AN2072 Freescale Semiconductor / Motorola, AN2072 Datasheet - Page 15

• Manufacturer Part Number: AN2072
• Description: AN2072, Decision Feedback Equalizer for StarCore-Based DSPs
• Manufacturer: Freescale Semiconductor / Motorola

3.4.1 Cholesky Factorization
The first step in finding the feed-forward and the feedback taps is to compute the lower triangular Cholesky factor
of matrix A (formed by replacing the lower triangle of the original matrix A by its Cholesky factor). This section
describes how the Cholesky factorization is implemented on the SC140 core. Two iterations of the algorithm are
presented. Iteration refers to the outermost loop. Iteration 1 refers to the entire operation as long as column 1 is the
base column, BASE_COL. Similarly, Iteration 2 refers to the entire operation when column 2 is the base column,
BASE_COL.
Iteration 1:
Freescale Semiconductor
1.
2.
Compute sqrt(a(1,1)) and 1/sqrt(a(1,1)).
The first step in filling up the matrix is replacing a(1,1) by sqrt(a(1,1)). Then each element of the first
column of the marix A is multiplied by 1/sqrt(a(1,1)) and these new values replace the existing first
column of matrix A in DSP memory. This process is shown by the lighter-shaded column which is
called the “BASE_COL” shown in the Figure 4.
Perform the operation:
A(i,j)=A(i,j)-A(i,k)*conj(A(j,k))
This implies replacing the second column (starting from the diagonal dash line) with the (first
iteration; k=1, j=2, and i=2) newly computed values:
A(2:12,2)=A(2:12,2)-A(2:12,1)*conj(A(2,1))
The darker-filled column in the matrix in Figure 4, shows the newly replaced columns. In the
assembly code, the start location of A(2:12,2)is stored in a register named, CURRENT_COL, and
the start location of A(2:12,1) is stored in a register named, BASE_ROW. The “BASE_ROW”
contains the starting row location in the “BASE_COL” as the algorithm proceeds.
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Decision Feedback Equalizer for StarCore™-Based DSPs, Rev. 1
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Figure 4. First Step in Computing the Cholesky Factor
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