Cooperative Diversity: Capacity Bounds and Code Designs - Adaptive Signal Processing in Wireless Communications - page 354

However, these strategies are useful in the medium- or low-SNR regimes. From (12.14)
and (12.15) we see that the gain of receiver cooperation comes from the terms | c 43 | 2 P 3
and | c 34 | 2 P 4 , which depend on the channel between the two receivers. Since this channel
is expected to be good (a node should cooperate with its “best neighbor”), this gain can
be very high. An interesting conclusion from [36] is that the gain from exploiting full
synchronization in receiver cooperation is very limited. Thus, in practice it is enough
to resort to the asynchronous cooperation, which significantly saves the hardware cost.
However, as pointed out in [37], optimal power allocation is essential in achieving the
full additive gain.

12.3.6 Transmitter Cooperation

In transmitter cooperation, two (close) single-antenna transmitters collaborate in com-
municating to two (remote) single-antenna receivers. The channel model is depicted in
Figure 12.3 (upper left) with c 43 = c 34 = 0. As in receiver cooperation, we restrict to the
full-duplex case, where nodes 1 and 2 can simultaneously transmit and receive.
It is shown in [36, 37] that, in contrast to receiver cooperation, synchronization helps
a lot when the transmitters cooperate. That is, if the two transmitters are synchronized,
they can completely cancel out the interference using DPC.
The DPC technique was exploited in [7, 38] to find the capacity of the Gaussian MIMO
broadcast channel. For the two-antenna broadcast channel with two receivers [7], the
main idea is to decompose the MIMO channel into two interference channels and per-
form successive encoding, in which the message for the second receiver is dirty-paper
encoded while assuming the previously encoded message for the first receiver is known
interference (the side information). In this way, the second receiver can completely can-
cel out the interference from the signal for the first receiver. However, to achieve full
capacity, the transmitter has to perform optimal channel decomposition using precod-
ing with the output vector x = b [ u 1 u 2 ] T , where b is a 2 × 2 precoding matrix that has
to satisfy the power constraint, and u 1 and u 2 are the encoded codewords (with unit
power) intended for the first and second receivers, respectively, and obtained via succes-
sive dirty-paper encoding. Assuming a 2 × 2 channel matrix H and unit-power Gaussian
noise, the achievable rates for the first and second receivers are

 

2





s 




11

R = log 1 +

1

2

1 + s

12

 

and R 2 = log(1 + | s 22 | 2 ), respectively, where s ij are the entries of matrix S = Hb .
The coding strategy of [7] is extended to transmitter cooperation in [36, 39]. In
[39], it is assumed that the channel between the two transmitters is orthogonal to the
channels between the transmitters and receivers (which can be achieved by means of
multiple access techniques). Thus, collaboration between the transmitters does not