MST Radar Signal Processing using PCA Based Minimum- Variance Spectral Estimation Method

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1 International Journal of Modern Electronics and Communication Engineering (IJMECE) ISSN: 31-1 Volume No.-, Issue No.-, November, 1 MST Radar Signal Processing using PCA Based Minimum- Variance Spectral Estimation Method G. Chandraiah Electronics and Communication Engineering Sri Venkateswara Universit College of Engineering Tirupati, India. gchandraece3@gmail.com T. Sreenivasulu Redd Electronics and Communication Engineering Sri Venkateswara Universit College of Engineering Tirupati, India. mettu@ahoo.co.in V. omala Devi Electronics and Communication Engineering Sri Venkateswara Universit College of Engineering Tirupati, India. devikomala@gmail.com Abstract: The sub-space methods based on Eigen decomposition have been used for etracting relevant information from large data sets. The paper proposes, the principal component based spectrum computation b using the minimum variance spectral estimation method (). In this work, we investigate the data received from the MST (Mesosphere-Stratosphere-Troposphere) radar installed at NARL (National Atmospheric Research Laborator) Gadanki using. We also tested the proposed algorithm () for broadband signal in presence of different noise levels (α). For the simulated signal, the has given a superior performance while detecting the number of frequencies in etremel noise corrupted data also. Finall, the is used to process the MST radar data for estimating the Doppler spectrum and thus in turn to find the Zonal and Meridional and wind velocit components from the Doppler. Compared with eisting algorithms, the works well at higher altitudes and the MST radar results were validated with the GPS data. ewords: Subspace methods, Eigenvalue decomposition, Principle component analsis, Spectrum estimation, MST Radar and GPS. computational cost respectivel. Other algorithms also applied I. INTRODUCTION to the aforementioned data, such as cepstral thresholding [] and wavelet-based denoising []. In signal processing, the power spectral densit estimation techniques are classified as parametric and non-parametric algorithms. These techniques suffer from problems of spectral leakages. Due to this, there is a restriction in frequenc resolution. Hence, there is need and scope to develop new methods and algorithms that give an accurate power spectrum, particularl at higher altitudes. In this paper, a new algorithm named as minimum variance spectral estimation based on the principal component analsis is introduced to estimate the precise Doppler spectrum for the MST radar data. MST radar gives wind data in the mesosphere-stratospheretroposphere with a resolution of 1 m from a height of 3.km. MST radar utilizes the Doppler Beam swinging (DBS) technique for gathering wind information in different directions (East, West, Zenith, North, and South). The radar collects the information using various beam positions with 1 µs coded pulse and an inter pulse period of µs. The online data processing for Doppler spectra for each bin can be obtained b using FFT (Fast Fourier Transform). The DC removal, mean noise level estimation, incoherent integration and removal of interference are the steps that are involved in offline data processing. The correct estimation of the Doppler frequenc is the vital one in the detection and estimation of the wind velocit b the radar. A package for processing MST radar data is developed b the NARL, Gadanki. It is called as Atmospheric Data Processor (ADP) [1]. The package (ADP) can be estimated Doppler frequencies accuratel up to certain heights onl. Since the data is highl corrupted with noise at higher range bins, so the ADP is unable to estimate wind profiles at higher altitudes. It can be seen in the literature that there are man authors introduced different strategies, techniques, and algorithms for denoising the Doppler spectrum for MST radar information, computing Doppler frequencies from the estimated spectrum and thus, in turninding the Zonal U, Meridional V and Wind velocit W components. An adaptive estimation technique is presented in [] to estimate the Doppler spectrum. In this technique, certain parameters were used to adaptivel track the radar signal in the range-doppler spectral frame. Multi-taper spectral estimation [3] and Bispectral-based estimation [] have been applied to The paper is organized as follows. In Section II, we discuss the proposed algorithm. In Section III, power spectral Densit for simulated signal and MST radar results are discussed and the paper is finall concluded in Section IV. II. PROPOSED ALGORITHM Principle Component Analsis is a mathematical process which uses an orthogonal transformation to change a set of observations of correlated variables into a set of uncorrelated variables. In PCA approach there is an advantage of dimensionalit reduction. There are different spectral estimation algorithms to estimate the frequenc. But in certain cases, we need to find onl the amplitudes and frequencies of the spectrum. There is no need to find the entire spectrum. These are called frequenc estimation methods. These techniques ma emplo the vectors that lie signal subspace or in noise subspace. The signal subspace techniques form a lowrank autocorrelation matri which is incorporated into a MST radar data, which have broadened spectral peak and high spectrum estimation algorithm. The principal component RES Publication Page

2 International Journal of Modern Electronics and Communication Engineering (IJMECE) ISSN: 31-1 Volume No.-, Issue No.-, November, 1 analsis is one of the signal subspace methods. In the frequenc estimation methods, the orthogonalit of the signal and noise subspaces could be used to remove the frequencies of p eponentials in white noise. There are another set of algorithms which can be use vectors that lie in the signal subspace. These algorithms are based on principal component analsis of the Autocorrelation Matri (ACM) and are denoted as signal subspace methods. The autocorrelation matri for the input data n ( ) consisting of p eponentials plus noise is a sum of autocorrelation matrices due to signal s and noise n [7]. Let R be a ACM of process that consists of p comple eponentials in the white noise. R R R (1) s n The Eigen decomposition of R, we have p H H H i i i i i i i i i i1 i1 i p1 R v v v v v v () Assuming that the Eigenvalues are arranged in descending order, 1. Since the second term in above equation is due to onl noise, we can write a reduced rank approimation to the signal R, b retaining the onl principal Eigenvectors of R. p H s i i i i1 R v v (3) This approimated principal components ma be used instead of R in case of spectral estimator such as maimum entrop method or minimum variance method. The PCA of the ACM can be used in conjunction with an of the spectral estimation methods and thus forming principle components spectrum estimation []. In this paper, we developed the minimum variance method for PCA based spectrum estimation. The equation of the principal component version of the minimum variance method is given b, ˆ j PMV ( e ) () H e v p i=1 i where e is the vector of comple eponentials orthogonal to eigenvectors v, i 1,,..., p i and i denotes eigenvalues of the covariance matri. Selecting the principal components Let R be the covariance matri calculated from the mean subtracted data n ( ) and R can be epressed as, 1 V RV = D () In (), V is the matri of eigenvectors and D is the diagonal matri of eigenvalues of a covariance matri R. i D m; [ ] = p p,q q m ; p q () th here denotes the m eigenvalue. The eigenvalues represent RES Publication Page 3 m the energ distribution of source data among each of the eigenvectors. The cumulative energ content E of the th m eigenvector is the sum of the energ content across all the eigenvalues from 1 through m. m E[m] = D [ q, q], m 1,..., (7) q1 Taking the first M columns of V and representing it as M matriw W[ p,q] = V [ p,q], p 1,... ; q 1,..., M () where 1M. The cumulative energ E[m] can be used as guide in choosing an appropriate value of M. The smallest value of M is chosen such that it gives a high value of energ E[m] on a percentage basis. We have to choose M, so that the cumulative energ E[m] is greater than 9%. The smallest value of M is selected such that, E[ m M] 9% D[ qq, ] q1 thus, the number of principal components to be selected. III. RESULT ANALYSIS A. Result Analsis for Simulation Data: In this section, we appl proposed method to the data generated b using Gaussian random input to a sstem function. The sstem is designed with a transfer function such that the output data can be a broadband signal. Finall, we add noise of different levels (α) to the data generated and estimated Power Spectral Densit (PSD). Let n ( ) be the data generated with Gaussian random input, en ( ) which is passed through a filter having transfer function H( z ), such that X( z) H( z) as shown in Fig. 1. H(z) is varied to produce Ez ( ) different broadband signals [9]. en ( ) H( z ) n ( ) Figure1. Generation of simulated data with Gaussian random input passed through a filter. For testing the proposed method in presence of noise, the data generated are passed through an Additive White Gaussian Noise (AWGN) channel which adds the Gaussian noise with zero mean and unit variance and let α be the amplitude associated with it. α is varied such that different levels of noise are added to data generated to produce noise signal. ( n) ( n) w( n) 1 () (9)

3 Height (km) Mean Square Error Mean Square Error Mean Square Error Power Spectral Densit(dB) Power Spectral Densit(dB) Power Spectral Densit(dB) Variance Variance Variance International Journal of Modern Electronics and Communication Engineering (IJMECE) ISSN: 31-1 Volume No.-, Issue No.-, November, 1 The broadband nois signal is being generated using the Moving Average (MA) model and the differential equation as follows: ( n) e( n). e( n 1).1 e( n ) (11) where N denotes data length and en ( ) is a normal white noise with zero mean and unit variance. The corresponding transfer function is X( z) 1 H ( z) 1.Z.1Z () Ez ( ) for numerical simulations, N is taken as samples. To test the performance of in the presence of AWGN, we generated a new signal ( n ) 1 as ( n ) ( n ) w ( n ), n,1,,..., N 1. (13) Alpha= TRUE PER Alpha= Normalized Frequenc(w/pi) Alpha= Figure. Estimation of Power spectral densit (PSDs) using and PER in presence of noise associated with amplitudes α=., α=1 and α= PER Alpha=. Alpha=1 Alpha= Normalized Frequenc(w/pi) Figure3. Estimation of Mean Square Error (MSEs) using and PER in presence of noise associated with amplitudes α=., α=1 and α= Alpha= PER Alpha= Normalized Frequenc(w/pi) 1 Alpha= Figure. Estimation of Variance using and PER in presence of noise associated with amplitudes α=., α=1 and α=1.. B. Result Analsis for MST Radar Data: Atmospheric radars operate in VHF and UHF bands. The fluctuations in the refractive inde of the atmosphere serve as an object (target) for those radars. We applied for the data received from MST radar located at NARL Gadhanki. The MST radar data contains 1 bins; each bin has comple time series data points. For a particular beam, the Doppler frequencies and Doppler velocities can be calculated b, f NFFT Inde NFFT 1 (1) and NFFT v Inde.9 (1) here NFFT is the FFT points and velocit of light and (3MHz) fc c fc, c is the is the operating frequenc PER 3 Output SNR (db) Figure.Height profiles of SNR estimated for the east beam of radar data. RES Publication Page

4 Height (km) International Journal of Modern Electronics and Communication Engineering (IJMECE) ISSN: 31-1 Volume No.-, Issue No.-, November, 1 Likewise, the Doppler frequencies and Doppler velocities are computed for all si beams i.e. f E W Z Z N S and v E W Z Z N S respectivel. The formula for calculating wind velocit components using the above Doppler velocities as follows: 1 v ve vw.3 v *.173 vn vs v z v ZX vzy (1) where v and v z are the zonal U, meridional V, and vertical velocities respectivel. The vertical velocit component v does not used in the computation of wind z speed. Hence the wind speed (velocit) is computed as follows. W 1/ v v (17) The height profiles of the SNR [] derived from the spectrum estimated using periodogram (PER) and for the east beam of data is shown in Fig. (). From the SNR figure, it is observed that ields good SNR improvement as compared to that of PER. The Doppler profiles for four scans of the east beam obtained using ADP and are shown in Fig. (a) and (b) respectivelor the MST radar data received on Feb th, 1. The mean Doppler profiles obtained b using and ADP is compared in Fig. (c) and in the same wa, the standard deviations are compared in Fig. (d). Until the height of 1 km, the standard deviation for lies close to the zero line, but, ADP displas a clear variation from zero line. (a) (b) (c) (d) Doppler (Hz) - Doppler (Hz) - Doppler (Hz) ADP Standard Deviation Figure. Doppler height profiles for four scan ccles of the east beam using (a) ADP and (b). (c) Mean Doppler profile. (d) The standard deviation for the east beam of MST data Feb th, 1. RES Publication Page

5 GPS Height (km) International Journal of Modern Electronics and Communication Engineering (IJMECE) ISSN: 31-1 Volume No.-, Issue No.-, November, 1 1 (a) 1 (b) 1 (c) GPS ADP Zonal Velocit (m/s) - Meridional Velocit (m/s) 3 Wind Velocit (m/s) Figure7. Wind speed comparisons for the radar data collected on Feb th, 1 using ADP, and GPS. The zonal ( v ), meridional ( v ) and wind velocities computed using GPS [11], and ADP are shown in fig.7. This has been eecuted for the data collected on Feb th, 1 to show the consistenc of the. From the fig.7, it can be noted that the wind speed profiles obtained using are following the path of those calculated using GPS measure particularl in the altitude range of - km. The scatter graph of fig. displas the correlation between ADP, and GPS. B using, We get a correlation coefficient of.93 which is better than ADP with R1=.93 () R=. (ADP) Correlation Analsis the computational compleit reduces due to forming a lowrank approimation. Here we considered variance and mean square error (MSE) are the performance measures to test the. The real power of can be seen at higher altitudes. All the other eisting methods not succeed at those heights and find the wind speed inaccuratel. But it is not the case with. The proposed algorithm is showing Signal-to- Noise Ratio (SNR) improvement approimatel over.db overall heights. Standard deviation is also low when compared to the eisting approach. ACNOWLEDGMENT We would like to thank the Centre of Ecellence in the Electronics and Communication Engineering department, S.V. Universit College of Engineering, Tirupati for providing technical assistance and also thank to NARL, Gadanki for providing MST radar data. 1 REFERENCES ADP 3 ADP and Figure. Correlation between ADP, and GPS wind speeds for MST data. IV. CONCLUSION We proposed principal component based spectral estimation algorithm using the minimum variance spectral method. Since the major role is onl finding the Doppler frequencies from the radar echoes. B using Principal Component Analsis (PCA), [1] Anandan V., Atmopheric data processor-technical user reference manual, NMRF, DOS publication, Gadanki,. [] V.. Anandan, P. Balamuraliddhar, P.B. Rao, and A.R. Jain, A method for adaptive moments estimation technique applied to MST radar echoes, in Proc. prog. Electromagn. Res. Smp., 199.pp.3-3. [3] V.. Anandan, G. Ramachandra Redd, and P.B. Rao, Spectral Analsis of atmospheric signal using higher orders spectral estimation technique, IEEE Trans. Geosci. Remote sens.ol. 39, no.9, pp , Sep, 1. [] V.. Anandan, C.J. Pan, T.Rajalakshmi, and G. Ramachandra Redd, multi taper spectral Analsis of atmospheric radar signal, Ann. Geophs.ol., no. 11, pp.399-3, Nov.. RES Publication Page

6 International Journal of Modern Electronics and Communication Engineering (IJMECE) ISSN: 31-1 Volume No.-, Issue No.-, November, 1 [] T. Redd and G.R. Redd, MST radar signal processing using cepstral thresholding, IEEE Trans. Geosci. Remote Sens., vol., no., pp. 7-7, Jun. [] S. Thatiparthi, R. Gudheti, and V. Sourirajan, MST radar signal processing using wavelet based denoising, IEEE Geosci. Remote Sens., lett.ol., no., pp. 7-7, Oct. 9. [7] Monson H, Haes, Statistical Digital Signal Processing and Modeling, John Wile & Sonsm 199. [] D. U. M. Rao, T. S. Redd, atmospheric radar signal processing using principle component analsis, Digit. Signal Process. vol.3, pp. 79-, Sep. 1. [9] P.Stoica and N.Sandgren, Total-Variance Reduction Via Thressholding: Application to Cepstral Analsis, IEEE Trans. Signal Process.ol., no. 1, pp. -7, Jan 7. [] D.A. Hooper, Signal and noise level estimation for narrow spectral width returns observed b the Indian MST radar, Radio sci. 3()(1999) 9-7. [11] V. M. Jagannadha Rao, D. Naraana Rao, M. Venkata Ratnam,. Mohan, and S.V. B. Rao, Mean vertical velocities measured b Indian MST radar and comparison with indirectl computed values, J. Appl. Meteorol.ol., no., pp. 1-, Apr. 3. AUTHOR S BIOGRAPHIES G. Chandraiah received the B.Tech degree in ECE from Jawaharlal Nehru Technological Universit (JNTU) in And M.Tech in Electronics Instrumentation and Communication Sstems from Sri Venkateswara Universit College of Engineering, Tirupati in 11. Currentl, he is Ph.D full-time Scholar with the Department of Electronics and Communication Engineering, S.V.U College of Engineering, Sri Venkateswara Universit. His research interest includes radar signal processing and signal processing. T. Sreenivasulu Redd received the B.Tech Degree in ECE from Sri Venkateswara Universit, Tirupati, India, in 199, the M.Eng. Degree in Digital Electronics from arnataka Universit, Dharwad, India, in 199 and Ph.D. degree in Radar Signal Processing from Sri Venkateswara Universit, Tirupati. Currentl, he is Professor with the Department of Electronics and Communication Engineering, S.V.U College of Engineering, Sri Venkateswara Universit. His research interests include radar signal processing and image processing. Mr. Redd is a Fellow of the Institution of Electronics and Telecommunication Engineers and a member of the Indian Societ for Technical Education. V. omala Devi received the B.Tech degree in ECE from Jawaharlal Nehru Technological Universit (JNTU) in and M.Tech from Sree Vidhanikethan College of Engineering, Tirupati in. Currentl, he is Academic consultant with the Department of Electronics and Communication Engineering, S.V.U College of Engineering, Sri Venkateswara Universit. Her research interest in radar signal processing. RES Publication Page 7