Digital Signal Processing Reference
In-Depth Information
transmitting and receiving signal power levels). A simpler setup is half-duplex relaying,
in which the relay does not simultaneously receive and transmit. Half-duplex relaying
[24, 27-30] can be implemented with lower complexity by using either time division,
frequency division, or code division, which are equivalent from an information theory
point of view [8]. In the following, we will focus on time-division half-duplex relaying
and discuss both capacity bounds and practical designs.
In time-division relaying, a frame of length
n
is divided into two parts: a relay-receive
period of length
n
α, 0 ≤ α ≤ 1, and a relay-transmit period of length
n
(1 - α). In the relay-
receive period, the source transmits a codeword
x
s
1
. The relay overhears this transmis-
sion, processes its received signal
y
r
in some way, and transmits a codeword
x
r
=
f
r
(
y
r
) in
the relay-transmit period. While the relay transmits, the source simultaneously trans-
mits another codeword
x
s
2
. he codeword
x
s
2
is not heard by the relay, as it is in transmit
mode, and is therefore transmitted directly to the destination. One way to accomplish
this is to split the message
m
∈{1, …,
M
} into two parts,
m
1
and
m
2
, at the source. hen,
m
1
is encoded into the
n
α-length codeword
x
s
1
(
m
1
), and the remaining
m
2
is encoded into
an
n
(1 - α)-length codeword
x
s
2
(
m
2
). At the symbol level, the received signals at the relay
and destination during the relay-receive period are
yn cx mnzn
r
[]
=
( []
+
[]
(12 . 5)
rss
11
rs
and
yncxmnzn
d
[]
=
( []
+ ,
[]
(12 .6)
1
dss
1
1
ds
respectively, where
z
rs
and
z
ds
are independent white Gaussian noises with unit
power. During the relay-transmit period in the asynchronous case, the relay sends an
n
(1 - α)-length codeword
x
r
(
m
1
) to the destination, which receives
yncx mncxmnzn
d
[]
=
( []
+
( []
+,
[]
(12 .7)
2
dss
2
2
dr
r
1
where
z
is again a white Gaussian noise with unit power.
In the synchronous case, the system can additionally use the antennas at the source
and the relay as a two-antenna transmit array. Suppose that the source is able to com-
pletely predict what the relay will send in the relay-transmit period; then the source can
transmit the same signal with a phase shift calibrated so that the two signals add up
coherently at the destination. The received signal is then
yncx mnccAx mnz
d
[]
=
( [] (
+ +
)
( []
+
n
],
[
(12 .8)
2
dss
2
2
dr
ds
r
1
where
A
is a complex constant subject to a power constraint and with such a phase that
|
c
dr
+
c
ds
A
| is maximized. If the source can only partially predict what the relay will
transmit, it is still possible to take advantage of this partial coherency.
The optimum operation at the relay is not known, but several coding schemes have
been proposed [2, 23, 25, 27] to obtain achievable bounds on the rate region. These
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