International Journal of Scientific & Engineering Research Volume 8, Issue 5, May ISSN
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1 International Journal o Scientiic & Engineering Research Volume 8, Issue 5, May A New FACTOR and Interpolation Based DOA Estimation Technique Yashoda B.S Research Scholar, Jain University Bangalore, India. Yashoda_bs@yahoo.com Dr. K.R. Nataraj Proessor ECE, SJBIT Bangalore, India. nataraj.sjbit@gmail.com Abstract: Smart Antenna increases the capacity o the Mobile Communication System by making use o either Maximal Ratio Combining or Diversity combining techniques. Smart Antenna has to perorm a duplex operation. It has to receive signals as well as transmits signals. The reception part mainly requires the detection o user directions. In this paper a novel Signal Subspace, Factor method is proposed which detects the users with better bias and Resolution. The algorithm also makes use o interpolation o steering vector without any ardware resources so that the resolution is improved in a better way. The Factor Method is compared with existing DOA (Direction o arrival) algorithms namely Bartlett, MLM (maximum likelihood method), MEM (Maximum entropy method), MUSIC (Multiple Signal Classiication) and QR method. From the Results one can conclude that with respect to bias, resolution and RMSE the Factor method is the best. I. INTRODUCTION Smart Antenna is a combination o multiple antennas. The smart antenna has major blocks namely Direction o Arrival (DOA) and Beam orming. DOA is responsible or locating the mobile sources by computing the power spectrum while beam orming transmits the radiation in the look direction based on input rom DOA. There are many DOA algorithms in the literature each o the approaches have their own way o determining the power spectrum in the network. II. BACKGROUND There is a huge amount o work that is perormed on the direction o arrival algorithms and this is the latest technology used in mobile communication The Normalized Power method is an inheritance o Fourier-based spectral analysis [] to sensor array data. It maximizes the beam or a speciic direction. In the papers [], [3] statistical based estimation methods such as MLM is derived. In the paper [4] the antenna array is divided into doublets and then independent eigen vectors will be ound on the irst L- antenna elements covariance matrix and last L- covariance matrix. The direction o arrival estimation is perormed by using the tangent ormula rather than computing the power spectrum. In the paper [5] source localization is done with planar array or sensors both conditional and unconditional source signal models and in [6] minimal bounds on MSE estimator or general Gaussian observation model is given. In the paper [7] estimation o quasistationary signals is perormed and Khatri-Rao (KR) subspace is used to ind the DAO in such a way that the noise correlation is reduced but the computation time is very high due to the act that i other existing DOA methods takes N iterations this methods takes N- iterations. In papers [8], [9], [0] expression or Cramer Rao lower bound on the covariance o unbiased estimators o constrained parametric model is derived. In paper[] irst and second order extended inite impulse response ilters are addressed or sub optimal estimation o nonlinear discrete time state space models with AWGN. MUSIC [], [3], [4] is an acronym which stands or Multiple Signal Classiication. MUSIC provides the estimates o the source directions and then inds out the values in such a way that the bias is less. In the papers [5], [6], [7] DOA resolution limits in MIMO is discussed. In paper [8] expressions or partition matrix, inverse matrix and hermitian matrix can be obtained. In paper [9] sub space tracking algorithms are discussed. 07
2 International Journal o Scientiic & Engineering Research Volume 8, Issue 5, May III. Existing DOA ALGORITMS A. Normalized Power Method (Bartlett) In normalized power method irst the amplitude matrix is computed and then the steering vectors are computed or all the directions and once they are computed the combination is perormed to obtain maniold vector. Once it is obtained then the source correlation matrix and noise correlation matrix are ound out and inally the power spectrum is obtained or the variability between -90 degree to +90 degree. The power spectrum or the normalized power method is given by the ollowing equation S RS PNormalized Power ( ) = () L elements as a reerence. D. MUSIC Method (Multiple Signal Classiication) MUSIC method makes use o Noise Subspace in order to ind the actual source directions. The Noise Subspace is obtained as the combination o noise Eigen a vector which corresponds to low magnitude. The MUSIC method power spectrum is given by the equation P = MUSIC a( ) E N E N a( ) (4) a( ) is steering vector or an angle and E N is L x L-M matrix comprising o noise Eigen vectors. S is steering vector associated with the direction, R array correlation matrix and L E. QR Method This method perorms the QR decomposition antenna elements o equation (). in order to obtain the power spectrum ater inding the noise subspace and then arranges the Eigen values B. Maximum Likelihood Method (MLM) based on the decreasing order. The perormance o QR method is similar to that o MUSIC Method. Maximum likelihood method ollows the same phenomenon o Normalized Power Method but it The array correlation matrix can be deined computes the inverse o total correlation matrix so that using the ollowing equation. the likelihood is maximized. The power spectrum is computed using the ollowing equation R = A S A + σ I (5) PMLM = () a ( ) Rinv a( ) A = Array Maniold Vector a ( ) is the hermitian transpose o a ( ) S = Signal Correlation Matrix and R inv is the inverse o autocorrelation matrix. A = ermitian transpose o correlation matrix σ = var iance o noise C. Maximum Entropy Method (MEM) I = Identity Matrix MEM DOA method assumes that the entropy is maximized at a time in one speciic direction o source. It is build on top o normalized power method and ater computation o total correlation matrix it inds the column vector o the correlation matrix which corresponds to maximum entropy and utilizes it in the power spectrum. The power spectrum is given by the equation P = ME [ S C C S ] (3) C is column o R - and S is the steering vector. P ME () is based on selecting one o L th array The QR decomposition is perormed or R. R QR = QR( R) R = QR Decomposition QR equivalent o corelation matrix For the QR decomposed matrix Noise Eigen vectors are ound out and substituted in the power spectrum equation. 07
3 International Journal o Scientiic & Engineering Research Volume 8, Issue 5, May F. I Method Factor and Interpolation Method inds the Eigen subspace and then ind the Factor and determine the directions and then inally substitute the value in the power spectrum equation. Interpolated Maniold vector. M AM Step3: The amplitude vector or N i number o users is computed using the ollowing equation with the assumption o cross correlation is zero. * a a 0 * Notation Meaning 0 a a... 0 N Number o Antenna a N Number o Mobile Users Av = M d Distance between antenna elements S Steering Vector or an angle v * a a N N M M Maniold vector or multiple steering M AM vectors A Amplitude vector v th ai = i amplitude value σ Variance o Noise Step4: The total correlation matrix is computed using Sub Noise Subspace the ollowing equation Noise Sub Signal Subspace signal TC = M AM Av M AM + Cnoise (6) th ev i Eigen vector or i eigen value Factorization Step5: The Eigen values are ound out or the total correlation matrix and then the Eigen values are S Interpolated Steering Vector grouped which are having high dimension. The roots I o the ollowing equation are ound to get Eigen P Power Spectrum or Factor spectrum values λ Wavelength TC λi = (7) i i th angle TC Total Correlation Step 6: The signal subspace or the Eigen values is ound out or a set o higher magnitude Eigen values. C Noise Correlation noise Consider a set { λ, λ,..., λ N } which are M signal Eigen values then Eigen vectors are ound out Step: The I Method irst computes the or all N Interpolated maniold vector which provides the delay M. computation o em waves or various angles Let Sub signal represent the signal subspace which combines the Eigen vectors or all the Eigen values Step 7: Perorm the Factorization or Signal Subspace Step 8: The power spectrum is then computed using the ollowing equation. Step: Compute the hermitian transpose o the 07
4 International Journal o Scientiic & Engineering Research Volume 8, Issue 5, May P S = steering vector or angle S spectrum = S = hermitian transpose = S Factorization = hermitian transpose IV. Simulation Results: (8) or actorization Resolution Comparison: Case: Low RF Elements and Far Away Users Name Number o Antenna Elements 8 Number o Users 3 Amplitude o Sources in volts [v v 3v] Direction o Sources [ ] Set Up Name Type o Antenna Dipole Type o Array Uniorm Linear Array Variability Antenna Separation λ s or Simulation:. Resolution: The capability o an algorithm to distinguish between equal energy sources Fig: Perormance Analysis with nearly equal angles Fig shows the Perormance Analysis as shown in. Bias: The bias is computed using the the igure the proposed I Method, QR, MUSIC and ollowing equation. MEM perorm better as compared to MLM and Bartlett. B = true actual (9) true = true direction = actual direction actual I the bias is less then algorithm is good. 3. RMSE: The RMSE error is ound by taking the values o bias or various variations o angles. Case: Low RF Elements and Nearby Users Name Number o Antenna Elements 8 Number o Users 3 Amplitude o Sources [v,v,3v] Direction o Sources [ ] RMSE = initial initial end + 5 true 0 actual end = initial value o direction = end value o direction (0) 07
5 International Journal o Scientiic & Engineering Research Volume 8, Issue 5, May Case4: Large RF Elements and Nearby Users Name Number o Antenna Elements 00 Number o Users 3 Amplitude o Sources in volts [v,v, 3v] Direction o Sources [0 3 6] Fig: Perormance Analysis Fig shows the Perormance Analysis as shown in the igure I, QR, MUSIC perorms the best as compared to MLM and Bartlett. Case3: Large RF Elements and Far Away Users Name Number o Antenna Elements 00 Number o Users 3 Fig4: Perormance Analysis 4 Amplitude o Sources [v v 3v] Fig4 shows the Perormance Analysis4 as shown in Direction o Sources [ ] the ig all algorithms perorm better. Bias Comparison : Name Number o Antenna Elements 8 Number o Users Amplitude o Sources in volts v Direction o Sources 45 Fig 3: Perormance Analysis 3 Fig3 shows the Perormance Analysis3 as shown in the igure all algorithms perorm better but the sharpness o I method is the best 07
6 International Journal o Scientiic & Engineering Research Volume 8, Issue 5, May-07 5 The direction or the mobiles have been taken in increments o degree starting rom 0 to 70. Fig6: RMSE Computation Fig6 shows the RMSE computation as shown in ig the proposed I method has lowest RMSE o 0.05 as compared to remaining methods namely Bartlett, MLM, MEM, MUSIC and QR have RMSE closer to 0.8. V. CONCSION The various algorithms namely Bartlett, MLM, MEM, MUSIC,QR and I algorithms are simulated on various mobile conigurations. The ollowing conclusions can be drawn rom the results.. For the case o Mobile Users which are Far Fig5: Bias Computation Away and have less RF Sources then I,QR MUSIC and MEM perormed better and are able to detect the users but Bartlett and MLM Fig5 shows the bias computation as shown in igure the proposed I method has lowest bias o as compared to remaining methods namely Bartlett, MLM, MEM, MUSIC and QR have bias. method ailed to detect For the case o Mobile Users which are Nearby and have less RF Sources then I,QR, MUSIC perorms better and are able closer to 0. to detect the users but Bartlett, MEM and RMSE Comparison: MLM method ailed to detect 3. For the case o Mobile Users which are Far Name Away and have More RF Sources then all the algorithms perorm better Number o Antenna Elements 8 4. For the case o Mobile Users which are Number o Users 3 Nearby and have More RF Sources then all Amplitude o Sources in volts v the algorithms behave well. Direction o Sources 0::70 5. The bias o the proposed method is lowest as compared to MEM, MLM, MUSIC, Bartlett, MUSIC and QR method. 6. The RMSE o the proposed method is lowest as compared to MEM, MLM, MUSIC, Bartlett, MUSIC and QR method. REFERENCES [] N.D. Sidiropoulos, R.Bro, and G.B Giannakis, Parallel actor analysis in sensor array processing, Signal processing, IEEE Transactions on vol.48,no.8,pp ,000. [] P. Stoica and A. Nehorai, Perormance study o conditional and unconditional direction-o-arrival estimation, IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 38, no. 0, pp , October 990. [3]. L. Van Trees, Optimum Array Processing Part IV o Detection,Estimation and Modulation Theory. Wiley- Interscience, 00. [4] Marot, J.Fossati,C.:Bourennane,S., Fast subspace-based source localization methods, sensor array and multichannel signal processing Workshop,008. SAM th IEEE,vol.,no.,pp.03,06,-3 july
7 International Journal o Scientiic & Engineering Research Volume 8, Issue 5, May-07 5 [5] D. T. Vu, A. Renaux, R. Boyer, and S. Marcos, Some results on the weiss weinstein bound or conditional and unconditional signal models in array processing, Elsevier Signal Processing, vol. 95, no. 0, pp. 6 48, 04. [6] A. Renaux, P. Forster, P. Larzabal, C. D. Richmond, and A. Nehorai, A resh look at the bayesian bounds o the weiss-weinstein amily, Signal Processing, IEEE Transactions on, vol. 56, no., pp , November 008. [7] Wing-Kin Ma; Tsung-an sieh; Chong-Yung Chi, DOA estimation oquasi-stationary signals via Khatri-Rao subspace, Acoustics, Speech and Signal Processing, 009. ICASSP 009. IEEE International Conerence on, vol., no., pp.65,68, 9-4 April 009. antenna arrays. Synthesis Lectures on Antennas 3. (008): -76. [8] P. Stoica and B. Ng, On the cramer-rao bound under parametric constraints, IEEE Signal Processing Letters, vol. 5, no. 7, pp , July 998. [9] T. J. Moore Jr., A theory o cram er-rao bounds or constrained parametric model, Ph.D. dissertation, University o Maryland, College Park,Department o Mathematics, College Park, Maryland, USA, 00. [0] F. R omer and M. aardt, Deterministic cram er-rao bounds or strict sense non-circular sources, in International ITG/IEEE Workshop on Smart Antennas (WSA), February 007. [] Y.-. Li and P.-C. Yeh, An interpretation o the moore-penrose generalized inverse o a singular isher inormation matrix, IEEE Transactions on Signal Processing, vol. 60, no. 0, pp , October 0. [] P. Laxmikanth, Mr. L. Surendra, Dr. D. Venkata Ratnam, S. Susrutha babu, Suparshya babu Enhancing the perormance o AOA estimation in wireless communication using the MUSIC algorithm SPACES-05, Dept o ECE, K L UNIVERSITY [3] D. Schulz and R. S. Thom a, Search-based MUSIC techniques ord DoA estimation using EADF and real antenna arrays, in 7th International ITG Workshop on Smart Antennas 03 (WSA 03), Stuttgart, Germany, [4] Schmidt, R.O., Multiple emitter location and signal parameter estimation, Antennas and Propagation, IEEE Transactions on, vol.34, no.3, pp.76,80, Mar 986. [5] M. Landmann, Limitations o experimental channel characterisation, Ph.D. dissertation, Ilmenau University o Technology, Electronic Measurement Research Laboratory, Ilmenau, Germany, 007. [6] M. Landmann, M. K aske, and R. Thom a, Impact o incomplete and inaccurate data models on high resolution parameter estimation in multidimensional channel sounding, IEEE Transactions on Antennas and Propagation, vol. 60, no., pp , February 0. [7] M. Landmann, A. Richter, and R. Thom a, DoA resolution limits in MIMO channel sounding, in IEEE Antennas and Propagation Society International Symposium, vol., June 004, pp [8] Y. Tian and Y. Takane, More on generalized inverses o partitioned matrices with banachiewicz schur orms, Linear Algebra and its Applications, vol. 7430, no. 5 6, pp , 009. [9] Foutz, Jerey, Andreas Spanias, and Mahesh K. Banavar. Narrowbanddirection o arrival estimation or 07
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