17-08-2012, 03:19 PM
Outage Rate Regions for the MISO IFC
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Abstract
We consider the two-user multiple-input singleoutput
(MISO) interference channel (IFC) and assume that the
receivers treat the interference as additive Gaussian noise. We
study the rates that can be achieved in a slow-fading scenario,
allowing an outage probability. We introduce three definitions
for the outage region of the IFC. The definitions differ on
whether the rates are declared in outage jointly or individually
and whether there is perfect or statistical information about
the channels. Even for the broadcast and the multiple-access
channels, which are special cases of the IFC, there exist several
definitions of the outage rate regions. We provide interpretations
of the definitions and compare the corresponding regions via
numerical simulations. Also, we discuss methods for finding the
regions. This includes a characterization of the beamforming
strategies, which are optimal in the sense that achieve rate pairs
on the Pareto boundary of the outage rate region.
INTRODUCTION
In this paper, we consider the two-user multiple-input
single-output (MISO) interference channel (IFC), consisting
of two base station (BS) - mobile station (MS) pairs. The
BSs employ n transmit antennas and the MSs a single receive
antenna. The transmissions are concurrent and cochannel;
hence, they interfere with each other. The BSs choose their
beamforming vectors in either a coordinated or an uncoordinated
manner. The fundamental question raised is which rates
can be simultaneously achieved.
The MISO IFC was studied in [1], where the authors characterized
the transmit strategies, which yield Pareto-optimal
operating points, assuming that the BSs have channel state
information (CSI). Herein, CSI refers to the scenario that
the BSs perfectly know the channel realizations. In [2], we
extended the characterization in [1] to the ergodic rate region,
assuming that the BSs have channel distribution information
(CDI). That is, the BSs know that the channels are zero-mean
complex Gaussian random variables with given covariance
matrices.
OUTAGE RATE REGIONS FOR CDI
In this section, we assume that the BSs have CDI, so that
they can only adapt their beamforming vectors to the statistical
distributions of the channels. Under this assumption, we would
like to find the outage rate region, which consists of all the
rate pairs (r1, r2) that can be simultaneously achieved given
an outage specification. We say that a rate pair (r1, r2) has
individual outage probabilities 1 and 2 when there exists a
pair of beamforming vectors, such that r1 is achieved in at
least a fraction 1 − 1 of the possible fading states or r2 is
achieved in at least a fraction 1 − 2 of the possible fading
states. We say that a rate pair (r1, r2) has a common outage
probability if there exists a pair of beamforming vectors such
that r1 and r2 are achieved simultaneously with a probability
at least 1 − .
OUTAGE RATE REGION FOR CSI
In this section, we assume that the BSs have CSI and,
therefore, are able to adapt their beamforming vectors to the
current fading state. Based on this, we provide an alternative
definition for the outage rate region of the MISO IFC. We
again follow a two-step approach. First, we consider a given
realization of the channels; thus, the rate in (4) is a function
of the beamforming vectors. Then, we define the region Rh
consisting of the rate points that can be achieved using all
possible pairs of beamforming vectors. It is apparent that for
each channel realization we yield a different rate region Rh.
CONCLUSIONS
In this paper, we discussed the outage rate region of the
MISO IFC. We proposed three different definitions which
correspond to different scenarios of channel knowledge and
outage specification. We justified these definitions by the
fact that similar definitions exist for the MAC and the BC.
Also, we described the methods we used to find the regions
and characterized the Pareto-optimal beamforming vectors for
CDI. Finally, we illustrated the differences between the regions
via a numerical example.