Cooperative Transmission for a Vector Gaussian Parallel Relay Network

In this paper, we consider a parallel relay network where two relays cooperatively help a source transmit its message to a destination. We assume the source and the destination nodes are equipped with multiple antennas. Three basic schemes and their achievable rates are studied: Decode-and-Forward (DF), Amplify-and-Forward (AF), and Compress-and-Forward (CF). For the DF scheme, the source transmits two private signals, one for each relay, where dirty paper coding (DPC) is used between the two private streams, and a common signal for both relays. The relays make efficient use of the common information to introduce a proper amount of correlation in the transmission to the destination. We show that the DF scheme achieves the capacity under certain conditions. We also show that the AF and CF schemes are asymptotically optimal in the high relay power limit if the relays-to-destination channel is full rank. The relative advantages of the three schemes are discussed with numerical results.