mohatta2015.pdf

MORE MATH 87
IQ' 1
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Eb/NO (dB)
Figure 4.5 BER vs. Et,/No for QPSK, root-raised-cosine pulse shaping (Ü.22 rolloff),
static, two-tap, symbol-spaced channel, with relative path strengths 0 and —1 dB, and path
angles 0 and 90 degrees, LE results.
4.4.1 ZF solution
In Chapter 3, we explored zero-forcing (ZF) solutions for decision feedback equalization.
ZF linear equalization solutions are similar, except that we don't subtract
the influence of past symbols first. Thus, we need additional degrees of freedom to
cancel past symbols as well.
We won't dig into the ZF solution. The advantage of this solution is that the
noise power or covariance function does not need to be known or estimated. The
disadvantage is that performance suffers at low to moderate SNR values. When we
consider block equalization, which also applies to the MIMO/cochannel scenario,
we will return to the ZF solution.
4.4.2 MMSE solution
In the previous section, we learned that if the decision variable can be written in
the form of (4.66), then the MMSE weight solution can be obtained by solving
(4.77), where R and p are defined in (4.72) and (4.71), respectively. Expressions
for R and p were obtained by using a model for the received samples.
In this section, we will use the extended system model to obtain more general
expressions for R and p. The weights will be applied to chip samples, so the result
will be a chip-level equalizer. Recall from (1.23) that after partial MF, the received