Capacity Performance of Relay Beamformings for MIMO Multirelay Networks With Imperfect ${\cal R}$-${\cal D}$ CSI at Relays

In this paper, we consider a dual-hop multiple-input-multiple-output (MIMO) wireless relay network in the presence of imperfect channel state information (CSI), in which a source-destination pair, both equipped with multiple antennas, communicates through a large number of half-duplex amplify-and-forward (AF) relay terminals. We investigate the performance of three linear beamforming schemes when the CSI of the relay-to-destination ( ℜ-
D
) link is not perfect at the relay nodes. The three efficient linear beamforming schemes are based on the matched-filter (MF), zero-forcing (ZF) precoding, and regularized ZF (RZF) precoding techniques, which utilize the CSI of both the
S
-ℜ channel and the ℜ-
D
channel at the relay nodes. By modeling the ℜ-
D
CSI error at the relay nodes as independent complex Gaussian random variables, we derive the ergodic capacities of the three beamformers in terms of instantaneous signal-to-noise ratio. Using the Law of Large Number, we obtain the asymptotic capacities, upon which the optimized MF-RZF is derived. Simulation results show that the asymptotic capacities match the respective ergodic capacities very well. Analysis and simulation results demonstrate that the optimized MF-RZF outperforms MF and MF-ZF for any power of the ℜ-
D
CSI error.