Achievable Spatial Degrees of Freedom for the
MIMO Interference Channel with Local CSIT
Shixin Peng, Yingzhuang Liu
Dep. of Electronics and Information Engineering
Huazhong University of Science & Technology
Wuhan, China
Email: psx6050@gmail.com, liuyz@mail.hust.edu.cn
Zhengmin Kong
Dept. of Automation
Wuhan University
Wuhan, China
Email: zmkong@whu.edu.cn
Abstract—This paper discusses spatial degrees of free-
dom(DoFs) characterizations and achievable schemes for the 3-
user symmetric MIMO interference channel without channel
extensions over time and frequency dimensions. It is assumed
that only the local channel state information (CSI) is avail-
able at the transmitters. We provide a constructive proof of
achievability on the total spatial DoFs based on interference
zero forcing for the 3-user MIMO interference channel. The
DoFs and achievable scheme are presented by comparing the
number of equations and the number of variables for 3-user
interference channel with specific antenna configuration. Then
we apply interference zero forcing scheme and signal subspace
analysis approach to generalize the idea of interference man-
agement for this special case to the common 3-user symmetric
MIMO interference channel and establish that the total spatial
Dofs min(3 min(M
t
, N
r
), max(M
t
, N
r
)) is achievable in 3-user
M
t
× N
r
symmetric MIMO interference channel when only local
CSI is available at each transmitter.
Index Terms—Local channel state information, degrees of free-
dom, interference channel, multiple-input-multiple-output (MI-
MO), interference zero-forcing.
I. INTRODUCTION
Multiple-input-multiple-output (MIMO) technology can re-
markably increase system channel capacity by providing ad-
ditional spatial dimensions for communication and yields a
spatial multiplexing gain. Spatial multiplexing gain is also
called capacity prelog or degrees of freedom (DoFs). For
multi-user MIMO interference channel, the DoFs as a metric
to approximate the information theoretic capacity in the high
SNR regime represents the available interference-free signal
dimensions in the wireless interference networks and can be
defined as
DOFs = lim
SNR→∞
C
Σ
(SNR)
log SNR
. (1)
where C
Σ
(SNR) is the ergodic sum capacity at signal-to-
noise rate. [1], [2] argues that the available spatial DoFs of
a point-to-point (PTP) MIMO system with M inputs and
N outputs is equal to min(M, N). Reference [4] shows the
exact number of spatial DoFs for a two user nondegenerate
(full rank channel matrices) MIMO Gaussian interference
channel with M
1
, M
2
antennas at transmitters 1, 2 and
N
1
, N
2
antennas at the corresponding receivers, and per-
fect channel knowledge at all transmitters and receivers, is
min (M
1
+ M
2
, N
1
+ N
2
, max(M
1
, N
2
), max(M
2
, N
1
)). For
the K-user interference channel, in the case of independently
faded parallel channels (i.e. time or frequency selective), it
was shown [5] that up to
K
2
DoFs is achievable, which means
each user can achieve one half of the total DoFs free from
interference no matter how many of other users share the
wireless medium. For cellular network, [3] characterized the
DoF of the network when the channel coefficients are time- or
frequency-varying, which is, the DoFs per cell is
KM
K+min(M,k)
,
where M and K denotes the number of receiver antennas
and the number of users in a cell, respectively. However,
these exciting results depend critically on the assumption
that global channel state information (CSI) is available at
the transmitter, which implies excessive training and an over-
whelming feedback overhead in a realistic system. In addition,
the conclusion in [5] is made on the condition that the number
of independently faded parallel channels, i.e. the channel
extensions (over time or frequency), is unbounded. A realistic
communication always has only a finite channel extension
or tries to avoid channel extension due to the limitation of
available wireless channel resource.
Recently, some related work has been developed to consider
the DoFs of MIMO interference network in absence of channel
state information at the transmitters (CSIT). In [6], authors
provided an outer bound on the DoFs for a 2-user MIMO
interference channel on the assumption of no CSIT, which
was shown to be tight for all possible combination of the
number of antennas at each node except for one special class
of channels where the DoFs region remain unknown. They
argued that the loss of DoFs due to lack of CSIT depended on
the relative magnitudes of the number of antenna at each node.
The complete DoFs region of 2-user interference channel in
absence of CSIT was determined in [7]. However, for K-user
(K > 2) MIMO interference channel, the DoFs of network in
absence of CSIT is still an open problem.
In distributed interference management, each transmitter
ideally use no CSI to eliminate interference while the system
can achieve required DoFs. However, in the absence of channel
knowledge, it is well known that the DoFs of interference
channel collapse entirely to what is achievable simply by
orthogonal time-division or frequency-divisions among users.
Reference [8], [9] proposed a blind interference alignment
scheme to do interference management through exploiting the
2013 2nd IEEE/CIC International Conference on Communications in China (ICCC): Communication and Information Theory
(CIT)
978-1-4673-2815-9/13/$31.00 ©2013 IEEE 68