Partialinterferencealignmentfordownlinkmulti-cellmulti-input

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### 部分干扰对齐在下行多小区多输入多输出网络中的应用 #### 概述本研究探讨了部分干扰对齐（Partial Interference Alignment, PIA）技术在下行多小区多输入多输出（Multi-Cell Multi-Input Multi-Output, MC-MIMO）网络中的应用，旨在通过有效管理干扰来提高无线通信系统的自由度。大型多小区网络中，完全的干扰对齐（Full Interference Alignment, FIA）模型通常需要大量的发射/接收天线以及广泛的信道状态信息交换，这在实际场景中难以实现。因此，本文提出了一种新颖的部分干扰对齐方案，该方案能够利用异构路径损耗特性，在较少数量的收发器天线情况下提升多小区网络的吞吐量。 #### 关键技术点 1. **背景与挑战**：在无线通信网络中，干扰是限制网络吞吐量和频谱效率的主要因素之一。传统方法通过简单的信道正交化来避免干扰，但这并非总是最优的解决方案。因此，寻找一种能够高效管理干扰同时保持较高系统性能的技术显得尤为重要。 2. **干扰对齐技术简介**：干扰对齐是一种新型技术，它通过有效管理无线通信系统中的干扰来达到最佳自由度。FIA是一种理想情况下的技术方案，但在实践中可能因所需的大量天线和复杂的信道状态信息交换而变得不可行。 3. **部分干扰对齐方案**： - **目标**：为了解决上述问题，研究者们提出了PIA方案。该方案能够通过相对较少的天线数量实现，适用于现实世界的应用场景。 - **原理**：PIA利用了网络中不同路径的异构路径损耗特性。通过精心设计信号传输策略，使得不同用户的信号能够在接收端对齐，从而减少相互之间的干扰。 - **实现**：为了将PIA问题公式化，研究者将其转化为一个混合整数双层非线性优化程序，并进一步将其分解为两个子问题，以降低计算复杂度。此外，还引入了两种算法用于选择干扰链接。 4. **仿真结果与分析**：研究通过仿真实验验证了所提出的PIA方案的有效性。在一个包含19个六边形环状小区的布局中，PIA方案即使在发射天线数量较少的情况下也显著优于传统的多用户MIMO技术。 5. **实际应用前景**：鉴于PIA方案能够在有限的天线数量下实现较好的性能，该技术有望在未来得到广泛应用，特别是在需要高吞吐量且受限于硬件资源的场景中。 #### 技术细节 - **混合整数双层非线性优化程序**：这是PIA问题的核心数学模型，通过定义一系列变量和约束条件来描述信号发送和接收过程中的各种参数及关系。 - **子问题分解**：为了简化计算过程并提高算法效率，原始问题被分解为两个子问题进行求解。第一个子问题主要关注信号发射策略的设计；第二个子问题则着重于接收端的信号处理方式。 - **干扰链接选择算法**：研究中提出的两种算法分别用于确定哪些信号链接需要进行干扰对齐操作，这些算法基于网络拓扑结构、路径损耗等因素进行决策。部分干扰对齐技术为解决大型多小区网络中面临的干扰管理难题提供了一个切实可行的方案。通过对现有技术的改进和完善，可以预期该技术将在未来的无线通信领域发挥重要作用。

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Partial interference alignment for downlink

multi-cell multi-input–multi-output networks

ISSN 1751-8628

Received on 16th May 2014

Accepted on 19th November 2014

doi: 10.1049/iet-com.2014.0504

www.ietdl.org

Yang Zhang

✉

, Zheng Zhou

, Bin Li

, Chaozhi Gu

, Ruo Shu

College of Computer and Communication Engineering, China University of Petroleum (UPC), Qingdao 266580, People’s Republic of China

School of Information and Communication Engineering, Beijing University of Post and Telecommunications (BUPT), Beijing 100876,

People’s Republic of China

✉ E-mail: zhangyang@upc.edu.cn

Abstract: Interference alignment (IA) is a novel technique to achieve the optimal degree of freedom of wireless

communication systems through efficient interference management. In a large size multi-cell network, IA over a full

connected model requires the impracti cal number of transmit/receive antennas. Moreover, extensive channel state

information is delivered over the backhaul between different base-stations. For realistic scenarios with limited quantity

of transceiver antennas, such a full IA scheme may even become infeasible. In this study, by exploiting the

heterogeneous path losses, the authors propo se a nov el parti al IA scheme to enhan ce the throughput of multi-cell

networks, which requires relatively small amounts of antennas and hence can be practically implemented. They first

formulate the partial IA prob lem in terms of a mixed integer bi-lev el non-li near opti mal program . Then, they

decompose the problem into two sub-problems to reduce the computation complexity and, furthermore, introduce two

algorithms for interference links selection. It is shown that, in a 19 hexagonal wrap-around-cell layout, their proposed

algorithm outperforms a standard multi-user multi-input–multi-output technique with far less transmit antennas. The

present scheme is therefore of great promise to practical applications.

1 Introduction

Interference is one of the key challenges of wireless communication

networks, which limits the throughput of networks and, therefore,

restricts the spectral efﬁciency seriously. Conventional schemes

avoid interference by simply using channel orthogonalisations.

However, they are not optimal for throughput in general. As an

efﬁcient approach to deal with mutual interference, interference

alignment (IA) provides a novel insight to mitigate interference by

aligning the aggregate interference into a lower dimensional

subspace at each receiver, such that interference free subspace

becomes available for the desired signal. It is shown that IA will

achieve the maximum degrees of freedom (DoF) of the K-user

interference channel [1]. To make this promising scheme a reality,

extensive investigations have been devoted to implementing IA by

aligning interference using signal levels, time or frequency channel

extensions, and multiple antennas at interfering users. Among

these schemes, aligning the interference over the spatial dimension

is the most practical approach. Therefore most of IA schemes

focus on the multi-input–multi-output (MIMO) IA. For more

details, one may refer to [2–4] and other references therein.

Recently, the IA approach is further extended to multi-cell systems

and, consequently, is emerged as an effective technique to suppress

inter-cell interference (ICI) and inter-user interference (IUI) of

multi-cell MIMO sys tems. IA for multi-cell networks is ﬁrst

introduced in [5], where a scheme called subspace IA is proposed.

The idea is to align all interference into multi-dimensional subspace

instead of one-dimensional (1D) subspace. The iterative IA

algorithms on MIMO interference channels are extended to

multi-cell networks in [6–8]. Furthermore, several efﬁcient IA

stra tegies are proposed for downlink multi-cell systems [9–11]. The

downlink scenario of multi-cell networks is also coined as the

interfering broadcas t channel (IFBC), while the uplink channel is

called interfering multiple access channel (IMA C). For a two-cell

MIMO IFBC, a nov el IA scheme using a closed-form expression

without iterative computation is proposed in [12]. Inspired by

previous work, several IA algorithms are designed in [13–15]to

support more than two cells and also more than two users per cell.

Lately, the feasibility of linear IA for MIMO-IFBC is analysed in [16].

It is noteworthy that, in previous works, the fully connected

interference model is assumed. Unfortunately, because of the

limitation of spatial dimensions at transceivers, such a

conﬁguration can only be applied to scenarios with a few cells and

users. It is not realistic that a scaling of IA using an arbitrarily

quantity of antennas per user grows with the size of the networks.

However, in practical multi-cell network scenarios, the distance

between a mobile station (MS) and its interfering base-station (BS)

may vary signiﬁcantly. If the distance is very large, the

corresponding interference can be neglected. Intuitively, aligning

partial interference may contribute to improving system throughput

subject to the constraint of limited spatial dimensions. This issue

has been addressed in works [17–20]. However, methods in [17,

18] are designed based on predeﬁned partial connection

topologies, and the problem of ﬁnding the optimal partial topology

still unsettled. The algorithm in [19] is proposed for MIMO

cellular networks with spatial correlation, and its computation

complexity is very high. The design of the partial IA (PIA)

scheme proposed in [

20] rely on the distribution of mobile users.

Yet, in order to fully exploit the potential advantage of PIA, it is

very important to joint design the schemes of aligned interference

links selection and PIA with certain interference topologies.

In this work, a novel PIA algorithm is proposed to tackle this

challenge by ignoring some weak interference links properly. We

formulate a mixed integer bi-level non-linear optimal program to

design the precoding matrices and receiving ﬁlter matrices.

Moreover, we decompose the bi-level optimal program into two

sub-problems which may alleviate the computation complexity

effectively. One of the sub-problems is designed to select the

interference links to be aligned and another sub-problem is used to

design precoding matrices and receiving ﬁlter matrices by a

close-form algorithm. Based on this scheme, a ﬂexible IA scheme

is implemented, which can be applied to large-size multi-cell

networks with realistic limited antennas. Finally, the proposed

algorithms are compared with the conventional iteration match

IET Communications

Research Article

IET Commun., 2015, Vol. 9, Iss. 6, pp. 836–843

836

The Institution of Engineering and Technology 2015

ﬁltering algorithm and the IA over full connection model via

simulations. The simulation results demonstrate that our proposed

algorithms maintain a good balance between throughput gain and

required antennas, which is hence of great signiﬁcance to practical

uses.

The rest of this paper is organised as follows. In the following

section, we describe the system model and IA technique in brief.

In Section 3, we propose the PIA scheme and formulate it in term

of bi-level mixed integer programming. To reduce the computation

complexity, we decompose the bi-level mixed integer

programming to two sub-problems in Section 4. Simulation results

are depicted in Section 5. Finally, we give the conclusions in the

last section.

Notations: Matrices and vectors are represented by bold upper and

lower case letters, respectively. Inversion, conjugation, transpose,

Hermitian transpose and expectation are denoted by (†)

−1

,(†)*,

(†)

,(†)

†

, E[†], respectively. Tr(†) represents the trace of a

matrix, and diag(†) denotes a block diagonal matrix. |†| is the

cardinality of a set.

2 System model

We consider a multi-cell network with G cells, there are 1 BS (denote

as BS g) and K

MSs in cell g, g =1,…, G, as illustrated in Fig. 1.

We denote M

, N

g,k

as the number of antennas at BS g and the kth

MS of cell g (we denote as MS (g, k)), respectively. D

g,k

is the

number of data streams transmitted to the MS (g, k)fromBSg.

The transmit signal for MS (g, k) is given by

g,k



g,k

d =1

g,k

= V

g,k

(1)

where x

g,k

= x

g,k

, ..., x

g,k

, ..., x

g,k



, and x

g,k

is the information

symbol for the dth data stream of the MS (g, k), while satisfying

the average power constraint, E





g,k





≤ P and v

g,k

[ C

×1

the linear precoding vector corresponding to the symbol x

g,k

, with

a unity norm constraint, that is, v

g,k



= 1. Therefore the

precoding matrix for the MS (g, k)isV

g,k

= v

g,k

, ..., v

g,k



, and

its corresponding data signal vector is represented as

g,k

= x

g,k

, ..., x

g,k



The received signal at the MS (g, k) is given by

g,k

= H

g,k



i=1,i=k

g,k

g,i



′



′

i=1

′

g,k

′

+ n

g,k

(2)

The ﬁrst term of (2) is the desired signal, the second term is IUI and

the third term is ICI. Here, n

g, k

is the additive white Gaussian noise

vector with variance σ

per entry at the MS (g,k), H

′

g,i

[ C

g,i

×M

′

the channel matrix from BS g′ to MS (g, i). ∀g, g

′

[ {1, 2, ..., G}

and ∀i [ 1, ..., K



, H

′

g,i

is composed of two factors namely path

loss

′

g,i

and small scale fading

′

g,i

, that is, H

′

g,i



′

g,i



′

g,i

. The

entries of small scale fading

′

g,i

are assumed as independently

and identically distributed complex Gaussian random variables

with zero mean and unit variance.

Each MS decodes the desired signal coming from its

corresponding BS by multiplying the receiving ﬁlter matrix, and

the received signal at the MS (g, k) is represented as

g,k

= U

†

g,k

+ U

†

g,k



i=1,i=k

g,k

g,i

+ U

†

g,k



′



′

i=1

′

g,k

′

+ U

†

g,k

(3)

where U

g,k

= u

g,k

, ..., u

g,k



[ C

g,k

×D

g,k

is the receiving ﬁlter

matrix of MS (g, k) and U

†

g,k

is the equivalent noise which is

distributed according to CN(0, 1).

We assume that perfect CSI is available at all BSs and MSs. Thus,

the IA approach is adopted to maximise the DoF of networks. In

order to decode the desired signal efﬁciently, both the ICI and IUI

should be aligned into the low-dimensional interference subspace

at MS, and the desired signal should be linearly independent of

the interference. Without symbol extension, the following

condition must be satisﬁed for MS (g, k)

rank U

†

g,k



= D

g,k

(4)

†

g,k

g,i

= 0, ∀i = k (5)

†

g,k

′

g,i

′

= 0, ∀g

′

= g (6)

Equation (4) is a rank constraint to convey the desired signals for

each MS. Equations (5) and (6) are the zero-forcing (ZF)

Fig. 1 Illustration of a multi-cell networks with heterogeneous path loss

IET Commun., 2015, Vol. 9, Iss. 6, pp. 836–843

837

The Institution of Engineering and Technology 2015

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