Diversity Gain Regions for MIMO Fading Broadcast Channels

In wireless communication systems, users with heterogeneous information content constrain the network by having different reliability requirements. In this paper an information-theoretic framework is proposed to study communication systems which provide heterogeneous reliabilities for the users. This is done by defining individual probabilities of error for the users in the network and obtaining their fundamental tradeoffs. Using this framework, a system can be realized, which can provide a tradeoff of reliabilities among the users for a fixed vector of users' rates. This adds a completely new dimension to the performance tradeoff in such networks, which is beyond what is given by the conventional performance versus rate tradeoff in single-user systems. Although this is a very general concept and can be applied to any multi-terminal communication system, in this paper we consider multiple-input multiple-output (MIMO) fading broadcast channel. In particular, we quantify the reliability tradeoff by introducing the notion of diversity gain region (DGR), which specifies the set of diversity gain vectors that are simultaneously achievable by the users for a fixed vector of users' multiplexing gains. We show the existence of a tradeoff among the users' diversity gains by deriving inner and outer bounds for the DGR.