AN2072 Freescale Semiconductor / Motorola, AN2072 Datasheet - Page 7

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

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This section presents an implementation of the algorithm using Matlab and the corresponding DSP implementation
techniques. The Matlab implementation uses practical requirements of a typical communication system (such as;
GSM), with the goal of implementing the algorithm on the SC140 core. Table 1 presents the design parameters.
The DSP software is tailored to the needs of the communication system using the DFE. Feedback and feed-forward
filter coefficients for the DFE are obtained as follows:
Code Listing 1 shows the Matlab code for steps 1–3.
Freescale Semiconductor
channel-impulse response
Channel memory
Complex channel-impulse
response length
Estimate of the SNR
Feed forward filter length
Optimum feedback taps by
delay optimization
SNR
Symbol spaced
equalizer
Parameter Considered
Implementation of the Algorithm
1.
2.
3.
Generate the convolution matrix H for an N
impulse response memory length ν (typically obtained from a channel estimation block).
This combination produces a convolution matrix of size C. For our example it is 8 × 12.
Compute the matrix; A = H × H + (1/SNR_lin)*I.
The (1/SNR_lin)*I creates a diagonal matrix with all the diagonal terms equal to 1/SNR_lin. (SNR_lin
= SNR is expressed in linear scale). The H × H (size 12
with N
size = 4). When the term 1/SNR_lin is added to all the diagonal entries, the matrix becomes strictly
positive-definite.
Compute the Cholesky factorization of Matrix A using the outer product version of the factorization.
This algorithm computes a lower triangular G*, such that A = GG*. For all i > j, A(i,j) is over-written
by G(i,j).
f
(N
f
= 8) numbers of positive eigan values, and four, zero eigan values (channel memory
Table 1. Parameter Considerations for Communication Systems
Decision Feedback Equalizer for StarCore™-Based DSPs, Rev. 1
channel-impulse
Parameter Value
response length
5 dB — 25 dB
N/A
N/A
N/A
1
5
8
Assumed available
The length of the channel-impulse response for GSM
Assumed available
Chosen arbitrarily, typically enough for GSM channel. The only
constraint is that the size of the convolution matrix must be a
multiple of 4.
Minimizes ISI and maximizes SNR at the decision point
Typical range of operation
Chosen over a T/l spaced case because its computational
complexity is “l” times less. Performance does suffer.
f
tap feed forward filter (N
×
12) matrix is a positive semi-definite matrix,
Comments
f
Implementation of the Algorithm
= 8) and a complex channel-
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