Abstract
The capacity region of the Gaussian multi-antenna
broadcast channel was characterized recently in [19]. It was
shown that a scheme based on Dirty Paper Coding [2] achieves
the full capacity region when the transmitter has perfect channel
state information. However, this scheme potentially involves
considerable amounts of feedback and complex algorithms for
coding and user selection. This has led to a quest for practical
transmission schemes and ways to reduce the amount of channel
state information required. In particular, it has been shown that
when the total number of users is large, the sum capacity can
be closely approached by transmitting to a small subset of nearorthogonal
users.
In order to further quantify the latter observation, we study
a Gaussian broadcast channel with two transmit antennas and
K statistically identical, independent users each with a single
receive antenna. We obtain an exact asymptotic characterization
of the gap between the full sum capacity and the rate that
can be achieved by transmitting to a suitably selected pair
of users. Specifically, we consider various simple schemes for
user-pair selection that take into account the channel norms
as well as the relative orientation of the channel vectors. We
conclude that a scheme that picks the strongest user and selects
a second user to form the best pair, is asymptotically optimal,
while also being attractive in terms of feedback and operational
complexity. Numerical experiments show that the asymptotic
results tend to be remarkably accurate, and that the proposed
scheme significantly outperforms a beam-forming strategy for a
typical number of users.
Original language | English |
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Title of host publication | Proceedings 4th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt'06, Boston MA, USA, April 3-7, 2006) |
Publisher | Institute of Electrical and Electronics Engineers |
Pages | 278-285 |
ISBN (Print) | 0-7803-9550-6 |
Publication status | Published - 2006 |