mohatta2015.pdf

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