The effect of coherent integration on the periodogram method to estimate the power spectra of MST radar signals is examined. The spectrum estimate usually is biased, even when care is taken to reduce the aliasing effects. Due to this bias, the signal power for Doppler shifted signals is underestimated by as much as 4 dB. The use of coherent integration in reducing the effect of aliased power line harmonics is pointed out

Rastogi, P. K.

English

NASA Technical Reports Server

509 
8.3B A NOTE ON THE USE OF COHERENT INTEGRATION I N  PERIODOGRAM 
ANALYSIS OF MST RADAR SIGNALS 
P, K. Rastogi 
Haystack Observatory 
Massachusetts I n s t i t u t e  of Technology 
Westford, MA 01886 
ABSTRACT 
The e f f e c t  of coherent-integration on the periodogram method of estimating 
t h e  power spectra of MST radar  s igna l s  i s  examined. The spectrum estimate 
usually i s  biased, even when care i s  taken t o  reduce the a l i a s i n g  e f f ec t s .  Due 
t o  t h i s  bias,  the s ignal  power fo r  Doppler sh i f t ed  signals i s  underestimated by 
as much as 4 dB. The use of coherent integrat ion i n  reducing the e f f ec t  of 
a l iased power-line harmonics i s  pointed out. 
INLNzBODUCf ION 
In experiments used t o  probe the atmosphere with sens i t i ve  high power 
radars, the autocovariance functions (ACF) or power spectra  of atmospheric 
r e tu rns  are estimated by a processor. Coherent i n t eg ra t ion  i s  a technique t h a t  
reduces the da t a  input rate t o  the processor without unduly d i s to r t ing  the 
information-bearing pa r t  of the returns.  I n  experiments t h a t  use phase codes 
and decoding t o  obtain a f i n e  range resolution, it i s  possible t o  cut down on 
computations i n  the processor by relegat ing the  decoding operation till a f t e r  
coherent integration. The use of coherent integrat ion has been discussed f o r  
ACF processing by WOODiMBN and GUILLFN (1974), and SCEMIDT e t  al. (1979). 
Discrete Fourier transform (DFT) methods, especial ly  for  estimation of power 
spectra as time-averaged periodograns (OPPENEEIM and SCHAFER, 1975; COOLEY e t  
al., 1979). increasingly are being used i n  atmospheric radar  experiments (GAGE 
and BALSLEY, 1978; WOODMAN, 1980; BALSLEY, 1981). I n  t h i s  note, the use of 
coherent i n t eg ra t ion  i n  periodogram analysis  of MST radar s igna l s  i s  examined. 
SPECTRAL WINDOW AND ALIASING 
Let z ( t )  be the complex signal a f t e r  coherent demodulation f o r  a given 
range. 
r e p e t i t i o n  in t e rva l  (PRI), t o  the processor. 
f i n i t e  number N of samples f o r  each range. 
obtains  first their N-point DFT Z(f) ,  and then estimates the power spectrum S(f)  
of the atmospheric r e tu rns  as the time-averaged periodogram 
Samples of z ( t )  are input a t  d i sc re t e  i n t e rva l s  T, usually the pulse 
The processor can handle only a 
For these samples the processor 
P(f)  5 CZ(f) Z*(f)> (1) 
The periodogran estimate is obtained over the frequency range (-F,F), where 
F 1/2T, a t  N points with a frequency resolut ion 113N. A t  each point i n  the 
above range P(f)  is obtained as a d i s c r e t e  convolution of S(f)  with the 
standard periodogram window H(f) (COOLEY e t  al., 1979). 
For l a rge  B, H ( f )  approximates a d e l t a  function. 
ever, smearing of a strong undesirable f ea tu re  such as the ground c l u t t e r  can 
mask the atmospheric signal.  Components of S(f)  outside the range (-F,F) are 
al iaeed or folded-in. 
siderably wider than a baseband containing features  of i n t e r e s t  i n  S(f). 
coherent integrat ion of e ( t )  over several  radar sweep, it i s  possible t o  reduce 
the  frequency range and t o  improve the frequency resolution. 
For modest values of N, how- 
For most MST radar  experiments, t h i s  range i s  con- 
With 
https://ntrs.nasa.gov/search.jsp?R=19840019095 2020-03-22T09:45:57+00:00Z
510 
W i t h  coherent integration, M successive samples of z ( t )  are accumulated and 
it i s  these accumulated samples t h a t  are fed t o  the processor. 
i n t eg ra t ion  i s  equivalent t o  f i r s t  obtaining a process g ( t )  t h a t  i s  the moving 
average of z ( t ) .  
Thus coherent 
and 
the 
way 
then coarsely sampling g ( t )  a t  multiples of MT. 
time-averaged periodogratn from N-point sequences of samples of g ( t ) ,  i n  the 
outlined above fo r  z ( t ) .  
The e f f ec t  of the moving average operation i n  (3) i s  t o  weight S(f)  with a 
The processor now obtains 
frequency window 
This window i s  a comb function (SCEMIDT e t  al . ,  1979) with maxima a t  multiples 
of 1/T. Between any two maxima there  are M-1 minima with zero weight a t  mul- 
t i p l e s  of l/MT. 
F/M), sampled a t  N points  with a frequency r e so lu t ion  2FIMN. Th components out- 
s ide t h i s  range a re  weighted by G(f) and aliased. To reduce undesired e f f e c t s  
of t h i s  a l i a s ing  it i s  necessary t o  ensure t h a t  the expected Doppler s h i f t s  of 
the atmospheric r e tu rns  renain smaller than F/M. 
DISCUSS ION 
Due t o  sample t i m e  MT, the  basic  frequency range i s  now (-F/M, 
The behavior of the frequency window G and the folded pa r t s  i s  i l l u s t r a t e d  
The  fo r  two values of M i n  Figure 1. 
pa r t s  of S(f)  outs ide the normalized range (-0.5,+0.5) a re  aliased. 
The  frequency ax i s  i s  normalized as fTM. 
When care i s  taken t o  avoid the a l i a s ing  e f f ec t  discussed above, the 
averaged periodogram provides a reasonable estimate of the signal spectrum S(f). 
Over the basic  window (-F/M, F/M), these estimates are s t i l l  biased by the 
window G(f). 
pared t o  the folding frequency F/M. The e f f ec t  of frequency weighting i s  there- 
f o r e  negl igible  on the estimates of Doppler s h i f t  and spectral  width. 
s igna l  power, however, depends on the Doppler s h i f t .  Figure 2 shows the bias  i n  
s ignal  power as a function of the normalized frequency fTM. 
s ignals  t h i s  bias  may cause the signal power t o  be underestimated by as  much as 
4 dB. For s ignals  t h a t  are al iased only once. a Doppler p r o f i l e  can usually be 
constructed, but the signal power is underestimated by an even l a rge r  amount. 
Usually the Doppler-shifted r e tu rns  have a bandwidth small com- 
The 
For unaliased 
I n  most radar experiments, the computational advantage with the use of 
coherent integrat ion outweighs the small b i a s  i n  the spectrum estimates. 
some experiments, however, t h i s  bias  can be c r i t i c a l .  This i s  especially true 
of the aspect-sensit ivity experiments (GAGE and GREEN, 1978; FUKAO et  al., 1980) 
t h a t  have been used t o  detect  enhanced specular r e f l ec t ion  a t  quasi-vertical  
incidence. 
reduction of s ignal  power estimates fo r  off-ver t ical  echoes i s  expected a s  a 
r e s u l t  of t h i s  bias  alone. 
I n  
Unless the Doppler s h i f t s  are s m a l l  compared t o  F/M, a 2-4 dB 
The occurrence of n u l l s  i n  the part  of the spectrum t h a t  i s  folded can be 
When the used t o  reduce the contribution of the al iased power-line harmonics. 
number I of coherently integrated samples is large, both M and the PRI T can 
be adjusted t o  ensure t h a t  the power-line harmonic frequencies coincide with (or 
are close t o )  the n u l l s  i n  G(f). 
511 
1 .e 
u 
2e.s 
4 
8.8 
1 .e 
(3 
c'es .- s 
8.8 
- 1 0 4 - 8 - 4 - 2  0 2 4 d 8 10 
Normalized Freqmcy i T M  
Figure 1. Gain of the frequency window G due to coherent 
integration over M samples as a function of the normal- 
ized frequency fMT, where T is the sampling rate. The 
frequency components outside (-0.5,+0.5) are folded in. 
0 
-I 
3 "  
f "  
P -7 
b 
" -3 
I-. 
i;* 
-9 
-ie 
Figure 2. Periodogram bias due to coherent integration 
as a function of the normalized frequency fMT for 
different values of M. 
512 
ACKNOWLEDGEMENT 
This material is  based on work supported by the National Science Foundation 
under grant number ATM-8000060. 
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A note on the use of coherent integration in periodogram analysis of MST radar signals

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