The effects on the signal detectability of varying the pulse repetition rate (PRF), peak pulse power (p(pk)) and pulse width (tau(p)) (tp) are examined. Both coded and uncoded pulses are considered. The following quantities are assumed to be constant; (1) antenna area, (z)echo reflectivity, (3) Doppler shift, (4) spectral width, (5) spectral resolution, (6) effective sampling rate, and (7) total incoherent spectral averagaing time. The detectability is computed for two types of targets

Carter, D. A.

English

NASA Technical Reports Server

100 
2.2B THE EFFECTS OF PULSE RATE, POWER, WIDTH 
AND CODING ON SIGNAL DETECTABILITY 
U. A. Carter 
Aeronomy Laboratory 
National Oceanic and Atmospheric Administration 
Boulder, CO 80303 
When deciding upon radar and s ignal  processing parameters f o r  MST radars,  
the quant i ty  t h a t  one attempts t o  maximize within ex i s t ing  constraints  i s  the  
s ignal  de t ec t ab i l i t y .  For Doppler spectral analysis  the de t ec t ab i l i t y  can be 
defined (see BALSLEY, 1978 or  GAGE and BALSLEY, 1978) a s  the r a t i o  of the 
amplitude of the l a rges t  spectral  peak of the received s ignal  t o  the noise l e v e l  
f luctuat ion,  D = Sr/ASN (see Figure 1) .  
pulse r e p e t i t i o n  r a t e  (PRF), peak pulse power (Pp@ and pulse width ( T p ) .  
coded and uncoded pulses w i l l  be considered. 
following quan t i t i e s  w i l l  be assumed t o  be constant: 
r e f l e c t i v i t y ,  Doppler s h i f t ,  spec t r a l  width, spec t r a l  resolut ion,  e f f ec t ive  
sampling r a t e ,  and t o t a l  incoherent spectral  averaging t i m e .  The d e t e c t a b i l i t y  
w i l l  be computed fo r  two types of t a rge t s :  
echoing region smaller than the smallest pulse width). 
This paper w i l l  examine the e f f ec t s  on the d e t e c t a b i l i t y  of varying the  
Both 
During t h i s  discussion the 
antenna area, echo 
1 )  d i s c r e t e  t a rge t  ( i .e . ,  a s ing le  
F i r s t  l e t  us examine the e f f e c t s  of coded pulses.  The received s igna l  from 
a coded pulse i s  decoded by convolving the received vol tage with the code. 
phase of the received s ignal  from the echoing region w i l l  be the mirror image of 
the transmitted code. Since the autocorrelat ion function of a code of length L, 
has a peak value of L,, the  decoding process enhances the echo s ignal  power by 
a f ac to r  of Le2. 
code, the convolution w i l l  add the power incoherently and thus the noise power 
w i l l  be increased by a factor  of L,. The above i s  t rue  regardless  of the type 
of code used. 
random codes) the s ignals  from successive codes must be added coherently t o  
obtain the desired autocorrelat ion sidelobe response. However, a s  long a s  the 
number of codes used i s  less than the normal number of coherent averages, multi- 
code processing w i l l  not have any addi t ional  e f f ec t  on the s ignal  de t ec t ab i l i t y .  
Of course, the sidelobes of the code autocorrelat ion functions w i l l  a f f ec t  range 
contamination of s ignals  and influence the choice among various codes. 
The 
For white noise which i s  uncorrelated between each b i t  of the 
For multicode processing (using complementary codes o r  pseudo- 
Now we w i l l  determine the s ignal  de t ec t ab i l i t y  for  coded and uncoded pulses 
as a function of PRF, t ransmit ter  power, pulse width, and code length. Let us 
define the fundamental b i t  length or resolut ion pulse width of a coded pulse t o  
be T~ and the t o t a l  pulse length to  be T~ E L , T ~ .  The same symbols can be used 
f o r  uncoded pulses by l e t t i n g  L, = 1 and T~ = T ~ .  The returned s ignal  power, 
Ps,  i s  proportional t o  peak t ransmit ter  power for d i sc re t e  targets  and t o  peak 
power and pulse width fo r  diffuse targets .  
uncoded pulses, 
Specif ical ly ,  for  both coded and 
"s a 'pk Lc (d i sc re t e  t a rge t s )  
Ps = Ppk T ~ L , ~  (diffuse t a rge t s ) .  
The noise power can be wri t ten as  
PN a B Lc/m a L /T m 
c o  
https://ntrs.nasa.gov/search.jsp?R=19840019025 2020-03-22T09:39:40+00:00Z
101 
I I 1 
.Of  ma, 0 , + Of max - Doppler Shift - 
Figure 1. Typical Doppler spectrum ( a f t e r  BALSLEY, 1978a). 
where B a l / r o  i s  the receiver bandwidth and m i s  the number of coherent 
averages. The signal-to-noise r a t i o ,  SNR = Ps/PNa then becomes 
SNR a Ppk m r o  Lc 
SNR a P m-r 2L (diffuse)  pk o c 
(d i sc re t e )  
Following the der ivat ion of s ignal  de t ec t ab i l i t y ,  D, used by BALSLEY (1978) 
and eliminating dependencies on the f ixed quan t i t i e s  given previously, it can be 
shown tha t  
D a P (PRF) -roLc PAv (d i sc re t e )  
D a P (PRF)-ro Le = PAv T~ (diffuse) .  
Pk 
Pk 
2 
Table 1 summarizes these r e s u l t s  fo r  4 cases with varying values of PRF, 
-rea and L, for  a constant average t ransmit ter  power (PAV = Ppk (PRF) L~T,,) P 
TRek'"reference" values of each quant i ty  are PRF 5: f a  Ppk =: P, To 
L, = 1. Each quant i ty  i s  mult ipl ied i n  turn by an integer  constant N, keeping 
the  average power constant i n  each case. The receiver bandwidth, B, i s  set t o  
l / r o  and the number of coherent averages n, i s  adjusted t o  maintain a constant 
e f f e c t i v e  sampling rate, PRF/nc. The r e su l t i ng  dependencies of the signal-to- 
noise r a t i o  and de tec t ab i l i t y  are shown i n  the last two columns. 
IC, and 
Table 1 can be simplified by wri t ing the f i r s t  3 independent var iables  i n  
terms of dimensionless quan t i t i e s  PRF/f, P kip, T ~ / T  and thus showing only the 
dependency on N. This has been done i n  Tagle 2. 
can see tha t  a l l  4 cases have the same signal-to-noise r a t i o  and the same 
de tec t ab i l i t y .  For the d i f fuse  case, because of the dependence on the resolu- 
t i o n  pulse width, the long uncoded pulse has a de t ec t ab i l i t y  which i s  a factor  
of N greater  than the other 3 cases. 
For the d i sc re t e  t a rge t s  we 
In those d i f fuse  cases where high resolut ion i s  obtained, w e  note t h a t  
using coded pulses gives the same s ignal  de t ec t ab i l i t y  as using short  uncoded 
pulses with e i the r  higher PRF o r  higher peak power. 
desirable ,  then, when high resolut ion i s  needed and when the peak power cannot 
be increased due t o  t ransmit ter  l imitat ions and the PRF cannot be increased, 
perhaps because of range a l i a s ing  problms. 
Pulse coding becomes 
Note t h a t ,  given a s e t  of Doppler power spectra obtained with any of the 
high resolut ion systems (cases 5, 6 or 8 i n  Table 2)  t he  de t ec t ab i l i t y  can be 
increased by N1l2, a t  the expense of range resolut ion,  by averaging the spectra 
across  N range gates. This e f f e c t  occurs because the spectral  noise power 
102 
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f luc tua t ions  are proportional t o  N-II2. 
processing, these high resolut ion systems can give range resolut ion improved by 
a factor  of I i n  region of good SNR and, i n  regions of low SNR, a detectabi-  
Thus by using two types of post- 
l i t y  degraded only by N k/2, compared t o  the long pulse case. 
REFERENCES 
Balsley, B. B. (19781, Design considerations for  coherent radar systems f o r  
' probing the troposphere, stratosphere,  and mesosphere, Preprint  Vol., 18th 
Conf. on Radar Meteorology, March 28-31, Atlanta,  GA, AMS, Boston, pp. 387- 
390. 
Gage, K. S. and B. B. Balsley (19781, Doppler radar  probing of the c l ea r  atmo- 
sphere, Bull. Am. Meteorol. SOC.. 59, 1074-1093. 


The effects of pulse rate, power, width and coding on signal detectability

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