Dualities for the MIMO BC and the MIMO MAC with Linear Transceivers

In the past few years, dualities were successfully employed as the linking element between the MAC and the BC and thus, they have gained in importance in the signal processing and information theory communities. If a domain (e.g., rate, mean square error, or signal-to-interference-and-noise ratio domain) in the BC is dual to the corresponding one in the MAC, then both regions coincide and every problem setting and analysis can be investigated and performed either in the BC or in the dual MAC. Consequently, any conclusion drawn in the MAC remains valid in the BC and vice versa. Optimality in one system translates itself into optimality in the other one as well. Besides the capability of proving the congruency of two regions, dualities also deliver explicit conversion formulas how to switch from one domain to the other. While the dual system has some fundamental properties in common with the original system such that the two underlying regions coincide, it additionally features some attributes that differ and hence can be exploited.