On the diversity-multiplexing tradeoff of the Gaussian MIMO brcadcast Channel

The optimal set of multiplexing gain tuples for the users in a broadcast network with K receivers having Nr antennas each and Nt antennas at the base station, given a minimum diversity gain constraint of d for each user, is investigated. An outer bound on this region is computed by analyzing the outage probability, where outage is defined as the event that the given rate tuple lies outside the capacity region of the broadcast channel. For the special but important case of single antenna receivers with K les N_t, the lattice reduction based precoding recently proposed in [1] is shown to achieve the outage outer bound.