The Geometry of the MIMO Broadcast Channel Rate Region Under Linear Filtering at High SNR


R. Hunger, P. d. Kerret, M. Joham,


        We present a high SNR analysis of the rate region
geometry when linear filtering is applied in the MIMO broadcast
channel and time sharing is not considered. In particular, the set
of weakly Pareto optimal points of the asymptotic rate region
is derived. While all different permutations of user sorting have
to be investigated for the complete rate region when nonlinear
dirty paper coding is applied, we show that the analogon to
different sorting orders is the number of active streams per
user when linear filtering is applied. Furthermore, we reveal
that only a small fraction of weakly Pareto optimal points is
in charge of maximizing an asymptotic weighted sum rate and
points belonging to that fraction are all obtained when every
user applies full multiplexing. In contrast, switching off some
data streams may be optimal when it comes to balancing or
maximizing a user's rate while keeping the other users' rates
constant. Many of the derived results are not only applicable
to systems with enough antennas at the base station, but also
to configurations with too few degrees of freedom, which so far
have never been discussed in any asymptotic analysis before.

BibTEX Reference Entry 

	author = {Raphael Hunger and Paul de Kerret and Michael Joham},
	title = "The Geometry of the {MIMO} Broadcast Channel Rate Region Under Linear Filtering at High SNR",
	booktitle = "Asilomar Conference on Signals, Systems, and Computers",
	address = {Pacific Grove, California},
	month = Nov,
	year = 2009,


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