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  1. 1. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012Comparative Study on Performance Analysis ofHigh Resolution Direction of Arrival Estimation Algorithms Chetan.L.Srinidhi, Dr.S.A.Hariprasad Abstract-Array processing involves manipulation of The application of the array processing requiressignals induced on various antenna elements. Its either the knowledge of a reference signal or thecapabilities of steering nulls to reduce co channel direction of the desired signal source to achieve itsinterferences and pointing independent beams toward desired objectives. There exists a range of schemes tovarious mobiles, as well as its ability to provide estimatesof directions of radiating sources, make it attractive to a estimate the direction of arrival with conflictingmobile communications system designer. This paper demands of accuracy and processing power.presents a performance evaluation of robust and high-resolution direction-of-arrival (DOA) estimation The technique used for estimating directions ofalgorithms such as MUSIC, ESPRIT and Q-MUSIC used arrival of signals using an antenna array has beenin the design of smart antenna systems. A comparative study of interest in recent years. Direction of arrivalstudy is carried out by evaluating the performance of methods has been widely studied in the literature andthese DOA algorithms for a set of input parameters that can be grouped into two categories. In the firstinclude the size of the sensor array, number and angular category, they are called as classical methods whichseparation of incident signals from the mobile terminals, provides a representation of the sources field (poweras well as noise characteristics of the mobile and angular positions of the sources) by projectingcommunication channel. MUSIC, ESPRIT and Q-MUSIC algorithms provide high angular resolution the model vector (directional vector) on the space ofamong the other current DOA estimation techniques and observation without considering the determination ofhence they are explored in detail. The simulation results the number of sources. However, these conventionalshows that Q-MUSIC algorithm is highly accurate, stable methods do not get a good resolution. The secondand provides high angular resolution even for category is known as "parametric" or high-resolutionmultidimensional complex data signals compared to method which requires prior knowledge of theESPRIT and MUSIC. number of uncorrelated sources before estimating their characteristics (angular position, power). TheIndex Terms - Direction of arrival (DOA), MUSIC, estimation problem is first solved by estimationESPRIT, Quaternion MUSIC. methods of the number of sources. Then a high- resolution method is applied to estimate the angular 1. INTRODUCTION position of these sources. These high-resolution methods are known to be more robust than The application of antenna array processing has conventional techniques.been in extensive research in recent years for mobilecommunication systems to cope up with the problem The origin of high-resolution methods was firstof limited channel bandwidth and to satisfy an ever proposed by Prony .This approach has been modifiedgrowing demand that a large number of mobiles put by Pisarenko to estimate the sinusoids [1]. Both theseon the channel. methods are based on linear prediction technique which characterizes the signal model. The modern high-resolution method is based on the concept of Manuscript received May, 2012. subspace, such as MUSIC developed by Schmidt [2], Chetan.L.Srinidhi is with the Department of Electronics andCommunication Engineering, Visvesvaraya Technological which requires a comprehensive search algorithm toUniversity Belgaum India, R.V.College of Engineering, Bangalore, determine the largest peaks for the estimatedIndia (srinidhipy@gmail.com). direction which is a computationally intensive Dr.S.A.Hariprasad is with the Department of Electronics and process. MUSIC fails to resolve coherent sources,Communication Engineering, Visvesvaraya TechnologicalUniversity Belgaum India, R.V.College of Engineering, Bangalore, sources with less number of snapshots and with lowIndia (hariprasad@rvce.edu.in). SNR conditions. To overcome these drawbacks Root- All Rights Reserved © 2012 IJARCET 67
  2. 2. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012MUSIC [3] was proposed which has better II. SIGNAL MODELprobability of resolution than MUSIC and alsoestimates coherent sources, but not applicable for all In this section, we present the general-rank signalarray geometry. Further ESPRIT [4] was developed models which frequently appear in array signalwhich has identical performance as Root-MUSIC, but processing for communication. The following signalis less computationally intensive than the other two model is applicable for MUSIC and ESPRIT, lateralgorithms because of the selection of sub arrays. the polarization signal model for Q-MUSIC isHowever in all these methods, the multidimensional discussed in Section V. The conventional data modelcollection of an EM vector sensor array is organizedinto a long vector to enable matrix formulation. As a assumes that the signal impinging upon an array ofresult, the relevant DOA estimators somehow destroy sensors to be narrow-band and emitted from a pointthe vector nature of the incident signals carrying source in the far field region. The far field wave ismultidimensional information in space, time and incident at a DOA upon a uniform linear arraypolarization. consisting of M identical antenna elements. Consider K narrowband signals S1(t), S2(t), ..., SK(t) at To overcome this drawback in array signalprocessing, recently quaternion based algorithms frequency f0 arriving with directions qk (k = 1,.., K)were proposed [5]. This quaternion model based and received by a linear array of M identical elementsalgorithms use vector sensors for multidimensional (M > K) spaced by a distance d, in an additive whitecomplex data signals, for recovery of vector nature of Gaussian noise, Fig.1. These signals can be fullyincident signals and also for polarization estimates of correlated as in the case of multiple paths or notEM waves. As vector sensors become more and more correlated as in the case of multiple users.reliable, polarization has been added to estimationprocess as an essential attribute to characterize Depending on the analytical representation, thesources, in addition to their DOAs. In recent years, received signal in baseband can be written as:MUSIC-like methods for polarized arrays arepresented in [6], [7] and ESPRIT techniques [8], [9],[10] which can be used to estimate spatially coherentsources, whereas MUSIC and ESPRIT is only for (1)uncorrelated sources. In this paper we discussquaternion based MUSIC algorithm for vector sensorarray which exploits spatial and polarization diversity Where is thefor multi-component complex data signals. It also reception signal or observation vector signal of (M-1)results in accurate estimation of signal subspace on a dimension representing the measured complextwo component vector sensor array. The quaternion envelopes of K signals on each antenna.MUSIC provides more robust resolution than theother subspace method even at low SNR conditionsand also with less number of samples. Q-MUSICallows a more accurate estimation of the noisesubspace for a two component data, compensating forthe loss of performance due to the reduction of datacovariance matrix size. This paper is organized as follows. Section II,describes receiving signal model. Section III,presents description of the MUSIC algorithm alongwith the simulation results. Section IV, discusses theESPRIT algorithm. A short description ofquaternion’s and polarization model along withQUATERNION MUSIC is introduced in Section V.Section VI, presents the Comparison of MUSIC,ESPRIT and Q-MUSIC. Finally Section VII, presentsthe conclusion of the work. Fig.1 Network of M antennas and receiver system with K incident signals. All Rights Reserved © 2012 IJARCET 68
  3. 3. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 Where N is the number of samples or observationSymbol T denotes transpose. is the steering or vectors, and X is the N×K complex envelopes matrixdirection vector of the kth source defined at the central of K measured signals.frequency: From the decomposition of this autocorrelation matrix of observation vectors into orthogonal subspaces, we will compare the performance of the (2) two methods (MUSIC, ESPRIT) of high resolution based on the concept of subspace. With m=1... where III. MUSIC ALGORITHMM is the geometric phase shift introduced at theelement m of the network and the kth signal A. Algorithmdepending on the angle of arrival. Sk is the complexenvelope of the analytic signal of the kth source MUSIC exploits the technique of eigenvectorsemitted and is the Gaussian vector of noise on the decomposition and eigenvalues of the covariancenetwork. It is noted that noises are stochastic matrix of the antenna array for estimating directions-processes assumed to be stationary with zero mean. of-arrival of sources based on the properties of the signal and noise subspaces. For this, the initial Using matrix notation, the matrix of observationscan be expressed as: (3) hypothesis is that the covariance matrix ܴ is notWhere: singular. This assumption physically means that sources are totally uncorrelated between them. MUSIC algorithm assumes that signal and noiseA is a MxK matrix formed by M steering vectors of subspaces are orthogonal. The signal subspacesources , S is the Kx1 vector of complex envelopes of consists of phase shift vectors between antennasK sources, and is the noise vector on the network. depending on the angle of arrival. All orthogonal vectors to constitute a subspace called noise If the number of sources K is less than the number subspace.of elements M of the network, then K directionalvectors are linearly independent and generate a vector MUSIC algorithm being based on the properties ofsubspace of the observation space of dimension M signal and noise subspaces, vectors derived fromassuming that signals and noises are stationary and generate a signal subspace collinear with steeringuncorrelated. The correlation matrix or covariance of vectors of sources and vectors derivedsignals will be given by: from generate a noise subspace orthogonal to steering vectors of these sources. (4)Noisy observation = Signal space + Noise space If the number of signals impinging on M element array is D, the number of signal eigenvalues and Where is the conjugate transpose of X, eigenvectors is D and number of noise eigenvalues is the MxM correlation matrix of the and eigenvectors is M-D. The array correlationnoise vector, I is the identity matrix and σ² is the matrix with uncorrelated noise and equal variances isnoise power identical for each element of network. then given by: is the KxK square matrix of covariance of the (6)signal vector given by is adiagonal of full rank. However, it becomes singular Wherewhen at least two sources are totally correlated. is array steering matrix. In practice, the correlation matrix or covariance is (7)estimated by an average over N observations asfollowing: (5) All Rights Reserved © 2012 IJARCET 69
  4. 4. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 has D eigenvectors associated with signals For the set of input parameters, MUSIC algorithmand M – D eigenvectors associated with the noise. has been tested for the following cases.We can then construct the M x (M-D) subspacespanned by the noise eigenvectors such that: Case.1. Varying number of array elements MUSIC algorithm has been tested in MATLAB for (8) two different sizes of array elements (8 and 16) considering previously defined set of input The noise subspace eigenvectors are orthogonal to parameters.array steering vectors at the angles of arrivals θ1, θ2,θ3, θD and the MUSIC Pseudo spectrum is given as: 4 x 10 MUSIC SPECTRUM 6 m-- array elements=8 b b array elements=16 5 (9) 4 pseudospectrum(db) However when signal sources are coherent or noisevariances vary the resolution of MUSIC diminishes. 3To overcome this we must collect several timesamples of received signal plus noise, assuming 2ergodicity and estimate the correlation matrices viatime averaging as: 1 0 -100 -80 -60 -40 -20 0 20 40 60 80 100 angle in degrees (10) Fig.2: Music spectrum for array elements 8 and 16. (SNR= 25 db and number of snapshots = 200) and From Fig.2 it is observed that with the increase in number of array elements, peak becomes more sharp(11) indicating an increase in ability to resolve two closely spaced targets and hence resulting in an enhancedWe find the ‘D’ largest peaks of PMUSIC ( ) in DOA estimation.eqn(9) to obtain DOA estimates. Estimated DOAB. Simulation Results Actual DOA Array Array DOA estimation using MUSIC algorithm is elements=8 elements=16performed based on a set of input parameters viz. 25 25 25Angle of arrival, inter element spacing, number of 80 80 80elements in an array, SNR range and number ofsnapshots. The input parameters for simulation of Table 2: DOA estimation for arrays elements 8 andMUSIC algorithm is given in Table 1. 16 (SNR= 25 db and number of snapshots = 200) Parameter Value Table.2 depicts the case where SNR is 25 dB and Angle of arrival of 25 , 80 hence the DOA estimation is equal for both array signals elements. For a lesser SNR value accurate angularInter element spacing estimation is possible for higher number of array (d) elements.Number of elements in 8 ,16 an array Case.2. Varying number of SNR values SNR range (dB) 0 to 25Number of snapshots 200,1000 DOA estimation varies with respect to variations in SNR values. Here MUSIC algorithm has been tested for different values of SNR (0dB and 25dB). Table 1: Input parameters for music algorithm All Rights Reserved © 2012 IJARCET 70
  5. 5. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 4 5 MUSIC SPECTRUM x 10 MUSIC SPECTRUM x 10 6 6 m-- SNR=0dB m-- Snapshots=200 b SNR=25dB b Snapshots=1000 5 5 4 pseudospectrum(db) 4 pseudospectrum(db) 3 3 2 2 1 1 0 -100 -80 -60 -40 -20 0 20 40 60 80 100 0 angle in degrees -100 -80 -60 -40 -20 0 20 40 60 80 100 angle in degrees Fig.4: MUSIC spectrum for snapshots 200 and 1000.Fig. 3: MUSIC spectrum for SNR of 0dB and 25dB. (SNR= 25 db and number of arrays elements=8) (Number of array elements = 8 and number of snapshots =200) From the Fig.4 it is clearly observed that accuracy of DOA estimates is directly proportional to the From Fig.3 it is observed that as SNR value number of snapshots. The estimated DOA for twoincreases, DOA estimates of MUSIC are more different snapshots is as shown in Table.4.accurate and almost near to estimated DOA. WhenSNR is very low (close to 0dB) accurate estimation Estimated DOAof DOA fails. The actual and estimated DOA’s are Actual DOA Snapshots=200 Snapshots=1000shown in Table 3. 25 24.82 25 Estimated DOAActual DOA 80 79.29 80 SNR=0dB SNR=25dB Table 4: DOA estimation for snapshots 200 and 1000 25 24.70 25 (SNR= 25 db and number of arrays elements=8) 80 79.41 80 VI. ESPRIT ALGORITHM Table 3: DOA estimation for SNR 0dB and 25dB (Number of array elements = 8 and number of A. Algorithm snapshots =200) ESPRIT (Estimation of Signal Parameters viaCase.3. Varying number of snapshots Rotational Invariance Techniques) was developed by Roy and Kailath in 1989 [4]. It is based on the Simulations are carried out for two different rotational invariance property of the signal space tosnapshots viz. 200 and 1000 keeping other input make a direct estimation of the DOA and obtain theparameters specified in Table 1 constant. angles of arrival without the calculation of a pseudo- spectrum on the extent of space, nor even the search for roots of a polynomial. This method exploits the property of translational invariance of the antenna array by decomposing the main network into two sub-networks of identical antennas which one can be obtained by a translation of the other, Fig.5 All Rights Reserved © 2012 IJARCET 71
  6. 6. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 i=0,1,2,…D (21) DOA can be calculated by (22) B. Simulation Results DOA estimation using ESPRIT algorithm is performed based on the same set of input parameters specified for MUSIC algorithm and are shown in Fig.5 Principle of the ESPRIT algorithm Table 5. The main advantage of this method is that it avoids Parameter Valuethe heavy research of maxima of a pseudo-spectrum Angle of arrival of 25 , 80or a cost function (therefore a gain calculation) and signalsthe simplicity of its implementation. In addition, this Inter element spacingtechnique is less sensitive to noise than MUSIC. It is (d)based on the array elements placed in identical Number of elements in 8 ,16displacement forming matched pairs, with M array an arrayelements, resulting in m=M/2 array pairs called SNR range (dB) 0 to 25“doublets”. Number of snapshots 200,1000 Computation of signal subspace for the two sub Table 5: Input parameters for ESPRIT algorithmarrays, P1 and P2, results in two vectors V1 and V2,such that Range[S]=Range[B]. Also, there should DOA estimation using ESPRIT technique has beenexist a non singular matrix T of D×D such that tested for the following cases. , where can be decomposed into V1 andV2. Case.1. Varying number of array elements , (16) ESPRIT algorithm has been tested for two different sizes of array elements (8 and 16) by considering other parameters as shown in Table 5.(17) ESPRIT 4 If D×D is diagonal,unitary matrix with phase shifts pseudospectrum (dB)between doublets for each DOA , there exists aunique rank D matrix FεC such that 3 V1W1+V2W2=BTW1+B TW2=0 (18) 2Rearranging eqn(18), we get: 1 BT =B T (19) With B as full rank and sources are having distinct 0 0 50 100 150DOA, then angle in degree (20) Fig.6: ESPRIT spectrum for array elements 8 and 16. (SNR= 25 db and number of snapshots = 200) Eqn(20) indicates that if we are able to find outeigenvalues of, which are diagonal elements of ,wecan estimate DOA as where All Rights Reserved © 2012 IJARCET 72
  7. 7. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 ESPRIT spectrum provides almost similar DOAestimates for different array elements with lesser Table 7: DOA estimation for SNR 0dB and 25dBvariance than MUSIC algorithm. (Number of array elements = 8 and number of snapshots =200) From Table 7 it is observed that ESPRIT provides better resolution than MUSIC even at lower SNR. Estimated DOA Case.3. Varying number of snapshots Actual DOA Array Array elements=8 elements=16 ESPRIT algorithm has been tested for two different 25 25.0031 25.0010 snapshots 200 and 1000 by considering input parameters as shown in Table 5. 80 79.9565 79.9873 ESPRIT Table 6: DOA estimation for arrays elements 8 and 5 16 (SNR= 25 db and number of snapshots = 200) pseudospectrum (dB) From Table 6 it is observed that as array size 4increases from 8 to 16, DOA estimates of signals arealmost close to actual DOA which is superior to 3performance of MUSIC. 2Case.2. Varying number of SNR values 1 ESPRIT technique has been tested for two differentSNR values 0dB and 25dB as in the case of MUSIC 0algorithm. 0 50 100 150 angle in degree ESPRIT Fig.8: ESPRIT spectrum for two different snapshots 1 200 and 1000. (SNR= 25 db and number of arrayspseudospectrum (dB) elements=8) 0.8 From Fig.8 it is observed that DOA estimates for 0.6 ESPRIT technique are almost close to actual DOA even at lesser number of snapshots and hence it 0.4 outperforms MUSIC algorithm. 0.2 Table 8: DOA estimation for snapshots 200 and 1000 (SNR= 25 db and number of arrays elements=8) 0 0 50 100 150 angle in degree Estimated DOA Actual DOA Snapshots=200 Snapshots=1000 Fig.7: ESPRIT spectrum for SNR of 0dB and 25dB. 25 25.0056 25.0047 (Number of array elements = 8 and number of 80 80.1840 80.0013 snapshots =200) The observation made from Table 8 clearly Pseudo spectrum obtained using ESPRIT technique indicates that ESPRIT provides more precisefor different S.N.R values is shown in Fig.7 and their estimation of DOA than MUSIC.DOA estimates are shown in Table 7. VI. QUATERNION MUSIC ALGORITHM Actual DOA Estimated DOA SNR=0dB SNR=25dB A. Quaternions 25 24.92 24.9658 80 79.1016 80.0026 All Rights Reserved © 2012 IJARCET 73
  8. 8. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 Quaternions are a four dimensional hyper complex polarized signal quaternion model proposed in thenumber system. Discovered by Sir R.W. Hamilton in next section.1843 [11], they are an extension of complex numbersto 4D space. A quaternion q is described by four B. Polarization modelcomponents (one real and three imaginaries). It canbe expressed in its Cartesian form as: Consider a scenario with one polarized source, assumed to be a centred, stationary stochastic process, emitting a wave field in an isotropic, (23) homogenous medium. This wave field is recorded on a two-component noise free sensor, resulting in twoWhere highly correlated temporal series , . In this case, the two signals are linked by phase and amplitude coefficient called polarization parameters (supposed constant in time and frequency). Consider that the two signals in time are transformed in the Fourier domain as ,with and then the two-component signal recorded on a vector –sensor can be expressed in the frequency Several properties of complex numbers can be domain such as:extended to quaternions. Some of them are givenbelow: (28)- The conjugate of q, noted , is given by: This signal is pure quaternion valued. Taking the- A pure quaternion is a quaternion which real part is first component as reference and with thenull: previous assumptions on polarization parameters, can be rewritten as:- The modulus of a quaternion q is = = = (1+ (29) = = and its inverse is Where , and are the amplitudegiven by ratios and the phase shifts for the second and third component respectively, with respect to the first one. (24) In the following, the working frequency will be omitted, assuming that we consider narrowband- A quaternion is said to be null if a = b = c = d = 0; signals or that we work independently at each frequency.- The set of quaternion’s, denoted by , forms anon-commutative normed division algebra, that C. Quaternion-MUSICmeans that given two quaternion’s q1 and q2: (25) MUSIC-like methods are based on the projection of a steering vector on the estimated noise subspace. Here we discuss a new approach based on- Conjugation over is an anti-involution: hypercomplex number system discovered by (26) Hamilton[11],they are an extension of complex numbers to four-dimensional(4-D) space. This new It is that a quaternion is uniquely expressed approach improves the signal subspace estimationas: , where = and = accuracy and reduces the computational burden. .This is known as the Cayley-Dickson form. It Additionally, the discussed algorithm presents ais also possible to express q in an alternate Cayley- better resolution power for direction of arrival (DOA)Dickson form. Thus, any quaternion q can be written estimation than the long-vector approach, foras: , where = and equivalent statistical performances and also results in This notation will be used in the All Rights Reserved © 2012 IJARCET 74
  9. 9. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012a reduction by half of memory requirements for expression of the quaternion spectral matrixrepresentation of data covariance model. becomes: The Quaternion Music can be summarized as (33)follows [12]:Step1: Consider a linear, uniform vector-sensor arrayof N sensors .Assume that the far-field waves from K Where and is asources (K-known, K < N) impinge on an antenna as matrix containing noise second order statistics.shown in Fig.9. Sources are supposed to bedecorrelated, spatially coherent and confined in the Step6: We associate the first K eigenvalues to thearray plane. Their polarizations are also stationary in signal part of the observation and the rest of N-K totime and space (distance). Noise is spatially white the noise part. Thus, the projector on the noiseand not polarized. subspace is defined as: (34) Step7: The quaternion steering-vector is then generated:  1 + i ρ e jϕ  Fig.   9 Acquisition Scheme q (θ , ρ , ϕ ) = N (1 + ρ ) 2 e + i ρ e j (ϕ −θ ) − jθ   e − j ( N −1)θ + i ρ e j (ϕ − N −1)θ   Step2: The source direction of arrival (DOA) canthen be calculated using the following formula: (35) (30) Where q is a three-parameter unitary vector, modelling the arrival of a source of DOA andWhere is the inter-sensors distance, is the polarization parameters on a 2C sensor array.wave propagation velocity and v is the working Step8: Quaternion-MUSIC estimator (Q-MUSIC) isfrequency. then computed by projecting the steering-vectorstep3: The output of the vector-sensor array is given on the noise subspace:by a column quaternion vector equal to thesum of the K sources contributions (added with anoise term): (36) eqn (36) for Q-MUSIC estimator similar to the well- known form of MUSIC algorithm for scalar-sensor (31) array. The functional in (36) has maxima for sets of ( corresponding to sources present in theStep4: We introduce the equivalent second order signal.representation for a vector-sensor array usingquaternion formalism. Quaternion spectral matrix D. Simulation Results is defined as: DOA estimation using Q-MUSIC algorithm has been tested for one polarized source impinging on a (32) two component (2C) - sensor array for inputStep5: Assuming the decorrelation between the noise parameters shown in Table 9.and the sources and between sources themselves, the All Rights Reserved © 2012 IJARCET 75
  10. 10. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 Parameter Value Table 10: DOA estimation for array of sensor 8 and Angle of arrival of 0.44rad 25 16 (SNR= 25 db, number of snapshots = 200, =3 signals and ) Inter element spacing (d) Case.2. Varying number of SNR valuesNumber of elements in 8 ,16 an array Q-MUSIC algorithm simulation has been carried SNR range (dB) 0 to 25 out for two different SNR values 0dB and 25dB for Number of snapshots 200,1000 input parameters shown in Table 9.constant modulus ratio 3 QMUSIC ( ) 0.4 m-- snr=25dB constant phase shift 0.27rad 0.35 r snr=0dB ( ) 0.3 Pseudospectrum(dB) Table 9: Input parameters for Q-MUSIC algorithm 0.25 0.2Q-Music algorithm has been tested for the followingcases. 0.15 0.1Case.1. Varying number of array elements 0.05 For two different array elements 8 and 16 Q- 0MUSIC algorithm has been tested with input 0 0.2 0.4 0.6 0.8 Angle in radians 1 1.2 1.4 1.6parameters shown in Table 9. QMUSIC Fig.11: QMUSIC spectrum for S.N.R values 0dB and 0.5 m-- array=16 25dB. (Number of array elements = 8 and number of 0.45 r array=8 snapshots =200) 0.4 0.35 From Fig.11 it is observed that even when SNR is Pseudospectrum(dB) 0.3 0dB, Q-MUSIC still provides better estimation of 0.25 DOA of signals when compared to MUSIC. The estimates are provided in Table 11. 0.2 0.15 Actual DOA Estimated DOA 0.1 SNR=0dB SNR=25dB 0.05 25 25.0675 25 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Angle in radians Table 11: DOA estimation for two different SNRFig.10: Q-MUSIC spectrum for two different array of 0dB and 25dB (array of sensor=8, number of sensor 8 and 16. (SNR= 25 db and number of snapshots = 200, =3 and ) snapshots = 200) Case.3. Varying number of snapshots From the Fig.10 it is observed that as arrayelements increases from 8 to 16 the 3dB detection Q-MUSIC algorithm has been tested for twolobe width for Q-MUSIC becomes narrower different snapshots 200 and 1000 by consideringcompared to MUSIC and ESPRIT and hence input parameters shown in Table 9.provides accurate DOA and polarized estimates formultidimensional signals. Actual DOA Estimated DOA Sensors=8 Sensors=16 25 24.97 25 All Rights Reserved © 2012 IJARCET 76
  11. 11. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012 0.8 QMUSIC Array elements=8 m-- Snapshots=200 Algorithm Actual Estimated % Error 0.7 r Snapshots=1000 DOA DOA 0.6 MUSIC ESPRIT Pseudospectrum(dB) 0.5 Q- 0.4 MUSIC 0.3 Array elements=16 Algorithm Actual Estimated % Error 0.2 DOA DOA 0.1 MUSIC 0 ESPRIT 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Angle in radians Q- MUSIC Fig.9: QMUSIC spectrum for snapshots 200 and 1000. (SNR= 25 db and number of arrays Table 13: DOA estimation for array elements 8 and elements=8) 16 (SNR= 25 db and number of snapshots = 200) The estimation of DOA using Q-MUSIC algorithm From Table 13, it is clear that as the number ofis directly proportional to the number of snapshots array elements increase, accurate DOA estimationsimilar to MUSIC. But from Fig.9, it is observed that can be achieved. Amongst the three algorithmsQ-MUSIC provides better estimation of signal arrival discussed above, Q-MUSIC has a lesser % error andeven at lower number of samples than MUSIC and the estimated DOA is almost equal to the actualthe estimated DOA is equal to actual DOA as shown DOA.in Table 12. Case.2. Varying number of SNR values For SNR= 0 dB and 25dB, all the three discussed algorithms have been simulated and results are tabulated in Table 14. SNR=0dB Actual Estimated DOA Algorithm Actual Estimated % Error DOA Snapshots=200 Snapshots=1000 DOA DOA 25 25.0092 25 MUSIC ESPRIT Table 12: DOA estimation for snapshots 200 and Q- 1000 (SNR= 25 db, number of sensors = 8, =3 MUSIC and ) SNR=25dB Algorithm Actual Estimated % ErrorVII. COMPARISON OF MUSIC, ESPRIT AND Q- DOA DOA MUSIC ALGORITHMS MUSIC ESPRIT Section IV, V and VI discussed the various Q-algorithms used in smart antenna systems for robust MUSICDOA estimation. The performance analysis ofMUSIC, ESPRIT and Q-MUSIC algorithm based on Table 14: DOA estimation for SNR 0db and 25dB.high resolution direction of arrival estimation is (Number of array elements=8 and number ofcompared in this section for the following cases. snapshots = 200)Case.1. Varying number of array elements In general, performance of DOA estimation degrades as signal to noise ratio decreases. But Q- For array elements 8and 16 all the three algorithms MUSIC accurately estimates DOA even at a veryhave been simulated and results are tabulated in lower gain of 0dB.Table 13. All Rights Reserved © 2012 IJARCET 77
  12. 12. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012Case.3. Varying number of snapshots snapshots than scalar techniques (MUSIC, ESPRIT). Thus Q-MUSIC can be quite successfully used in The comparison table for performance of three radar’s to improve clutter rejection and discriminatediscussed algorithms is shown in Table 15 for two between different types of target. It also providesdifferent snapshots 200 and 1000. more efficient spectrum utilization for mobile communication systems. Snapshots=200Algorithm Actual Estimated % Error DOA DOA REFERENCES MUSIC ESPRIT [1] V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophysical J. of the Royal Astron. Q- Soc., vol. 33, pp. 347–366, 1973. MUSIC [2] R. O. Schmidt, “Multiple emitter location and signal Snapshots=1000 parameter estimation,” IEEE Trans. Antennas Propagation,Algorithm Actual Estimated % Error vol. 34, no. 3, pp. 276–280, Mar. 1986. [3] A. J. Barabell, “Improving the resolution performance of DOA DOA eigenstructure based direction-finding algorithms,” Proc. of MUSIC ICASSP, Boston, MA, USA, pp. 336–339, 1983. ESPRIT [4] Richard Roy and Thomas Kailath, “ESPRIT-Estimation of signal parameters via rotational invariance techniques,” Q- IEEE Transactions on Acoustics, Speech, and Signal MUSIC Processing, vol. 37, N° 7, pp. 984-995, July 1989. [5] H. D. Schutte and J. Wenzel, “Hypercomplex numbers inTable 15: DOA estimation for snapshots 200 and digital signal processing,” Proc. IEEE Int. Symp. Circ. Syst., pp. 1557–1560, 1990.1000 (SNR= 25 db and number of array elements=8) [6] K. T. Wong and M. D. Zoltowski, “Self- initiating MUSIC direction finding and polarization estimation in spatio From Table 15, it is observed that Q-Music polarizational beamspace,” IEEE Trans. Antennasprovides better detection capability for lower number Propagation, vol. 48, pp. 1235–1245, Sept. 2000.of samples compared to the other two algorithms. [7] K. T. Wong and M. D. Zoltowski, “Diversely polarized root- MUSIC for azimuth- elevation angle of arrival estimation,”Hence Q-MUSIC algorithm is best suited in Digest of the 1996 IEEE Antennas Propagation Soc. Int.multipath environment whereas the received signal is Symp., Baltimore, pp. 1352–1355, July 1996difficult to estimate accurately. [8] M. D. Zoltowski and K. T. Wong, “ESPRIT-based 2D direction finding with a sparse array of electromagnetic vector-sensors,” IEEE Trans. Signal Processing, vol. 48, pp. VIII. CONCLUSION 2195–2204, Aug. 2000. [9] K. T. Wong and M. D. Zoltowski, “Uni-vector-sensor In this paper, we discussed three high resolution ESPRIT for multi-source azimuth, elevation and polarizationdirection finding algorithms based on their estimation,” IEEE Trans. Antennas Propagation, vol. 45, pp. 1467–1474, Oct. 1997.performance for different number of array elements, [10] J. Li and J. R. Compton, “Angle and polarization estimationsnapshots and different SNR’s. From the simulated using ESPRIT with a polarization sensitive array,” IEEEresults, it is observed that MUSIC and ESPRIT Trans. Antennas Propagation, vol. 39, pp. 1376–1383, Sept.provides an accurate estimation of DOA with 1991. [11] W.R.Hamilton, “ On quaternions,” in Proc. Royal Irishimproved resolution power than the other direction Academy,1843finding techniques. But in the case of diversely [12] Miron S., Bihan N.L. and Mars J. “Quaternion-MUSIC forpolarized antenna arrays where the SNR values and Vector-Sensor Array processing,” IEEE Trans. Signalnumber of snapshots are less, these two algorithms Processing, 2006, 54(4):1218-1229. [13] N. Le Bihan and J.Mars,” Singular value decomposition offailed to achieve precise estimation of DOA of matrices of quaternions: A new tool for vector-sensor signalsignals. To overcome these drawbacks we have processing.” Signal Process, vol.84, n0 7, pp 1177-1199,discussed a new technique for vector sensor array 2004.processing using Quaternion’s for diversely polarized [14] CUI Wei, “A Novel Quaternion DOA estimation algorithm based on magnetic loop antenna”.array. This Quaternion based algorithm (Q-MUSIC)of EM vector sensors can achieve better performance [15] J.P. Ward, Quaternions and Cayley Numbers, Algebra andthan scalar–sensor arrays, while occupying less space applications,Kluwer Academic, 1997and cost for hardware implementation. However, theprocessing requirements are somewhat higher for the [16] F. Zhang, “Quaternions and matrices of quaternions,” Linear algebra and its applications, vol. 251, pp. 21–57, 1997.diversely polarized array. Further we have shown thatQ-MUSIC provides higher direction finding accuracy [17] Kantor and A. Solodovnikov, Hypercomplex numbers, anand higher resolving power even with lower SNR and elementary introduction to algebras. Springer-V erlag, 1989. All Rights Reserved © 2012 IJARCET 78
  13. 13. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 4, June 2012[18] Kantor and A. Solodovnikov, Hypercomplex numbers, an elementary introduction to algebras. Springer-V erlag, 1989.[19] L.C. Godra, “Application of antenna arrays to mobile communications-PartI: Performance improvement, feasibility and system considerations,” Proc. IEEE, vol. 85, pp. 1031- 1060, Jul, 1997.[20] L.C. Godra,”Application of antenna arrays to mobile communications_Part II: Beam – forming and direction-of- arrival considerations,” Proc. IEEE,vol. 85,pp.1195-1245, Aug 1997. BIOGRAPHIES Chetan.L.Srinidhi graduated in Electronics and Communication Engineering from Nitte Meenakshi Institute of Technology, Bangalore India. He is Currentlty pursuing his M.Tech degree in Communication syatems, at R.V.College of Engineering, Bangalore, India. His research interests are in the fields of digital Signal Processing, Antennas and Digital Communication. Dr.S.A.Hariprasad obtained his PhD from Avinashilingam University for Women, Coimbatore in the area of digital controller’s .He is having teaching experience of 22 years and five years of research experience. He has published nearing 35 papers in international/national journals and conferences. He has also published a text book on advanced Microprocessor and reviewed books on Microwave engineering and won best teacher award (twice) from RSST and appreciation award from ISTE. His research areas of interest are embedded systems and RF systems. All Rights Reserved © 2012 IJARCET 79