Digital Signal Processing Reference
In-Depth Information
35
2 Transmit Antennas
Upper Bound (sync)
Synchronous (3 DPCs)
Synchronous (1 DPC)
Asynchronous
No Cooperation Upper
No Cooperation Lower
30
25
20
15
10
5
0
−10
0
10
20
30
40
50
SNR [dB]
FIgure 12.8
he bounds on the sum-rate
R
1
+
R
2
as a function of the received SNR at the direct
link between nodes 1 and 3 for transmitter cooperation. The received SNR at the link between
nodes 1 and 2 is 30 dB higher than that at the direct link. The average powers of all four nodes are
the same. The upper bound is for the synchronous system.
By exchanging nodes 1 and 2 with nodes 3 and 4, we get another symmetric rate bound.
Besides the multiplexing gain of
r
= 1, DPC achieves a high-SNR additive gain of
2
c
(
)
+
2
21
a
=
log
c
t
+
t
log
.
(12 .18)
41
12
22
2
c
41
Comparing (12.17) and (12.18), we see that the additive gain of using DPC is approxi-
mately equal to that from the upper bound when |
t
12
|
2
≈
P
1
and |
t
22
|
2
≈
P
2
, which cor-
responds to the scenario with weak interference, i.e., |
c
41
|,|
c
32
|
1. In this case, the
gain compared to no cooperation in (12.15) is min{log(|
c
12
|),log(|
c
21
|)}, which can be sig-
nificant, because the channel between the two transmitters is expected to be good. This
is illustrated in
Figure 12.9
, which shows the high-SNR additive gain for a symmetric
cooperative channel (|
c
41
| = |
c
32
|, |
c
21
| = |
c
12
|). Note that under strong interference, i.e.,
|
c
32
|,|
c
41
|
1, there is no gain from cooperation, which might seem somewhat surpris-
ing and is in contrast to receiver cooperation. For weak interference, on the other hand,
there is a high gain from cooperation. This is true even when the link between the trans-
mitters is weak (|
c
21
|
2
= -6 dB in Figure 12.9), and it can be explained by the fact that
there is no known signaling for the interference channel with weak interference, while
cooperation can help in this scenario.
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