Data Compression:

Due to the high data rate and consequently the large amount of data, which is collected for each image, the need for data compression is imperative to meet both storage and downlink requirements. The requirements for a compression algorithm for a SAR system are [PARK-99]:

-Good data output quality -Compression with 2,3 or 4 bits -High data rate compression -Low power consumption -Low mass

In SAR systems, due to the random nature of the returned echoes and the non-correlation between subsequent data points, lossless compression algorithms can gain, at most, a 1.4:1 compression'ratio. This is not high enough to reduce the data to adequate levels. Therefore, lossy compression algorithms are used, limiting the compression ratio to maintain good picture quality. The most popular compression algorithm is the Block Adaptive Quantizer, BAQ, and will be used for this system. This is a simple algorithm without complex hardware and is well documented [BENZ-95]. The BAQ also offers a compression ratio of nearly 4:1, and limits the errors caused by losses due to the compression. The BAVQ, block adaptive vector quantizer, begins with the same BAQ algorithm, but places the output of this into vector format and matches this to a codebook and outputs the standard deviation from the BAQ and the codebook address for the vector [BENZ-95]. Other compression algorithms have been examined and used, but become more complex in hardware and therefore negate their benefit for this system.

Kwok et al. first presented the BAQ for the Magellan mission [KWOK-89]. It is an algorithm to estimate the statistics of the source data and attempts to match the quantizer to the observed statistics. Figure 3.10 offers a block diagram of the algorithm.

Figure 3.10 BAQ Block Diagram [KWOK-89]

As was found by Kwok et al., the optimum number of range samples per block is easiest and most accurate when limited to the size of one to two range resolution cells, however, as the block must exhibit Gaussian characteristics, the typical size is between 50 to 100 samples. Given this constraint, the simulation result show that a thermal S/N of 8dB was optimal as an increase in S/N did not improve image quality, and a lower S/N degraded it [KWOK-89].

The algorithm is based on the properties of the echo signal. The return from a radar signal is understood to be the super-position of the responses of several small scatterers, i.e. the convolution of the signal with the complex ground reflectivity. The amplitude and phases are statistically independent of each other and of other scatterers within the scene, which leads to the assumption that each range sample is uncorrelated with the previous and preceding sample. The phases can be considered uniformly distributed between —n and n radians [PARK-99]. Given these characteristics of the signal, it can be

considered that the real and imaginary parts of the complex radar return signal have a zero-mean Gaussian distribution, unknown average power and uncorrelated real and imaginary parts. This is the basis for the BAQ [PARK-99].

T h e re tu rn s ig n a l fo r th e sy ste m is m o d e le d as:

A ( x , y , z ) = ^ a ke J<!,k [3.10]

i

w h e re N s is th e n u m b e r o f s a m p le s p e r b lo c k , ak is th e re fle c ta n c e a m p litu d e a n d (jfc is th e p h a s e d e la y . T h is sig n a l fo llo w s th e c h a ra c te ris tic s s ta te d in th e p r e v io u s d isc u ssio n

[K W O K -8 9 ].

T h e f irs t s te p in th e a lg o rith m is to s e p a ra te th e la rg e d a ta b lo c k in to s m a lle r b lo c k s, w h e re th e s ig n a l’s s ta n d a rd d e v ia tio n is e x p e c te d to b e ro u g h ly c o n s ta n t a n d th e G a u s s ia n s ta tis tic s w ith in th e b lo c k a re e v id e n t [B E N Z -9 5 ],

N e x t, th e c o n tro l s ta tis tic s fo r th e b lo c k a re e s tim a te d . T h e s ig n a ls o f th e I a n d Q c h a n n e ls a re u s e d to f in d th e a v e ra g e s ig n a l m a g n itu d e , th e s ta tis tic c h o s e n to c h a r a c te riz e th e sig n a l [K W O K -8 9 ]. T h e a v e ra g e s ig n a l m a g n itu d e c a n b e fo u n d by:

w h e re p (x ) is th e G a u s s ia n d is trib u tio n fu n c tio n , x n is th e s ig n a l m a g n itu d e o f th e n s a m p le , a n d a is th e s ta n d a rd d e v ia tio n o f th e in p u t [K W O K -8 9 ]. T h e th re s h o ld se ttin g , th e c o n tro l s ta tis tic , is d e te rm in e d b y c a lc u la tin g th e a v e ra g e sig n a l o f th e d a ta b lo c k fo r N s a m p le s a n d E q u a tio n 3 .1 1 is u s e d to d e te rm in e a . T h is v a lu e is f o u n d in a 4 K R O M % lo o k -u p ta b le , w h o s e 8-b it w o rd o u tp u t is th e h e a d e r fo r th a t s e rie s o f d a ta c o m p re s s io n a n d c o n ta in s th e c o n tro l p a ra m e te r fo r th e b lo c k . T h e n e x t s te p is th e q u a n tiz e r, w h e re e a c h 8-b it d a ta s a m p le is e n c o d e d in to 2 b its u s in g th e c o n tro l p a ra m e te r fo u n d in th e p re v io u s s te p (se e F ig u re 3 .1 0 f o r th e b lo c k d ia g ra m ). T h e d a ta s a m p le is c o n v e rte d in to a 2 -b it s a m p le b a s e d u p o n th e G a u s s ia n d is trib u tio n a n d th e th re s h o ld v a lu e . T h e s a m p le is p la c e d w ith in th e lim its o f th e fu n c tio n . T h e first b it o f th e o u tp u t is th e sig n b it, a 0 fo r a n e g a tiv e a n d a 1 fo r a p o s itiv e , p la c in g th e sig n al o n e ith e r s id e o f th e s ta tis tic fu n c tio n . T h e se c o n d b it p la c e s th e s a m p le a t th e c e n tre o f a

tra n s itio n s e g m e n t to a llo w fo r m in im u m d is to rtio n w ith in th e re c o n s tru c te d d a ta [B E N Z - 9 5 ]. It is p o s s ib le to c o m p re s s th e e a c h d a ta p o in t to 1 b it, b u t to d o th is re q u ire s a s a m p lin g r a te o f tw ic e th a t to q u a n tiz e to 2 b its , a n d th e re fo re a d d s no re d u c tio n in im a g e siz e , b u t in c re a s e s th e c o m p le x ity o f th e h a rd w a re .

W ith th e fin a l o u tp u t to th e c o m p re s s io n a lg o rith m b e in g th e 8-b it c o n tro l s ta tis tic , p la c e d as th e h e a d e r to th e d a ta stre a m , a n d th e c o m p re s s e d 2-b it d a ta s a m p le s , a c o m p re s s io n ra tio o f n e a rly 4 is p o s s ib le . T h e to ta l o u tp u t to th e s y s te m w ill b e 4 .4 M b its o f c o n tro l s ta tis tic d a ta , ta k e n fo r 4 8 p u ls e s o v e r th e 16 tim e s a m p le s . T h e c o m p re s s e d d a ta is 845 M b its, a t 2 b it s a m p le s fro m th e I a n d Q c h a n n e ls o f th e c o m p re s s e d p u ls e . T h e to ta l c o m p re s s e d d a ta s iz e is 8 5 0 M b its p e r p ic tu re , i.e . a c o m p re s s io n ra tio o f n e a rly 4 :1 .