Transceiver optimization for multi-hop MIMO relay multicasting from multiple sources

In this paper, we consider a multicasting multiple-input multiple-output (MIMO) relay system where multiple transmitters multicast their own messages to a group of receivers over multiple hops, and all nodes are equipped with multiple antennas. The joint transmit and relay precoding design problem has been investigated for multicasting multiple data streams based on min-max mean-squared error (MSE) criterion. We aim at minimizing the maximal MSE of the signal waveform estimation among all receivers subjecting to power constraints at the transmitters and all the relay nodes. 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 by solving convex subproblems. By exploiting the optimal structure of the relay precoding matrices, we then propose a low complexity solution for the problem under some mild approximation. In particular, we show that under (moderately) high signal-to-noise ratio assumption, the min-max optimization problem can be solved using the semidefinite programming technique. Numerical simulations demonstrate the effectiveness of the proposed algorithms.