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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34 MATCHED FILTERING<br />
the individual symbol copy powers). We say the noise and ISI add noncoherently<br />
(sometimes constructively, sometimes destructively), whereas the symbol copies add<br />
coherently (constructively).<br />
Sometimes we want an upper bound or upper limit on the SINR after equalization.<br />
To obtain this bound, we imagine an ideal situation in which we perfectly<br />
remove ISI before matched filtering. In this case, the output SINR would be the<br />
output SNR, which would be<br />
SINRMFB = , i 181 L = 1-81 = 2.6 dB. (2.9)<br />
(10 2 +9 2 v<br />
)100<br />
'<br />
We will see that output SINR values for other equalizers will be less than this value.<br />
2.2.1 General dispersive scenario<br />
In general, for the dispersive scenario, the MF decision variable for s\ is given by<br />
z l =cr l +dr 2 . (2.10)<br />
Substituting the model equations for r\ and r 2 from (1.5) into (2.10) gives<br />
«i = (c 2 + d 2 )si + cd(si) + s 2 ) + (cni + dn 2 ). (2.11)<br />
The resulting output SINR is<br />
(c 2 + d 2 ) 2 1<br />
2(cd) 2 + (c 2 + d 2 )a 2 h + a 2 /(c 2 + d 2 ) '<br />
y ' '<br />
where<br />
We can rewrite this as<br />
where<br />
12<br />
^ 2c 2 d 2 _ 2c 2 rf 2<br />
(c 2 + d 2 ) 2 2c 2 d 2 + c 4 + d 4 y '<br />
* = / 1+ oiW<br />
(2 ' 14)<br />
h=d 2 /c 2 . (2.15)<br />
Let's assume that c 2 is bigger than d 2 , so that /i and f 2 are positive fractions (less<br />
than 1).<br />
Now consider using only r-i to detect s 2 . Recall that r 2 can be modeled as<br />
Applying one-tap MF in this case gives<br />
The resulting output SINR, is<br />
ri = csi + ds n + ni. (2-16)<br />
2/1 = cr\ = c 2 s\ + cdsn + cn\. (2-17)<br />
C<br />
SINR =<br />
c ¿ d ¿ + c ¿ a ¿<br />
= ^^,,. (2.18)<br />
/i + a'/c*