Linear precoder based on minimum Euclidean distance for multicast channels

Assuming the maximum likelihood (ML) receiver at each user, a linear precoding algorithm is proposed for multiple-input multiple-output (MIMO) multicast channel with two users by maximizing the minimum Euclidean distance between two received data vectors. With perfect channel knowledge known a priori, the optimization problem based on the minimum Euclidean distance for multicast channels is first provided and then transformed into a QoS-aware one, where different users can be flexibly constrained to different QoS levels. The proposed precoding matrix can be decomposed into a non-singular matrix multiplied by a diagonal one and an orthogonal one, where the orthogonal one can be approximately obtained resorting to the results for the unicast scenario, and the other two can be acquired by means of the non-orthogonal joint diagonalization and linear programming techniques, respectively. Simulation results validate the efficiency of the proposed precoder for the special case of 2×2 multicast system.