Cryptography Reference
In-Depth Information
Figure 11.21 - Error probability of the first user as a function of the signal to noise
ratio
Eb/N
0
for constant intercorrelation coecients
ρ
=0
.
2
, for K=6 users sharing
the resource.
by the equivalences:
Max
b
f
y
(
y
)
⇔
Min
b
Max
b
2
b
T
Ay
b
T
ARAb
2
R
−
1
y
−
RAb
⇔
−
(11.64)
An exhaustive search for the optimal solution is relatively complex.
Decorrelator detector
Decorrelator detectors involves multiplying observation
y
by the inverse of the
intercorrelation matrix of the codes:
R
−
1
y
=
Ab
+
R
−
1
S
T
n
.Thisequation
shows that the decorrelator enables the multiple access interference to be can-
celled completely, which makes it robust in relation to the
Near Far Effect
.On
the other hand, the resulting additive Gaussian noise has greater variance. In-
deed, we have:
R
−
1
S
T
n
N
(0
,σ
2
R
−
1
)
. The error probability of the
k
-th user
canthenbewrittenintheform:
P
e,k
=
P
b
k
∼
=
b
k
=
Q
A
k
σ
(
R
−
1
)
kk
(11.65)
Linear MMSE detector
The MMSE detector involves finding the transformation
M
that minimizes the
mean squared error: Min
M
∈R
K×K
E
2
. This transformation is no
b
−
My
