Multiplexing Gain for Wireless Networks (Cooperative Diversity)

The results presented so far considered a single destination. Consider now a 2 x 2 wireless network with two source nodes and two sink nodes (see Figure 5.5). Source u, u = 1,2, wishes to send a message to sink node u + 2. We pose the question: can one achieve MIMO multiplexing gains in such cooperative systems?

Wireless network with two source nodes (1 and 2) and two sink nodes (3 and 4).

Fig. 5.5 Wireless network with two source nodes (1 and 2) and two sink nodes (3 and 4).

Channel models with two transmitting and two receiving ends.

 

Fig. 5.6 Channel models with two transmitting and two receiving ends.


Before answering this question, we compare the model in Figure 5.5 with several other models having two transmit and two receive antennas (see Figure 5.6):

(i) MIMO broadcast channel with two transmit antennas;

(ii) MIMO multiaccess channel with two receive antennas;

(iii) MIMO channel;

(iv) interference channel.

For the MIMO channel shown in Figure 5.6(3), physical links exist between the two transmitting antennas and between the two receive antennas. At high SNR, we know that the best MIMO system rates behave as 2log(Y). Similarly, the sum capacity of the two multiuser systems in Figures 5.6(1) and (2) also behave as 2log(Y) [23, 34]. Thus, full cooperation at either the transmitters or the receivers suffices to achieve the multiplexing gain of 2. On the other hand, the interference channel in Figure 5.6(4) has a multiplexing gain of 1 [77]. With respect to the amount of information shared at the transmitters and/or receivers, the cooperative system in Figure 5.6(5) falls between the MIMO and the interference channels.

Unfortunately, the sum-capacity multiplexing gain of the cooperative system in Figure 5.6(5) is only r = 1 even when all nodes have perfect CSIR and CSIT, perfectly synchronized transmissions, and full-duplex capabilities [78]. One can further show that this cooperative system achieves a much poorer diversity-multiplexing tradeoff than the MIMO system [196, 197].

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