TIME OF ARRIVAL BASED LOCALIZATION IN WIRELESS SENSOR NETWORKS: A LINEAR APPROACH

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1 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 IME OF ARRIVA BASED OCAIZAION IN WIREESS SENSOR NEWORKS: A INEAR APPROACH Ravindra S 1 and Jagadeesha S N 1, Jawahara Nehru Nationa Coege of Engineering, Shimoga Visvesvaraya echnoogica University, Beguam, Karnataka, India. rsp.cse@gmai.com jagadeesha_003@yahoo.co.in ABSRAC In this paper, we aim to determine the ocation information of a node depoyed in Wireess Sensor Networks (WSN. We estimate the position of an unknown source node using ocaization based on inear approach on a singe simuation patform. he Cramer Rao ower Bound (CRB for position estimate is derived first and the four inear approaches namey inear east Squares (S, Subspace Approach (SA, Weighted inear east Squares (WS and wo-step WS have been derived and presented. Based on the simuation study the resuts have been compared. he simuation resuts show that the wo- step WS approach is having higher ocaization accuracy. KEYWORDS Source ocaization, ime of Arriva, inear east Squares, Subspace Approach, Weighted inear east Squares (WS, wo-step WS and CRB 1. INRODUCION Wireess Sensor Network (WSN consists of a arge number of tiny ow cost, ow-power, mutifunctiona sensors which are capabe of sensing, computing and communicating between these wireess devices which are depoyed in a arge geographic area[1]. WSN can be appied to a wide variety of diverse areas[], such as environmenta monitoring, miitary appications, target tracking, medica care, space exporation, ocation based services such as Emergency 911 (E-911 [3], ocation sensitive biing, fraud detection, inteigent transport systems, ocation based Socia Networking and Mobie yeow pages etc, [4]. Due to the deveopments in wireess communication WSN have been a new area of research [5-7]. Many appications of WSN require the sensor nodes to acquire the position information of the sensor nodes depoyed. Data gathered by sensors shoud be associated with the sensors positions and it is worthess without the information about the pace of its origin. Despite the huge research effort, sti a we accepted approach on how to sove the ocaization issue is being reaized. Since the sensor nodes are inexpensive and are in huge number it is not practica to equip these sensors with a Goba Positioning System (GPS receiver. Various ocaization approaches have been proposed and can be seen in the iterature [8-13] and there is not a singe approach which is simpe, distinct and gives decentraized soution for WSNs. he DOI : /sipij

2 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Utra Wide Band (UWB techniques [14] give very decent ocaization accuracy but the systems are expensive. he commony used approaches for measuring position estimate in WSN are ime of Arriva (OA [15], ime Difference of Arriva (DOA[16], Received Signa Strength (RSS[17] and Ange of Arriva (AOA a.k.a., Direction of Arriva (DOA[18]. Where, the OA, DOA, and RSS measurement gives the distance cacuation between the source sensor and the receiver sensors whie DOAs provide the information of the ange and the distance measurements from the source and the receiver. Cacuating these distance and ange measurements is not simpe because of the noninear reationships with the source. Given the OA, DOA, RSS and DOA information, the main focus of this paper is based on OA positioning agorithms. We consider a two dimensiona (D rectanguar area where the sensors are depoyed in ine-of-sight (OS transmission, i.e., there is a direct path between the source and each receiver [19]. Aso, we concude that the measurements are we inside the expected range in order to obtain reiabe ocation estimation. he rest of the paper is organized as foows. In section we present, the measurement mode of OA, and their positioning principes. In section 3, we provide the inear approach of finding the position by four methods i.e., inear east Squares (S, Subspace Approach (SA, Weighted inear east Squares (WS and wo-step WS. In section 4, the mean square position error comparison of the above approaches is made. Finay, the concusions are drawn in section 5.. OA MEASUREMEN MODE AND PRINCIPES OF SOURCE OCAIZAION he mathematica measurement mode for OA based Source ocaization Agorithm is given as: r = f(x + n (1 Where x is the source position which needs to be estimated, r the measurement vector, n is an additive zero-mean noise vector and f(x is a known noninear function in x..1. ime of Arriva OA is the one-way propagation time of the signa traveing between a source and a receiver. his means that the source and a the receivers are accuratey synchronized to measure the OA information, and such an identica system is not needed if two way or round trip OA is computed. he computed OA is then mutipied with a known propagation speed, usuay denoted as c, gives the measured distance between the source and the receivers. he measured OA represents a circe with its centre at the receiver and the source must ie on the circumference in a wo Dimensiona (D space. hree or more such circes obtained from the noise free OAs resut in a distinct intersection point which represents the source position and is as shown in Figure 1(a and 1(b, specifying that a minimum of three sensors is necessary for two dimensiona position estimate [0]. If the number of sensors is ess than three there is a possibiity that there may not be any intersecting points and hence not a feasibe soution. Hence, a minimum of three sensors is required to obtain the intersection and these can be represented as a set of circuar equations, based on the optimization criterion the source position can be estimated with the knowedge of the known sensor array geometry [1, ]. 14

3 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 (a riateration (b Mutiateration Figure 1: Geometricay representation of OA Positioning system. he OA measurement mode is deveoped as foows. et [ ] coordinates of the th sensor, 1,,...,. = and x = [ x y] x = x y be the known be the unknown position of the source to be estimated. he number of receivers must be greater than or equa to 3. he distance between the source and the sensor, denoted by d is simpy: d x x y y = x-x = ( + (, = 1,,... ( he source radiates a signa at time 0 and the th sensor receives it at time t. hat is, { t } are the OAs and is represented in a simpe reationship between t and d : d t =, = 1,,..., c (3 OAs are prone to measurement errors. As a resut, the range based measurement based on mutipying t by c, denoted by r oa,, is modeed as: r d n x x y y n OA, = + OA, = ( + ( + OA,, = 1,,... (4 where noa, is the range error in r OA,, which is resuted from OA disturbance. r = f ( x + n (5 OA OA OA where, r OA = roa, 1 roa,..., roa, (6 and n OA = noa, 1 noa,..., noa, (7 15

4 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 f ( x = d = OA ( x x + ( y y 1 1 ( x x + ( y y M ( x x + ( y y (8 Here, f OA (x represents the known function which is parameterized by x and in fact, it is the noise free distance vector. he source position estimation probem based on OA measurements is to estimate x given {r OA, } or r OA. A zero mean uncorreated Gaussian process with variances {σ OA, } is assumed for the range error {n OA, }. his heps in to faciitate the agorithm deveopment and anaysis as we as Cramer Rao ower Bound (CRB Computation. It is noteworthy that the zero mean property indicates OS transmission. he Probabiity Density Function (PDF for each scaar random variabe r OA,, denoted by p (r OA,,, has the form of 1 1 ( p( roa, = exp r OA, d πσ πσoa, OA, (9 And is characterized by its mean and variance, d and {σ OA, }, respectivey. In other words, we can write r OA, N( d, σ OA, (10 Whie the PDF for r OA, denoted by p(r OA, is 1 1 p(r OA = exp / roa d COA roa d C ( π 1/ OA -1 ( ( (11 where C = diag( σ, σ,..., σ (1 OA OA,1 OA, OA,.. Cramer Rao ower Bound It is known that the MSPE of a biased estimator cannot be ess than the CRB. he mean square position error of the various positioning agorithms is computed and compared with CRB which gives a ower bound on variance attainabe by any unbiased estimators for the same data set [3]. Given the conditiona PDF, we may derive the CRB for OA based ocation estimation and the same is given as foows [4, 5]: Cacuate the second order derivatives of the ogarithm of the measured PDF with respect to x, that is n p( r / ( x x.. ake the expected vaue of n p( r / ( x x. o yied I( x = E{ n p( r / ( x x } 16

5 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Where I(x denotes the Fisher Information Matrix (FIM. And the ower bound for x and y are given by I -1 (x 1,1 and I -1 (x, respectivey. Aternativey, when the measurement errors are zero-mean Gaussian distributed, the FIM, whose eements are defined as: f ( x 1 f ( x I( X = C x x (13 where C is the covariance matrix. he FIM based on OA measurements denoted by: f ( x foa ( x = OA OA 1 ( IOA X C x x (14 It is straightforward to show that x x1 y y1 ( x x1 + ( y y1 ( x x1 + ( y y1 x x y y x M M x x y y ( x x + ( y y ( x x1 + ( y y1 foa ( x = ( x x + ( y y ( x x + ( y y x x y y d 1 d 1 x x y y 1 1 f O A ( x = d d x M M x x y y d d (15 (16 Empoying eq. (16 and eq. (1, eq. (14 becomes I ( x x ( x x ( y y = 1 σoa, d = 1 σoa, d ( x = ( y y OA ( x x ( y y = 1 σoa, d = 1 σoa, d Where the ower bound for x and y are denoted by -1 I ( x and 1,1 (17-1 I ( x respectivey, and the, 17

6 CRB ( OA x, is Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 CRBOA( x = I ( x + I ( x -1-1 OA 1,1 OA, (18 3. INEAR APPROACHES FOR SOURCE OCAIZAION Given the noninear expressions, the inear ocaization methodoogy tries to convert the noninear expressions of eq. (4, into a set of inear equations with zero mean disturbances. And a goba soution is obtained based on the corresponding optimization cost function. In this paper four inear positioning approaches namey inear east Squares (S, Subspace Approaches (SA, WS and two Step WS are presented inear east Squares he S approach utiizes the ordinary east Squares (S technique to estimate the position of x by reorganizing eq. 4 into inear equations [6]. And an intermediate variabe is added which is a inearization function to estimate the source position. he inear OA measurement mode in x can be obtained by squaring eq. 4 on both sides, where = 1,,..., et ( ( ( ( OA, OA, OA, r = x x + y y + n + n x x + y y, (19 ( ( OA, OA, OA, m = n + n x x + y y (0 be the noise term in eq. (19 and introduce a dummy variabe R of the form: R = x + y. (1 Substituting eq. (0 eq. (1 into eq. (19 yieds: ( ( OA, = + + OA, r x x y y m r = x x x + x + y y y + y + m OA, OA, x x y y + R + m = r x y, = 1,,..., ( OA, OA, et x1 y1 1 x y 1 A = (3 M M M x y 1 18

7 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 [ x y R] θ = (4 and = moa,1 moa, moa, q (5 he matrix form for eq. ( is then: roa,1 x1 y 1 roa, x y b = (6 M roa, x y Aθ + q = b (7 where the observed r OA of eq. (5 is now transformed to b, θ contains the source ocation to be determined and A is constructed from the known receiver positions. When { m OA, } are sufficienty sma such that noa,1 ( x x1 + ( y y1 q noa,1 ( x x + ( y y (8 M noa,1 ( x x + ( y y can be considered a zero-mean vector, that is E{ q } 0, we can approximate eq. (7 as: he S cost function based on eq. (9, denoted by J S, OA ( J = S, OA Aθ b. (9 % θ, is: ( θ% ( Aθ% - b ( Aθ% - b = θ% A Aθ% θ% A b + b b (30 Which is a quadratic function in % θ, and is a soe minimum in JS, OA ( corresponds to: S, OA ( % θ %. he S estimate θ = arg min J θ (31 θ% which can be easiy computed by differentiating eq. (30 with respect to θ % and equating the resuting expression to zero: 19

8 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 J S, OA ( θ% = 0 θ% θ% = θ A Aθ A b = 0 A Aθ = A b θ = A A A b (3 ( 1 he S position estimate can be obtained from the first and second entries of θ, that is, x = θ 1 θ (33 Eq. (33 is aso known as the east squares caibration method [7]. 3. Subspace Approach he subspace positioning approach using OA measurement is presented as foows. We first define a ( x matrix X: x1 x y1 y x x y y X = M M (34 x x y y which is parameterized by x. With the use of X, the mutidimensiona simiarity matrix [8], denoted by D, is constructed as: whose ( m, n entry can be shown to be D = XX (35 [ D ] = ( ( ( ( x, m - x x m n n - x + ym - y yn - y ( ( ( ( = 0.5 x ( ( m x + ym y + xn x + yn y xm xn ym y n where ( ( d d d = + + ( m n mn d = d = x x + ( y y is of known vaue because it represents the mn nm m n m n distance between the m th and n th receivers. We then represent D using Eigen Vaue Decomposition (EVD: D = UΛU (37 0

9 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Where = [ 1 ] vectors and Λ = diag ( λ λ λ U u u u is an orthonorma matrix whose coumns are corresponding eigen 1,,..., is the diagona matrix of eigen vaues of D with λ1 λ λ 0. Noting that the rank of D is, we have λ 3 = λ 4 = λ = 0. As a resut eq. (37 can aso be written as: D = U Λ U S S S = U Λ U Λ ( 1/ 1/ ( 1/ 1/ S S S S S S S S = U Λ Ω U Λ Ω ( U S u 1 u ΛS diag 1 and ΛS = diag λ1, λ denote the signa subspace components whie Ω is the rotation matrix such thatωω = I. Comparing eq. (35 and eq. (38 yieds: Where = [ ], = ( λ, λ We then determine the unknown rotation matrix X = U Λ Ω (39 S 1/ ( S S 1/ S Ω = U Λ X ( 1/ ( 1/ 1 U ( 1/ SΛS USΛ S S S = U Λ X 1/ =Λ U X (40 S S where is moore penrose pseudo inverse. Substituting eq. (40 into eq. (39 resuts in X = U U X (41 which impies that the position x can be extracted from the eigen vectors of the signa subspace. As d, = 1,,...,, is not avaiabe, we construct a practica D according to S S [ ] = ( + + D 0.5 d m, n m dn dmn. (4 1/ If the measurement error is present [8], U SΛ S is the S estimate of X up to a rotation. And hence eq. (41 becomes an approximate reation. o derive the position estimate, we first rewrite X as Where X = Y 1x (43 1

10 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Y x x M x 1 1 = y y M y (44 Using the subspace reation U SU S = I UnU n where U n = [ u3 u4 u ] corresponds to the noise subspace and Substituting eq. (43 into eq. (41, we get: U U 1x U U Y (45 n n n n Foowing, the S procedure in eq. (9 eq. (3, the subspace estimate of x using OA measurements is computed as: (( n n 1 n n x = U U U U Y (46 Y UnUn 1 = 1 U U 1 n n (47 he cassica mutidimensiona scaing approach [9] is a modified subspace technique. 3.3 Weighted inear east Squares Approach Since S is a simpe approach and provides an optimum estimation performance ony when the disturbances in the inear equations are independent and identicay distributed. From eq. (8, it is cear that because of the noise vector q the S OA-based positioning approach is suboptima. he ocaization accuracy can be improved if we incude a symmetric weighting J θ %. he fina obtained expression is the matrix, say, W, in the cost function, denoted by WS, OA ( WS cost function which is of the form: J ( θ% ( Aθ% - b W ( Aθ% - b WS, OA = = θ% A WAθ% θ% A Wb + b Wb (48 According to eq. (7 eq. (8, we have { b} E = Aθ which corresponds to the inear unbiased data mode. he optimum W, can be obtained simiary as best inear unbiased estimator (BUE [30, 31], which is equa to the inverse of the covariance of q. hat is, the weighting matrix is simiar to that if the maximum ikeihood methodoogy. Empoying eq. (8, we obtain: W = E { qq } 1 ( 4 OA,1 1,4 OA,,...,4 OA, diag σ d σ d σ d = diag,,..., 4 σ d σ d σ d OA,1 1 OA, OA, 1 (49

11 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 As { d } are not avaiabe, a sma error condition can be obtained by repacing d with roa, which is vaid an optimum W, for sufficienty sma error condition: W = diag,,... (50 4 OA,1 roa,1 OA, roa, OA, r σ σ σ OA, Foowing eq. (31 eq. (3, the WS estimate of θ is: θ = arg min J = θ ( A WA WS, OA 1 A Wb ( θ% he Weighted inear east Square position estimate is given by eq. (33. (51 With ony a moderate increase of computationa compexity [31], eq. (51 is superior to eq. (3 in terms of estimation performance. he ocaization accuracy can be improved by making use of θ according to the reation eq. (1 as foows. When x of eq. (51 is sufficienty cose to x, 3 we have: Simiary, for θ : ( ( x( θ x θ x = θ + x θ x ( (5 θ y y θ y (53 Based on eq. (1 and with the use of eq. (5 eq. (53, we construct: where h = Gz + w (54 h = θ 1 θ θ ( G = 0 1 ( z = x y (57 and ( ( w = x x y x R θ 1 θ θ (58 3 3

12 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Note that z is the parameter vector to be determined. he resut of BUE is used to compute the covariance of w in x and is of the form [31]: { } = ( E θ x θ y θ R θ x θ y θ R A WA (59 Empoying eq. (58 eq. (59, the optima weighting matrix for eq. (54, denoted byφ, is then: Φ 1 = diag ( x, y,1( diag ( x, y,1 A WA (60 As a resut, the WS estimate of z is ( 1 z = G ΦG G Φh (61 As there is no sign information for x in z, the fina position estimate is determined as: ( [ ] ( [ ] x = sgn sgn θ z 1 1 θ z (6 Where sgn represents the signum function [3]. his technique is caed the two-step WS estimator [33] where eq. (1 is used in an impicit manner. Simiary an expicit way is to use agrangian mutipiers [34, 35] to minimize eq. (48 subject to the constraint of eq. (1. 4. SIMUAION RESUS he performance evauation of the various inear OA based ocaization approaches is simuated using MAAB[M] Version (R010A on Microsoft Windows XP, Professiona Version 00, Service Pack 3, 3 bit operating system instaed on Inte[R], Core[M] Duo CPU, of Ram. he simuation is done in a - Dimensiona region with a size of (1100m x 1100m, where the unknown source is assumed to be at position (x, y = (00, 300, and the receivers are positioned in known coordinates at (0, 0, (0, 1000, (1000, 1000 and (1000, 0 respectivey. And the sensors are depoyed in a rectanguar area where the source is surrounded by four receivers and is shown in Figure. It is aso assumed that { n OA, } with variances { σ OA, } variance σ is proportiona to OA, 1 are zero- mean uncorreated Gaussian process, and zero- mean property indicates OS transmission. he range error d with SNR = d / σ. he signa-to- noise-ratio (SNR = 30dB has been assumed. A the methods estimate the position. he impementation fow of the two step WS and the CRB is shown in Figure 3 and 4 respectivey. Figure 5, shows the pot of x x y E + y of different inear OA, { } Mean Square Position Error (MSPE defined as ( ( approaches and CRB for SNR in the range [-10, 5] db, based on 1000 independent runs, which is given by 1000 ( x ( /1000 i 1 i x + yi y, where = ( xi, yi, denotes the position estimate of the i th run. From the Figure, it can be seen that the wo-step WS estimator achieves the optima estimation performance, whie the S, SA and WS approaches are suboptima. 4

13 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Figure : Position of Source and Receivers abe 1: Estimated OA positions obtained using different inear approaches. Method x in meters y in meters inear east Squares Subspace Approach Weighted inear east Squares wo Step Weighted east Squares abe 1 gives the resuts of the position estimate, and resuts of the two step WS approach is better when compared with the other inear approaches. he two step WS accuratey estimates the positions. he accuracy is higher in case of wo- step WS whie the other approaches have ower ocaization accuracy. 5

14 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Figure 3: Fowchart showing the computation of wo- Step WS approach 6

15 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Figure 4: Fowchart showing the computation of CRB Figure 5: Mean Square Position Error Computation of the different inear based approaches 7

16 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August CONCUSIONS he work presented addresses the probem of position estimation of a sensor node in a Wireess Sensor Network, using OA measurements in OS environments. he CRB for the position estimation probem has been derived first and ater four methods namey S, SA, WS and wo Step WS methods of inear approach have been derived and presented. Extensive simuations have been carried out and the resuts of different methods have been compared. he comparison reveas that the two step WS method is superior to the rest of the inear approaches in OS environments. We have restricted our studies to the inear approaches. he work can be extended to the noninear approaches aso and sha be reported in a future communication. racking mobie nodes is an interesting probem which may require a combination of two or more approaches to improve the accuracy of the position estimate. ACKNOWEDGEMENS he authors woud ike to thank Dr. Yerriswamy, (PDI Hospet, and their Coeagues at Dept. of CSE, JNNCE Shimoga, for the vauabe inputs and the reviewers for their usefu comments and suggestions. REFERENCES [1] Ravindra. S and Jagadeesha S N, (013, A Noninear Approach for ime of Arriva ocaization in Wireess Sensor Networks, 6 th IEE Nationa Conference on RF and Wireess IConRFW-13, Jawahara Nehru Nationa Coege of Engineering, Shimoga, Karnataka, India May, pp [] Yerriswamy. and Jagadeesha S. N, (011, Faut oerant Matrix Penci method for Direction of Arriva Estimation, Signa & Image Processing: An Internationa Journa, Vo., No. 3, pp [3] he Federa Communications commission about Emergency 911 wireess services, [4] Pawe Kuakowski, Javier Vaes-Aonso, Esteban Egea-opez, Wiesaw udwin and Joan Garcia- Haro, (010, Ange of Arriva ocaization based on antenna arrays for wireess sensor networks, artice in press, Computers and Eectrica Engineering Journa Esevier, doi: /j.compeeceng [5] Kar H, Wiing A, (005, Protocos and architectures for wireess sensor networks. John Wiey and Sons. [6] Stojmenovic I, (005, Handbook of sensor networks agorithms and architectures. John Wiey and Sons. [7] Wang C, Xiao. (007, Sensor ocaization under imited measurement capabiities. IEEE Network, 1:16 3. [8] Patwari N, Ash J N, Kyperountas S, Hero III AO, Moses R, Correa NS, (005, ocating the nodes: Cooperative ocaization in Wireess Sensor Networks. IEEE Signa Process Mag., : [9] H. Wymeersch, J. ien and M. Z. Win, (009, Cooperative ocaization in Wireess Networks, IEEE Signa Processing Mag., vo.97, no., pp [10] R Zekavat and R. M Buehrer (011, Handbook of Position ocation: heory, Practice and Advances, Hoboken, NJ: John Wiey & Sons, INC. [11] A. H. Sayed, A. arighat, and N. Khajehnouri, (005, Network based Wireess ocation: Chaenges faced in deveoping techniques for accurate wireess ocation information, IEEE Signa Processing. Mag., Vo., no. 4, pp, [1] Nea Patwari, Afred O Hero III, Matt Perkins, Neiyer S Correa and Robert J O dea. (003, Reative ocation estimation in Wireess Sensor Networks, IEEE ransactions on Signa Processing, 51(8: [13] Yerriswamy. and Jagadeesha S. N, (01, IFKSA- ESPRI Estimating the Direction of Arriva under the Eement Faiures in a Uniform inear Antenna Array, ACEEE Internationa Journa on Signa & Image Processing, Vo. 3, No. 1, pp. 4 46, 01. 8

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18 Signa & Image Processing : An Internationa Journa (SIPIJ Vo.4, No.4, August 013 Authors Ravindra. S. received his B.E., in Eectrica and Eectronics Engineering., and M.ech., in Networking and Internet Engineering, from Visvesvaraya echnoogica University, Begaum, Karnataka, India in 006 and 008 respectivey. He is currenty working towards a Doctora Degree from Visvesvaraya echnoogica University, Begaum, Karnataka, India. At present he is working as Assistant Professor, in Computer Science and Engineering department of Jawahara Nehru Nationa Coege of Engineering (affiiated to Visvesvaraya echnoogica University, Shimoga, Karnataka, India. Dr. S.N. Jagadeesha received his B.E., in Eectronics and Communication Engineering, from University B. D. Coege of Engineering., Davangere affiiated to Mysore University, Karnataka, India in 1979, M.E. from Indian Institute of Science (IISC, Bangaore, India speciaizing in Eectrica Communication Engineering., in 1987 and Ph.D. in Eectronics and Computer Engineering., from University of Roorkee, Roorkee, India in He is an IEEE member. His research interest incudes Array Signa Processing, Wireess Sensor Networks and Mobie Communications. He has pubished and presented many papers on Adaptive Array Signa Processing and Direction-of-Arriva estimation. Currenty he is professor in the department of Computer Science and Engineering, Jawahara Nehru Nationa Coege of Engg. (Affiiated to Visvesvaraya echnoogica University, Shimoga, Karnataka, India. 30