Atmospheric radar signal processing using principal component analysis

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Atmospheric radar signal processing using principal component analysis D. Uma Maheswara Rao, T. Sreenivasulu Reddy ∗ , G. Ramachandra Reddy Sri Venkateswara University College of Engineering, Department of Electronics and Communication Engineering, Tirupati, Andhra Pradesh, 517 502, India

a r t i c l e

i n f o

Article history: Available online xxxx Keywords: Principal component analysis MST radar GPS sonde Wavelet-based denoising Cepstral thresholding

a b s t r a c t Principal Component Analysis (PCA) is a simple non-parametric method for extracting relevant information from high-dimensional data sets. In this paper, we analyze the data collected from the Indian MST (Mesosphere, Stratosphere, Troposphere) radar at Gadanki (13.5◦ N, 79.2◦ E) using PCA. We tested the PCA for various simulated signals like narrowband, wideband and exponential signals which may contain more than one frequency both in absence and presence of noise. For the simulated data, it is observed that PCA works for low SNR, i.e. it successfully detects the frequency in the highly noise-corrupted signal also. Finally, we applied PCA to the radar data for estimating the power spectrum and thus in turn estimating the Doppler frequency components. We estimate the zonal (U), meridional (V), wind speed (W) etc. from the Doppler frequencies. Compared with existing algorithms, PCA works well at higher altitudes and results have been validated using the GPS sonde data. © 2014 Elsevier Inc. All rights reserved.

1. Introduction Indian MST radar provides information on wind data in the mesosphere, stratosphere and troposphere with a resolution of 150 m starting above 3.5 km. The radar uses Doppler Beam Swinging (DBS) method to determine the three wind components U, V and W [1]. The spectral data are collected by the radar using multiple beam positions (east, west, zenith-X, zenith-Y, north and south) with 16 μs coded pulse and 1000 μs Inter Pulse Period (IPP). The complex time series of the decoded and integrated signal samples are subjected to the process of Fast Fourier Transform (FFT) for on-line computation of the Doppler power spectra for each bin of the selected range window. The off-line data processing involves the following steps: the removal of dc, estimation of average noise level, the removal of interference, incoherent integration and computation of low-order (0th, 1st and 2nd) moments. The three moments are signal strength, weighted mean Doppler shift and half-width parameters of the spectrum respectively. Up to a certain height (≤18 km), this technique estimates the Doppler frequencies of the returned echoes accurately. At heights greater than 18 km, estimation fails. It is also observed that in many cases that when noise interferes with data at lower altitudes (3.5 km to 12 km), we get incorrect results. Several authors proposed various algorithms for denoising the spectrum, finding the Doppler frequencies from

*

Corresponding author. E-mail address: [email protected] (T. Sreenivasulu Reddy).

http://dx.doi.org/10.1016/j.dsp.2014.05.009 1051-2004/© 2014 Elsevier Inc. All rights reserved.

the estimated spectrum and thus the U, V and W components. Bispectral-based estimation algorithm eliminates the noise [2]. But, this algorithm involves a complex mathematical computation. Multitaper spectral estimation algorithm produces broadened spectral peak [3]. Wavelet-based denoising method has been applied for spectrum cleaning and thus estimating the Doppler frequencies and wind components [4]. The Cepstrum thresholding approach also has been applied to the radar data to estimate the frequencies [5]. These methods have an advantage of total variance reduction of the estimated spectrum. But, they fail at higher heights where SNR will be very low. Hence, there should be an algorithm which yields correct results at medium as well as higher altitudes and take an advantage of reduced variance. PCA is such method which reduces the complexity and gives us the good results. The remainder of this paper is organized as follows. In Section 2, the PCA concept and its properties for exponentials are explained. In Section 3, we showed the reduction in variance and mean square error (MSE) when PCA is applied to the simulated data and illustrate the detection of frequencies of one or more sinusoids in presence of high noise. We applied our approach to the MST radar data to estimate the Doppler shift in Section 4. Wind velocities are computed from the estimated Doppler shifts. In Section 5, the concluding remarks are given. 2. Principal component analysis PCA is a mathematical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated

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variables into a set of values of uncorrelated variables called principal components (PCs). The main advantage of PCA is dimensionality reduction. There are various spectrum estimation algorithms to estimate the frequency. But, there will be certain cases where we need to estimate only the frequencies and amplitudes of the spectral components. There is no need to estimate the entire spectrum. These are known as frequency estimation techniques and are applicable to a harmonic process that consists of a sum of sinusoids or complex signals. These methods may use the vectors that lie in noise subspace or signal subspace. The signal subspace methods form a low-rank approximation to the autocorrelation matrix which is then incorporated to a spectrum estimation algorithm. PCA is one of such signal subspace methods. The autocorrelation matrix (ACM) for the given set of data x(n) consisting of p exponentials plus noise is a sum of autocorrelation matrices due to signal s and noise n [6]. Let the size of ACM be M × M. Thus,

Rx = Rs + Rn

(1)

The Eigen decomposition of the ACM can be expressed as below assuming that the eigenvalues (λi ) are arranged in the descending order (λ1 ≥ λ2 ≥ . . . ≥ λ M ),

Rx =

M 

λi vi viH =

i =1

p 

λi vi viH +

i =1

M 

λi vi viH



i = p +1

where vi is eigenvector corresponding to eigenvalue λi . The first term of (2) is due to signal alone and second term of (2) is due to noise alone. If we retain only the principal eigenvectors of (2), a reduced rank approximation is formed to the signal ACM. Thus,

ˆs = R

p 

λi vi viH

(3)

i =1

Now, any spectral estimator can be used for the above approximated ACM of (3). The noise part of (2) is eliminated and only signal part is retained. Thus, the estimation of spectral component due to signal is enhanced. The principal components representation of (2) imposes a rank-p constraint on Rx since it is assumed that the signal has p exponentials and also the rank of the ACM due to the signal is p. The number of principal components is less than or equal to the number of original variables. The first principal component has high variance as it accounts for as much of the variability in the data as possible. The succeeding component in turn has the highest variance possible under the constraint that it has to be orthogonal to (uncorrelated with) the preceding components. Its operation can be thought of as revealing the internal structure of the data in a way which best explains the variance in the data. Fig. 1 shows the steps involved in PCA spectral estimate. The PCA of the ACM may be used in conjunction with any of the spectrum estimation techniques and thus forming principal components spectrum estimate. The following are some of the methods used for this PC spectrum estimate. 1. Blackman–Tukey Frequency Estimation method (PCA-BT), 2. Minimum variance Frequency Estimation method (PCA-MV) and 3. AR Frequency Estimation method (PCA-AR). In this paper, we implemented the first two methods. The equations of the PC version of the above first two methods are given by,



Pˆ PCA-BT e

jw



=

1 M

ˆ se = e R H

1  p

M

i =1

 2 λi e H vi 

Fig. 1. Flowchart of the steps involved in PCA.

(2)

(4)



Pˆ PCA-MV e j w =  p

M 1

i =1 λ i

| e H v i |2

(5)

where e is the vector of complex exponentials orthogonal to vi , i = 1, 2, . . . , p. Selecting the number of PCs Let R be the M × M covariance matrix obtained from the mean subtracted data vector, x(n). R can be expressed as,

V−1 RV = D

(6)

In (6), V is the matrix of eigenvectors that diagonalizes the covariance matrix R and D is the diagonal matrix of eigenvalues of R. D is an M × M diagonal matrix, where



D[ p , q ] =

λm , p = q = m p = q

0,

(7)

with λm being the mth eigen value and the elements of the diagonal matrix D are in descending order. The eigenvalues represent the distribution of source data’s energy among each of the eigenvectors. The cumulative energy content E of the mth eigenvector is the sum of the energy content across all of the eigenvalues from 1 through m.

E[m] =

m 

D[q, q],

m = 1, . . . , M

(8)

q =1

Save the first L columns of V as the M × L matrix W.

W[ p , q] = V[ p , q],

p = 1, . . . , M , q = 1, . . . , L

(9)

where 1 ≤ L ≤ M. The E[m] can be used as a guide in choosing an appropriate value of L. The value of L is as small as possible while achieving a reasonably high value of E on a percentage basis. For example, if we want to choose L so that the cumulative energy E[m] is above a certain threshold, like 90 percent. The smallest value of L is chosen such that,

E[m = L ] ≥ 90% M q=1 D[q , q ] Thus, the number of PCs is selected.

(10)

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Table 1 IMSE values with non-PCA methods (PER and WBDA) and PCA methods. SNR

PER

WBDA

PCA-BT

PCA-MV

0 dB −5 dB −10 dB −15 dB −20 dB

50.29575 288.1379 2341.993 21712.45 212486.3

25.06152 132.3433 1015.021 9596.22 90976.33

5.136076 26.39256 208.9833 1955.955 19073.43

0.226263 0.226277 0.226280 0.226281 0.226378

Denoising Approach are named WBDA [4]. The IMSEs of a narrow band complex system with various SNRs calculated with Periodogram (PER) method, WBDA, PCA-BT and PCA-MV approaches are shown in Table 1. From the figures and table, we can come to the following conclusions:

Fig. 2. (a), (b) Estimation of Power Spectral Density (PSDs). (c), (d) Mean Square Error (MSE). (e), (f) Variance with Periodogram (PER) approach, Principal Component– Blackman–Tukey (PCA-BT) approach and Principal Component–Minimum variance approach in presence of noise associated with amplitudes α = 0.5 and α = 1 — comparisons.

3. Simulation results for complex data In this section, we present the results for the estimation of the power spectrum of complex data based on PCA. Case 1: Narrow-band complex signal The data are generated by applying a Gaussian random input to a complex narrow-band system [7]. The mean square error and variance are taken as the performance measures. The narrowband complex signal y (n) is generated using the transfer function, H ( z) = (1 + cz−1 )/(1 + az−1 + bz−2 ), where a = 1.807e j0.349π , b = 0.903e − j0.3π and c = 0.979e − j0.199π . The corresponding difference equation is

y (n) + ay (n − 1) + by (n − 2) = e (n) + ce (n − 1)

(11)

for n = 0, 1, . . . , N − 1 where N represents the data length and e (n) is normal white noise with zero mean and unit variance. To test the performance of PCA in the presence of additive white Gaussian noise, a new signal y 1 (n) is generated as

y 1 (n) = y (n) + α v (n),

n = 0, 1 , . . . , N − 1 ,

(12)

where v (n) is a complex Gaussian noise with zero mean and unit variance and α is the amplitude associated with v (n). The number of samples in each realization is assumed to be 512, i.e., N = 512. The results based on the Monte Carlo simulation using Periodogram approach, PCA-BT and PCA-MV for Power Spectral Density (PSD), Mean Square Error (MSE) and Variance are shown in Fig. 2. To show the sensitivity of existing non-PCA methods with PCA methods as a function of SNR, we take Integrated Mean Square Error (IMSE) as a parameter. The estimated IMSE of a Periodogram can be interpreted as the average of mean square error over all frequencies and is defined as, N −1     ˆ k) = 1 ˆ k) − ∅(k) 2 IMSE ∅( E ∅(



N

1. From Fig. 2(a) and 2(b), it is clear that when the magnitude of the noise increases, it is difficult to detect the frequency peaks. But, PCA-BT and PCA-MV approaches successfully detect the frequency peaks even at higher magnitudes of noise. Also, both PCA approaches yield the same results of PSD. So, we can adopt any one method for our Doppler frequency estimation problem. 2. As the noise magnitudes increases, there is a considerable increase in MSE in Periodogram and PCA-BT approaches. However, PCA-MV approach tends to a very small change in MSE as α increases. These are illustrated in Fig. 2(c) and 2(d). 3. As the noise level increases, variance also increases as shown in Fig. 2(e) and 2(f). 4. The IMSE increases as SNR of the signal decreases in all the methods. If we compare between non-PCA and PCA methods as a whole, IMSE is very low for the PCA methods. 5. Even in PCA methods also, IMSE is almost negligible in PCAMV approach when compared to that of PCA-BT approach. 6. As far as the concepts of minimum variance and IMSE are considered, PCA-MV is the best approach compared to the other approaches. Case 2: Complex signal Let us consider a complex signal x(n) consisting of two different frequencies with random phase as,

x(n) = e j (nπ f 1 +φ1 ) + e j (nπ f 2 +φ2 ) + w (n)

(14)

with f 1 = 0.2π and f 2 = 0.4π . w (n) is AWGN(0, σ ). To test the efficiency of PCA, σ 2 is varied to have SNR values from −10 dB to −20 dB in steps of −5 dB. The plots of PSDs are shown in Fig. 3. Since, the exponential signal contains two different frequencies at f 1 = 0.2π and f 2 = 0.4π , power spectrum has to show peaks at those respective frequencies. The graphs are plotted for various SNR values. For higher SNR values, normal Periodogram approach can also give frequency peaks. But, as SNR values goes on decreasing, the Periodogram approach fails and PCA method gives correct results up to the SNR value of −15 dB. For SNR = −20 dB, PCA methods also fail to produce correct frequency peaks. Thus, we can draw a conclusion that PCA can be applied to the data corrupted with noise to estimate the frequencies without applying the denoising algorithms and thus reducing the complexity of the system. 2

4. Results for MST radar data

(13)

k =0

where N is the number of FFT points, ∅(k) is the true spectrum ˆ k) is the spectrum estimated through any of the non-PCA and ∅( or PCA methods. The results developed with the Wavelet Based

Atmospheric radars operate typically in VHF (30–300 MHz) and UHF (300 MHz–3 GHz) bands. The turbulent fluctuations in the refractive index of the atmosphere serve as a target for these radars. We applied PCA for the data collected from the troposphere and lower troposphere by operating the MST radar located at National

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Fig. 3. Estimation of Power Spectral Densities (PSDs) of exponential signal consisting of two frequencies with Periodogram approach, Principal Component–Blackman– Tukey (PCA-BT) approach and Principal Component–Minimum variance approach under various SNR values (−10, −15, −20) (in dB) — comparisons.

Fig. 5. (a) Typical spectra. (b) Height profiles of SNR estimated through PCAA and WBDA. (c) Estimating the peaks at Doppler frequencies (Doppler-height profile) — of the east beam for October 6, 2012 data. (d) Height profiles of mean SNR estimated through PCAA and WBDA for data from July 13 to 18, 2012.

The height profiles of the signal-to-noise ratio (SNR) [10] derived from the spectra computed using WBDA and PCAA for east beam is shown in Fig. 5(b). From the SNR plot, it is observed that PCAA yields good SNR as compared to that of WBDA. As we know PCAA finds only the frequency peaks, the respective peaks at the Doppler frequencies are shown in Fig. 5(c) which is the Doppler height profile. For more consistency of the proposed approach, we applied PCA to the data from July 13 to 18, 2012 and means of SNRs obtained through WBDA and PCAA are plotted in Fig. 5(d) for the south beam. Methodology for computing the Doppler frequencies, Doppler velocities and Wind components Let Index be the vector of indices of frequency peaks at all bins of one beam. The Doppler frequencies and Doppler velocities are computed as [1], Fig. 4. Spectrum at bins numbered 2, 52, 112 and 147 of all beams using PCA for October 6, 2012 data.

Atmospheric Research Laboratory (NARL) near Tirupati, India. The MST radar is a monostatic coherent pulse Doppler radar operating at 53 MHz with a peak power-aperture product of 3 × 1010 W m2 . The detailed system description and the signal processing technique used are given elsewhere [8]. The MST radar data are collected in the form of scans. Each scan contains six beams (east, west, zenith-Y, zenith-X, north and south) and each beam contains 147 bins with a resolution of 150 m. Each bin will have the complex time series data of 512 samples. The results developed with the PCA approach are named PCAA. The results are compared with WBDA [4]. PCAA is applied to all 147 bins of all six beams. Fig. 4 shows the spectrum obtained at bins 2, 52, 112 and 147 of all beams. From Fig. 4, we can infer that at lower bins, PCAA is able to determine the peak only at a single frequency more smoothly. But, as we go upwards, several peaks appear other than the signal peaks which are due to noise. Previous approaches failed to determine the Doppler frequencies at those layers completely. Since PCAA can detect the frequency peaks up to an SNR level of −15 dB as shown in Fig. 3, we can say that PCAA succeeds in tracking the Doppler frequencies at those higher noise levels also. The typical spectra of the data collected on October 6, 2012 for the east beam without applying PCAA is shown in Fig. 5(a).



f = Index − and



v = Index −

NFFT 2

NFFT 2



−6 ×



7.56 + 7.8 NFFT − 1

− 6 × 0.029 × λ



(15)

(16)

where NFFT is the number of FFT points used for calculating the peak, λ = c / f c , c is the velocity of light. f c is the operating frequency of the Doppler radar (53 MHz). Similarly, they are calculated for all six beams. Thus, the computed Doppler frequencies are fN , fS , fZx , fZy , fE , fW and Doppler velocities are vN , vS , vZx , vZy , vE , vW , where the subscript indicates the respective beam. The general formula for computing the zonal (V x ), meridional (V y ) and vertical (V z ) velocities at each bin is as shown below [1],

⎡

⎤

Vx ⎣ Vy ⎦ Vz

⎤−1    2 cos θxi cos θ yi i i cos θxi cos θ zi  i cos θxi  = ⎣ i cos θxi cos θ yi  i cos2 θ yi cos θ yi cos θzi ⎦ i 2 cos θ cos θ cos θ cos θ xi zi yi zi i i i cos θ zi ⎤ ⎡  i v i cos θxi × ⎣ i v i cos θ yi ⎦ (17) i v i cos θ zi ⎡

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Fig. 6. Doppler Height profiles for four scans of the east beam using (a) WBDA and (b) PCAA. (c) Mean Doppler Height profile of the east beam using WBDA and PCAA. (d) Standard deviation for the east beam using WBDA and PCAA for October 6, 2012 data.

5

Fig. 7. Doppler velocities of the first scan of all six beams for October 6, 2012 data using PCAA and WBDA — comparisons.

where i represents the beam, v i is the Doppler velocity of particular bin of ith beam, θxi , θ yi and θzi are the angles that the radar beam makes with the X , Y , Z axes with respect to various beams. For Indian MST radar at NARL, the above formula reduces to,

⎡

⎤

⎤−1

⎡

Vx 0.0603 0 0 ⎣ Vy ⎦=⎣ 0 ⎦ 0.0603 0 0 0 0.0603 Vz

⎡

⎤

0.1736( v E − v W ) × ⎣ 0.1736( v N − v S ) ⎦ 0.1736( v Z x − v Z y )

(18)

Thus, the zonal, meridional and vertical velocities are computed at each bin. Since, zenith-X and zenith-Y beams are in vertical directions, there will be no contribution of vertical velocity to the total wind velocity and it is almost zero. The wind speed can be calculated as,



W = V x2 + V y2

 12

(19)

The Doppler profiles of the east beam from four different scans are computed using WBDA and PCAA are shown in Fig. 6(a) and (b). The mean Doppler Height profiles of the east beam extracted from the spectrum are shown in Fig. 6(c). The standard deviation versus height profiles are shown in Fig. 6(d) for the east beam. From Fig. 6(d), we can say that the standard deviation is zero at lower altitudes and as we go to higher altitudes, standard deviation also increases, but not as that of WBDA. Fig. 7 shows the Doppler velocities of all beams using both PCAA and WBDA. The zonal (V x ), meridional (V y ) and Wind speed (W ) components calculated using GPS Radio sonde [9], PCAA and WBDA are shown in Fig. 8. From the graph, it is clear that, beyond 20 km, the WBDA fails to detect the Doppler profiles accurately; as a result, it is failing to follow the profiles (zonal, meridional and Wind speed) obtained using the GPS sonde. It is also clear that the V x , V y and W components calculated using PCAA are somewhat closely following the trends obtained from the GPS sonde even at higher altitudes. The minor deviation from 15 km to 17.5 km can be attributed to the fact that the data used in PCAA are collected from the reflected echoes from the layers of the atmosphere in the vertical direction without any drift in the horizontal direction, whereas in the data collected through GPS, there can be horizontal drift

Fig. 8. Zonal, Meridional and Wind Velocities for October 6, 2012 data using GPS Radio Sonde, PCAA and WBDA — comparisons.

of the balloon due to high wind speeds. The scatter plot of Fig. 9 shows the correlation between GPS and PCAA. We get a correlation coefficient of 0.90429 between GPS and PCAA which is better than WBDA with 0.76793. 5. Conclusion We presented Principal Component Spectral Estimate Approaches using both Blackman–Tukey and Minimum-Variance methods. Since our interest is only in finding the Doppler frequencies, we can use any one of these two methods as both of the methods give us the same results at any level of noise as shown in the graphs. By using PCA, the complexity reduces since we form a low-rank approximation. When we consider variance to be minimum, the second method gives us good results. The IMSE of PCA-MV method is also negligible when compared with nonPCA methods and PCA-BT method. The real power of PCA method can be seen at higher. All the other methods fail at those altitudes and calculate the wind velocities inaccurately. But, it is not the case with PCA. PCA is showing an SNR improvement of almost over 10 dB over all heights. Standard deviation and Mean Square Error are also low when compared to the previous approaches.

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[9] V.V.M. Jagannadha Rao, D. Narayana Rao, M. Venkat Ratnam, K. Mohan, S.V.B. Rao, Mean vertical velocities measured by Indian MST radar and comparison with indirectly computed values, J. Appl. Meteorol. 42 (4) (Apr. 2003) 541–552. [10] D.A. Hooper, Signal and noise level estimation for narrow spectral width returns observed by the Indian MST radar, Radio Sci. 34 (4) (1999) 859–870.

D. Uma Maheswara Rao received his B.Tech. degree in ECE from SIETK in 2010 and M.Tech. degree in Communication Engineering from VIT University in 2012. He secured University 3rd rank in B.Tech. over all affiliated colleges of JNTU and received gold medal from VIT University in M.Tech. He also got first prize twice for the two papers presented in First and Second International Science, Engineering and Technology (SET) conferences held by VIT University biannually. He got two times merit scholarship and endowment award from chancellor of VIT University. He worked as Junior Research Fellow from June, 2011 to May, 2012 in ISRO and is working as Project Engineer in Wipro Limited till date. Fig. 9. Correlation between GPS and PCAA wind speeds for data from July 13 to 18, 2012.

Acknowledgments We would like to thank Department of Science and Technology (DST), New Delhi under grant No. SR/S4/AS:2010 for providing financial assistance and National Atmospheric Research Laboratory (NARL), Gadanki for providing radar data and technical assistance. References [1] V.K. Anandan, Atmospheric Data Processor—Technical and User Reference Manual, NMRF, DOS Publication, Gadanki, India, 2002. [2] V.K. Anandan, G. Ramachandra Reddy, P.B. Rao, Spectral analysis of atmospheric signal using higher orders spectral estimation technique, IEEE Trans. Geosci. Remote Sens. 39 (9) (Sep. 2001) 1890–1895. [3] V.K. Anandan, C.J. Pan, T. Rajalakshmi, G. Ramachandra Reddy, Multitaper spectral analysis of atmospheric radar signal, Ann. Geophys. 22 (11) (Nov. 2004) 3995–4003. [4] Thatiparthi Sreenivasulu Reddy, G. Ramachandra Reddy, MST radar signal processing using wavelet-based denoising, IEEE Geosci. Remote Sens. Lett. 6 (4) (Oct. 2009) 752–756. [5] T. Sreenivasulu Reddy, G. Ramachandra Reddy, MST radar signal processing using cepstral thresholding, IEEE Trans. Geosci. Remote Sens. 48 (6) (Jun. 2010) 2704–2710. [6] Monson H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley & Sons, 1996. [7] P. Stoica, N. Sandgren, Smoothed non parametric spectral estimation via Cepstral thresholding, IEEE Signal Process. Mag. 23 (6) (Nov. 2006) 34–45. [8] P.B. Rao, A.R. Jain, P. Kishore, P. Balamuralidhar, S.H. Damle, G. Viswanathan, Indian MST radar 1. System description and sample vector wind measurements in ST mode, Radio Sci. 30 (4) (Jul./Aug. 1995) 1125–1138.

T. Sreenivasulu Reddy received the B.Tech. degree in ECE from Sri Venkateswara University, Tirupati, India, in 1990, the M.Eng. degree in Digital Electronics from Karnatak University, Dharwad, India, in 1996 and Ph.D. degree in Radar Signal Processing from Sri Venkateswara University, Tirupati. He is currently an Associate Professor with the Department of Electronics and Communication Engineering, Sri Venkateswara University College of Engineering. His research interests include radar and image signal processing. Mr. Reddy is a Fellow of the Institution of Electronics and Telecommunication Engineers and a member of the Indian Society for Technical Education. G. Ramachandra Reddy received the M.Sc. and M.Sc. (Tech.) degrees from the Birla Institute of Technology and Science, Pilani, India, in 1973 and 1975, respectively, and the Ph.D. degree from the Indian Institute of Technology, Madras, India, in 1987. In 1976, he joined the Department of Electrical and Electronics Engineering, College of Engineering, Sri Venkateswara University, Tirupati, India, and worked till 2010. He is currently Senior Professor in VIT University, Vellore. Also, he is holding the position of Dean for the School of Electronics Engineering and Accreditation and Academic Committee. From February 1989 to May 1991, he was with the Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, Canada, as a Visiting Scientist. Dr. Ramachandra Reddy is a Fellow of the Institution of Electronics and Telecommunication Engineers and a member of the Indian Society for Technical Education.