The operation of an active retrodirective array (ARA) in an ionospheric environment (that is either stationary or slowly-varying) was examined. The restrictions imposed on the pilot signal structure as a result of such operation were analyzed. A 3 tone pilot beam system was defined which first estimates the total electron content along paths of interest and then utilizes this information to aid the phase conjugator so that correct beam pointing can be achieved

Nandi, A. K.

Tomita, C. Y.

English

NASA Technical Reports Server

IONOSPHERIC EFFECTS IN ACTIVE RETRODIRECTIVE iZRR;\Y 
AKD PITTIGATISG SYSTEM DESIGN 
A. K. Nandi and C.  Y. Tomita 
Rockwell I n t e r n a t i o n a l  
Abstract  
The ope ra t i on  of  an a c t i v e  r e t r o d i r e c t i v e  a r r a y  ( A M )  i n  an ionospheric  
environment ( t h a t  i s  e i t h e r  s t a t i o n a r y  o r  slowly-varying) i s  examined. The 
r e s t r i c t i o n s  imposed on t h e  p i l o t - s i g n a l  s t r u c t u r e  a s  a  r e s u l t  of such opera- 
t i o n  a r e  analyzed. A 3-tone p i l o t  beam system is  def ined  which f i rs t  es t imates  
t h e  t o t a l  e l e c t r o n  conten t  along pa ths  of i n t e r e s t  and then  u t i l i z e s  t h i s  
information t o  a i d  t he  phase conjugator  so  t h a t  c o r r e c t  bean1 po in t i ng  can be 
achieved.  
I .  INTRODUCTION 
In  o rde r  t o  make t h e  s o l a r  power s a t e l l i t e  system perform c o r r e c t l y ,  it 
i s  necessary t o  po in t  t h e  h igh  power downlink beam towards a  s p e c i f i c  po in t  
on ground. The downlink beam i s  narrow and poin t ing  accuracy requirements 
a r e  s t r i n g e n t .  One way of achieving t h i s  o b j e c t i v e  i s  t o  use t h e  r e t r o d i r e c t i v e  
a r r ay  such t h a t  t h e  down-going power beam po in t s  i n  t h e  same d i r e c t i o n  from 
which a  ground-originated p i l o t  s i g n a l  came. I n  t h i s  approach, t h e  downlink 
wavefront i s  obtained by conjugat ing t h e  phases of  va r ious  segments o f  t h e  
upl ink ( p i l o t )  wavefront.  For ope ra t i ona l  reasons ,  t h e  upl ink and downlink 
f requenc ies  cannot be i d e n t i c a l .  Both t h e  up l ink  and downlink wavefronts a r e  
r equ i r ed  t o  t r a v e l  through the  ionosphere. The ob j ec t  o f  t h i s  no t e  is t o  
examine system opera t ion  c o n s t r a i n t s  imposed by t h e  ionosphere and f i n d  
pos s ib l e  remedies. The d iscuss ion  t h a t  fol lows i s  based on t h e  assumptior1 
t h a t  t h e  ionosphere i s  s t a t i o n a r y  o r  slowly-varying. Also, hea t ing  e f f e c t s  
on t h e  medium due t o  t h e  downlink power beam a r e  no t  t aken  i n t o  account,  
11. IONOSPHERIC EFFECTS ON SINGLE-TONE PILOT BEAM 
I t  is well-known t h a t  an important  f e a t u r e  of  t h e  r e t r o d i r e c t i v e  a r r ay  
is t h a t  t h e  down-coming beam is phase coherent  when it a r r i v c s  a t  t h e  s0u rce . l  
This s ta tement  i s  r i go rous ly  co r r ec t  on ly  i f  t h e  propagat ion medium isnon-dispersive 
s p a t i a l l y  homogeneous and temporally s t a b l e .  I n  case  o f  t h e  ionosphere, one o r  
more o f  t h e  above condi t ions  a r e  v i o l a t e d .  Under c e r t a i n  condi t ions ,  beam 
poin t ing  e r r o r  can occur  and phase coherence a t  t h e  source  can be l o s t .  
Consider t h e  s i t u a t i o n  shown i n  Figure 1. Assume t h e  upl ink and downlink 
f requenc ies  a r e  given by f, and f ~ ,  r e spec t i ve ly  ( fU # f~). The (path-dependent) 
phase s h i f t  a t  f U  on one p a r t i c u l a r  r a d i o  l i n k  can be w r i t t e n  a s2  
where 
e2 b = -  e  = e l e c t r o n  charge, m = e l e c t r o n  mass, 2 c0 m' 
c0 = f ree-space  p e r m i t t i v i t y  
= 1.6 x lo3  mks 
https://ntrs.nasa.gov/search.jsp?R=19810008032 2020-03-21T15:12:07+00:00Z
Conjugating Network 
Rectenna f o r  
wnlink Power Beam 
p i lo t -  Beam 
Source 
Figure 1. 
L 
L i s  the  physical  pa th  length involved a n d L  N dE i s  the  in t eg ra t ed  e l ec t ron  
dens i ty  along t h e  pa th  under considerat ion (=1017 - 1019). Note t h e  second 
quan t i t y  on t h e  r i g h t  hand s i d e  of  Equation (1) accounts f o r  ionospheric e f f e c t s  
on a CW tone.  On using appropr ia te  cons tants ,  one can w r i t e  
Since one is  i n t e r e s t e d  i n  knowing t h e  phase s h i f t  a t  f D ,  a reasonable 
es t imate  o f  t h e  phase can be obtained by mult iplying Q(fu) by fD/ fu  ( t h i s  
es t imate  becomes increas ingly  accura te  a s  f U  -+ fg ) .  Thus, 
On conjugating t h i s  phase, one ob ta ins  
The downlink signal at the transmitting end can be written as 
The downlink signal at the receiving end is given by 
R Sdo,m(t) = COS [uDt - D K~ (Ku - -11 
D 
For a temporally stable ionosphere and ignoring second-order effects, one 
can set Ku = KD in Equation (6) and obtain 
If, in addition, the propagation medium is assumed non-dispersive, then 
the second term on the right hand side of Equation (7) involving Ku could 
be equated to zero. In the present situation, this kind of assumption is 
highly unrealistic. Note in Equation (7), Ku applies to a particular 'adio 
path and will, in general, be different on different paths because of 
ionospheric inhomogeneity. A consequence of this fact is that the phase 
coherence (at source) property of the downlink signal mentioned earlier 
does no longer hold good. Furthermore, if a coherent phase perturbation 
occurs due to some ionospheric large-scale features (such as a wedge), 
then even a beam pointing error is possible. The magnitude of these 
effects need to be evaluated for worst-case ionospheric conditions. The 
two tone pilot beam system which aims at alleviating some of the ionospheric 
problems mentioned above is discussed next. 
111. TWO-TONE PILOT BEAM SYSTEM 
If two tones (symmetrically situated around the downlink frequency) 
are used on the uplink transmission, then under appropriate conditions an 
average of the phases of the uplink tones can be taken to be a good estimate 
of the phase at the downlink frequency. The idea here is that the phase 
errors caused by a stationary ionosphere can be largely eliminated by this 
approach. Let fl and f2 be the two tones consituting the pilot beam and 
symmetrically located around the downlink frequency f ~ .  The choice of the 
offset Af is based on conflicting requirements and is not discussed here. 
Using the notation as before, for a given link one can write 
and 
Then 
Note is  a des i rable  quanti ty as  f a r  as c o r r e c t .  r e t rod i rec t ive  array 
operation is  concerned. Normally, a l l  one needs t o  do is  t o  conjugate 
t h i s  quanti ty and use it as  the  phase of the  downlink s ignal  leaving the 
space antenna. However, the  ari thmetic averaging indicated i n  Equation (10) 
can give wrong answers f o r  (often ca l l ed  II ambiguities). This can happen 
i f  
( i )  $( f2)  - $(f l )  = K (2II) + A ;  1 A !  < 211 and K is odd in teger  
( i i )  asynchronous dividers  a r e  used. 
I t  i s  c l e a r  tha t  i n  s p i t e  of  i ts  inherent a t t r ac t iveness ,  the  2-tone p i l o t  
beam system cannot be used because of the  Il ambiguities t h a t  can occur 
during phase averaging. 
I V .  THREE-TONE PILOT BEiU1 SYSTEM 
Before proceeding with the  main task of  solving the  phase conjugation problem 
i n  an ionospheric environment, it is worthwhile t o  f ind out whether $1 and 42 
could indeed d i f f e r  by in tegra l  mult iples of 2X when typical  SPS parameters 
a r e  used. For the  present problem, it is su f f i c i en t  t o  show tha t  ionospheric 
e f f e c t s  alone can give r i s e  t o  phase differences which a re  mult iples of 2Il. 
A measure of  t h i s  e f fec t  i s  obtained by multiplying $11 (Equation (8))  by f 2 / f l  
and subtracting $2 (Equation 9 ) ) .  Thus 
Let 
fD = 2,45 x lo9 
then, the  number of 2II phase changes obtained f o r  d i f fe ren t  values of IN dR 
and Af is shown i n  Table 1. 
Tahle 1. Nw.ber of  Ambicuities (n) V s .  Af 
I t  is c l e a r  from Table i t h a t  i n  order  t o  avoid ionospheric  ambiguity f o r  
t he  s t ronges t  concent ra t ion  under cons idera t ion ,  Af should not exceed 1 bMz. 
Other opera t iona l  c o n s t r a i n t s  render  such a choice unacceptable. 
In what fol lows,  a 3-tone approach due t o  Burns and Fremouw i s  used t o  reso lve  
t h e  ambiguity problem. I t  i s  based on a d i r e c t  measurement of  J N  dR along 
t h e  pa ths  of  i n t e r e s t  and then us ing  t h i s  information t o  es t imate  t h e  pa th  
r e l a t e d  phase s h i f t  a t  t h e  downlink frequency fD.  
Consider a frequency-amplitude p a t t e r n  a s  shown i n  Figure 2 where t h e  t h r e e  
upl ink tones f l ,  f 2  and f 3  a r e  coherent a t  ground. Indeed, t h e  t h r e e  tones  
can be  generated by a low-deviation phase-modulated t r a n s m i t t e r .  Thus, using 
equatiorls s i m i l a r  t o  Equation (8) f o r  t h r e e  frequencies  f l ,  f 2  and f 3 ,  one 
can w r i t e  
and 
The second d i f f e r ence  o f  phase s h i f t  is given by 
Figure 2. 
For s u i t a b l y  chosen Af, one ob t a in s  
Suppose one needs t o  avoid a 360° ambiguity i n  624 f o r  va lues  of /N dl. 
l e s s  than  1019. From Equation (16) ,  one e a s i l y  f i n d s  
2I1 
~f2.-6~( x fI3/(- x 40.5 x 2 x J N  dl.) 
C 
Let 
PI = 2.45 + 0.153125 ( t h i s  choice  w i l l  bc j u s t i f i e d  l a t e r )  
= 2,603125 GHz 
Then 
3 
&f2 - (2n) x (2.6 x lo9)  x C/(2ll x 81 x 1019) 
= 0.651 x 1016 
or 
A f  = 80.6 MHz 
Thus, wi th  A f  s 80.6 MHz and assuming t h a t  624 can be measured, then f N dll 
can be ca l cu l a t ed  r a t h e r  e a s i l y  from Equation (16).  An implementation t h a t  
measures 624 with r e l a t i v e  ease  i s  shown i n  Figure 3 .  
b % 
Figure 3. Measurement of  62@ 
Reordering Equation (16), one e a s i l y  obta ins  
= computed value of I N  d l  
c 3 
For f = 2.603 GHz and Af = 80.0 EMz, one can compute 1 
* 
Based on S/N r a t i o  cons idera t ions ,  t h e  accuracy of  t h e  N computation i n  
Equation (20) i s  determined by t h e  accuracy of 62+ measurement and i s  
given by 
Once an es t imate  of f N  dL f o r  a  given l i n k  i s  found, one needs t o  
perform seve ra l  s t eps  o f  s igna l  processing s t a r t i n g  with the  phase 
a t  f j  and f in i sh ing  with t h e  conjugated phase a t  f ~ .  These s t eps  
a r e  shown i n  Figure 4 .  
I t  is  f a i r  t o  poin t  out  t h a t  t h e  conjugator  used i s  a modified 
version of the  one i n  Reference 1. With t h e  add i t i ona l  boxes, t he  
new conjugator c l e a r l y  takes  i n t o  account s teady-s ta te  ionospheric  
e f f e c t s .  
For t h e  present  configurat ion,  t h e  uplink and downlink frequencies a r e  
r e l a t e d  by t h e  equation* 
For f D  = 2.45 GHz and n = 32, one obta ins  
f l  = 2.603125 GHz (see Equation (18)).  
I t  i s  i n t e r e s t i n g  t o  examine t h e  output $* (fD) of t he  conjugator i n  Figure 4 .  
On t ak ing  d i f f e r e n t i a l s ,  one obta ins  
One us ing  f D  = 2.45 GHz and f l  = 2.603 GHz, t he  above equation s impl i f i e s  t o  
*Note t h e  mode of  operat ion indica ted  here  i s  d i f f e r e n t  from t h a t  i n  Ref, 1. 
7.65 

so  t h a t  
Suppose one r equ i r e s  an rqs  accuracy o f  lo0  (= -174 rad)  on +*( fD) ,  Then 
t h e  required accuracy on M i s  given by 
On going back t o  Equation (22), one f i n d s  
Squaring t h e  quant i ty  on the  r i g h t  hand s i d e  o f  Equation (28) and on using 
some r e s u l t s  i n  Reference 3, one obta ins  a value f o r  (PR/(r2) .** Thus, 
pR/(r2 = (S/N) r a t i o  a t  t h e  r ece ive r  sketched i n  Figure 3 
A s  f a r  a s  FigureA4 i s  concerned, s eve ra l  comments a r e  i n  order .  F i r s t l y ,  t h e  
use o f  t h e  same N f o r  both uplink and downlink phase compensations need j u s t i -  
f i c a t i o n .  Secondly, t h e  conjugator s u f f e r s  from d iv ide r  ambiguity problems. 
This makes it necessary t o  phase conjugate a t  IF and then su i t ab ly  mult iply 
t h e  conjugator output frequency t o  2.45 GHz. Preliminary design of  a 3-tone 
conjugator  operat ing a t  IF has been completed and w i l l  be reported elsewhere. 
V. CONCLUSION 
An attempt has been made above t o  incorporate t h e  r o l e  of  t h e  ionosphere i n  
ARA system design. A conjugator has been sketched t h a t  compensates f o r  steady- 
s t a t e  ionospheric  e f f e c t s .  Work i s  cu r ren t ly  i n  progress t o  eva lua te  t h e  
magnitudes of  ionospheric  wedge e f f e c t s .  Based on ( l imi ted)  ava i l ab le  data2 
and because of  geometry considerat ions ( the  proximity of  t h e  ionosphere t o  
t h e  rec tenna) ,  it appears unl ike ly  t h a t  any compensation towards ionospheric  
e f f e c t s  would be necessary. However, i n  order  t o  make a d e f i n i t e  conclusion, 
more d a t a  on wedge s t r u c t u r e  a r e  des i r ab le .  In  addi t ion ,  t h i s  problem needs 
examination i n  t h e  l i g h t  of  ionospheric  hea t ing  e f f e c t s  due t o  t h e  downlink 
power beam. 
**PR is t h e  t o t a l  3-tone s igna l  power received and o2 is  t h e  noise  power 
out of any one of  t h e  tone f i l t e r s  t h a t  have i d e n t i c a l  bandwidths. 
1 6 7  
REFERENCES 
1. Chernoff,  R. C . ,  "Large Active Re t rod i r ec t i ve  Array f o r  Space Application," 
IEEE Trans. on Antennas and Propagation, pp 489-496, J u l y  1979. 
2. Lawrence, R.  S., L i t t l e ,  C. G . ,  and Chivers,  H. J . ,  "A Survey of 
Ionospheric  E f f ec t s  Upon Earth-Space Radio Propagation," Proc. IEEE, 
pp 4-27, January 1964. 
3.  Bulns, A. A. and Fremouw, E. J . ,  "A Real-Time Correct ion Technique f o r  
Transionospheric  Ranging Error," IEEE Trans. on Antennas and Propagation, 
pp 785-790, November 1970. 


Ionospheric effects in active retrodirective array and mitigating system design

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