|Ph.D Thesis||Department of Electrical Engineering|
|Supervisors:||Assoc. Prof. Steinberg Yossef|
|Distinguished Prof. Shamai )Shitz( Shlomo|
|Full Thesis text|
The multi-antenna Broadcast Channel (BC) is considered. In a BC one transmitter transmits different messages with different rates to several users who can not cooperate. In the multi-antenna version of the BC both the transmitter and the receivers are equipped with one or more antennas. The channel is characterized by a region which is the set of all achievable rates and is referred to as the capacity region.
This model is of great interest as it lies at the heart of current cellular systems.
Caire and Shamai suggested using a transmission scheme called dirty paper coding (DPC). They showed that in some cases, DPC obtains the maximum sum-rate of the channel. The maximum sum-rate corresponds to a limited set of points on the boundary of the capacity region. In this work we show that the DPC rate region coincides with the entire capacity region, thus solving a long standing problem. This result is of particular interest as the multi-antenna broadcast channel does not belong to any of the subclasses of the BC for which there is a known information theoretical expression for the capacity region.
To that end, a new notion of an enhanced BC 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 BC and that dirty paper coding is optimal for the non-degraded 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.
We also consider two other configurations of this BC. The first one is that of a two user BC with common messages where the transmitter sends three messages. Two messages are private, one for each user, and one message is common to both users. The capacity region of this case is defined by a three dimensional region and is still unknown. However, we provide several results showing that the DPC rate region is tight over some sections of its boundary. The other model is that of a BC where there are two groups of users and the transmitter sends two messages, one for each group. The capacity region of this configuration is found for the case where there is some degradedness order between the two groups of users.