July 2015
Intermediate to advanced
600 pages
17h 41m
English
Content preview from Trends in Digital Signal Processing
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June 16, 2015 15:12 PSP Book - 9in x 6in 14-Yong-Ching-Lim-c14
Implementation of Multiuser/MIMO Detector 445
by its other elements, and we assume that the elements of d are
independent of one another. This implies
ln
P (d
(n)
−k
, d
k
=+1|λ
e
2
)
P (d
(n)
−k
, d
k
=−1|λ
e
2
)
= ln
P (d
(n)
−k
|λ
e
2, −k
)
P (d
(n)
−k
|λ
e
2, −k
)
+ ln
P (d
k
=+1|λ
e
2
(d
k
))
P (d
k
=−1|λ
e
2
(d
k
))
= ln
P (d
k
=+1|λ
e
2
(d
k
))
P (d
k
=−1|λ
e
2
(d
k
))
= λ
e
2
(d
k
), (14.17)
where λ
e
2, −k
is λ
e
2
with λ
e
2
(d
k
) dropped from it and the last identity
follows from the definition of L-value. The third line in (14.16)
follows since p(y|d) =
1
(2πσ
2
n
)
N/2
e
−|y−Hd|
2
/2σ
2
n
.
Once λ
(n)
1
(d
k
) is obtained, recalling that
P (d
k
=−1|y, d
(n)
−k
, λ
e
2
) = 1 − P (d
k