mohatta2015.pdf

THE MATH 83
where
*m n = ν ^ ^ ^ ' ν (4.88)
S mo (0) = Es^C^h. (4.89)
We can write z mo as the output of a linear equalizer, giving
where w is the solution to the set of equations
«(mo) = w"v, (4.90)
C„w = y/W s h. (4.91)
Observe that the weights are the same for each symbol period. The amplitude
reference is
¿(mo) = v^w H h, (4.92)
which is also independent of m 0 .
We see that the ML solution is similar to the MMSE solution, except that C v
has been replaced by C u . Using the matrix inversion lemma, it is possible to show
that these weight vector solutions are equivalent in the sense that one is a positively
scaled version of the other.
4.3.3 Output SINR
A useful measure of performance is output SINR. We can compute SINR using the
model in (4.79) and (4.80). Given a weight vector w, the signal and impairment
powers are given by
The resulting SINR is then
s = |w H [v^:h]i 2
= £ s |w H h| 2 (4.93)
I + N = E{|w H u[ 2 }
= w H E{uu H }w
= w H C u w. (4.94)
SINR^i^'
2 . (4.95)
Keep in mind that the relationship between this SINR and performance depends
on how well we use the signal energy present in the complex plane. For ideal
receivers, the term w H h will be purely real, giving a purely real amplitude reference.
Sometimes, in practical situations, this term is not purely real even though it is
assumed to be. In this case, a more sophisticated computation of SINR is needed.
Now let's evaluate SINR for the ML solution. From (4.91), the weight vector
can be expressed as
WML = v^C^h. (4.96)