of a beamforming array can be expressed as (4) (5) We now consider a distributed source as a generalization of the collection of -point sources. Such a source is usually described by a distributed source density (or directional density) that indicates the amount of source power coming from each direction. Herein, we concentrate on the distributed source density for which the plane wave approximation (narrowb in frequency) is valid. In this paper, the distributed source is represented in terms of spatial harmonics, the output of an array is obtained by integrating the effect of a single plane wave source over all azimuth directions weighted by the distributed source density. Note that in modeling of noise, a similar approach was studied in [5] [10]. is temporally spatially uncorrelated with Note that if is a model abstraction, then from (3) (5) (6)

3 962 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 4, APRIL 1997 (a) A parametric source can therefore be characterized by the two parameters: DOA (representing the center direction) distribution parameter (representing the extent). These two parameters together form a generalization of DOA. Under this parametric model, the goal of DOA estimation is to estimate Defining, the distributed source composed of parametric sources can be expressed as (7) (b) The geometric series (7) is absolutely convergent when all represents point sources when all because (c) Fig. 1. (a) Some point sources. (b) Three examples of distributed sources. (c) Some examples of parametric sources. when all is In addition, the covariance function of This shows that (5) is a generalization of (1). Some examples of distributed sources are shown in Fig. 1. For example, the distributed sources in Fig. 1(b) may be obtained from weighted functions of the point sources in Fig. 1(a). A. A Parametric Source Model Many distributed sources composed of various weighted functions, as shown in Fig. 1(b), cannot easily be dealt with. To obtain specific concrete results, we will consider a class of the distributed sources. In this section, we concentrate on a class of distributed sources, for which the output of an array is (8) (9) with, as shown in Fig. 1(c). Note that some of the sources in Fig. 1(b) can be expressed as a weighted sum of the sources in Fig. 1(c). Let us call a source (10) is the steering vector under the parametric model. It should be noted that defined with a parametric source. The parametric source is thus unimodal symmetric about We require that for two closely spaced parametric sources, if, then In other words, the distributed source density of the two combined sources located at any point between their centers is less than the source density of either one at its center. Closely spaced sources not satisfying this condition will not be considered in this paper. from (4). Now, the covariance matrix of is Note that (11) is quite similar to the equation (11) (12)

4 LEE et al.: DISTRIBUTED SOURCE MODELING AND DIRECTION-OF-ARRIVAL ESTIMATION TECHNIQUES 963 used in the point source model. It should be noted that the term with in (8) is equivalent to the spatial auto-correlation function in [15]. B. A Nonparametric Source Model Let us next consider the nonparametric model. A nonparametric source in this paper is defined to be a general function defined for The goal under the nonparametric model is thus generalized to estimating the distributed source, as opposed to the conventional goal of identifying the number of sources their locations under the point source model. Although a source is theoretically exped into an infinite series, a finite truncation of the series may often be used as an approximation. Under the assumption that is piecewise continuous differentiable with respect to, we have from (3) (13) is the model order, an abstraction, which is not to be interpreted as the number of sources. For the nonparametric source, the source covariance function is (14) that is, in (4) for or The output of an array for the source is, with the substitution (13) into (5) (15) Now, it is easy to see that the covariance matrix of the output of an array is C. Some Discussions on the Distributed Source Models Since rank is full rank, the rank of the matrix is equal to when the number of sources in the parametric model is It is required that the number of sensors should be greater than when DOA estimation methods based on eigenstructure are to be used. Practically, the rank of the sample covariance (as estimated from the data) determines if the parametric model can be used; if rank, then the parametric model may be used. If the full-rank matrix can be approximated by a reduced rank matrix through a rank reduction scheme if rank, then we may again use the parametric model. One rank reduction scheme retains only the largest eigenvectors. Thus, if then we use (18) (19) are the th largest eigenvalue its corresponding eigenvector, respectively, of ( It should be noted that when a parametric source is specified with three or more parameters, alternative parametric models can be developed that adequately represent higher dimensional systems. When the information of the source distribution cannot be obtained at all, the nonparametric model may be useful. After some prior knowledge (e.g., the number of sources the distributed source shape) are obtained from nonparametric estimation, the parametric estimation can be applied with the acquired information. III. DOA ESTIMATION UNDER DISTRIBUTED SOURCE MODELS A. DOA Estimation under the Parametric Model This section considers an eigenstructure-based method analogous to the MUSIC method. Consider an eigendecomposition of the covariance matrix Assume that we can obtain the signal noise subspaces range range, respectively, which are defined by (16) is the steering vector under the nonparametric model. We now define to obtain (17) with the eigenvector of corresponding to the th largest eigenvalue of Then, we have from (11) span the two spaces span span span (20) are orthogonal. Thus, the

5 964 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 4, APRIL 1997 DOA s distribution parameters can be found from the following orthogonality property: iff (21) Now, we investigate some properties of the vector Suppose that the th element of the vector is. Then, the th element of is (22) Let. Then, (23), the integration is in the clockwise sense. By the Cauchy integral formula, we have If the receiver is a uniform linear array, i.e., have (24),we (25) It is noteworthy that in this case, Thus, the only difference between the steering vectors under the point parametric models is the factor when the phase of is a linear function of for In this case, if is close to 1 in addition, the difference obviously becomes less significant. B. Distributed Source Estimation under the Nonparametric Model In general, the DOA of a nonparametric source can be estimated from in (14), with determined from (17), since both are known. (Practically, the sample covariance matrix is used in place of.) The matrix is obtained from the covariance matrix as follows. From (17), it is easy to see that (26) Fig. 2. Conventional MUSIC null-spectrum for two parametric sources (1; 1) = (2=18; 0:9) (2; 2) = (7=18; 0:7) when the number of sensors L = 10(3); 30(+); 50(1); 55(0): well known [6] that use of the pseudoinverse concept imposes a least-squares constraint with the result (27) Thus, if, a nonparametric source is expected to be correctly estimated by examining the covariance function because of the uniqueness of When, the direct method may result in poor performance due to indeterminacy of It should again be noted that the goal under the nonparametric model is generalized to estimating the distributed source as opposed to the conventional goal of identifying the number of sources their locations under the point source model. IV. STATISTICAL PROPERTIES In this section, we consider the asymptotic statistical properties of the estimates of the DOA s distribution parameters obtained from the MUSIC-based method discussed in Section III-A. Let the th eigenvector of be denoted by corresponding to the th largest eigenvalue The estimates of the DOA distribution parameter are denoted by, respectively. Using the orthogonality property (21), these estimates can be determined by taking the values that minimize the cost function (28) When rank, the matrix can uniquely be obtained using the pseudoinverse of When is full rank, there are many matrices that satisfy (26). In these cases, some constraints must be imposed to find a matrix It is That is (29)

6 LEE et al.: DISTRIBUTED SOURCE MODELING AND DIRECTION-OF-ARRIVAL ESTIMATION TECHNIQUES 965 the asymptotic distribution of the estimation error vector is a zero-mean normal rom vector with covariance (33) (34) is the asymptotic value of (see the Appendix), (a) (35) with (36) Using the Cauchy Schwartz inequality, it is easily shown that the asymptotic Hessian given in (34) is a nonnegative definite matrix. When (37) (b) Fig. 3. (a) Nonparametric source. (b) Conventional MUSIC null-spectrum for the nonparametric source in Fig. 3(a) when the number of sensors L = 10(3); 30(+); 50(1); 55(0): It is easy to see that is a continuous bounded function of The gradient Hessian of are respectively. We have (30) (31) the matrix is a positive definite matrix, we use an optimization technique such as the steepest descent method to obtain (33). We now consider the case the distribution parameters are known. Conditioned on the distribution parameters, the covariance of the estimation errors of the DOA is cov (38) which is similar to the covariance obtained from the MUSIC method under the point model [14]. The covariance is naturally smaller than that unconditioned on the distribution parameter unless the correlation between the estimation errors is 0, or the two row vectors are orthogonal. Since the statistical analysis of the nonparametric sources strongly parallels that of the point sources, we will not reconsider the analysis here. under the assumption that (32) is sufficiently close to As shown in the Appendix, V. NUMERICAL EXAMPLES AND SIMULATION RESULTS In this section, examples of the distributed sources are considered to illustrate previous results explicitly. The direction of a signal source is denoted in radians the SNR in decibels.

7 966 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 4, APRIL 1997 Fig. 4. Covariance functions of the nonparametric source shown in Fig. 3(a) when the number of sensors L = 10(3); 20(+); 30(1); 50(0); 55(0): Fig. 5. Contour of V (; ) obtained with the parametric method for the nonparametric source in Fig. 3(a). A. solution Ambiguity of a Point Source Model applied to Distributed Sources Assume that the number of sensors of a uniform linear array is 10, 30, 50, 55 in Examples 1 2. Example 1: Let the number of parametric sources be two We estimate the DOA s with the conventional MUSIC method under a point source assumption, assuming that The conventional MUSIC null-spectrum is shown in Fig. 2. Only one local minimum can be found (around The other DOA (around ) cannot exactly be obtained using this method, even when the number of sensors is increased. Example 2: In this example, the nonparametric source is the 50th-order approximation of [i.e., in (13)],, as shown in Fig. 3(a). Assuming that, the conventional nullspectrum is as shown in Fig. 3(b); again, we cannot locate the two DOA (around ) exactly. These examples show that the MUSIC-based DOA estimator may fail when depending on use of a point source assumption, even when the number of sensors is increased. The following section will give an example of the performance using the nonparametric model. The parametric model will be used in the simulation of Section V-C. B. solution Ambiguity of Distributed Source Models Example 3: For the nonparametric source of Example 2, the source covariance function is shown in Fig. 4 for 55. As the value of becomes larger, it becomes clearer from the figure that the extent of the source is between between From Fig. 4, we see that if, the estimation of a nonparametric source can be achieved by examining the covariance function. To obtain a good estimate of the covariance function for a nonparametric source, we need This example shows that the nonparametric DOA estimator can be successfully used under the nonparametric source assumption. Fig. 6. Covariance functions of two parametric sources in Example 1 when the number of sensors L = 50(3); 70(+); 80(1); 100(0): Example 4: Assume that the number of sensors of a uniform linear array is 10. For the nonparametric source of Example 2, we estimate the DOA with the parametric method, assuming that The contour of the nullspectrum is as shown in Fig. 5: Only one peak can be found around This example shows that the parametric DOA estimator may fail when erroneously applied to a nonparametric source. Example 5: Consider the two parametric sources of Example 1. The source covariance function is shown in Fig. 6 for 100: When the number of sensors is 50, we may (incorrectly) estimate that one nonparametric source exists with the extent between On the other h, when is 70, 80, or 100, we can obtain a good approximation of the parametric source. This example shows that the nonparametric DOA estimator may fail when applied to a parametric source when the number of sensors is small. This example also shows, however, that the estimator may produce a good result when the number of sensors the model order are sufficiently large.

8 LEE et al.: DISTRIBUTED SOURCE MODELING AND DIRECTION-OF-ARRIVAL ESTIMATION TECHNIQUES 967 TABLE I VARIANCES OF THE DOA AND DISTRIBUTION PARAMETER ESTIMATION ERRORS UNDER THE MUSIC-BASED METHOD (a) When, the contour of the cost function (28) is shown in Fig. 7(a): Two peaks around may be obtained through the implementation of (29), in which the plane is searched for the minima of To better locate the two peaks, we plot the (conventional) sample spectrum (that is, the cross-section of the contour) with 0.92, as shown in Fig. 7(b). It is clearer now that a local minimum exists around Similarly, when we plot the cross-section with,asin Fig. 7(c), the second local minimum is found to exist around We next consider the estimation errors. Table I shows the variances of the estimation errors when is perturbed with fixed at Simulation results are obtained from 30 trials, theoretical values of the variances are calculated from (33). We observe that the variances of the estimation errors decrease as the difference of the two DOA s increases. (b) (c) Fig. 7. (a) Contour of V (; ) obtained with the MUSIC-based method when L =10;M =2;N = 100; SNR =20dB, ( 1 ; 1 )=(2=18; 0:9); ( 2 ; 2 ) = (7=18; 0:7): (b) Cross-sections of the contour in Fig. 7(a) at ^ =0:88(+); 0:9(0); 0:92(3): (c) Cross-sections of the contour in Fig. 7(a) at ^ = 0:68(+); 0:7(0); 0:72(3): C. Simulation sults In this section, we assume that, the number of snapshots, is 100, SNR 20 db, two parametric sources are temporally spatially uncorrelated. VI. CONCLUDING REMARK When signal sources are angularly distributed, we consider two distributed source models: parametric nonparametric. One signal source considered is a generalization of the point source. This parametric source is characterized by two parameters: the DOA distribution parameters. In the parametric model, the estimation of a source could alternatively be viewed as a 2-D estimation problem analyzed using a MUSICbased method. A direct method under a nonparametric model was also investigated. The asymptotic distribution of estimation errors is obtained to show statistical properties under the parametric model. Some simulation results discussions on the estimation of sources are given for the two distributed source models. We think the models considered in this paper would be appropriate in many cases including a) when the sources are correlated with each other (parametric model) b) when several sources form an inseparable source (nonparametric model). APPENDIX THE ASYMPTOTIC DISTRIBUTION OF THE ESTIMATION ERROR VECTOR IN THE MUSIC-BASED METHOD From the statistical results of [14], we can replace the Hessian of (31) by the asymptotic Hessian

9 968 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 45, NO. 4, APRIL 1997 without affecting the asymptotic properties of the estimation error vector. With the orthogonal property of (21), we also obtain that Then, (32) becomes (A.1) the asymptotic Hessian is obtained from (28) (31) (A.2) the gradient is obtained from (28) (30) (A.3) Since [14], we can approximate the gradient by (A.4) Let us now obtain the mean of the estimation error vector Since is known to be a zero-mean normal rom vector [7], [14] for, it is easy to see that the estimation error vector is a zero-mean vector from (A.1). Next, let us obtain the covariance matrix From (A.1), we have For convenience, let us define Then, we have (A.5) (A.6) (A.7) Since [7], [14], for, we have Therefore, we get (A.8) (A.9) ACKNOWLEDGMENT The authors are very grateful to the anonymous reviewers for their helpful constructive comments suggestions for their grammatical advice. REFERENCES [1] T. P. Jänti, The influence of extended sources on theoretical performance of the MUSIC ESPRIT methods: Narrow-b sources, in Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, San Francisco, CA, Mar. 1992, pp. II [2] J. Choi I. Song, Asymptotic distribution of the MUSIC null spectrum, IEEE Trans. Signal Processing, vol. 41, pp , Feb [3] J. Choi, I. Song, S. Kim, Y. K. Jhee, A generalized null-spectrum for direction of arrival estimation, IEEE Trans. Signal Processing, vol. 42, pp , Feb [4] J. Choi, I. Song, S. Kim, S. Y. Kim, H. M. Kim, A statistical analysis of MUSIC null-spectrum via decomposition of estimation error, Signal Processing, vol. 34, pp , Nov [5] H. Cox, Spatial correlation in arbitrary noise fields with application to ambient sea noise, J. Acoust. Soc. Amer., vol. 54, pp , Nov [6] G. H. Golub C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, [7] M. Kaveh A. J. Barabell, The statistical performance of the MUSIC minimum-norm algorithms in resolving plane waves, IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp , Apr [8] S. R. Lee, I. Song, Y. U. Lee, T. Chang, H. M. Kim, Estimation of two-dimensional DOA under a distributed source model some simulation results, IEICE Trans. Fundamentals, vol. E79A, pp , Sept [9] Y. U. Lee, S. R. Lee, H. M. Kim, I. Song, Estimation of direction of arrival for angle-perturbed sources, IEICE Trans. Fundamentals, vol. E80A, pp , Jan [10] A. Nuttall J. H. Wilson, Estimation of the acoustic field directionality by use of planar volumetric arrays via Fourier series method the Fourier integral method, J. Acoust. Soc. Amer., vol. 90, pp , Oct [11] S. U. Pillai, Array Signal Processing. New York: Springer-Verlag, [12] R. O. Schmidt, Multiple emitter location signal parameter estimation, IEEE Trans Antennas Propagat., vol. 34, pp , Mar [13] T. Shan, M. Wax, T. Kailath, On spatial smoothing for directionof-arrival estimation of coherent signals, IEEE Trans. Acoust., Speech, Signal Processing, vol. 33, pp , Aug

10 LEE et al.: DISTRIBUTED SOURCE MODELING AND DIRECTION-OF-ARRIVAL ESTIMATION TECHNIQUES 969 [14] P. Stoica A. Nehorai, MUSIC, maximum likelihood Cramer- Rao bound, IEEE Trans. Acoust., Speech, Signal Processing, vol. 37, pp , May [15] S. Valaee, B. Champagne, P. Kabal, Parametric localization of distributed sources, IEEE Trans. Signal Processing, vol. 43, pp , Sept Yong Up Lee was born in Seoul, Korea, on October 15, He received the B.S. degree in electronics engineering from Seoul National University, Seoul, Korea, in 1985, the M.S. Ph.D. degrees in electrical engineering from the Korea Adavanced Institute of Science Technology, Daejeon, in , respectively. Since September 1986, He has been with the Department of the Wireless Communication search Team, Telecommunication R/D Center, Samsung Electronics Co., Ltd., he is currently on the technical staff. His current research interests include array signal processing mobile communication theory. Iickho Song (S 80 M 87 SM 96) was born in Seoul, Korea, on February 20, He received the B.S. (magna cum laude) M.S.E. degrees in electronics engineering from Seoul National University, Seoul, Korea, in February 1982 February 1984, respectively. He also received the M.S.E. Ph.D. degrees in electrical engineering from the University of Pennsylvania, Philadelphia, in August 1985 May 1987, respectively. He was a Member of Technical Staff at Bell Communications search, Morristown, NJ, from March 1987 to February In March 1988, he joined the Department of Electrical Engineering, the Korea Advanced Institute of Science Technology, Daejeon, as an Assistant Professor became an Associate Professor in September His research interests include detection estimation theory, statistical signal processing, communication theory. Dr. Song served as the Treasurer of the IEEE Korea Section in 1989 as an Associate Editor of the Journal of the Acoustical Society of Korea (ASK) in He has served as an Associate Editor of the Journal of the Korean Institute of Communication Sciences (KICS) since February 1995 as an Associate Editor of the Journal of the ASK (English edition) since January He is also a Member of the ASK, KICS, Korean Institute of Telematics Electronics (KITE), Institution of Electrical Engineers (IEE). He was a recipient of the Korean Honor Scholarship in of the Korean American Scholarship in He received the Academic Awards from KICS in the Best search Award from ASK in Jinho Choi (M 94) was born in Seoul, Korea. He received B.E. degree in electronics engineering in 1989 from Sogang University M.S.E. Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science Technology, Daejeon, in , respectively. He was with Electronics Telecommunication search Institute (ETRI) as an research associate from December 1992 to May He is now with the DACOM R/D Center as a senior researcher. His research interests include wireless communications array/statistical signal processing. Seong Ro Lee was born in Gog Sung, Korea, on October 28, He received the B.S. degree in electronics engineering from Korea University, Seoul, in 1987 the M.S. Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science Technology, Daejeon, in , respectively. His current research interests include array signal processing DOA estimation.