The capacity region of a compound multiple-antenna broadcast channel is characterized when the users exhibit a certain degradedness order. The channel under consideration has two users, each user has a finite set of possible realizations. The transmitter transmits two messages, one for each user, in such a manner that regardless of the actual realizations, both users will be able to decode their messages correctly. An alternative view of this channel is that of a broadcast channel with two common messages, each common message is intended to a different set of users. The degradedness order between the two sets of realizations/users is defined through an additional, fictitious, user whose channel is degraded with respect to all realizations/users from one set while all realizations/users from the other set are degraded with respect to him.

The capacity region of a compound multi-antenna broadcast channel is characterized when the users exhibit a certain degradedness order. For this purpose, we bring to bear a new extremal inequality for information theory and utilize a channel enhancement technique.

In this paper we discuss a two user Multi-Antenna Gaussian broadcast channel with common messages and explore the achievable region suggested by Jindal and Goldsmith. We present simple outer-bounds which are shown to be tight at certain regions. We investigate the aligned channel with common messages and show that beyond a certain threshold on the common rate, the achievable region coincides with the capacity region and we also give a full characterization of the capacity region of the degraded message sets case.

The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the nondegraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints

The dirty paper coding rate region is shown to be the capacity region of the Gaussian MIMO broadcast channel. To that end, a new notion of an enhanced broadcast channel is introduced.

We investigate the fading multiple-antenna channel. The decoder is assumed to possess imperfect channel fading information. A modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information (GMI), the achievable rate, is obtained. We show that under certain conditions the achievable rate is equivalent to that of a fading multiple-antenna Gaussian channel where fading is known to the receiver and is equal to the channel estimation, and where noise is due to both the channel noise and the channel estimation error. We show that for our communication scheme, the minimum mean square error (MMSE) channel estimator is optimal in the sense that it achieves the highest value of GMI, and hence the highest communication rate. Additionally, a training based multiple-input multiple-output (MIMO) scheme in a block-fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal-to-noise ratio (SNR).