mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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MORE MATH 87<br />
IQ' 1<br />
OC<br />
111<br />
ω<br />
10 2<br />
10" 3 -2 0 2 4 6 8 10 12 14<br />
Eb/NO (dB)<br />
Figure 4.5 BER vs. Et,/No for QPSK, root-raised-cosine pulse shaping (Ü.22 rolloff),<br />
static, two-tap, symbol-spaced channel, with relative path strengths 0 and —1 dB, and path<br />
angles 0 and 90 degrees, LE results.<br />
4.4.1 ZF solution<br />
In Chapter 3, we explored zero-forcing (ZF) solutions for decision feedback equalization.<br />
ZF linear equalization solutions are similar, except that we don't subtract<br />
the influence of past symbols first. Thus, we need additional degrees of freedom to<br />
cancel past symbols as well.<br />
We won't dig into the ZF solution. The advantage of this solution is that the<br />
noise power or covariance function does not need to be known or estimated. The<br />
disadvantage is that performance suffers at low to moderate SNR values. When we<br />
consider block equalization, which also applies to the MIMO/cochannel scenario,<br />
we will return to the ZF solution.<br />
4.4.2 MMSE solution<br />
In the previous section, we learned that if the decision variable can be written in<br />
the form of (4.66), then the MMSE weight solution can be obtained by solving<br />
(4.77), where R and p are defined in (4.72) and (4.71), respectively. Expressions<br />
for R and p were obtained by using a model for the received samples.<br />
In this section, we will use the extended system model to obtain more general<br />
expressions for R and p. The weights will be applied to chip samples, so the result<br />
will be a chip-level equalizer. Recall from (1.23) that after partial MF, the received