Digital Signal Processing Reference
In-Depth Information
We consider E[
W
k,n
2
] = κ
-
, which is a measure of the enhancement of the white noise
compared to the MRC combiner [45]. We also assume that the combiners
W
k,n
and
Ŷ
n
′,
k
′
n
Thus, we derive the variance of the residual interference as follows:
∑
C
∑
K
∑
n
+
1
=
( ))
u
ˆ
d
d
d
Var δ
+
δ
+
δ
V
ξ ξ
κ
Var
Y
nkn
MAIkn
,,
ICIkn
,,
ISIkn
,,
′′
,,
u
u
=
1
kK
′=−
nn
′= −
1
≠
d
∑
′=−
′≠
K
∑
n
+
1
+
( )
ˆ
d
V
ξ ξ
ρκ
Var
Y
nkn
′′
,,
kK
kk
nn
′= −
1
(10. 59)
∑
n
+
1
+
( )
d
ˆ
V
ξ ξ
ρκ
Var
′′=−
′≠
Y
,
nkn
′
,,
nn
nn
1
=
( )
d
ˆ
V
ξ ξ
ρκVar
I
.
kn
,
In the developments of equation (10.59), we exploited the fact that we transmit different
data sequences over distinct subcarriers for a given user, and hence assumed that the
cross-correlation terms from different subcarriers are zero.
In the following, we will derive the values of
V
ξ
and ρ
ξ
under the following three
assumptions: (1) the error indicating variables ξ
k
′,
n
′
and λ
k
′,
n
are independent; (2) all the
random sequence variables (ξ
k
′,
n
′
) and (λ
k
′,
n
) are independent and identically distributed;
and (3) E[λ
k
′,
n
]. Given these assumptions we derive
V
ξ
as follows:
=
=
u
u
u
*
u
*
u
*
u
*
u
u
*
V
E
ξλξλ ξ
E
ξ
E
λ λ
ξ
kn
′′ ′ ′ ′ ′
,
kn
,
kn
,
kn
,
k
′′
,
n
kn
′′
,
kn
′
,
kn
′
,
(10.6 0)
=+
u
u
*
=
E
λλ
1 ρ
λ
.
kn
′
,
kn
,
In order to evaluate
V
ξ
, we exploit the expression of the variance of the power control
error in [51]. Hence, ρ
λ
varies with the maximum Doppler frequency
f
D
(equation (10.51)
in [51]), yielding:
×
( )
−
2
2
4
π
F
P
τ
DPC
ρ
λ
=
,
(10. 61)
1
where τ
PC
is the power control feedback delay. Below we derive the expectation
2
ξ
=
=
=
ρ
E
ξ λξλ
u
u
u
′∗
u
′∗
E
ξ
u
E
ξ
u
′∗
E
λ
u
E
λ
u
′∗
E ξ
kn
u
.
kn
′′ ′
,
kn
,
kn
′ ′
,
kn
′
,
k
′
n
′
kn
′ ′
,
kn
′
,
kn
′
,
′′
,
If
S
rec
1, the value of ρ
ξ
can be derived as follows [45]:
(
)
(
)
2
−−
( )
ρ
ξ
11
cos
2
π
M
i
S
.
(10.62)
rec
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