Precoding design for MIMO relay multicasting

In this paper, we consider a two-hop multicasting multiple-input multiple-output (MIMO) relay system where one transmitter multicasts common message to multiple receivers with the aid of a relay node, and all nodes are equipped with multiple antennas. Joint transmit and relay precoding design problems are investigated for multicasting multiple data streams based on two design criteria. In the first scheme, we aim at minimizing the maximal mean-squared error (MSE) of the signal waveform estimation among all receivers subjecting to power constraints at the transmitter and the relay node. This problem is highly nonconvex with matrix variables and the exactly optimal solution is very hard to obtain. We develop an iterative algorithm to jointly optimize the transmitter, relay, and receiver matrices through solving convex subproblems. By exploiting the optimal structure of the relay precoding matrix, we then propose a low complexity solution which decouples the optimization of the transmitter and relay matrices under the (moderately) high first-hop signal-to-noise ratio (SNR) assumption. In the second scheme, we propose a total transmission power minimization strategy subjecting to quality-of-service (QoS) constraints. By using the optimal structure of the relay precoding matrix and the (moderately) high first-hop SNR assumption, we show that this problem can be solved using the semidefinite programming (SDP) technique. Numerical simulations demonstrate the effectiveness of the proposed algorithms. Interestingly, we show that for the special case of single data stream multicasting, the relay precoding matrix optimization problem can be equivalently converted to the transmit beamforming problem for single-hop multicasting systems.