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Hybrid interference alignment for multi-user interference MIMO ...
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该文献提出了一种混合干扰对齐的方法,该方法中发射机满足Max-SLNR原则,接收机满足Max-SINR原则。在此基础上,又研究了基于网格搜索和注水法的功率分配算法。
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RESEARCH PAPER
.
SCIENCE CHINA
Information Sciences
doi: 10.1007/s11432-012-4549-z
c
Science China Press and Springer-Verlag Berlin Heidelberg 2012 info.scichina.com www.springerlink.com
Hybrid interference alignment and power allocation
for multi-user interference MIMO channels
SHU Feng
1,2 ∗
, YOU XiaoHu
2
, WANG Mao
1
, HAN YuBing
1
,
LI Yang
3
& SHENG WeiXing
1
1
Institute of Wireless Communication and Sensor Network, EEOT, Nanjing University of Science and
Technology, Nanjing 210094,China;
2
National Mobile Communications Research Laboratory, Southeast University, Nanjing 210094,China;
3
Department of Electrical Engineering, University of Texas at D allas, TX 75080–3021,Texas,USA
Received April 15, 2011; accepted July 31, 2011
Abstract This paper proposes a hybrid interference alignment scheme which combines maximizing signal-to-
leakage-noise ratio (Max-SLNR) at transmitter and maximizing signal-to-interference-noise ratio (Max-SINR)
at receiver. The proposed scheme gives the same sum rate as the existing method using Max-SINR at both
transmitter and receiver by avoiding the operation of reversing channel, thus it provides a simpler solution.
Furthermore, two power allocation procedures are devised based on game theory and water filling. The gain of
these schemes over equal power allocation increases to 2 bit/s/Hz in correlated fading channels as large-scale
fading becomes significant. Additionally, user fairness is solved by introducing weighting factors.
Keywords interference alignment, power allocation, sum rate, Max-SLNR, Max-SINR
Citation Shu F, You X H, Wang M, et al. Hybrid interference alignment and power allocation for multi-user
interference MIMO channels. Sci China Inf Sci, 2012, 55, doi: 10.1007/s11432-012-4549-z
1 Introduction
Distributed MIMO networks have attracted significant research attention recently. Multi-user MIMO
systems represent an example. Interference is a challenging issue in such network, and interference
alignment (IA) [1–10] emerges as a viable solution due to its ability to achieve the degrees of freedom
(DoF) of network as a general tool for compressing the impact of interference to maximize sum rate of
the network. Ref. [3] constructs a combined scheme of dirty paper coding, successive decoding, and zero
forcing achieving 4M/3DoFsinMIMOX channel where M is the number of antennas at each node. Two
iterative algorithms using the reciprocity of wireless networks are also proposed in [1] to improve sum rate
via IA with only local channel knowledge. Ref. [4] formulates the IA and interference cancellation as a
convex problem in multi-hop wireless networks. In [5], a subspace tracking based IA is proposed to reduce
network interference. In [6], a minimum mean squared error based IA is designed, which is shown to be a
convex optimization solved by Newton iterations which replaces maximizing signal-to-interference-noise
ratio (Max-SINR). As there are no closed-form solutions available for Max-SINR based IA due to the
coupled nature of the resulting optimization, Ref. [7] proposes a gradient projection approach. In this
∗
Corresponding author (email: shufeng@mail.njust.edu.cn)
2 Shu F, et al. Sci China Inf Sci
paper, we propose a hybrid iterative IA and power allocation in a K-user interference channel which
provides improvement over the existing iterative IA schemes.
Notations: Throughout the paper, matrices, vectors, and scalars are denoted by letters of bold upper
case, bold lower case, and lower case, respectively. (·)
H
denotes conjugate transpose. I
n
denotes the n×n
identity matrix and E
n×m
denotes the n × m matrix of all ones. Also define K = {1, 2,...,K}.
2Systemmodel
We consider a K-user MIMO network with interference which consists of K transmitters and K receivers.
The transmitter i has M
i
antennas and the receiver k has N
k
antennas. To implement IA, transmit pre-
coding and receive beamforming are applied. The d
i
×1datavectors
i
from transmitter i is first precoded
by multiplying with the M
i
× d
i
transmit precoding matrix V
i
. The transmit power at transmitter i is
E
V
i
s
i
2
= P
i
. The corresponding N
k
× 1 received vector at receiver k is given as
y
k
=
K
i=1
H
ik
V
i
s
i
+ w
k
, ∀k ∈K, (1)
where H
ik
is the N
k
× M
i
channel matrix from transmitter i to receiver k,andw
k
is the N
k
× 1 zero
mean unit variance circularly symmetric additive white Gaussian noise (AWGN) vector at receiver k.
Next, the N
k
× d
k
receive beamforming matrix U
k
is applied to y
k
as
y
k
= U
H
k
y
k
=
H
kk
s
k
+
K
i=1,i=k
H
ki
s
i
+
w
k
, (2)
where
H
kj
= U
H
k
H
kj
V
j
is the d
k
× d
i
effective channel matrix from user i to user k,and
w
k
is the d
k
× 1
effective AWGN vector at receiver k. As indicated in [1], the feasible conditions of IA are V
H
k
V
k
= I
d
k
and U
H
k
U
k
= I
d
k
such that
H
kj
= 0
d
k
×d
j
, ∀ j = k, and rank(
H
kk
)=d
k
, ∀k ∈K. If the above conditions
are satisfied, then (2) is simplified into [1]
y
k
=
H
kk
s
k
+
w
k
. (3)
Below, the perfect channel state information is assumed at both receivers and transmitters.
3 Proposed hybrid IA scheme with pow er allocation
In this section, maximizing signal-to-leakage-noise ratio (Max-SLNR) is first used at transmitter to solve
V
k
given all U
j
and equal power allocation (EPA). Then, Max-SINR is adopted at receiver to attain U
k
given all updated V
j
and EPA. Repeat this process until convergence similar to [1]. Finally, two power
allocation schemes are designed to further improve the sum rate.
3.1 Max-SLNR precoder at transmitter
Firstly, Max-SLNR is adopted to compute each column of precoding matrix V
k
given U
j
, ∀j ∈K.From
(1), (2) and the concept of leakage in [2], the average signal leakage power from the ith substream of user
k to all other receivers is expressed as
L
ki
= E
⎧
⎨
⎩
K
n=1
d
n
z=1,nz=ki
s
H
ki
H
H
kn,z
H
kn,z
s
ki
⎫
⎬
⎭
=
K
n=1
d
n
z=1,nz=ki
v
H
ki
H
H
kn
u
nz
u
H
nz
H
kn
v
ki
p
ki
, (4)
where mj = nz means m = n and j = z, v
ki
is the ith column of matrix V
k
, u
H
nj
is the jth row of matrix
U
H
n
,andp
ki
denotes the power allocated to the ith substream of user k with
K
k=1
N
k
i=1
p
ki
= P where
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