Digital Signal Processing Reference
In-Depth Information
(
)
2
1
+
c
PP
+
41
1
2
R
≤
log
2
1
11
+
++
P
c
2
2
R
c
2
1
+−
1
c
1
41
41
2
P
21
1
in the synchronous case, and the sum-rate bound
R
1
+
R
2
is an increasing function of
R
1
.
If |
c
41
| > 1, the upper bound is
2
2
1
+ +
c
c
P
41
21
1
+
2
RR
+≤ +
log
1
cPP
+
log
1
2
41
1
2
2
1
+
cP
41
1
in the asynchronous case, and
2
2
1
+ +
c
c
P
+
(
)
41
21
1
2
RR
+≤ +
log
1
c
PP
+
log
(12 .16)
1
2
41
1
2
2
1
+
cP
41
1
in the synchronous case. There is also a symmetric set of rate bounds by exchanging
nodes 1 and 2 with nodes 3 and 4.
Achievable bounds in asynchronous (without DPC) and synchronous systems (with
three DPCs) can be found in [36]. The achievable bound for the scheme that used one
received SNR on the direct link between nodes 1 and 3. The simulation setup is similar
to that for receiver cooperation with the received SNR at the cooperative link (between
nodes 1 and 2) being 30 dB higher than that at the direct link, again indicating that the
cooperating transmitters are close together.
The achievable bounds of the synchronous system with DPC are usually close to the
upper bound, although noticeable gaps exist in certain SNR ranges. There is only a small
performance loss if only one DPC is used instead of three. The additive gain compared to
the noncooperative case is up to 15 dB in the high-SNR regime. Transmitter cooperation
with DPC performs close to using two transmitter antennas at low and medium SNRs,
giving a multiplexing gain of 2. However, at high SNRs, the multiplexing gain is only 1.
Similar to receiver cooperation, in the high-SNR regime, transmitter cooperation
only gives a multiplexing gain of
r
= 1 (in contrast to the two-antenna broadcast chan-
nel, which results in
r
= 2). The additive gain can be high. For example, when |
c
41
| < 1, in
the synchronous case it is bounded by
2
+
1
+
c
(
)
2
21
a
≤
log
c
PP
+
log
.
(12 .17)
41
1
2
2
c
41
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