Cryptography Reference
In-Depth Information
with:
K
I
s
j
s
j
Φ
K
=
−
(11.69)
j
=1
We can show that the error probability for the
k
-th user at iteration
m
can be
written in the following form, where
S
is the matrix of the codes and
A
is the
diagonal matrix of the amplitudes:
⎛
⎞
g
m,k
SAb
σ
g
m,k
g
m,k
1
2
K−
1
⎝
⎠
P
e
(
m, k
)=
Q
(11.70)
b
/b
k
=+1
Figure 11.25 gives an example of simulations of the SIC method with 5 users, a
spreading factor of 20 and an intercorrelation matrix given by:
⎛
⎞
1
,
30 0 0
0
,
31
,
3
,
3
,
1
0
,
31 0
⎝
⎠
R
=
0
,
2
0
,
30 1 0
0
,
1
−
−
0
,
20
1
Figure 11.25 - Simulation of a SIC receiver.
We note that after 3 iterations, the SIC converges towards the result obtained
with the decorrelator (we can prove mathematically that the SIC converges
towards this result when the number of iterations
M
tends towards infinity).
