The individual steps in the data processing scheme applied to most radars used for wind sounding are analyzed. This processing method uses spectral analysis and assumes a pulse Doppler radar. Improvement in the signal to noise ratio of some radars is discussed

Strauch, R. G.

English

NASA Technical Reports Server

528 
8.5A DATA ANALYSIS TECHNIQUES: SPECJXAL PROCESSING 
R. 6. Strauch 
NOAA/ERt/Wave Propagation Laboratory 
Boulder, GO 80303 
Most radars used fo r  wind sounding use a data-processing scheme similar  t o  
Radial p ro f i l e s  of the f i r s t  three 
t h a t  i l l u s t r a t e d  i n  Figure 1. 
ana lys i s  and assumes a pulse Doppler radar. 
moments of the Doppler spectra  a r e  estimated: s igna l  power P, mean r a d i a l  velo- 
c i t y  V, and spectrum width W. The input s ignal  i s  the backscattered s igna l  
f o r  each radar  r e so lu t ion  c e l l  a f t e r  t r a n s l a t i o n  t o  a convenient frequency. The 
receiver  l i m i t s  the bandwidth with a f i l t e r  t h a t  i s  (usually) matched t o  the 
transmitted pulse. Complex video i s  obtained by baseband mixing with a 
reference voltage. Samples of video a r e  generated f o r  each pulse r e p e t i t i o n  
period T and fo r  each range resolut ion c e l l  centered along the antenna axis ;  
these voltage samples represent the.composite amplitude and phase of the 
sca t t e r ing  process i n  the resolut ion volume. 
s t ep  of the data pr6cessing i s  examined i n  t h i s  paper. 
The processing method shown uses spec t r a l  
The averaging t h a t  occurs i n  each 
The signal-to-noise r a t i o  SNR can be improved f o r  some radars by summing 
the  complex video samples from a number J of consecutive received pulses. Since 
the noise bandwidth i s  determined by the radar  pulse width, noise samples taken 
a t  the pulse r e p e t i t i o n  period w i l l  be uncorrelated; therefore  the noise power 
increases l i nea r ly  with the number of samples added. The signal.  however, 
remains wel l  correlated f o r  approximately 0.2 A/W seconds (NATIIANSON, 1969) 
where A i s  the radar wavelength. 
t i o n  t i m e  i s  milliseconds with microwave radars  and seconds with VHF radars. 
I f ,  i n  addi t ion t o  being correlated,  the phase of the s ignal  samples changes 
very l i t t l e  between samples, then s ignal  samples can be added SO t h a t  s ignal  
power increases with the square of the number of samples added. This occurs f o r  
radars  whose unambiguous ve loc i ty  X/(4T) i s  much greater  than the r a d i a l  velo- 
c i t y  of the sca t t e re r s .  The SNR improves by the number J of samples averaged, 
and the unambiguous ve loc i ty  w i l l  decrease t o  A/(4JT). 
noted. 
detection. 
domain averaging minimizes the calculat ion burden i n  succeeding processing 
stages without s ac r i f i c ing  sens i t i v i ty .  ( 2 )  Time domain averaging f i l t e r s  the 
input signal so t h a t  s ignal  components with ve loc i ty  g rea t e r  than A/(4JT) w i l l  
be a l i a sed  and may be g rea t ly  attenuated (SCHMIDT e t  a l . ,  1979). Without t i m e  
domain averaging when s igna l  components a r e  a l i a sed  they a r e  not attenuated. We 
s e l e c t  J as large as possible such t h a t  X/(4JT) i s  greater  than the maximum 
expected mean r ad ia l  veloci ty  and such t h a t  the s ignal  is correlated f o r  much 
longer than JT. 
Typically W i s  about 1 m/s, so the correla- 
Two points should be 
(1) It i s  not necessary t o  use t i m e  domain averaging t o  improve 
The SNR improvement can be obtained i n  l a t e r  processing, but t i m e  
The next s tep i n  s ignal  processing i s  t o  compute the power spectrum of K 
(averaged) s ignal  samples. K i s  selected such t h a t  the ava i l ab le  coherent i n t e -  
grat ion i s  realized. I f  K i s  too small, s e n s i t i v i t y  i s  reduced; i f  K i s  too 
large,  the calculat ion burden is increased without 
r e t r i ev ing  addi t ional  information. Figure 2 shows 
domain improves as  dwell time TD = JKT increases.  
given by 
improving s e n s i t i v i t y  or 
how the SNR i n  the spectral  
The improvement f ac to r  is 
K erf - [ 22*] 
https://ntrs.nasa.gov/search.jsp?R=19840019100 2020-03-22T09:45:38+00:00Z
529 
Tirnebmain 
Averaging 
3 
Spectral 
Analysis 
K 
c 
t 
Spectral 
Averaging 
L 
Signal 
Noise 
Receiver 
Figure 1. Data processing sequence. Spectral processing 
for a pulse Doppler radar is illustrated. 
+ -- -- ---- 
-95% I. 
1 
-0 5 Yo I 
I 
dV = w 
I 
A - I - 
4 w  2 w  
TO 
Figure 2. Signal-to-noise ratio improvement by spectral pro- 
cessing. The limiting value is A I ( 2 T G  w). Dwell times 
longer than X/2W improve spectral resolution but yield little 
SNR improvement. 
530 
where AV i s  the ve loc i ty  resolut ion of the spec t r a l  processor A/(2TD). 
small K the  improvement f ac to r  increases l i nea r ly  with K; spec t r a l  resolut ion i s  
so poor t h a t  a l l  the s ignal  power remains i n  one veloci ty  resolut ion element. 
A s  observation t ime  increases,  the noise power i n  each ve loc i ty  resolut ion 
element decreases, while s igna l  power remains constant. When the dwell t i m e  i s  
increased such t h a t  s ignal  power starts t o  occupy more than one spec t r a l  point,  
SNR improvement no longer increases l i nea r ly  with dwell t i m e .  When the  dwell 
t i m e  i s  A/(2W) o r  K = A/(2JTw), 95% of the avai lable  coherent integrat ion i s  
achieved. Longer dwell t i m e s  y i e ld  l i t t l e  SNR improvement because both noise 
power and s ignal  power decrease i n  the veloci ty  resolut ion element t h a t  contains 
maximum signal.  Note, however, t h a t  fo r  l a rge  K, spec t r a l  points can be 
averaged and the  spectrum w i l l  s t i l l  be resolved. I f  t h i s  is  done, SNR improves 
as TD1/2 as expected f o r  incoherent integration. Thus, t o  minimize calculat ions 
w e  choose K = A/(2JlW) and use any addi t ional  observation t i m e  t o  measure new 
spectra,  
For 
The next processing s t ep  i s  the averaging of L spectra,  each obtained from 
JK radar  pulses. 
exponentially d i s t r ibu ted  with a standard deviation equal t o  the mean 
(HILDEBRAND and-SEKEON, 1974). We expect averaging t o  improve the spec t r a l  
domain SNR by h; however, t h i s  improvement w i l l  occur only i f  the mean wind i s  
the same f o r  each dwell t i m e .  I f  the mean wind i s  not the same, then the width 
of the averaged spectrum increases during the averaging and the SNR improvement 
w i l l  be less than a. 
abruptly by more than W, then the SNR can actual ly  decrease with averaging t i m e .  
The dependence of spec t r a l  width on averaging t i m e  can be deduced by examining 
the dependence of spec t r a l  width on averaging distance as studied by FRISCH and 
CLIFFORD (1974) and LABITT (1981). They der ive the r e l a t ionsh ip  W a d1I3 where 
d i s  the maximum dimension of the observation volume (beamwidth or range 
resolut ion,  whichever i s  g rea t e r )  and d i s  less than the outer scale  of 
turbulence Lo. 
Taylor's hypothesis, W a (T T,)1/3 where v i s  the mean wind speed. 
i f  the averaging t i m e  i s  less than dfi, then the width of the averaged spectrum 
i s  about the same as the width of the individual spectra;  fo r  greater  averaging 
t i m e ,  the width of the averaged spectrum increases as TO1/3. 
advantage of a improvement i n  SNR by averaging spectra,  L should be l imited t o  
about dl(JKTi7). 
The L power estimates fo r  each frequency or veloci ty  w i l l  be 
It i s  readily seen t h a t  i f  the mean wind changes 
I f  w e  average fo r  t i m e  T,such that  d < B To < Lo, then, using 
Therefore, 
To take f u l l  
The next data-processing step i s  the estimation of the important spectral  
The s ignal  spectrum must moments from the averaged Doppler veloci ty  spectrum. 
be i so l a t ed  from the measured signal-plus-noise spectrum before the moments can 
be found. The methods used t o  do t h i s  (and t o  remove undesired spec t r a l  
components such as ground c l u t t e r  near zero ve loc i ty )  are usually empirical. 
The average value of the complex t i m e  s e r i e s  i s  usually removed pr ior  t o  cal- 
culat ing the  power spectrum. 
threshold, e i the r  a specif ied amount above the mean noise l eve l  or below the 
peak l eve l .  Another method t o  loca t e  the signal i s  t o  f i n d  the maximum power i n  
a veloci ty  window of width equal t o  the expected s ignal  width. The method used 
with the 6711 radar a t  P l a t t e v i l l e ,  Colorado ( the P l a t t e v i l l e  radar i s  operated 
cooperatively by NOAA' s Aeronomy Laboratory and Wave Propagation Laboratory) i s  
as follows (CARTER, 1982). The mean value of t he  complex t i m e  series i s  removed 
p r i o r  t o  calculat ing t h e  individual power spectra. This f i l t e r i n g  i s  s u f f i c i e n t  
t o  remwe any c lu t t e r .  
transmission is  detected),  and the mean noise level  is  found by applying an 
object ive technique (HILDEBRAND and SEKHON, 1974) for  each spectrum. 
noise l eve l  cannot be assumed because the noise is governed by cosmic back- 
ground. 
averaged spectrum apd including a l l  those contiguous spectral  points t h a t  exceed 
the noise level.  The c l a s s i c  de f in i t i on  of the moments i s  then applied t o  the 
i so l a t ed  s ignal  spectrum a f t e r  subtracting the mean noise l eve l  from each of the 
Noise r e j ec t ion  i s  accomplished by applying a 
The noise spectra are white .!except when in t e r f e r ing  
A f ixed 
The s ignal  spectrum i s  isolated by locating the peak value of the 
531 
selected spec t r a l  points. 
noise only, the algorithm selects the peak and one or two addi t ional  spectral  
points;  i t  therefore  becomes a maximum-likelihood estimator of the mean veloci ty  
(WEALEN, 1971). 
random value between (+h/(4JT)) for  the mean veloci ty) .  
portion of the noise i n  the i so l a t ed  spec t r a l  points t h a t  exceeds the mean noise 
as "signal", both power and width estimates a r e  s l i g h t l y  biased by the noise. 
This method appears t o  work w e l l  for  a wide v a r i e t y  of conditions. 
I n  very weak signals ,  or i f  the input consis ts  of 
It i s  an unbiased estimator of the mean ( i n  noise it se l ec t s  a 
Since i t  se l ec t s  t h a t  
Final ly ,  estimates of spectral  moments can be averaged. The averaging time 
depends on the type of information sought and the temporal evolution of the 
sca t t e r ing  phenomena. For example, the P la t twi l le  radar is used primarily t o  
obtain hourly estimates of tropospheric winds; during an hour M r a d i a l  p ro f i l e s  
of mean veloci ty  are measured. 
random because of low SNR. Some of the p r o f i l e s  i re  a l s o  contaminated by inter-  
ference from other  t ransmit ters  or by sca t t e r ing  from a i r c r a f t .  
are averaged by applying a simple version of Random Sample Consensus (FISCHLER 
and BOLLES, 1981). 
examined t o  f ind  the l a rges t  subset of points within X m / s  of each other. 
t he  subset includes fewer than Y data  points,  the data are rejected f o r  that  
height;  otherwise the subset i s  averaged t o  obtain the mean r a d i a l  wind. 
algorithm r e j e c t s  data when the SNR i s  too low and a l so  r e j e c t s  random points 
caused by interference.  
c i t y  i s  219 m/s), and the  smallest subset allowed i s  4 of 12 measurement 
points. 
A t  the upper heights the mean v e l o c i t i e s  are 
The p ro f i l e s  
The set of M data  points a t  each measurement height a r e  
I f  
This 
I n  pract ice  X i s  1 m/s (where the maximum rad ia l  velo- 
REFERENCES 
Carter, D. A. (19821, Pr ivate  communication, Aeronomy Laboratory, NOAA. 
Fischler,  M. A. and R. C. Bolles (1981), Random sample consensus: A paradigm 
f o r  model f i t t i n g  with appl icat ions to  image analysis  and automated carto- 
graphy, Commun. Assoc. Comput. Mach.. 24, 381-395. 
Frisch, A. S. and S. F. Cl i f ford (19741, A study o f  convection capped by a 
s t a b l e  layer using Doppler radar and acoust ic  echo sounders, J. Atmos. Sci. 
& 1622-1628. 
Bildebrand, P. E. and R. S. Sekhon (19741, Objective determination of the noise 
l eve l  i n  Doppler spectra,  J. Appl. Meteorol., 13, 808-811. 
Labi t t ,  M. (19811, Coordinated radar and a i r c r a f t  observations of turbulence, 
Project  Report ATC 108, MIT Lincoln Laboratory. 39 pp. 
Nathanson, F. E. (19691, Radar Design Principles ,  McGraw-Hill, N e w  York, 
626 pp. 
Schmidt, G., R. Ruster and P. Czechowsky (19791, Complementary code and d i g i t a l  
f i l t e r i n g  fo r  detect ion of weak WF radar s ignals  from the mesosphere, 
IEEE Trans. Geosci. Exec.. GE-17, 154-161. 
Whalen, A. D. (1971), Detection of Signals i n  Noise, Academic Press, New 
York, 411 pp. 


Data analysis techniques: Spectral processing

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