Asymptotic High Power Analysis of the MIMO BC

The detailed analyses of the weighted sum rate maximization problem in the previous two chapters have revealed that the optimum transmit covariance matrices and the accompanied maximum weighted sum rate are usually not available in closed form for a multi-user MIMO broadcast channel system setup. In fact, the global optimum can be found by means of iterative algorithms in case of dirty paper coding (see Chap. 6) but only few qualitative conclusions can be deduced therefrom. For linear transceivers, the situation is even worse. Up to now, a globally optimum algorithm does not seem to exist although we conjecture that the combinatorial stream allocation algorithm presented in Chap. 7 achieves this global optimum in most of the cases.