On the multiple antenna broadcast channel

This paper summarizes, with a tutorial flavor, the "quest" for the capacity region of a Gaussian broadcast channel with vector input and scalar outputs, where the channel is linear time-invariant and perfectly known to all terminals. Determining the capacity region of this channel is a challenge, since this model belongs to the class of non-degraded broadcast channels, for which a complete information-theoretic characterization is still open. Nevertheless, a series of previous results shed light on several aspects: a coding strategy and its achievable region were given, and it was shown that, as far as the throughput (rate sum) is concerned, this coding strategy is optimal. In this paper we review these results and add our original point of view. Moreover, we point out some new observations and directions for future study on the subject.