Las servidumbres

3.6.1 Time:

A k e y e le m e n t in th e s y n c h ro n iz a tio n o f th e tw o sy ste m s is b a se d on a c c u r a te tim in g . In b i-s ta tic S A R , a c c u ra te tim in g c a n a ls o b e u s e d to m e a su re o f th e b a s e lin e d ista n c e b e tw e e n th e tra n s m itte r a n d re c e iv e r. T h e re n e e d s to b e sy n c h ro n iz e d c lo c k s o n b o th th e tr a n s m ittin g a n d re c e iv in g s a te llite . I f th e re a re e rro rs in th e c lo c k tim e s, th is w ill c a u s e e rro rs b o th in th e ra n g e re s o lu tio n , re s u ltin g in im a g e d e -fo c u sin g . In a m o n o -s ta tic S A R sy ste m , th e tim e s y n c h ro n iz a tio n is sim p le , as th e c o m p o n e n ts are lin k e d to a c o m m o n c lo c k s o u rc e . H o w e v e r, in b i-s ta tic S A R , tra n s m itte r a n d re c e iv e r s u b s y s te m s a re o n s e p a ra te p la tfo rm s , th e re fo re , th e c lo c k s m u s t b e k e p t s y n c h ro n iz e d , e ith e r o n e to th e o th e r, o r b o th to a n o u ts id e m a s te r c lo c k , f o r e x a m p le , o n e d e riv e d fro m th e G P S s a te llite n e tw o rk .

A s th e s a te llite s w ill b e u s in g a G P S r e c e iv e r in th e g u id a n c e a n d n a v ig a tio n s y ste m , it is lo g ic a l to s la v e b o th o n -b o a rd c lo c k s to th e tim e o n th e G P S re c e iv e r. T h is w ill re q u ire a c lo c k s ta b ility o n th e o rd e r o f a fr a c tio n , ty p ic a lly 14, o f th e tr a n s m itte d c o m p re s s e d p u ls e w id th [W IL L d -9 1 ]. In th is s y ste m , th e c lo c k s ta b ility d u rin g th e im a g in g tim e o f 4 s, w ith th e r e q u ir e d tim e a c c u ra c y o f 2 .5 n s, is 6 .2 5 x 10' 10 o r a b o u t 2 p a rts p e r 109 fo r 4 s. T h is s ta b ility is e a s ily a c h ie v a b le w ith c u rr e n t te c h n o lo g y o f q u a rtz c lo c k s [W IL L d -9 1 ].

A s th e r e la tiv e tim e in th e sy s te m , i.e. th e tim e o f th e tra n s m ittin g c lo c k a n d th e tim e o f th e re c e iv in g c lo c k , is im p o rta n t, a n d n o t a u n iv e rs a l tim e , th e G P S c lo c k b ia s e s w ill n o t in tro d u c e e rro rs in to th e s y ste m . H o w e v e r, th e d iffe re n c e in p ro p a g a tio n tim e b e tw e e n th e G P S s a te llite a n d th e tra n s m ittin g a n d re c e iv in g s a te llite s w ill c a u s e th e tw o c lo c k s to b e o ffs e t b y an erro r. T o re m o v e th is e rro r fro m th e tim in g , it is n e c e s s a ry to u s e a p u ls e d e la y ra n g in g b e tw e e n th e tw o s a te llite s .

T h e tr a n s m ittin g sa te llite , as th e m a s te r s a te llite , w ill b e a s s u m e d to h a v e th e c o rre c t tim e . A s th e tra n s m itte r tr a n s m its its p u ls e s , a - 2 0 dB s p litte r w ill b e u s e d to tra n s m it to th e

re c e iv e r a c o p y o f th e p u ls e . T h e tra n s m itte r w ill s ta rt tra n s m ittin g at tim e t0, w h ic h is k n o w n o n b o th th e sa te llite s. T h e re c e iv in g s a te llite w ill re c e iv e th is ra n g in g sa m p le at th e tim e t0+ttravei+£, w h e re ttravei is th e a c tu a l tim e fo r th e sig n a l to tra v e l th e b a se lin e a n d e is th e e rro r in th e re c e iv e r tim e c o m p a re d to th e tra n s m itte r. H o w e v e r, th e re c e iv e r w ill a ssu m e th a t th e p u ls e w a s tr a n s m itte d a t tim e tD, a n d w ill in te rp re t th e tra v e l tim e as ttravei + 8, a n d c o m p u te a b a s e lin e d is ta n c e fro m th is. It w ill c o m p a re th is d is ta n c e to th a t d e te rm in e d b y th e G P S re c e iv e r. T h e d iffe re n c e s in th is v a lu e w ill m a in ly b e th e re s u lt o f th e c lo c k erro r, w ith a s m a ll e r r o r d u e to th e in a c c u ra c y o f th e G P S m e a s u re m e n t, i.e. a fe w cm s. T h is p ro c e s s c a n b e c o n tin u e d th ro u g h th e im a g in g tim e so th a t an a c c u ra te v a lu e o f th e c h a n g e in th e b a s e lin e c a n b e d e te rm in e d , a n d th e c lo c k e rro r c a n b e h e ld to a m in im u m . F u rth e rm o re , th e c lo c k s c a n b e sy n c h ro n iz e d p rio r to th e s ta rt o f im a g in g , so th a t n o c o rre c tio n s fo r c lo c k e rr o r w ill n e e d to b e m a d e d u rin g sig n a l p r o c e s s in g b y th e g ro u n d sta tio n .

3.6.2 Phase:

S im ila r to m o n o -s ta tic sy s te m s , th e tra n s m itte r a n d re c e iv e r n e e d to m a in ta in a h ig h le v e l o f p h a s e sta b ility to e n s u re c o h e re n c e w ith in th e s y ste m . T h is tra n s la te s to sta b ility o f th e lo c a l o sc illa to r. H o w e v e r, th is s ta b ility w ill n e e d to b e o v e r th e c o h e re n t in te g ra tio n tim e o f th e sy ste m , a p p ro x im a te ly 0 .2 3 s, as th e re w ill b e p o s s ib ility f o r re -s y n c h ro n iz in g th e sy ste m d u rin g e a c h in te g ra tio n tim e . A lso , d u e to th e d is trib u te d n a tu re o f th e sy ste m , th e to ta l s ta b ility is th e s u m o f th e in d iv id u a l sta b ility o f th e tra n s m ittin g lo c a l o s c illa to r a n d th e re c e iv in g lo c a l o s c illa to r. G iv e n th e p o s s ib ility o f a 5° p h a s e e rro r f o r th e e n tire sy ste m , th e to ta l s ta b ility fo r th e o s c illa to rs is 2 .3 x lO “ n . T h is tra n s la te s to an e rro r o f 1.15 x lO -H fo r e a c h o s c illa to r o v e r th e 0 .2 3 s in te g ra tio n tim e. T h is s ta b ility is p o s s ib le w ith th e q u a rtz c lo c k [W IL L d -9 1 ].

3.6.3 Signal:

P e rh a p s th e m o s t c h a lle n g in g a s p e c t o f s y n c h ro n iz a tio n o f th e tra n s m itte r a n d th e re c e iv e r is th e s y n c h ro n iz in g o f th e sig n a l. A s sta te d p re v io u s ly , th e o n -b o a rd re c e iv e r w ill be

re s p o n s ib le o n ly fo r d o w n - c o n v e rtin g th e s ig n a l, d iv id in g in to I a n d Q c h a n n e ls, d ig itiz in g a n d s to rin g th e d a ta . H o w e v e r, to a c c o m p lis h th is, th e re c e iv e m u s t h a v e an a c c u ra te c o p y o f th e tr a n s m itte d p u ls e . T h is c a n b e d o n e d ire c tly fro m re c e iv in g th e tra n s m itte d p u ls e an d c o rre c tin g f o r D o p p le r s h iftin g a n d p ro p a g a tio n e rro rs to u se it as th e m ix in g s ig n a l. H o w e v e r, th is a p p ro a c h w ill a lw a y s ad d e rro rs to th e sy ste m , th e re b y , re d u c in g th e q u a lity o f th e s y s te m ra w d a ta . T h e u s e o f D ire c t D ig ita l S y n th e sis, D D S , so lv e s th is p ro b le m .

T h e c o n c e p t b e h in d D D S is to s to re in m e m o ry , a d ig ita l c o p y o f th e w a v e fo rm , o r s u b s e q u e n tly to sto re lo o k -u p ta b le s f o r th e p h a s e , fre q u e n c y an d a m p litu d e v a lu e s, a n d th e s to re th o s e a d d re s s e s [G A L L -88]. In e ffe c t, it re p la c e s th e a n a lo g e x c ite r, re s p o n s ib le f o r p ro d u c in g th e lin e a r F M c h iip w a v e fo rm , w ith a d ig ita lly s to re d v e rsio n . T h e D D S s y s te m w o u ld re q u ire h ig h - s p e e d ra n d o m a c c e s s m e m o ry to s to re th e d ig ita l w a v e fo rm a n d a h ig h -s p e e d d ig ita l to a n a lo g c o n v e rte r (D A C ) [G A L L -88]. T h e D A C o f th e sy ste m w o u ld o u tp u t th e a n a lo g b a s e -b a n d v e rs io n o f th e d e s ire d w a v e fo rm , w h ic h w o u ld th e n b y u p -c o n v e rte d to S -b a n d f o r u s e . T e s tin g re s u lts fro m su c h s y ste m s, sh o w th a t it is p o s s ib le to g e t n e a r th e o re tic a l w a v e fo rm g e n e ra tio n , in c lu d in g a R M S p h a s e e rro r o f 1.4°

[G A L L -88],

U s in g a D D S sy ste m w o u ld p ro v id e , a n e a r th e o re tic a l w a v e fo rm g e n e ra te d fro m th e tra n s m itte r, a n d , w ith a n id e n tic a l s y s te m p la c e d o n th e re c e iv e r, w o u ld p ro v id e a n e ar- e x a c t r e p lic a o f th e tr a n s m itte d p u ls e to d o w n -c o n v e rt th e sig n a l. T h is sy ste m w o u ld lim it th e a m o u n t o f e rro rs in tr o d u c e d in to th e s y s te m by th e d is trib u tio n o f th e tra n s m itte r an d re c e iv e r. T h e D D S s ig n a l c a n a lso b e s to re d in th e g ro u n d s ta tio n fo r p ro c e s s in g , u p d a te d w ith e rro r re a d in g s f ro m th e tr a n s m ittin g s a te llite .