Digital Signal Processing Reference
In-Depth Information
of any single source. However, the performance can be further improved by exploiting
knowledge of the local channel state information (CSI) at the users [13]. For example, if
a user experiences bad channels, it should reduce its transmission probability to avoid
collision with the other users. This is the subject of this section.
In a multiuser system, it is well known that, with knowledge of the CSI, the through-
put of the system can be increased by scheduling users with the best channel to transmit
in each time slot. This advantage is referred to as multiuser diversity in the literature [31].
To exploit this in a random access system, one can adopt a channel-aware transmission
control function, as proposed in [32, 33], that determines the transmission probability
of each user based on its local channel state in each time slot. Specifically, instead of
transmitting with a fixed transmission probability, we assume that each user, say user
i
,
adjusts its transmission probability based on its local channel state γ
i
[
m
] according to the
function
s
i
(γ
i
[
m
]). The average transmission probability is defined as
=
∫
()
p
s
γ
dF
( ,
γ
i
i
i
γ
i
i
where
F
γ
i
(γ
i
) is the distribution function of the channel state γ
i
.
Consider a cooperative network that consists of two users and assume that both users
are fully loaded. Similar to the case without channel awareness, the cooperative queue
states {
CQ
1
[
m
],
CQ
2
[
m
]}
m
=0
form a four-state Markov chain where the stationary distri-
bution can also be derived. The service rates under the fully loaded assumption are given
by
µ
(
ssqq
,,, =+
)
(
π πβ
)
q
(
1
− +−
p
)
[(
2
1
π
+
πβ
)](
q
1
− ,
p
)
1
,
CSI
1
212
1
322
1
311
2
(11.10)
µ
(
ssqq
,,, =+
)
(
π π
)
q
β
(
1
−+−+
p
)[ (
1
π πβ
)
q
](
1
−,
p
)
2
,
CSI
1
212
2
3311
2
1
3
22
1
for users 1 and 2, respectively, where β
i
=
e
γ
i
[
s
i
(γ
i
)Ψ(γ
i
)]. By Loynes' theorem, the fully
loaded region for fixed
s
1
,
s
2
,
q
1
, and
q
2
is
R
coopCSI
(
ssqq
,,, =,
)
{(
λλ λµ
)
:
<
(
ssqq
,,, , <
)
λµ
(
ssqq
, ,, .
)}
(11.11)
,
12 12
12
1
1
,
CSI
12 12
2
2
,
CSI
12 12
For fixed
s
1
(γ
1
),
s
2
(γ
2
), we take the union of the regions in (11.11) over
q
1
,
q
2
to obtain
β
(
1
−+−
β
p
pp p
p
)
(
1
)
R
coopCSI
,
, = , : <
(
ss
)
{(
λλ λ
)
2
1
1
2
ppVss
x
(
1
−≡ , ,
,
)
(
)
12
12
1
1
2
1
1
2
β
(
1
−+ −
)
(
1
)
2
1
1
2
β
(
1
−+−
−+ −
p p
pp p
)
β
(
1
)
λ
<
1
2
2
1
p
(
1
−
p
1
)
≡
,
Vs s
(
, ,
)
(11.12)
2
2
2
y
12
β
(
1
)
(
1
)
1
2
2
1
λλβ
+< −+−≡
(
1
p
)
β
(
1
p
)
ks
(
11
, .
s
)}
1
2
1
2
2
1
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