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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THE MATH 83<br />
where<br />
*m n = ν ^ ^ ^ ' ν (4.88)<br />
S mo (0) = Es^C^h. (4.89)<br />
We can write z mo as the output of a linear equalizer, giving<br />
where w is the solution to the set of equations<br />
«(mo) = w"v, (4.90)<br />
C„w = y/W s h. (4.91)<br />
Observe that the weights are the same for each symbol period. The amplitude<br />
reference is<br />
¿(mo) = v^w H h, (4.92)<br />
which is also independent of m 0 .<br />
We see that the ML solution is similar to the MMSE solution, except that C v<br />
has been replaced by C u . Using the matrix inversion lemma, it is possible to show<br />
that these weight vector solutions are equivalent in the sense that one is a positively<br />
scaled version of the other.<br />
4.3.3 Output SINR<br />
A useful measure of performance is output SINR. We can compute SINR using the<br />
model in (4.79) and (4.80). Given a weight vector w, the signal and impairment<br />
powers are given by<br />
The resulting SINR is then<br />
s = |w H [v^:h]i 2<br />
= £ s |w H h| 2 (4.93)<br />
I + N = E{|w H u[ 2 }<br />
= w H E{uu H }w<br />
= w H C u w. (4.94)<br />
SINR^i^'<br />
2 . (4.95)<br />
Keep in mind that the relationship between this SINR and performance depends<br />
on how well we use the signal energy present in the complex plane. For ideal<br />
receivers, the term w H h will be purely real, giving a purely real amplitude reference.<br />
Sometimes, in practical situations, this term is not purely real even though it is<br />
assumed to be. In this case, a more sophisticated computation of SINR is needed.<br />
Now let's evaluate SINR for the ML solution. From (4.91), the weight vector<br />
can be expressed as<br />
WML = v^C^h. (4.96)