Ground reflections which are similar for all (Yagi) elements of a phased array and change the radiation pattern of the single elements are discussed. This consequently yields a change of the radiation pattern of the entire array. It is assumed that the radiation pattern of a Yagi antenna can be treated in a good approximation for the present purpose, similar to the pattern of a single dipole, if one confines to radiation angles which are roughly perpendicular to the main beam of the Yagi antenna

Rottger, J.

English

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5.1B MIST DESIRABLE TERRAIN, e.g., FLAT VS VALLEY LOCATION 
J. Rottger 
EISGAT S c i e n t i f i c  Association 
981 27 Kiruna, Sweden 
TEE INFLUENCE OF GROUND REFLECTIONS ON TEE ANTENNA DIAGRAM AT LOW ELEVATION 
ANGLES AND THEIR EFFECT ON RADAR GROUND CLUTTER AND INTERFERENCE 
For obtaining an es t imate  it i s  assumed t h a t  ground r e f l e c t i o n s  a r e  s i m i -  
l a r  for  a l l  (Yagi) elements of a  phased array and they jus t  change the radia- 
t i o n  pa t t e rn  of the s ing le  elements. This. consequently y ie lds  a  change of the 
r ad ia t ion  pa t t e rn  of the e n t i r e  array.  I t  i s  furthermore assumed and deemed t o  
be j u s t i f i e d  t h a t  the r ad ia t ion  pa t t e rn  of a  Yagi antenna can be t r ea ted  i n  a  
good approximation f o r  the present purpose, s imi la r  t o  the  pa t t e rn  of a  s ing le  
dipole,  i f  one confines t o  r ad ia t ion  angles which a re  roughly perpendicular t o  
the  main bean of the Yagi antenna (e.g. a t  low elevat ion angles f o r  v e r t i c a l l y  
pointing Yagis). 
Assume the geometry given i n  Figure 1. Antenna A i s  located a t  a  height 
z  above the ground. The d i r e c t  path length between the antenna and the  
c f u t t e r  t a rge t  C i s  rl,  and the  path length of the wave, r e f l ec ted  a t  R on 
the  ground surface,  i s  r2. The hor izonta l ly  s t r a t i f i e d  ground surface has 
the  complex r e f l e c t i o n  coef f i c i en t  p .  The height of the  c l u t t e r  t a r g e t  above 
the ground surface i s  zC, and the ground dis tance between antenna A and c lut -  
t e r  t a rge t  C i s  d. 
Let E be f i e l d  s t rength  a t  C f o r  f r e e  space propagation, and ER the 
reeu l t ing  f i e l d  with ground re f l ec t ion ,  then 
2n r 2n r 
E~ 1 
- = exp ( - i  ---r) + poerp (-i  -) X ' (1) 
Eo 
where X i s  the wavelength of the radar  s ignal .  
Let us assume some l imi t ing  values,  which appear reasonable (X = 6 m): 
then a l  = a = a < 1.5'. Ground r e f l e c t i o n  a t  R i s  wi thin  1OOA of antenna 
i f  a > 0.507 e.g. ground i s  assumed f l a t  ( inc l ina t ion  to  the hor izonta l  smaller 
than A )  out  t o  several  hundred meters from the antenna. 
The r e f l e c t i o n  coef f i c i en t  fo r  hor izonta l  polar iza t ion (propagation di- 
r e c t i o n  perpendicular t o  a x i s  of d ipole)  i s  
s i n  a  -Je, - COS-a 
Ph = 
s i n  a  +JT 
and f o r  ' 'vert ical ' '  polar iza t ion (propagation d i rec t ion  i n  d i rec t ion  of d ipole  
a x i s  ) 
* 2 
e * s i n  4 -JET - cos 4 
r 
p-- = 
c r * s i n  + 9-
'presently a t  Arecibo Observatcry, Arecibo, Puerto Rico, on leave from 
lax-Planck-Institut f u r  Aeronomie, Lindau, W. Germany. 
https://ntrs.nasa.gov/search.jsp?R=19850024200 2020-03-20T18:07:46+00:00Z
Figure 1. Geometry t o  ca lcu la te  in te r fe rence  f i e l d  a t  C of d i r e c t  
wave and ind i rec t  wave, r e f l e c t e d  on the ground surface a t  R. 
* 
where cr is the complex pe rmi t t iv i ty  given by 
with E~ = d i e l e c t r i c  constant ( r e l a t i v e ) ,  o = ground conductivity. 
For a < l.SO, these reduce t o  
P" * -1. 
(The devia t ion from -1 i s  f a i r l y  neg l ig ib le  f o r  low elevat ion angles and 
reasonable ground pe rmi t t iv i ty  and conductivity.  Using Q = -1 i n  equation (1) '  
fo r  rl + r2 elucidates  the c l u t t e r  reduction1 ) 
For zA < zC << d, we obta in  f o r  the two-way ( radar)  case 
-- E~ 2n zA0zC 
- = 4 s i n  . 
Eo 
- Since- zC i s  mostly much l a r g e r  than zA, the  a l t i t u d e  extension of the 
c l u t t e r  t a r g e t  e s sen t i a l ly  detennines the c l u t t e r  echo strength.  Inse r t ing  the 
l imi t ing  values  z < A, zC < 5X, d > 250X, equation (2)  y ie lds  
- A 
P, 
3 (, 0.07 (g -24 dB). E 
0 
To i l l u s t r a t e :  The ground r e f l e c t i o n  reduces the c l u t t e r  echo s t rength  by 
a t  l e a s t  24 dB f o r  t h i s  f a i r l y  exposed condition of a highly elevated t a r g e t  
, 
(e.g., top o t  an antenna tower a t  30 m height a t  1500 m d is tance) .  A tower 
with 10 m height would y ie ld  a c l u t t e r  s t rength  reduced by another 20 dB. 
It i s  evident t h a t  most of the c l u t t e r  contribution comes form the top 
par t  of s ~ s h  targets .  This i s  because of the quadrat ic  a l t i t u d e  weighting ( for  
= .=c << 3% ) given by (2),  and because the l a rge r  the e levat ion a, the more t i e  groun r e f l e c t i o n  coef f i c i en t s  deviate from -1. Of course the actual  c lu t -  
t e r  echo s t r en th  depends a l s o  on the t o t a l  r e f l e c t i o n  coef f i c i en t  of the c l u t t e r  
t a rge t s  (has t o  be in tegrated) ,  which, however, may not change so strongly a s  
the height dependence given by (2). C lu t t e r  r e tu rns  from local ized (point or 
l i n e )  t a r g e t s ,  e.g. TV towers or bgildings,  w i l l  be weaker than d i s t r ibu ted  
(area)  t a rge t s  because of t h e i r  r dependence. From equation (2)  it i s  de- 
duced t h a t  c l u t t e r  r e tu rns  may g e t  f a i r l y  strong i f  zC i s  large.  This would 
be, f o r  instance,  the case f o r  mountains extending up t o  several  hundred meters2 
o r  even higher  a l t i t u d e s .  Addi t ional ly ,  f o r  such extended t a r g e t s  only an r 
dependence appl ies  and the t a r g e t  r e f l e c t i o n  coeff ic ient  can be orders  of magni- 
tude larger  than f o r  s ing le  towers or buildings.  
One has t o  keep i n  mind t h a t  P v  devia tes  substant ia l ly  from -1 for  a l -  
ready very small e levat ion angles,  which i s  not the case f o r  Ph. It follows 
t h a t  i n  d i r e c t i o n  of the d ipo le  a x i s  the cancel la t ion of d i r e c t  and ground re- 
f l e c t e d  wave i s  no more e f f i c i e n t ,  except of f o r  very grazing e l w a t i o n  angles. 
Similar t o  c l u t t e r  probleus with elevated t a rge t s ,  the  reverse can happen 
a l so ,  namely probleas with an elevated antenna. Equation (2)  shows t h a t  t h i s  
problem can be t r ea ted  i n  an exactly equal way. It shows t h a t  obviously very 
c r i t i c a l  c l u t t e r  can occur even from f a i r l y  low targets .  Pa r t  of these c l u t t e r  
problens can be explained by the f a c t  t h a t  the d i rec t  r ad ia t ion  i s  f a i r l y  inef-  
f i c i e n t l y  cancelled by the ground-reflected rad ia t ion  because of the not grazing 
incidence angle t o  the e a r t h ' s  surface. 
Equation (21, of course, a l s o  y ie lds  an es t imate  f o r  in terference pick-up 
i f  one assumes a t ransmit ter  (TV, broadcast ,  etc.) with antenna height zC. 
Again, the  ground-reflected s igna l  a t  low e l w a t i o n  angles almost el iminates,  
o r  a t  l e a s t  strongly reduces, d i r ec t  s ignals .  Equation (2)  a l s o  indicates  t h a t  
the  ground c l u t t e r  suppression improves by lowering the  rada r  antenna; the  
s ing le  feed elements of the antenna (or t h e i r  phase centrum), however, must not 
be a quar ter  wavelength above the ground t o  obta in  the r a d i a t i o n  suppression a t  
- low angles. 
SUMMARY 
It i s  shown t h a t  ground r e f l e c t i o n  very  e f fec t ive ly  cancels the r ad ia i ion  
a t  grazing angles (a So)  because the reflected'wave su f fe r s  a phase reve r sa l  
during re f l ec t ion .  This even can suppress low  sidelobes 'of the a r ray  pa t t e rn  
vhich may be regarded a s  c r u c i a l  without taking i n t o  account ground re f l ec t ions .  
The loca t ion  of an a r ray  antenna a t  a f l a t  ground (extending out t o  several  100 
m) may be s u f f i c i e n t ,  but a shallow va l l ey  should generally be preferred t o  
e l iminate  the low angle r ad ia t ion  e f fec t s .  Bowever, high extending t a rge t s ,  
such a s  r ad io  towers o r  mountains i n  the close v i c i n i t y ,  w i l l  s t i l l  cause con- 
s ide rab le  c l u t t e r  echoes, w e n  when optimizing the  antenna array fo r  low angle 
r a d i a t i o n  suppres sion. 


Most desirable terrain, e.g., flat vs valley location, part 5.1B

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