L 
s (n, m) SUM £f (n, k) * b (n, k * m), [4] 
k=1 
where f(n,k) are the coefficients of the matched filter kernel, and L is 
the matched filter length. 
Inserting 1 into 3 and combining the coefficients gives: 
k=L  3=3 
s(n, m) =" SUM SUM g (j, n, k)^* a^€j^ p, deor m^ * [s] 
k=1 j=0 
where 8 (1, n,°k) = (j, n, 1) £3 1. [6] 
The SAR geometry varies slowly and monotonically with range. For fixed 
index k the coefficients g (j, n, k) do not change significantly from n 
to ntl, and the index p equals n plus an integer offset which changes 
only with major step increases of n; for a satellite SAR like ERS-1 the 
coefficients could be kept constant over e.g. 64 azimuth lines without 
significant SAR image degradation. 
With a fraction resolution of e.g. 1/128 there are 512 interpolation 
coefficients which can be calculated once for all; the determination of 
the c(j,n,k) related to the actual SAR geometry then reduces to a point- 
er set-up task. 
Similarly, the whole range of azimuth matched filter coefficients can be 
calculated once in advance with a sufficient fine stepping in centre 
frequency and frequency modulation rate. The appropriate sets of matched 
filter kernels (e.g. 80) can be selected at initialization of processin 
for SAR scene with respect to the actual geometry, and with equation [6 
the e.g. 320 coefficients g(j,n,k) for each index k can be calculated. 
3. A Time Domain Fast SAR Processor Architecture 
3.1 Overall Concept 
  
The range cell migration correction and the azimuth matched filtering 
can be performed together and for all range columns in parallel. For 
each range column the computations are piecewise convolutions with regu- 
lar changes of the kernels. 
This leads to the structure of an azimuth compression device which con- 
sists of as many parallel processing elements as there are range columns 
needed for the azimuth matched filter length. 
The suggested way to implement fast time domain SAR processing is by 
means of a synchronous machine as illustrated in figure 2. Let us call 
it Fast Time Domain Processor (FTDP) for convenience of reference. This 
forms the number crunching nucleus of the SAR processor, and it consists 
of the range compression module, the azimuth compression module and a 
controlling processor which synchronizes both and handles the interface 
to the host computer. The host computer provides the input data, re- 
ceives the resulting data, performs all preparatory calculations for 
coefficients, range cell migration corrections offsets and submits these 
data to the FTDP. It also provides the central clock pulse. 
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