The DFE also has two modes of operation: decision directed and training. They
have the same functions as previously described above. The equalizer output is represented as
(6.7) x(k) a NFF1
j0
bj(k) # r(k j) a NFB1
j0
aj(k) # xr(k j 1)
d ~
x(k) bT(k) # H(k) # d~(k)
x(k) bT(k) # r(k)
r (k) Fh0 c hN1 0 c 0
0 h0 c hN1 0
0 (
( f 0
0 0 0
0 c 0 h0 c hN1V# F d(k)
d(k 1)
(
d(k N K 1)V
r(k) [h0(k) h1(k) chN1(k)] # ?‰? d(k)
d(k 1)
(
d(k N 1) ??
d
r(k) hT(k) # d(k)
r(k) aN1
j0
hj(k) # d(k j)
RECEIVER DIGITAL SIGNAL PROCESSING 295
where NFF is the number of feed forward taps and NFB is the number of feed back taps. The DFE output
can also be represented in vector notation as
(6.8)
where is the time varying weight vector of the feed forward section and is the time varying
weight vector of the feed back DFE section.
The DFE weights can be optimized in a variety of ways. Approaching this solution from the aspect
of creating a MMSE solution by matrix manipulations; the feed forward and feed back weights can be
???stacked??? in the calculation. This MMSE approach will be discussed in more detail in the following
sections. Alternatively each adaptive filter can be separately controlled to arrive at the weight solution.
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