mohatta2015.pdf

106 MMSE AND ML DECISION FEEDBACK EQUALIZATION
where the elements of R n are given in (4.75). Thus, the MMSE weight solution is
given by
C„w = y/Ίζ h. (5.46)
As with MMSE linear equalization, the weight solution w and A(mo) are independent
of which symbol is being equalized (m () ). As with MMSE linear equalization,
the processing delay dj is a relative delay, relative to m^T. Thus, the elements in
y will change with different mo.
5.3.2 ML solution
As we saw with linear equalization, the ML solution is similar to the MMSE solution,
except that C y is replaced with C u , where
C = C„ - E s hh". (5.47)
5.3.3 Output SINR
The output SINR and SNR expressions have the same form as the expressions for
linear equalization. The only different is that the data and impairment covariance
matrices exclude ISI removed via subtraction. That assumes the ISI was removed
correctly. In practice, errors are made, so that the output SINR expressions give a
bound on SINR (SINR assuming perfect ISI subtraction).
5.3.4 Fractionally spaced DFE
DFE is fractionally spaced when the forward filter sampling period T s is less than
the symbol period T. The spacing of the feedback filter depends on whether it
removes ISI before the forward filter (same spacing as forward filter) or after the
forward filter (symbol-spaced). The story is basically the same as for fractionally
spaced LE (see previous chapter).
5.3.5 Performance results
Similar to the previous chapter, we consider QPSK, root-Nyquist pulse shaping,
and the two-tap, symbol-spaced channel with relative path strengths 0 and —1 dB
and angles 0 and 90 degrees (TwoTS). In Fig. 5.3, BER vs. Eb/N n is shown for the
matched filter, the analytical matched filter bound (REF), MISI DFE, and MMSE
DFE. The LE results are for 31 taps placed symmetrically about the first path
for the symbol of interest. The MISI DFE results are for 1 FF tap placed on the
first signal path. In this special case, ISI can be perfectly removed (assumed ideal
decision feedback), so that the MISI solution becomes the ZF solution discussed in
Chapter 3. The MMSE DFE results are for 16 taps, placed on the first path of the
symbol of interest and the first path of the next 15 future symbols. For both MISI
(ZF) and MMSE DFE, a single feedback tap is used for the symbol prior to the
symbol of interest.