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 61<br />
where<br />
«i = m - (d/f)n 2 . (3.20)<br />
Can we simply keep r 2 as is? No. The reason is that noise on x\ (u\) is now<br />
correlated with the noise on r 2 («2)· Specifically,<br />
E{ Ul n 2 } = E{n x n 2 - (d/f)n 2 2} = -(d/f)a 2 φ 0. (3.21)<br />
So let's consider a second combination of the form x 2 = r 2 + hr\, which can be<br />
modeled as<br />
x 2 = (e + hc)s 1 + (f + hd)s 2 + u 2 , (3.22)<br />
where<br />
u 2 =n 2 + hni. (3.23)<br />
We want to pick h such that u\ and u 2 are uncorrelated. Setting the correlation to<br />
zero gives<br />
E{uiu 2 } = E{(m - (d/f)n 2 )(n 2 + hm)} = ha 2 - (d/f)a 2 = 0, (3.24)<br />
which implies that we should set h = d/f.<br />
Putting this together in matrix form, we obtain<br />
1 -(d/f)<br />
(d/f) 1<br />
(3.25)<br />
which can be modeled as<br />
x \= Cs + u, (3.26)<br />
where the elements of u are uncorrelated and have power (1 + (d/f) 2 )a 2 and<br />
C = AH<br />
c - de/f 0<br />
e + dc/f f + d 2 /f<br />
(3.27)<br />
Success. Our channel matrix is now triangular. Note, we could have scaled the<br />
elements in A by 1/^/(1 + (d/f) 2 ) to force the elements in u to have power σ 2 .<br />
Instead, we allowed the signal and noise powers to increase, maintaining the same<br />
SNR.<br />
Now we detect si first, using y\. We can then detect s 2 using<br />
As for SINR, the SINR for detecting si is<br />
For detecting s 2 , an upper bound on SINR is given by<br />
y 2 = X2 - (e + dc/f)s!. (3.28)<br />
(c-de/f) 2<br />
S I N R ! = , , . > : : ; „ , ■<br />
(1 + (d//)> 2<br />
( ^<br />
SINR2 * (ΐ%//)> 2· ( 3·3°)