Digital Signal Processing Reference
In-Depth Information
of cooperation on one of the most fundamental random access protocols—the slotted
ALOHA system [27].
11.3.1 Slotted ALOHA in a Wireless Network
In this section, let us start by reviewing the conventional slotted ALOHA system before
incorporating the concept of cooperation in later sections.
Consider a network with
N
users, denoted by the set U = {1, 2,
…
,
N
}, transmitting to
an access point (AP) through the wireless fading channel, as shown in Figure 11.2. In the
slotted ALOHA system, the time is divided into equal-length time slots with the dura-
tion equal to the transmission time of one packet. The beginning and ending of each
time slot are synchronized for all users, and a transmission can only occur at the begin-
ning of a time slot. Let us assume, without loss of generality, that the length of each time
slot is equal to 1 such that the transmission in the
m
th
time slot occurs during the time
t
∈[
m
,
m
+1). If a user, say user
i
, has a packet to transmit, it will transmit in the current
time slot with probability
p
i
, which is independent from all users and over all time slots.
If more than one user is transmitting in the same time slot, a collision will occur and no
packet will be successfully received at the AP.
In contrast to conventional slotted ALOHA systems, where a transmission is assumed
to be successful as long as there is no collision, the transmission of a packet in a wireless
system may fail due to channel fading. Suppose that the channel experienced by user
i
in the
m
th
time slot is parameterized by the variable γ
i
[
m
]. For example, γ
i
[
m
] may be
the signal-to-noise ratio (SNR) of the signal received at the AP corresponding to the
transmission by user
i
in the
m
th
time slot. Assume that γ
i
[
m
] is independent and identi-
cally distributed (i.i.d.) over time with the distribution function
F
γ
i
. Given that user
i
is the only user transmitting in the current time slot, the probability that the destina-
tion receives the packet correctly can be modeled by the probability Ψ(γ
i
[
m
]), which is
a function of the channel state. Let {
H
i
[
m
]}
m
=0
be a sequence of i.i.d. Bernoulli random
variables with probability ψ
i
=
e
γ
i
[Ψ(γ
i
[
m
])], where the event
H
i
[
m
] = 1 indicates the
event of a successful transmission. After each time slot, the access point will feedback
{0,1,
e
}
information to the users, where
0
indicates an idle slot,
1
indicates a success, and
e
indicates an error, due to either collision or channel fading.
Access
point
Collision
Ψ
Success
γ
1
. . . .
. . . .
. . . .
2
m m + 1
1
γ
N
Time slots
γ
2
User 1
. . . . .
λ
1
User N
B
1
λ
N
User 2
B
N
λ
2
B
2
FIgure 11.2
Illustration of the slotted ALOHA system.
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