Cooperative Diversity: Capacity Bounds and Code Designs - Adaptive Signal Processing in Wireless Communications - page 350

2

Upper Bound
DF
CF
Multi−hop

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1

−10 −8 −6 −4 −2 0 2 4 6 8 10

|c rs | 2 [dB]

FIgure 12.6 The multihop bound and the upper bound on the capacity together with the
achievable bounds of DF and CF for the Gaussian half-duplex relay channel, assuming | c ds | 2 =
0 dB, | c dr | 2 = 10 dB, and P s = P r = 5 dB. The rate gain over direct transmission is shown as a func-
tion of | c rs | 2 .

transmission. Thus, even if the link between the source and relay is poor, the relay can
still help somewhat by using CF.
It is instructive to compare relay channel signaling with a traditional multihop ad hoc
network, where physical layer communication and networking are typically separated.
Such a comparison will show how cooperative diversity can help increase the perfor-
mance over traditional networking. In a traditional multihop network, the source trans-
mits a packet either directly to the destination or to the relay, which would decode it,
re-encode it, and transmit it to the destination. Relay channel signaling improves upon
this in several ways:

1. The destination uses the signals from both the source and relay for decoding, as
opposed to only one of them.

2. The relay uses a different codebook for encoding in DF than the source, which is
similar to using error-correcting codes rather than repetition coding.

3. The relay can use soft information, as in CF, which resembles using soft decisions
in decoding error-correcting codes rather than hard decisions.

4. The source is allowed to transmit new information simultaneously with the relay's
transmission, which at high SNR brings a large increase in rate.

5. In the synchronous case, the relay can use coherency to combine signals construc-
tively, achieving a gain similar to that in MIMO systems.

12.3.4 Receiver Cooperation
In receiver cooperation, two (closely located) single-antenna receivers cooperate to facil-
itate decoding messages from two remote single-antenna transmitters.