Doppler Profile Estimation in VHF Radar Signals

using Wavelets 1Leela Lakshmi. S.,

Assistant Professor(Sr.,)

Dept. of ECE, SKIT

Srikalahasti-517640

2Rajani Kanth .V,

Assoc. Professor

Dept. of EEE, SKIT

Srikalahasti-517640

3Varada Rajan. S.,

Professor

Dept. of EEE, SVU

Tirupati-517502

A.S.R.Reddy

Professor

Principal, SKIT

Srikalahasti-517640 1lakshmirajanikanth.veluru@gmail.com

2lakshmirajanikanth.veluru@hotmail.com

Abstract- The wind profile estimations are the fundamental

objective of the Indian MST radar with the received signal

ranging from nearly 3.5 25 Km height. A widely accepted

narrow band model is considered, for the analysis of the

signal received. Though the received signal SNR is stronger

at lower altitudes, as the height progresses the strength

becomes feeble and the noise dominates the received signal.

The classical Time-Frequency analysis is made on the

received signal from different altitudes and observed that the

zero Doppler influence is significant at higher altitudes along

with the noise. A Hilbert transform based DC bias removal is

proposed in contrast with the existing 3 point MA technique.

To handle the noise, in particular at higher altitudes a

wavelet based adaptive denoising is proposed and found

satisfactorily for the spectral cleaning of the Doppler

spectrum. The validation of the proposed algorithm is made

with the GPS data.

Key words: doppler, radial velocity, denoise, threshold

I. INTRODUCTION

Atmospheric research in India has a hoary tradition over

200 year old legacy by the then British India Company at

Colaba Observatory station near Mumbai for the purpose

of meteorological observations. To unravel the mysteries

of the topological of the Indian sub-continent many

programs were instigated, one such program was the

Middle Atmosphere Program (MAP) [1]. The principle

objective of the MAP is to explore the secrets of the

activity of the middle atmosphere on all temporal and

spatial scales and also to untangle the interactions between

the three different height regions viz. Mesosphere,

Stratosphere and Troposphere. The Radar is setup by the

ISRO at NARL (National Atmospheric Research

Laboratory), Gadanki (near Tirupati), Chittoor (dist), A.P.;

@ to study these

regions. This atmospheric radars are also known as clear

air radars and they operate typically in the VHF

( ) band; admirable instrumentation system

for atmospheric probing in the regions of Mesosphere,

Stratosphere and Troposphere (MST) covering up to a

height of about 100 Km generally [1]. It is also used for

coherent backscatter study of the ionosphere irregularities

above 100 km. These radars also used for meteor detection

in the as a tracer of background wind at 70-120 Km in the

astronomical studies. The necessary technology to setup

VHF radar is cheaper and easier to achieve [2]. However,

the VHF region is crowded, band widths are narrow,

external noise can be high, and beamwidths are broad.

Turbulent fluctuations in the refractive index of the

atmosphere serve as a target for these radars. Particularly,

the noise effect becomes more and more predominant as

the height progress beyond 12 Km in case of soft targets.

Therefore, there is a greater need for need to induct the

signal processing techniques for cleaning the Doppler

spectrum, used for wind profile estimation at different

altitudes.

II. 2.0 MST RADAR SIGNAL MODEL

A widely accepted model, without loss of generality, of

the radar signals i.e. narrowband signal model [2] is

considered as the velocity of the target (layers of the

atmosphere in the present case) is much lesser than the

speed of the propagation of the transmitted/received

signal. Accordingly [3], the received signal is given by:

where is the Doppler frequency, - time lag.

The classical Fourier transform (also in turn the

spectrum estimation) of the signal is given

mathematically as:

If, the received signal represented by eq. ( ) consists of

a single frequency component, it is very straightforward to

extract the information from the target like its velocity,

height, etc. In practice, the received signal is much

contaminated with noises that degrade the quality of the

signal received. Hence, it is a cumbersome process to

compute the spectrum of the signal and becomes intricate

to extract the parameters. Thus, the Atmospheric Signal

Processing has been one field of signal processing where

there is an ample scope for development of novel and

efficient tools for cleaning of the spectrum of the signal,

TABLE I: RESOLUTION DETAILS OF MST RADAR

(SOURCES NARL, ISRO, GADANKI, INDIA)

Sampled

Time ( )

Radial

velocity

resolution

(m )

Doppler

resolution

( )

Range of

Radial

Velocity

( )

Range of

Doppler

Shift ( )

256 512 256 512

4 2.8 1.4 1.0 0.5 ±353.75 ±125.0

8 1.4 0.7 0.5 0.25 ±176.87 ±62.5

16 0.7 0.35 0.25 0.12 ±88.44 ±31.25

32 0.35 0.17 0.12 0.06 ±44.23 ±15.63

36 0.17 0.09 0.06 0.03 ±22.10 ±7.81

128 0.09 -- 0.03 -- ±11.10 ±3.91

256 -- -- -- -- ±5.12 ±1.95

512 -- -- -- -- ±2.77 ±0.98

243978-1-4244-8594-9/10/$26.00 c©2010 IEEE

and estimation of the desired parameters. The MST radar

data processing is presented in the following sections.

III. MST RADAR DATA FORMAT

The Indian MST radar data is stored/available in two

formats for the scientists and/or user scientists. They are:

( ) the Time domain data (discrete time series data,

commonly referred as raw data), ( ) the Frequency

domain (spectrum computed using FFT) data, ( )

Moments data, ( ) Power spectrum + moments data and

( ) UVW data types. The data types ( ), ( ), ( ) & ( )

are preprocessed data computed from the discrete time

series data without applying any signal processing

techniques. The typical transformation is a simply the

Fourier transformed data and statistical data only. There is

a little to do by the signal processing engineer with this

data. However, the discrete time series data received from

the atmosphere is associated with enormous amount of

information [4]. The clear air turbulence is essentially a

volume target and the volume reflectivity in the

atmosphere ranges between to

or lower. Thus, the typically the power

aperture values of the order of to are

required for successful MST radar campaign. In most

cases the echo is buried below/under the background

noise/clutter ranges typically to . Therefore,

new advanced signal processing techniques and efficient

algorithms are required to extract the required information.

The spectral estimation of the radar return signal using eq.

(2), is simple and straight, finds useful in extracting the

desired information. The data processing is done in on-line

mode and off-line mode. The data processing operation

consists of applying spectral analysis techniques to the

received radar signal to estimate Doppler spectrum. This is

further useful in estimating the radial velocity and absolute

velocity of the wind. A typical Doppler spectrum of MST

radar is shown in fig 1. The profile of the Doppler

spectrum is clearly traceable at lower ranges of altitude.

As the height progress the spectrum is much contaminated

by the noise in turn the SNR becomes feeble and hard to

trace the wind profile. The table I depicts few technical

details of the Indian MST radar, NARL, Gadanki. To

understand the content of the signal it is required

mathematical tools other than Fourier transform due to the

fact that the classical Fourier transformation is localized in

frequency domain rather time-frequency. This limitation

can be overcome using time-frequency analysis.

IV. TIME-FREQUENCY ANALYSIS

The joint transforms were

used for the purpose of characterizing the time-varying

frequency content of a signal. The best known time

frequency representation of a time signal is short-time

Fourier Transform ( ), also referred as Gabor

transform. The most convenient approach to explore a

signal with content is to split the signal into many

segments in the time domain, and then taking the Fourier

transform. This slant is called as the short time Fourier

transforms ( ) and is given by:

Mathematically, the Gabor window function is given by

(time domain representation):

The fig.2 depicts the time domain representation of the

radar signal at different altitudes. An ample number of

window functions are available in the literature and are

useful to find the frequency content with in temporal

domain, is shown in fig. 3 & 4. The table II depicts figure

of merit made by the observations for different gating

functions when used as the kernel windows in the

analysis of equation ( ). It is observed that the effect of

DC bias in the signal is not much intervening at lower

altitudes particularly nearly below 12 Km and beyond this

Fig. 1: Typical Doppler Spectrum of MST radar (Doppler Frequency in

Hz Vs Height in Km). Fig. 2.a: Time domain representation of MST radar signal (received at nearly 4.25Km).

Fig. 2.b: Time domain representation of MST radar signal (received at

nearly 12.5Km).

Fig. 2.c: Time domain representation of MST radar signal (received at

nearly 22.5Km).

244 2010 International Conference on Signal and Image Processing

range the dominance of the DC component in the signal

progressively increases and causes for erroneous

estimations of wind velocities using the Doppler spectrum.

The wind velocities , using the Doppler frequency is

estimated mathematically as:

and vertical height corresponding to this velocity is

given quantitatively as:

where - velocity of light in free space, - carrier

frequency, - range time delay, - beam tilt angle.

It is noted that except Dolph-Chebyshev window [6], all

the windows introduces coherent/DC gain in the signal

(refer to the observation table II). However, the Dolph-

Chebyshev results are deterring at altitudes beyond 16Km

as shown in fig.5b.

To handle this DC bias present in the signal component,

a Hilbert transform based technique is proposed. At

present the NARL uses a moving average method for

reducing the effect of DC component in the Doppler

spectrum based on 3 point averaging technique.

However, it finds its own limitations that this method also

fails at altitudes beyond 12 Km. The proposed Hilbert

transform removes the DC component which is present in

the signal [6] and the results are shown in fig.6, which is

superior to the multi taper technique [11]. Yet, this

technique cannot eliminate the noise present in the signal.

Therefore, further effective signal processing techniques

require handling the noise for the improvement the SNR of

Fig. 3.a: Time Frequency plot using Rectangular windowforMST radar

signal (received at nearly 12 Km).

Fig. 3.b: Time Frequency plot using Gaussian windowforMST radar

signal (received at nearly 12 Km).

Fig.3c: Doppler Spectrum/Frequency domain representation of MST radar signal (received at nearly 12 Km).

Fig. 4.a: Time Frequency plot using Rectangular windowforMST radar signal (received at nearly 22.5Km).

Fig. 4.b: Time Frequency plot using Dolph-Chebyshev window for

MST radar signal (received at nearly 22.5 Km).

Fig. 4.c: Doppler Spectrum/Frequency domain representation of MST

radar signal (received at nearly 22.5 Km).

Fig. 5.a: Time Frequency plot using Rectangular window of MST radar

signal using proposed DC removal (received at nearly 22.5 Km).

Fig. 5.b: Time Frequency plot using Dolph-ChebyshevMST radarsignal using proposed DC removal (received at nearly 25 Km).

Fig. 5.c: Doppler Spectrum /Frequency domain representation of MST

radar signal using proposed DC removal using Hilbert Transform (received at nearly below 22.5 Km).

Fig. 5.d: Time domain representation of MST radar signal using proposed

DC removal using Hilbert Transform (received at nearly 22.5 Km).

2010 International Conference on Signal and Image Processing 245

the signal. The wavelets, a special class of time-frequency

tool, gives the signal information that is localized in both

time and frequency domain, because of their finite energy

and also finite duration of oscillatory in nature rather

harmonically continuous. This oscillatory behavior is the

desired property that a signal processing expert needs. In

the subsequent sections the analysis of the radar signals

using wavelet transform is presented.

V. WAVELET ANALYSIS

finite energy, localized in time. It has an oscillating

wavelike characteristic but also has the ability to

permit/allow simultaneous time and frequency analysis.

This makes wavelet to be a suitable tool for transient, non-

stationary or time-varying phenomena [7,8]. The basis

function in the recursion form is given by:

The coefficients are the inner product of

and . The transformation kernel is an

orthogonal basis. The desirable property seek by the

designers is orthogonalityi.e., the inner product of the

basis must be equal to zero. This means: is

orthogonal to all its dilations/scales and translations. The

wavelet basis, containing these basis functions

form an orthogonal basis. Mathematically:

In the first integral, equation , ,

whereas is positive and then negative over the

support defined. Thus the integral is zero.

Similarly on the second half-interval

where is positive and negative. The second

integral, equation , is therefore zero. The third integral,

equation , vanishes for a different reason that the

functions , do not overlap. One is zero

and where the other is nonzero simultaneously. So the

product , is vanishes everywhere [8] in

the domain as there is no overlap. However, the dyadic

analysis and dyadic synthesissystemobjects are used to

remove noise from a signal (discussed in the section 6).

These properties of wavelets find important applications in

signal denoising.

VI. ADAPTIVE DENOISING USING WAVELETS

The objective of the denoising or estimation function is

to recover the useful signal from the noisy version thereof.

The denoising is the major application of wavelets in

statistics. Let the signal model, equation ( ), has been

contaminated by the noise is given by:

where desired unknown noise free signal,

is an unobservable noise assumed to be

Gaussian in nature.

is the observed signal from the process.

The wavelet expansion of the above function can be

represented in the similar Fourier series analysis form

given mathematically as:

In many applications it is observed that the rapid

variations in the signal possess minimal magnitude. Thus,

a conceivable denoise stratagem consists of:

Fig. 6: Doppler Spectrum of MST radar using Hilbert Transform

(Doppler Frequency in Hz Vs Height in Km).

TABLE II: FIGURES OF MERIT OF WINDOWS

Window

Type

DC/Coherent

Gain

Side lobe

fall-off

(dB/octave)

Equivalent

Noise BW

Rectangle 1.00 -6 1.00

Blackman 0.46 -6 1.57

Blackman-

Harris 0.36 -6 2.00

Kaiser 0.42 -6 1.50

Triangular 0.50 -12 1.33

Bohman 0.41 -24 1.79

Taylor 0.57 -6 1.30

Dolph-

Chebyshev 0.53 0 1.39

Gaussian 0.51 -6 1.43

Bartlett-

Hanning 0.43 -18 1.61

Tapered

Cosine 0.64 -12 1.23

Hanning 0.42 -24 1.73

Hamming 0.54 -6 1.36

246 2010 International Conference on Signal and Image Processing

i. Keeping the approximations such that the noise is

absent or at least much attenuated the .

ii. Supplementing this approximation by parts if the

finer details , clearly ascribable to the

useful signal and rejecting the parts which are

regarded as stemming from the noise.

However, two modes of threshold schema are popular

referred as hard and soft. Therefore, by equality the

coefficients carry the noise component of the

equation . In order to reduce noise effect, through

equating to zero of equation and reconstructing

the result yields to , this is expected to

be free from noise.

The application of wavelet decomposition, unfasten the

high frequency sub-bands contain most of the noise

information and little signal information. Many denoising

methods are available in the wavelet literature for cleaning

the signal from contamination. Several denoising schema

like rigrsure, heursure, sqtwolog, minimaxi, etc., are

available for noise removal [9,10], from the contaminated

signal so as to improve the SNR of the signal. In the

current work the signal decomposition is made using non-

decimated wavelet analysis. This kind of redundant,

translation-invariant transform is especially useful for

denoising, which is one of the most important wavelet

applications. This transform however has a serious

limitation: ( ) the signal length must be a power of 2 and

( ) the periodized extension mode must be used for the

underlying DWT. In-spite of these limitations, this

technique eliminates the reconstructing the signal. The

fig.7illustrates the wavelet adaptive denoising

implementation of the radarreturn at various altitudes. The

SNR of the original signal and wavelet adaptive denoised

signal is shown at nearly 22Km. The effect of wavelet

adaptive denoised signal is also observed. The application

of the wavelet adaptive denoising is done in non-

decimated mode so as to preserve the useful content of the

signal through eliminating the convention down sampling.

However, this method is more redundant. The typical

Doppler spectrum of fig.1 after wavelet adaptive denoising

is illustrated in fig.8 and good improvement of the SNR is

keenly observed with the wavelet denoising. The fig. 9 &

10depict the SNR (dB) plot (Range intensity plot before &

after wavelet adaptive denoising respectively. From fig 10

in comparison with fig 9, it is viewed that the proposed

wavelet adaptive denoising method improves the signal

strength, particularly in the range beyond 12 Km. Thus,

the wind profile using doppler spectrum (refer fig 8)

becomes simple.

The proposed Hilbert transform method, the wavelet

based denoising technique is made a comparisonwith the

other techniques developed [12,13], are herewith

presented in the fig.11. It is observed that the wavelet

Fig. 7.a: MST radar signal in time domain using wavelet adaptive denoising (received at nearly 6 Km).

Fig. 7.b: MST radar signal in time domain using wavelet adaptive

denoising (received at nearly 22 Km).

Fig. 8: Typical Doppler Spectrum of MST radar using wavelet adaptive

denoising (Doppler Frequency in Hz Vs Height in Km).

Fig.9: Range Time intensity plot of MST radar.

Fig.10: Range Time intensity SNR plot of MST radar after proposed

wavelet adaptive denoising.

2010 International Conference on Signal and Image Processing 247

based methods are exhibiting superiority over other

techniques. However, the proposed wavelet based adaptive

denoising performance demonstrates less performance

than the simple wavelet based denoising due to the fact

that the proposed method is developed based on adaptive

method in which the denoising is done based on the range

bin signal received and the amount of noise associated

with the signal present.

VII. WIND VELOCITIES ESTIMATION

Estimating the various parameters form the radar return

is the objective of the present work, such that to satisfy the

fundamental requirement of MAP discussed earlier

(section 1 of the present work). The absolute wind velocity

( ) calculated using the radial velocity components of

different beam positions. The computation/estimation of

velocity components viz., requires at least three

non-coplanar beams of the radar data are required. Let

an orthogonal axis defined by , and which are

aligned to east, north and zenith directions.

The , and are the resolved wind velocities

in , and directions.The wind velocities , and are

computed as explained.

Consider a given set of beams ; (at

present NARL uses for computation of wind

vectors) and , , are the directional cosines

for the beam. The is the radial component of the

wind velocity measured for the beam using equation 5.

Then, the directional velocity components are estimated

using the following relation:

where,

,

, ,

, ,

Thus, the wind vector components are computed and

finds useful for further atmospheric investigations like

study of periodicity of waves, modeling & development of

the standard Indian Atmosphere model, etc.

VIII. RESULTS& APPLICATIONS

All the results shown are extracted from the

experimental data obtained on MST radar instrument

system, NARL, ISRO in the subsequent years 2005, 06,

07.The wind velocities and directional components are

computed using the equations (5) & (11) are computed.

The results are compared with the ADP software at

NARL, Gadanki, India. The results obtained using

proposed algorithm wavelet based adaptive denoising is

also validated with the GPS experiment, SHAR data and

the results are shown in fig. 12 [12], which illustrates GPS

data Wavelet adaptive denoised Data (ALG). The

results obtained are concurrent with GPS data with a

deviation of ±2%.

The computation of wind velocity components and thus

the wind profile obtained from the MST radar, NARL,

Gadanki is used during launching of the space vehicles at

Sateesh Dhawan Space Centre, ISRO, Sriharikota, A.P.,

India. This information is critical during take-off the space

vehicles because the stress on the launch vehicle due to

wind gusts have greater influence below 15Km. Therefore

the dynamics of the wind information is essentially needed

for the launching program to steer the launch of space-

crafts and to assess mechanical stress during ascent.

ACKNOWLEDGMENT

The authors sincerely express their deep sense of

gratitude to Mr. B.L.Prakash, Associate System Engineer,

IBM, Bangalore, India Ltd for his support in building the

robust and testing algorithm, the package developed for

the current work. The authors also wish to acknowledge to

Mr. P.Srinivasulu, Scientist-F, NARL, ISRO, India who

helped the authors for making use of the instrument

facility to validate the results.

REFERENCES

[1] G Viswanathan, MST Radar System An Overview, Second Winter School on Indian MST Radar, pp.1-21, Feb 1995, UGC-SVU

Centre for MST Radar Application, S V University, Tirupati.

[2] M.I Skolnik, Boston, Radar Hand Book, McGraw-Hill, 1990, pp. 1.16.

[3] Lora G. Win 1994 IEEE Signal Processing Magazine, pp. 13-31.

[4] Radar Observations of Winds and

Turbulence in the Stratosphere and Mesosphere J.Atmos.Sci., , pp 493-505, 1985.

[5] Kusuma G Rao and S C Chakravarty,MST RADAR Theory,

Techniques and Applications, ISRO, 2000.

Fig.12: Typical Wind Profile validation / comparison of the proposed

wavelet adaptive denoised algorithm (ALG) Vs GPS experiment data.

Fig.11: Typical Wind Profile validation / comparison of the proposed

wavelet adaptive denoised algorithm (ALG) Vs GPS experiment data.

248 2010 International Conference on Signal and Image Processing

[6] Vijay K.Madisetti and Douglas B.Williams, Digital Signal

Processing Hand Book,Chapter 6, CRC Press, 1999. [7] C Sidney Burrus, R A Gopinath, and HaitaoGuo, Introduction to

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Academic Press, 1999.

[9] Donoho, D.L.; I.M. Johnstone, Ideal de-noising in an orthonormal basis, C.R.A.S. Paris, t. 319, Ser. I, pp. 1317-1322.

[10] Donoho, D.L. (1995), "De-noising by soft-thresholding," IEEE

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techniques, Atmos. Sci. Letters, Royal Meteorological Society, UK,

pp 1221-1230[13]

Techniques

Development Cell, JNTU, pp 58, Anatapur, 2010.

2010 International Conference on Signal and Image Processing 249