The Global Optimality of the MIMO Cooperative System with Source and Relay Precoders for Capacity Maximization

This paper deals with the global optimality of the channel capacity of the multiple-input multiple-output (MIMO) cooperative system which is equipped with precoders at source and relay, and exploits the direct channel between source and destination. Each precoder of the system is individually designed by the Lagrangian method and the final precoders are decided by an iterative structure. To prove the global optimality for the channel capacity of the system with these joint precoders, we show that the channel capacity function of the system is a concave function and the constraints of the system are convex sets.