nd 
st 
  
With a full-custom VLSI implementation of the prototype architecture for 
complex time domain convolution, real-time range compression for SAR 
data of ERS-1 would be possible. 
However, azimuth compression is much more complicated. Due to the RCMC 
and the varying matched filter kernels it is not possible simply to use 
an arrangement of hundreds of range compression VLSI-processors in par- 
allel for azimuth compression. Applying time domain convolution requires 
not only parallelism in computations but also an architecture which al- 
lows simultaneous access to a large amount of data and avoids any unne- 
cessary memory access. This can only be achieved sufficiently fast with 
a design dedicated to the required processing. Attempts to go in this 
direction have already been proposed by K. Y. Liu (ref. 6). 
2.4 Peculiarities of the Azimuth Compression Process 
Assuming SAR data have been range compressed and are arranged in matrix 
form where columns from left to right correspond to successive radar 
pulses, and rows belong to samples of the same slant range (figure 1). 
The SAR geometry is supposed to be constant over the extension in azi- 
muth to be processed, however it varies with slant range. Before the 
azimuth matched filtering can be done the range cell migration correc- 
tion must be applied to the data, i.e. sample values corresponding to 
the RCM curvature have to be calculated by interpolation in range direc- 
tion for each sample. Taking for example a third order polynomial this 
requires multiplication of quadruples of adjacent samples in range with 
coefficients and accumulation: 
3 
bin,dO 9.::3UM. (0, (4, n, 9). apt ji, d, [1] 
3=0 
where a(i,k) are the complex range compressed matrix elements of row i 
and column k, b(n,k) are the range cell migration corrected samples and 
c(j,n,k) are the interpolation coefficients which depend on the relative 
offset: r(n,k) of the range curvature for line n at column k; the index 
p gives the total row offset position: 
p = n + Integer € (a,k)] [2] 
The range cell curvatures can well be approximated by sets of second 
order polynomials of azimuth position. The monotonic range dependent 
variations of these sets within a range column are adequately described 
by linear functions: 
r (n, k) = u (k) # n + v (k), [3] 
where u (k) and v (k) are quadratic functions of k. 
This leads to the effect that p as function of n for fixed k is mainly 
proportional to n with occasional steps of 1. 
The azimuth matched filtering operation can be written as: 
439