SMOOTHED DOPPLER PROFILE IN MST RADAR DATA- THE MODIFIED CEPSTRUM APPROACH

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1 SMOOTHED DOPPLER PROFILE IN MST RADAR DATA- THE MODIFIED CEPSTRUM APPROACH M. Venatanarayana 1 and T. Jayachandra Prasad 1 Department of ECE, KSRE, Kadapa, India RGET, Nandya, India E-Mai: narayanamoram@gmai.com ABSTRACT The concept of cepstrum threshoding (CT) is appied to estimate smoothed nonparametric spectrum. The CT method is appied to Mesosphere, Stratosphere and Troposphere (MST) radar data for spectra ceaning. This method is not superior as compared with the conventiona Periodogram method. So, to enhance the spectra visibiity in Dopper Profie (DP), the CT technique is modified. The modified cepstrum () is deveoped and impemented, to vaidate, it is appied to radar data. An adaptive spectra moment s estimation technique is utiized for anayzing the Dopper spectra of the MST radar signas. From the Dopper frequency components, the radia veocities in the direction of the zona (U), meridiona (V), and vertica (W) are estimated. In turn, the wind veocity is estimated from U and V components. The proposed method wors we even at higher atitudes and resuts are compared with the traditiona methods such as Pea detection technique and the matched fiter. Keywords: MST radar, cepstrum threshoding, dopper shift, matched fiter, spectra pea detection, spectra moments. 1. INTRODUCTION Nationa Atmospheric Research Laboratory (NARL) at Gadani (13.7 N, 79.1 E), India has been operating 53 MHz atmospheric Mesosphere, Stratosphere and Troposphere (MST) radar for studying structure and dynamics of ower, midde and upper atmosphere [1-]. MST Radar provides estimates of atmospheric winds on a continuous basis with high tempora and spatia resoutions. MST Radar uses the echoes obtained over the height range of 1-1 Km to study winds, turbuence. The Indian MST Radar is operationa for scientific studies of the atmosphere in the height range of - m (troposphere and ower stratosphere), -9 m (mesosphere), 1-15 m (E region) and 15- m (F region). The echoes from the atmosphere are due to neutra turbuence in the ower height regions and due to the irreguarities in eectron density in higher atitudes. The method adopted for identifying the signa and computing the three ow-order spectra moments is centra to the probem of extracting information from the Dopper spectrum of the MST radar signa. The conventiona method of anayzing the MST radar spectra data is based on identifying the most prominent pea of the Dopper spectrum for each range gate and computing the three ow order spectra moments and signa-to noise ratio (SNR) using the expressions given by [5]. Various methods were proposed to identify the Dopper profies under a wide range of signa to noise ratio (SNR) conditions [-1]. A these techniques are not superior at ow SNR conditions. The method of adaptive moments estimation was presented to perform consistenty we at distinct SNR conditions of atmospheric signas [11]. The method is appied to the radar spectra data and the resuts are presented for ow and high SNR conditions. The method has certain imitations in its appication such as (1) under severe weather conditions, the agorithm fais to estimate the moments propery which is mainy due to the difficuties arising from the mutipe echoes () the agorithm invoves five sets of moments estimation and six iterations for the fina moments extraction. This introduces compexity in computation. The research wor carried by S. Varadarajan of S V University, has overcome the above imitations using waveet denoising the time series data priori to spectrum processing. To fix the threshod, the cross vaidation scheme was used. The spectra visibiity range of the Dopper profie using waveet denoising is increased to 1Km at the expense of computationa compexity. In this paper, an attempt has been made to appy the concept of Cepstrum Threshoding (CT) for smoothed spectrum estimation [1]. The CT method is appied to radar to for the Dopper profie. It is observed that no superior than the existing techniques. To achieve better spectra ceaning, the cepstra coefficients are weighted by a Hamming or Hanning window. Since the higher indexed cepstra coefficients are reated to rapid fuctuations in estimated spectrum, the windowing process is performed by retaining the ower indexed cepstra coefficients and modifying the higher indexed cepstra coefficients. The modified cepstrum () approach is appied to the MST radar data. In this approach, the waveet denoising, dc remova, averaging operations are not used in the estimation of Dopper profie. The theory of the smoothed spectrum estimation using the is presented in section. A stepwise description of the agorithm appied to the MST radar data is given in section 3. The resuts and discussion are in section and the important concusions are in section 5.. SMOOTHED SPECTRAL ESTIMATION VIA THE MODIFIED CEPSTRUM Consider a stationary, discrete-time, rea vaued signa x ( n), n =,1,,..., with covariance sequence 13

2 { r } = and power spectra density (or spectrum) φ p (ω) where ω [ π, π ]. In practice, the spectrum φ (ω) is estimated from a set of observed sampes N { x ( n) } 1 t= of the signa. The periodogram estimate of φ(ω) is given by [13-] N 1 t= iωn ˆ 1 φ p ( ω) = x( n) e (1) N where the subscript p denotes the periodogram estimate. π Let ω =, =,..., N 1 () N denote the Fourier grid of the anguar frequency axis. ˆ φ p ( ω) can be computed efficienty by means of a Fast Fourier transform (FFT) agorithm. The cepstra coefficients are defined as: c 1 1 N = jω n[ φ ( ω )] e, =,1,... N 1 (3) N = where it is assumed thatφ (ω ) >,. The cepstra coefficients have severa interesting features, one of which is mirror symmetry: cn = c, =,1,..., N / () which mean that ony haf of the sequence c,..., cn /, is distinct. The other haf is obtained from c1,...., c( N / ) 1, as in (). Using the periodogram estimate in (1), a common estimate of the cepstra coefficients is obtained by repacing φ (ω) in (3) with ˆ φ p ( ω), which is given in [15]. N 1 1 c n[ ˆ = φ p ( ω )] e N = =,... M, jω ˆ + γδ, where 1 if = δ, = () ese M = N/ and γ = (the Euer s constant)., (5) It can be shown that in arge sampes, the M estimated cepstra coefficients { cˆ } = are independent normay distributed random variabes []: c ˆ ~ N( c, s ) (7) with s π = 3N π N if if =,..., M = 1,..., M 1 The cepstra coefficients are weighted by a Hamming or Hanning window. Since the higher indexed cepstra coefficients are reated to rapid fuctuations in estimated spectrum, the windowing process is performed by retaining the ower indexed cepstra coefficients and modifying the higher indexed cepstra coefficients. The modified cepstra coefficients are denoted by { c ~ }. The smoothed spectra estimate corresponding to { c ~ } is given by: ~ N 1 ( ) exp ~ = jω φ cep ϖ c e p ; =,... N 1 (9) = where the subscript cep signifies its cepstrum dependence. The fina scaed spectrum estimate ˆ φ cep ( ω ) is then given by: ˆ ~ φ ( ω ) = ˆ αφ ( ω ), =,..., N 1 (1) cep where N 1 = = p N 1 = cep ˆ ~ φ ( ω ) φcep ( ω ) ˆ α ~ (11) φ cep ( ω ) 3. EXISTING AND PROPOSED ALGORITHMS 3.1 The existing method The time series raw data (I and Q) has been used and then the coherent integration was performed. It improves the process gain by a factor inter puse period and aso improves the SNR by integrating the detected quadrature due to any other succeeding operation. The variance of the estimate decreases with the use of a window. It aso reduces the eaage and picet fence effects. The Fourier anaysis characterizes the frequency content of the signa. After performing power spectrum ceaning the Dopper profie is estimated by using max pea detection method. From the profies the Dopper frequencies are cacuated. By using Dopper frequencies radia veocities are cacuated, from which the zona, meridona and vertica veocity components are cacuated. ()

3 Wind speed is cacuated using zona and meridona veocities. The existing agorithm used in atmospheric signa processing can accuratey estimate the Dopper frequencies of the bacscattered signas up to certain height. However, the technique fais at higher atitudes and even at ower atitudes when data are corrupted with noise due to interference, cutter etc. Muti taper spectra estimation agorithm has been appied for radar data. This method has the advantage of reduced variance at the expense of broadened spectra pea. The FFT technique for power spectra estimation and adaptive estimates technique for estimating the moments of radar data has been proposed. This method considers a certain number of prominent peas of the same range gate and tries to extract the best pea, which satisfies the criteria chosen for the adaptive method of estimation. This method faied to give consistent resuts. Hence, there is a need for deveopment of better agorithms for more accurate estimation of wind parameters Estimation of dopper shift for atmospheric radar signas The atmospheric signas are accompanied with a ot of noise predominanty white Gaussian noise. In order to improve the probabiity of estimation of the Dopper on the said noise, a good spectra ceaning technique is required to compute the frequencies of the atmospheric signa. The agorithm based on an adaptive data processing technique, consists of sequence of steps given in [11] were used to determine the radar signa Dopper profie Moments estimation There are many methods adapted to find out the noise eve estimation. The method impemented here is based on the variance decided by a threshod criterion. The noise eve threshod sha be estimated to the maximum eve L, such that the set of spectra points beow the eve S, neary satisfies the criterion: {Variance(S)/Mean(S) }<=1 over number of spectra averaged. The extraction of zero, first and second moments is the ey reason for on doing a the signa processing and there by finding out the various atmospheric and turbuence parameters in the region of radar sounding. The basic steps invoved in the estimation of moments such as the zeroth moment or Tota power, the first moment or Mean Dopper, the second moment or variance (the spectra bandwidth), and Signa to Noise Ratio (SNR) are foowed from [5] UVW computation Cacuation of radia veocity and height For representing the observation resuts in physica parameters, the Dopper frequency and range bin have to be expressed in terms of corresponding radia veocity and vertica height. Height, H = Ct R cosθ / meters Veocity, V = Cf D /( f c ) or f Dλ / m/sec where C = the ight veocity in free space, f D = Dopper frequency, f c = the carrier frequency, λ = Carrier waveength, θ = Bean tit ange, t R = Range time deay. Computation of absoute wind veocity vectors (UVW) After computing the radia veocity for different bean positions, the absoute veocity (UVW) can be cacuated. To compute the UVW, at east three noncopanar beam radia veocity data is required. If higher numbers of different beam data are avaiabe, then the computation wi give an optimum resut in the east square method. Line of sight component of the wind vector V V, V, V ) is: V D = V ( x y z. i = Vx cosθ x + Vy cosθ y + V z cosθ where X,Y and Z directions are aigned to East-West, North-South and Zenith, respectivey. Appying east square method, residuaξ = V V ), where ( D Di V Di = f Di λ / and i represents the beam number to satisfy the minimum residua. Minimizing residua ξ aong X, Y and Z direction eads tovx, Vy andvz, which corresponds to U (Zona), V (Meridona) and W (Vertica) components of veocity. Estimation of wind-speed The winds speed can be cacuated by using the formua: Wind-speed W = U + V The horizonta component of the wind veocity is cacuated from the UV components which are estimated from the Dopper frequencies. 3. The proposed method The consistent method to reduce the variance estimate is the CT approach. Stoica and Sandgren () proposed the CT method for the smoothed spectrum estimation []. Practicay, the variance reduction in spectrum estimation using the CT method is not significant. To achieve better variance reduction, the CT method is modified, caed as the method. To vaidate, the approach is appied to MST radar data. The agorithm is based on an adaptive window technique, consists of a sequence of steps to determine the radar signa profie, in a Dopper spectra frame. Step-1: The cepstra coefficients are cacuated using FFT for the given time series of data Step-: Appy the Hamming or Hanning window on the cepstra coefficients Step-3: Dopper power spectrum is obtained from the cepstra coefficients z 15

4 Step-: The adaptive moment s estimation technique is used to obtain the smoothed Dopper profie. Step-5: The steps 1 to are repeated for the whoe frame in estimating the Dopper frequencies. After spectra ceaning, the genuine Dopper echoes are seected for drawing Dopper profies using adaptive window method and maximum sope detection method. The proposed agorithm performs spectra ceaning by mutipying the smoothing window with the cepstra coefficients. Remaining part of the moment s estimation, UVW computation and wind speed cacuation are same as that of the existing method. Range (Km) FFT based D Spectrum. RESULTS AND DISCUSSIONS The proposed method is appied for the East beam of radar data to extract the Dopper profie. The Dopper profie of the radar data based on FFT and is shown in Fig.1. From that, it is cear that Dopper profie using FFT is visibe upto 11Km, beyond which the atmosphere noise is dominating the spectra contents. The proposed agorithm is abe to smooth the spectra contents of Dopper profie for a heights. The periodogram, the CT and the techniques are appied to 5 th, 3 th, 55 th, th and 15 th bins (for cear comparison purpose, we seected few bins from ow range to high range i.e. in incrementa steps of 5 from starting 5 th bin to 15 th bin) of East beam radar data for spectra estimation. From Figs., 3 and, it is observed that simiar spectra contents are produced by the periodogram and CT methods. The resuts confirm that the estimated spectra based on technique are noise free, smoothed enveope when compared with the above methods. It increases the abiity to extract origina Dopper frequency from the Dopper profies. 1 FFT based D Spectrum 1 based D Spectrum Height (Km) Dopper(Hz) Figure FFT based spectra at various heights. CT based D Spectrum Dopper (Hz) Figure 3 CT based spectra at various heights. based D Spectrum Range (Km) 1 1 Range (Km) Dopper(Hz) -5 5 Dopper(Hz) Figure 1 The spectra of East beam dated on nd June 9 using FFT and. Range (Km) Dopper(Hz) Figure based spectra at various heights.

5 Using the AME technique, the Dopper profies for these methods are shown in Figs. 5 and. The Dopper profie for east beam data using Atmosphere Data Processor (ADP) software is shown in Fig. 7. The estimated Dopper profie using method is in agreement with that of the ADP software. From Figs. and 9, it is observed that the wind speed trace using the proposed method is simiar to the matched fiter and the pea detection technique with AME. To vaidate the Dopper wind veocity profie estimated by the method, independent observation is obtained using radiosonde. Fig. (d) shows a sampe pot of the comparison of wind veocities of Dopper profie based on FFT, and radiosonde data. The resuts confirm that the estimated wind veocity profie using the proposed method is in ine with radiosonde data. Range(Km) based D Dopper Profie Dopper(Hz) FFT based D Dopper Profie Figure. The based Dopper profie of East beam using AME technique. 1 Range(Km ) Dopper(Hz) Figure 5 The FFT based Dopper profie of East beam using AME technique. Figure 7. Dopper profie of East beam using ADP software. 17

6 U component of veocity 1 1 V component of veocity FFT Range(Km) 1 1 Range(Km) 1 1 FFT veocity(m/s) veocity(m/s) (a) (b) 1 W component of veocity 1 Wind speed Range(Km) 1 1 Range(m) 1 1 FFT FFT Rsonde veocity(m/s) Wind veocity(m/s) (c) (d) Figure : (a) U component (b) V component (c) W component veocities and (d) Wind speed of six beams of MST radar data using adaptive moments estimation technique. 1

7 1 Wind speed Range(m) 1 1 MF Rsonde Wind veocity(m/s) Figure 9. Wind speed of radar data using the matched fiter (MF), the and wind speed of radiosonde data. 5. CONCLUSIONS The CT method is appied to MST radar data for the smoothed spectrum estimation. The CT method fais to achieve better spectra ceaning compared with the conventiona techniques. The method is deveoped and impemented for the radar data. The existing agorithm coud detect upto 11 Km beyond which one has to manuay cacuate the moments and find the Dopper. The proposed agorithm is abe to smooth the spectra contents of Dopper profie for a heights. The numerica resuts suggest that the proposed method for spectra ceaning of MST radar data is much better than the CT and the periodogram. In addition, the resuts confirm that the estimated wind veocity using the approach is in agreement with the radiosonde data. REFERENCES [1] Anandan V. K. Atmospheric Data Processor- Technica and User reference manua. Nationa Atmospheric Research Laboratory, Gadani, Tirupati, Andra Pradesh, India. [] Briggs B. H. 19. Radar observations of atmospheric winds and turbuence: a comparison of techniques. Journa of Atmospheric and Terrestria Physics. : [3] Dovia R.J. and Zrnic. D.S. 19. Dopper radar and Weather Observations, Acadamic Press, London, U.K. [] Rötteger J. and M.F. Larsen. UHF/VHF Radar techniques for atmospheric research and wind profier. [5] Woodman R. F Spectra moment s estimation in MST radars. Radio Sci. : [] Cothiaux E. E., R. S. Rene, D. W. Thomson, T. P. Acerman and S. R. Wiiams A first-guess feature based agorithm for estimating wind speed in cear-air Dopper radar spectra. J. Atmos. Oceanic Techno. 11: -9. [7] Fischer M. A. and R. C. Botes Random sampe consensus: paradigm for mode fitting with appication to image anaysis and automated cartography. Commun. Assoc. Comput. Mach. : [] May P. T. and R. G. Strauch An examination of wind profier signa processing agorithms. J. Atmos. Oceanic Techno. : [9] Merritt D. A A statistica averaging method for wind profier Dopper spectra. J. Atmos. Oceanic Techno. 1: [1] Morse C. S., R. K. Goodrich and L. B. Cornman.. The NIMA method for improved moment estimation from Dopper spectra. J. Atmos. Oceanic Techno. 19:

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