mohatta2015.pdf

MORE DETAILS 101
2.5 -
ÍS 1.5
0.5
-0.15 -0.1 0.05 0.1 0.15
Figure 5.1
MSE vs. w-¡ for various values of w^ for DFE for si.
5.2 MORE DETAILS
From the previous section, the MSE as a function of the weights is given by
Ei = (wi(-10)+w 2 (9) - l) 2 + (wi(-10)) 2 + (w 2 + w 2 )100. (5.11)
Similar to the previous chapter, we can take the derivative of 2J 2 w.r.t. each weight
and set the derivatives to zero. This gives
0 = o + 2(-10)(w 2 (9)+wi(-10)- l)(l) + 2(9)(w 1 9)(l)+2w 1 (100)(5.12)
0 = 2(-10)(tu 2 (-10))(l) + 2(9)(to 2 (9) + u; 1 (-10)-l)(l)
+ 0 + 0 + 2ω 2 (100). (5.13)
Solving this set of equations for the MMSE weights gives w\ = —0.04158 and
w 2 = 0.01871.
With a traditional DFE, the feedforward filter would use r\ and r 2 when forming
ζχ, then use r 2 and r$ to form 2 2 . Thus, a sliding window of received values are
used. In this case, the weights turn out to be the same.
However, suppose we only have r\ and r 2 to work with. In this special case,
we find that the MSE for s 2 is minimized to a value of 0.5 when w\ = 0 and
w 2 = —0.05. Observe that in this case, wi = 0. This makes sense, because after
subtracting the influence of s\ and s () , there is no signal term in y\\ there is only
noise that is unrelated with the noise in r 2 .