Three-hop MIMO relaying systems in Gaussian broadcast channels

In this paper, we consider the three-hop MIMO relaying systems, based on the amplify-and-forward (AF) protocol, where there are two relay nodes both of which are equipped with multiple antennas, over Gaussian broadcast channels. We also consider that the base station (BS) broadcasts the signals to multiple distributed users via two relay nodes, that is, three hops, using a zero-forcing dirty paper coding (DPC). We propose three different relaying strategies depending on adopting the power loading from the antennas of each reay node. We calculate both the lower and the upper bounds of the sum capacity of the different relaying strategies we proposed and compare these lower and upper bounds with the sum capacity of the decode-and-forward (DF) protocol based system. In our paper we derive the optimal power allocation at both relay nodes and the BS by using the geometric programming. The simulation results show that our proposed relaying strategies can achieve a similar sum capacity with the upper bound of the three-hop multiuser MIM relaying system, and these outperform the two-hop multiuser MIMO relaying system porposed in Chae et al. (2008) or the multiuser MIMO system without relays in terms of the sum capacity.