Third winter School on Indian MST Radar March 5-9, …wprass/andandan-lec.doc · Web viewThe radar works on the principle that when a pulse of electromagnetic waves is transmitted

IITM-NMRF-VKA-Training /Workshop programme on Wind profiler and Radio Acoustic Sounding System

Training /Workshop programme on Wind profiler and Radio Acoustic Sounding System

Signal detection and Processing techniques for Atmospheric radars

Dr. V.K.Anandan

National MST Radar Facility Dept. of Space

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1. Introduction

RADAR is the acronym for Radio Detection and Ranging. The radar

invention has its roots in the pioneering research during nineteen twenties by Sir

Edward Victor Appleton in UK and Breit and Tuve (1925) in USA on the

detection of ionization layers in the upper atmosphere. The radar works on the

principle that when a pulse of electromagnetic waves is transmitted towards a

remotely located object, a fraction of the pulse energy is returned through either

reflection or scattering, providing information on the object. The time delay with

reference to the transmitted pulse and the received signal power provide

respectively the range and the radar scattering cross-section of the target detected.

These class of radars are known as pulse radar. In case the target is in motion

when detected, the returned signal is Doppler shifted from the transmitted

frequency and the measurement of the Doppler shift provides the line-of-sight

velocity of the target. The radars having this capability are referred to as pulse

Doppler radars. In addition to the above, if the location of the target is to be

uniquely determined, it is necessary to know its angular position as well. The

radars having this capability employ large antennas of either phased array or dish

type to generate narrow beams for transmission and reception. Two major radars

of this kind used for scientific research are the phased array radar of Jicamarca

and dish antenna radar of Arecibo. Two important parameters that characterize

the capability of a radar are its sensitivity and resolution for target detection. The

sensitivity is determined by the peak power-aperture product and the resolution

by the pulse volume which depends on the pulse length and the radar beam width.

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There are several variants to the above type of pulse radars that have been

developed with varying degrees of complexity to meet the demands of application

in various fields.

2. Atmospheric Radars

Radar can be employed, in addition to the detection and characterization of

hard targets, to probe the soft or distributed targets such as the earth’s

atmosphere. The atmospheric radars of interest to the current study are known as

clear air radars and they operate typically in the VHF (30 –300 MHz) and UHF

(300 MHz – 3GHz) bands (Rotteger and Larsen, 1990). The turbulent fluctuations

in the refractive index of the atmosphere serve as a target for these radars

There is another class of radars known as weather radars which serve to

observe the weather systems and they operate in the SHF band (3- 30 GHz)

(Doviak and Zrnic, 1984). A major advance has been made in the radar probing

of the atmosphere with the realization in early seventies, through the pioneering

work of Woodman and Guillen (1974), that it is possible to explore the entire

Mesosphere-Stratosphere-Troposphere (MST) domain by means of a high power

VHF backscatter operating ideally around 50 MHz. It led to the concept of an

MST radar and this class of radars have come to dominate the atmospheric radar

scene over the past few decades.

An MST radar is a high power phase coherent radar operating typically

around 50 MHz with an average power-aperture product exceeding about 5x107

Wm2. Radars operating at higher frequencies or having smaller power-aperture

products are termed ST (Stratosphere-Troposphere) radars. In arriving at an

optimum radar frequency for MST application, the main considerations are the

frequency dependence of radar reflectivity for turbulent scatter and possible

interference from other sources of sporadic nature. The weak radar reflectivity of

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the turbulent scatter coupled with a requirement of a few tens of meters of range

resolution has called for the application of pulse compression and advanced signal

and data processing techniques. In the next few sections are presented some of the

basic concepts on pulse compression and signal and data processing as applied to

the MST radars, which form the background to the study.

3. Signal Detectability and Pulse Compression

The efficiency of the radar system depends on how best it can identify the

echoes in the presence of noise and unwanted clutter. The important parameters

from the system point of view influence the radar returns are the average power

of transmission and the antenna aperture size. Signal detectability is a measure of

the radar performance in terms of transmission parameters.

3.1 Signal Detectability

One of the important parameters which decides the received power can be in-

directly defined in terms of detectability factor (Farley, 1985). This important quan-

tity is the received signal power Psig to the uncertainty Pn in the estimate of the

noise power after averaging. For optimum processing

Where Ae is the effective antenna area, Pt is the peak power transmitted, is the

pulse length, PRF is the pulse repetition frequency, Pave = PtPRF is the average

transmitter power, Brec is the receiver band-width, Ts is the effective system noise

temperature, Nc is the number of samples coherently added, Ninc is the number of re-

sulting sums which are incoherently averaged, c 1/Bsig is the correlation time of

the scattering medium for the radar wavelength used, t is the total integration time,

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h is the range or height and h is the height resolution. Before the operation of the

coherent integration and incoherent integration, which comes in the digital domain,

the signal is maximized at the receiver with a “matched” filter whose impulse re-

sponse is the time inverse of the transmitted pulse. It is also assumed that the target

fills the scattering volume defined by the beam pulse and shape length.

From equation (1.1) it is obvious that the average power is the important pa-

rameter for the strong returns and this is function of pulse length. Short pulses are

required for good range resolution, and the shorter length of Inter pulse period (IPP)

generates the problem of range ambiguity. Therefore maximum limit on the PRF is

restricted due to the above problems. Pulse compression and frequency stepping are

techniques which allow more of the transmitter average power capacity to be used

without sacrificing range resolution.

3.2 Pulse Compression

As the name implies, a pulse of power P and duration is in a certain sense

converted into one of power nP and duration /n. In the frequency domain compres-

sion involves manipulating the phases of the different frequency components of the

pulse. In the time domain a pulse can be compressed via phase coding, especially

binary phase coding, a technique which is particularly amenable to digital process-

ing techniques. Since frequency is just the time derivative of phase, either can be

manipulated to produce compression. Phase coding has been used extensively in at-

mospheric radars and in commercial & military applications.

The codes in general use fall in to a number of general classes

Barker codes: These were first discussed by Barker (1953) and have been used in

Ionospheric incoherent scatter measurements. The distinguishing feature of these

codes is that, the range side-lobes have a uniform amplitude of unity. The compres-

sion process only works, if the correlation time of the scattering medium is substan-

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tially longer than the full-uncompressed length of the transmitted pulse. The decod-

ing involves adding and subtracting voltages, not powers. If the scattering centers

move a significant fraction of a radar wavelength between time of arrival of the first

and last baud of the pulse, the compression process will fail. This is never a problem

in practice in Mesosphere, Stratosphere, Troposphere (MST) observations, but it

can be a problem in ionospheric studies. Although 13 bauds is the longest possible

binary Barker sequence (Unity side lobe), there are many longer sequences with

side lobes that are only slightly larger which are used in radar observations (Wood-

man et al., 1980).

Complementary code pairs: Barker codes have range side lobes which are small,

but which may still cause problems in MST applications. Ideally a codes which sup-

ports high compression ratios (long codes) to get the possible altitude resolution, but

if we do so the signal from an altitude in the upper stratosphere, may be contami-

nated by range side lobe return from lower altitudes, since the scattered signal

strength is a strong function of altitude, typically decreasing by 2-3 dB/km (Farley,

1985). This side lobe problem can be eliminated by the use of complementary

codes.

The existence of complementary codes was first pointed out by Golay (1961)

and has been discussed further in the literature (Rabiner and Gold; 1975,), but the

severe restriction on their application to radar - phase changes introduced by the tar-

get must vary only a time scale much longer than the IPP - have prevented them be-

ing utilized in practice. The Doppler shifts encountered in military, civilian applica-

tion, and in incoherent scatter from the ionosphere are too large. The Doppler shifts

associated with MST radar observation on the other hand, are very small and are en-

tirely compatible with the use of such codes. The medium correlation time is typi-

cally tens or hundreds of times longer than IPP.

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Complementary phase codes are binary in their simplest form and they usu-

ally come in pairs. They are coded exactly as Barker codes, by a matched filter

whose impulse response is the time reverse of the pulse. The range side lobes of the

resulting ACF output for each pulse will generally be larger for a barker code of

comparable length, but the two pulses are complementary pair have the property

that their side lobes are equal in magnitude but opposite in sign, so that when out-

puts are added the side lobes exactly cancel, leaving only the central peak. This

code is used in SOUSY radar (Schmidt et.al., 1979), Arecibo (Woodman, 1980) and

Gadanki, India (Rao et.al., 1995).

4. Signal Processing

The decoding of the pulse compressed data and coherent integration need

to be realized in real time. The decoding operation essentially involves cross

correlating the incoming digital data with the replica of the transmit code. It is

implemented by means of a correlator/transversal filter. Since decoding would

normally require several tens of operations per sec, the implementation would

be difficult in software. One approach that can be adopted is to apply coherent

integration first and then decode the signal, which is implemented in Sousy radar

(Woodman, 1983; Woodman et.al., 1984).

Until recently, most of the signal processor designs were based LSI ICs re-

sulting in limited flexibility. The field of digital signal processing (DSP) has been a

very active area of research and application for more than two decades. This broad

development has paralleled in time the development of high-speed electronic digital

computers, microelectronics and integrated fabrication technologies. An ever in-

creasing assortment of integrated circuit parts specifically tailored to perform com-

mon DSP functions is available to the design engineers as system building blocks

on parts-in-trade. Effective utilization of advanced DSP IC and fast digital to analog

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converter has made possible the implementation of decoding without integrating

and the software coding in a later stage. In the new generation radars most of the

signal processing is realized in firmware with the help of DSP ICs.

4.1 Data processing and parameter extraction

Figure 1shows the functional block diagram of various processing stages involved

in the extraction and estimation of atmospheric parameters.

The complex time series of the decoded and integrated signal samples are

subjected to the process of FFT for the on-line computation of the Doppler power

spectra for each range bin of the selected range window. The Doppler spectra are

recorded on a Hard disk for off-line processing. There is a provision, however, to

record raw data (complex time samples) directly for any application, if so desired.

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Decoder(I&Q)

Coherent Integrator Normalization Windowing

Fourier Analysis&

Power SpectrumIncoherent Averaging

Spectrum Cleaning

Noise level Estimation

Moments UVW

Figure 1 Processing steps for extraction of parameters

Q-Channel

I-Channel

Power Spectrum

Time Series

Zonal, Meriodonal, Vertical wind velocity

Total Power, Mean Doppler, Doppler Width

Signal Processor On-line/Off-line Processing

Off-line Processing


The off-line data processing for parameterization of the Doppler spectrum follows

closely the procedure adopted at the poker flat radar (Riddle, 1983). The

computation involved in the various stages of operation and its advantages is

given below.

Coherent Integration

The detected quadrature signals are coherently integrated for many pulse returns

which lead to an appreciable reduction in the volume of the data to be processed

and an improvement in the SNR. The coherent integration is made possible

because of the over sampling of the Doppler signal resulting from the high PRF

relative to the Doppler frequency. In other words, the coherence time of the

scattering process c is much greater than the sampling interval given by the inter

pulse period tp. In the case of phase coding, a complementary pair of phase-coded

pulse constitutes one radar cycle with a time interval of Tp (= 2tp). The odd and

even pulses are coherently integrated and decoded separately before combining

them to provide the complex time series for spectral analysis for each range gate.

Since the integration is linear operation it can be performed before any decoding

is carried out of the phase coded pulse returns (Woodman et.al., 1980).

The operation of coherent integration amounts to applying a low pass filter,

whose time-domain representation is a rectangular window of Ti duration. The

effects of coherent integration on the signal power spectrum have been discussed

by Farley (1985). The signal spectrum is weighted by that of the integration filter

sin2x/x2, where x = fTi and f is the Doppler shift in Hz. The sampling operation

at the integration time interval of Ti leads to frequency aliasing with signal power

at frequencies f (m/Ti), where m is any integer, added to that at f. In the case of

a flat spectrum, the filtering and aliasing balance each other and white noise still

looks white, with no tapering at window edges. On the other hand, a signal peak

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with Doppler shift of 0.44/Ti Hz, near the edge of the aliasing window, will be

attenuated by 3 dB by the filter function, whereas a peak near the center of the

spectrum will be almost unaffected. One should, therefore, be conservative in

choosing Ni for coherent integration so as to ensure that all signals of interest are

in the central portion of the post-integration spectrum. The coherently integrated

complementary pairs of coded signals are decoded for each range gate and added

together to generate the final time series of the signal return for spectral analysis.

Normalization of the Pre-Processed data

The input data is to be normalized by applying a scaling factor

corresponding to the operation done on it. This will reduce the chance of data

overflowing due to any other succeeding operation. The Normalization has

following components.

a. sampling resolution of ADC

b. scaling due to pulse compression in decoder

c. scaling due to coherent integration

d. scaling due to number of FFT points.

if v - ADC bit resolution ( 10/16384),

w - Pulse width in microsecond,

M -Number of IPP integrated = Integrated time /inter pulse period,

N - Number of FFT points,

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then the Normalization factor

The complex time series { Ii , Qi where i = 0, . . ,N-1} at the output of the signal

processor is scaled as

Windowing

It is well known that the application of FFT to a finite length data gives rise

to leakage and picket fence effects. Weighting the data with suitable windows can

reduce these effects. However the use of the data windows other than the

rectangular window affects the bias, variance and frequency resolution of the

spectral estimates. In general variance of the estimate increases with the uses of a

window. An estimate is said to be consistent if the bias and the variance both tend

to zero as the number of observations is increased. Thus, the problem associated

with the spectral estimation of a finite length data by the FFT techniques is the

problem of establishing efficient data windows or data smoothing schemes.

Fourier analysis

Spectral analysis is connected with characterizing the frequency content of a

signal. A large number of spectral analysis techniques are available in the

literature. This can be broadly classified in to non-parametric or Fourier analysis

based method and parametric or modal based methods.

Fourier proposed that any finite duration signal, even a signal with

discontinuities, can be expressed as an infinite summation of harmonically related

sinusoidal component; that is

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Where AK and Bk are Fourier coefficients and 0 is the fundamental angular

frequency. Application of Fourier analysis to discrete series of data and its fast

computation algorithm Fast Fourier transform (FFT) made this technique so popular

in the spectral analysis. FFT is applied to complex time series {(I i, Qi), i =

0,1, . . . ,N-1} to obtain complex frequency domain spectrum { (Xi, Yi), i = 0, . . . . ,

N-1}

Power Spectrum

Power spectrum is calculated from the complex spectrum as

Incoherent Integration (Spectral averaging)

Incoherent integration is the averaging of the power spectrum number of times.

where m is the number of spectra integrated.

The advantage of the incoherent integration is that it improves the detectability of

the Doppler spectrum. The detectability is defined as

D = PS/S+N (8)

Where PS is the signal power and S+N is the standard deviation of the power spectral

density. Figure 2 shows the sample result of incoherent averaging of the data

obtained with MST radar.

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13Figure 2 Example of Incoherent Integration


Power spectrum cleaning

Due to various reasons the radar echoes may get corrupted by ground clutter,

system bias, interference, image formation etc.. The data is to be cleaned from these

problems before going for analysis.

Clutter/ DC removal: The presence of ground clutter presents a source of

additional problem. Different techniques have been used to cancel or minimize its

effect. Ground clutter signals have a spectral signature which consists essentially

of a single spectral line at the origin with a strength which depends on the ground

shielding of the radar. At tropospheric and stratospheric heights it is at least

comparable to the signal and often many orders of magnitude larger. Strictly it is

very difficult to remove these signals, one way to eliminate its biasing effect is to

ignore the frequencies around zero (dc) frequency. This is possible only when the

spectral offset is larger than its width.

The basic operation carried out here is,

This is also can be removed in time series by taking out the bias in I and Q channel

and then perform the Fourier analysis.

Spikes (glitches) in the time series will generate a constant amplitude band all

over the frequency bandwidth. Once Fourier analysis is done, it is difficult to

identify the correct Doppler in the range bin. These points may be removed from

the range bin and adjusted to noise floor or doing an incoherent integration of the

spectrum and replace the value with good value from the second spectrum.

However, this type of problem need to be corrected before doing Fourier analysis to

get a better result by finding out the out-liers in data.

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Constant frequency bands will form in the power spectrum by the

interference generated in the system or due to extraneous signal. Due to this reason

it is also possible the formation of multiple bands in spectrum. This is removed by

taking a range bin, which does not have echoes but the interference. This range bin

gets subtracted from all other range bins after the removal of mean noise. If the

interference is not affecting the original Doppler trace then the analysis may be

carried out in a window confined to the Doppler trace.

5 Parameter Estimation.

MST radar echoes are produced by fluctuations in the index of refraction of

the atmosphere. In most cases, these are turbulence-induced fluctuations. Because

of the random nature of the turbulence, radar returns from turbulence-induced

fluctuations represent stochastic processes and have to be characterized

statistically. The returns from any one height form a random time series and can

be considered stationary within an integration time and Gaussian in nature

(Woodman 1985; Zrnic 1979). A Gaussian and stationary process is fully

characterized by its autocorrelation function or equivalently by its Fourier

transform, the frequency power spectrum. To characterize the process, it is

essential to know the turbulence intensity, mean radial velocity and velocity

dispersion, which are a measure of physical properties of the medium. If the

spectrum is Gaussian, these three parameters contain all the information which

we can obtain from the radar echoes. Following section will give the parameter

extraction procedure.

5.1 Noise level estimation

There are many methods adapted to find out the noise level estimation. Basi-

cally all methods are statistical approximation to the near values. The method im-

plemented here is based on the variance decided by a threshold criterion, Hilde-

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brand and Sekhon (1974). This method makes use of the observed Doppler spec-

trum and of the physical properties of white noise; it does not involve knowledge of

the noise level of the radar instrument system. This method is now widely used in

atmospheric radar noise threshold estimation and removal.

The noise level threshold shall be estimated to the maximum level L, such that the

set of Spectral points below the level S, nearly satisfies the criterion,

Step 1:

Reorder the spectrum { Pi, i = 0, . . . N-1} in ascending order to form. Let this

sequence be written as{ Ai, i = 0, . . . N-1} and Ai < Aj for i < j

Step 2: compute

Where M is the number of spectra that were averaged for obtaining the data.

Step 3:

5.2 Moments Estimation

The extraction of zeroth, first and second moments is the key reason for on

doing all the signal processing and there by finding out the various atmospheric and

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turbulence parameters in the region of radar sounding. The basic steps involved in

the estimation of moments, Woodman (1985) are given below.

Step 1.

Reorder the spectrum to its correct index of frequency (ie. -fmaximum to

+fmaximum) in the following manner.

Step 1

Spectral index 0 1 N/2 N-1

ambiguous freq. -fmaximum Zero freq. +fmaximum

Step 2:

Subtract noise level L from spectrum

Step 3:

i) Find the index l of the peak value in the spectrum,

ii) Find m, the lower Doppler point of index from the peak point.

iii) Find n the upper Doppler point of index from the peak point

Step 4:

The moments are computed as

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represents zeroth moment or Total Power in the Doppler spectrum.

represents the first moment or mean Doppler in Hz

represents the second moment or variance, a measure of dispersion from central

frequency.

where

IPP - is interpulse period in microsec.

N - is the number of FFT points.

Calculation of spectral moments of spectrum with composite structure is

done in a slightly different way from the procedure explained above. This type of

spectrum normally comes in the upper atmospheric region (Ionosphere). Here the

spectra shows multiple spikes and wide, so after the removal of mean noise level the

spectra may be crossing from positive values to negative many times. Thus, the

peak and valley detection described above can not give the correct result. To

overcome this problem, a running template is taken with seven Doppler points

(Patra et.al., 1995). The Doppler point to be checked is the central point of the

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template. This template will move from the peak to the either side of the spectrum

to find the lower and upper point of Doppler index from the maximum peak. The

running average of seven points is checked against a threshold. The threshold is

kept 3dB above the mean noise level. The Doppler point is considered till the

template average is above the threshold. Remaining part of the moments calculation

is same as that of the calculation for the single peak Doppler spectrum.

5.3 UVW Computation

The prime objective of atmospheric radar is to obtain the vector wind

velocity. Velocity measured by a radar with the Doppler technique is a line of

sight velocity, which is the projection of velocity vector in the radial direction.

There are two different techniques of determining the three components of the

velocity vector: the Doppler Beam Swinging (DBS) method and Spaced Antenna

(SA) method. The DBS method uses a minimum of three radar beam orientations

(Vertical, East-West, and North-South) to derive the three components of the

wind vector (Vertical, Zonal and Meriodional), Sato (1988). In the spaced

antenna method, the backscattered signal is received by three non-coplanar

antennas, located usually at the corners of a right angle triangle. The horizontal

velocity and the characteristics of the ground diffraction pattern and thereby that

of the scattering irregularities can be obtained through the full correlation analysis

of Briggs (1984).

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Calculation of radial velocity and height:

For representing the observation results in physical parameters, the Doppler

frequency and range bin have to be expressed in terms of corresponding radial

velocity and vertical height.

where c - velocity of light in free space, fD- Doppler frequency, fC- Carrier

frequency, - Carrier wavelength ( here 5.86 m), - Beam tilt angle, tR - Range

time delay.

Computation of absolute Wind velocity vectors (UVW):

After computing the radial velocity for different beam positions, the absolute

velocity (UVW) can be calculated. To compute the UVW, at least three non-

coplanar beam radial velocity data is required. If higher number of different beam

data are available, then the computation will give an optimum result in the least

square method.

Line of sight component of the wind vector V (Vx, VY, Vz) is

VD = V . i = Vx cosx + Vy cosy + Vz cosz (20)

where X, Y, and Z directions are aligned to East-West, North-South and Zenith

respectively. Applying least square method, residual

2 = (Vx cosx + Vy cosy + Vz cosz - VD i)2 (21)

where VD i =fD i * /2 and i represents the beam number

To satisfy the minimum residual

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2 /Vk = 0 k corresponding to X,Y, and Z leads to

Thus, on solving equation (2.20) we can derive VX, VY, and VZ, which corresponds

to U (Zonal), V (Meridonal) and W (Vertical) components of velocity.

Reference:

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Barker, R.H., Group synchronizing of binary digital systems, in Communication

theory, ed. By W. Jackson, PP 273-287, Acadamic, Orlando, Fla., 1953.

Breit, G and M.A Tuve, A radio method of estimating the height of conducting

layer, Nature 116, 357, 1925.

Briggs, B., The analysis of spaced sensor records by correlation techniques,

Handbook for MAP, Vol. 13, pp 166-186, SCOSTEP Secretariat, University of

Illinois, Urbana, 1984.

Doviak, R.J., and Zrnic.D.S, Doppler radar and Weather Observations, Acadamic

Press, London 1984.

Farley, D.T., On-line data processing techniques for MST radars, Vol 20, No.6, Pp

1177-1184, 1985.

Golay, M.J.E., Complimentary series, IEEE Trans. Inf. Theory, IT-7, 82-87, 1961.

Hildebrand, P.H., and R.S Sekhon, Objective determination of the noise level in

Doppler spectra, J.Appl.Meterol., 13, 808-811, 1974.

Patra, A.K., V.K.Anandan, P.B.Rao, and A.R.Jain First observations of equatorial

spread –F from Indian MST radar, Radio Sci., 30, 1159-1165, 1995.

Rabiner, L.R., and B.Gold, Theory and application of Digital signal Processing,

Prentice Hall, Englewood Cliffs, N.J, 1975.

Rao, P.B., A.R Jain, P.Kishore, P.Balamuralidhar, S.H.Damle and G.Viswanathan.,

Indian MST radar1. System description and sample vector wind measurements in

ST mode., Radio sci., vol 30, No.4 pp 1125-1138 1995.

Riddle, A.C., Parameterization of spectrum, in Handbook for MAP, edited by S.A.

Bowhill and B.Edwards, 9. pp 546-547, SCSTEP Secr., Urbana, Ill., 1983.

Rötteger, .J., and M.F. Larsen, UHF/VHF Radar techniques for atmospheric

research and wind profiler applications, in Radar in Meteorology, edited by D.

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Atlas, chap. 21a, pp 235-281, American Meteorological Society, Boston, Mass.,

1990.

Sato, T., Radar Principles, ISAR, Lecture notes ed by Fukao, 1988.

Schmidt, R., Multiple Emitter Location and Signal Parameter Estimation, Proc. Of

the RADC spectrum Estimation Workshop, RADC-TR-79-63, Rome Air

Development Center, Rome, NY, , PP243, Oct 1979.

Woodman, R.F., Kugel R.P, and Rotteger, A coherent integrator-decoder

preprocessor for the SOUSY-VHF radar, Radio Sci., 15, 233-242, 1980.

Woodman R.F, M.P.Sulzer, D.T.Farley., Binary pulse compression techniques for

MST radars, Map Hand book. Vol. XIII, pp 155-165, 1984.

Woodman, R.F., and A Guillen, Radar observations of winds and turbulence in the

stratosphere and mesosphere, J. Atmos. Sci., 31, 493-505, 1985.

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Documents

Third winter School on Indian MST Radar March 5-9, …wprass/andandan-lec.doc · Web viewThe radar works on the principle that when a pulse of electromagnetic waves is transmitted