mohatta2015.pdf

70 LINEAR EQUALIZATION
C X
s o
S 1
®
d x
M Θ (V) S 3
Figure 4.1
Rmiived signal for linear equalization.
Fortunately, the answer is no. By scaling the received values by appropriate weights,
we can improve our figure-of-merit, output SINR.
In detecting S2, let's first look at the copy of S2 in r.v The model for r-¿ and the
next sample, Γ4, is
Γ4
-10s :i + 9s 2 +n:i
-10«4 + 9s.} + Π4-
(4.1)
(4.2)
If we use r;¡, we will introduce the ISI term — ΙΟβ^. However, there is a copy of S3
in Γ4 that we can use to cancel the ISI. If we try to completely cancel the ISI from
s,), a zero-forcing strategy, we need to multiply r± by 10/9 =1.11 and add it to r 3 ,
giving
2/2 = ^ + 1.1^4. (4.3)
This can be modeled as
t/2 = 9s 2 + 0s ;i + (-ll.l)s 4 + [n r( + l.lln 4 ]. (4.4)
Notice that we traded the term —10s :! in (4.1) for the term —II.IS4 in (4.4), increasing
ISI (we also increased the number of noise terms). Thus, we made things
worse.
This suggests we only use the copy of S2 present in Γ2, the larger copy. It turns
out we have flexibility in selecting the weight for Γ2, as long as it has the same sign
as c = —10. Let's use —1/10, so that
«2 -0.1r 2 ,
(4.5)
which can be modeled as
where
z 2 = s 2 + ui,
«2 = —0.9si — 0.1n 2 .
(4.6)
(4.7)
Notice that by using —1/10 for the weight, the model has a coefficient of 1 in front
of «2- We refer to this as unity gain. It allows us to think of 22 as an unbiased