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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MORE DETAILS 103<br />
Notice that this is a general expression, for any weight values. Substituting the<br />
MMSE weights gives an SINR of 1.405. Observe that this is larger than the SINR<br />
for MMSE LE (0.65714), showing that if the detected values are correct, it is better<br />
to remove them than to linearly suppress them. Also, 1.405 is larger than the upper<br />
bound for ZF DFE (1.0), showing that MMSE performs better than ZF. This is<br />
because MMSE collects signal energy from both images rather than just one. It is<br />
still less than the matched filter bound of 1.81, as expected.<br />
For the general dispersive case, assuming s"o = «o, the estimation error on z\ can<br />
be modeled as<br />
ei = [cw\ + dwi — \)s\ + CW2S2 + [wiTi\ + ω2«2]· (5.19)<br />
The average power in e\, denoted E%, is given by<br />
Ei = (c»i + dw 2 - l) 2 + (cw 2 ) 2 + {w\ + w 2 )a 2 . (5.20)<br />
As in the previous chapter, we can take the derivative of E\ (MSE) w.r.t. w\ and<br />
W2 and set them to zero. This gives a set of equations of the form (4.36) where<br />
R<br />
c 2 + σ 2 cd , h=[ C cd c 2 +d 2 + σ d]. (5.21)<br />
2<br />
As before, R can be interpreted as a matrix of data correlations, only now it is the<br />
data correlations for y\ and yi, which have so removed.<br />
The solution to this set of equations is<br />
„, = c(c 2 + d 2 + a 2 )-cd 2<br />
1<br />
(c 2 + d 2 + a 2 ){c 2 + σ 2 ) - c 2 d 2 { '<br />
d{c 2 + σ 2 ) - c 2 d<br />
W2<br />
~ (c 2 + d 2 + a 2 )(c 2 + σ 2 ) - c 2 d 2 (<br />
'<br />
'<br />
For the MIMO case, we need to rethink the triangularization process. Recall the<br />
first step, when we eliminated S2 from r\ by forming X\ = r\ — (d/f)r2- What we<br />
were really doing is detecting s\ using a form of ZF linear equalization with weights<br />
w\ = 1 and v>2 = (d/f). We would do better if we used the MMSE linear equalizer<br />
as described in the previous chapter.<br />
Recall the second step, in which we formed X2 with noise uncorrelated with x\,<br />
subtracted the influence of si on X2 used s\, then detected S2. We still need to<br />
form X2 with noise uncorrelated with x\. Let w\ and »2 be the weights used in the<br />
first step to form y\, i.e.,<br />
x\ = w\T\ + ω 2 Γ 2 . (5-24)<br />
Let's form X2 as before, using<br />
x 2 = r 2 + hr 1 . (5.25)<br />
As before, we determine h such that the noise on x\ and X2 are uncorrelated. This<br />
gives<br />
E{«i«2} = E{(w)iTii + W2Ti2)(hni + TI2)} = hw\a 2 + w 2 a 2 = 0, (5.26)