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In this paper, the authors address the optimal source and relay matrices design for the Multiple-Input Multiple-Output (MIMO) relaying Broadcast Channels (BC) with Direct Links (DLs) based on weighted sum-rate criterion. This problem is non-linear non-convex and its optimal solution remains open. To develop an efficient way to solve this problem, they first set up an equivalent problem, and solve it by decoupling it into two tractable sub-problems. Finally, they propose a general linear iterative design algorithm based on alternative optimization. This iterative design algorithm is convergent since the solution of each sub-problem is optimal and unique. The advantage of the proposed iterative design scheme is demonstrated by numerical experiments.
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