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RESEARCH PAPER

SCIENCE CHINA

Information Sciences

doi: 10.1007/s11432-012-4549-z

 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

, WANG Mao

, HAN YuBing

LI Yang

& SHENG WeiXing

Institute of Wireless Communication and Sensor Network, EEOT, Nanjing University of Science and

Technology, Nanjing 210094,China;

National Mobile Communications Research Laboratory, Southeast University, Nanjing 210094,China;

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. (·)

denotes conjugate transpose. I

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

antennas and the receiver k has N

antennas. To implement IA, transmit pre-

coding and receive beamforming are applied. The d

×1datavectors

from transmitter i is ﬁrst precoded

by multiplying with the M

× d

transmit precoding matrix V

. The transmit power at transmitter i is



V





= P

. The corresponding N

× 1 received vector at receiver k is given as



i=1

+ w

, ∀k ∈K, (1)

where H

is the N

× M

channel matrix from transmitter i to receiver k,andw

is the N

× 1 zero

mean unit variance circularly symmetric additive white Gaussian noise (AWGN) vector at receiver k.

Next, the N

× d

receive beamforming matrix U

is applied to y



= U





i=1,i=k





, (2)

where



= U

is the d

× d

eﬀective channel matrix from user i to user k,and



is the d

× 1

eﬀective AWGN vector at receiver k. As indicated in [1], the feasible conditions of IA are V

= I

and U

= I

such that



= 0

×d

, ∀ j = k, and rank(



)=d

, ∀k ∈K. If the above conditions

are satisﬁed, then (2) is simpliﬁed into [1]







. (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

given all U

and equal power allocation (EPA). Then, Max-SINR is adopted at receiver to attain U

given all updated V

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

given U

, ∀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

= E

⎧

⎨

⎩



n=1



z=1,nz=ki



kn,z



kn,z

⎫

⎬

⎭



n=1



z=1,nz=ki

, (4)

where mj = nz means m = n and j = z, v

is the ith column of matrix V

, u

is the jth row of matrix

,andp

denotes the power allocated to the ith substream of user k with



k=1



i=1

= P where

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