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Joint quantisation levels and power

optimisation in uplink network multiple-input

and multiple-output under constraint

backhaul

ISSN 1751-8628

Received on 19th January 2015

Revised on 17th June 2015

Accepted on 17th July 2015

doi: 10.1049/iet-com.2015.0358

www.ietdl.org

Shipeng Wang

✉

, Li Chen, Xiaohui Chen, Guo Wei

Key Laboratory of Wireless-Optical Communications, Chinese Academy of Sciences, School of Information Science and Technology,

University of Science and Technology of China, No. 96 Jinzhai Road, Hefei, Anhui Province, 230026, People’s Republic of China

✉ E-mail: shpwang@mail.ustc.edu.cn

Abstract: This article studies the performance of the cooperative system where each base station (BS) is connected to a

central process or (CP) via a noiseless and rate-limited backhaul link. The single-user compress-and-forward scheme is

deployed at the BSs, and the problem for jointly setting the quantisation noise and the transmit power levels is left

open. The authors formulate the weighted sum-rate (WSR) problem of optimi sing quantisation and transmit power

levels for K-users and B-BSs situation. However, the problem is non- convex and difficult to be sol ved directly by

conventional convex methods. In this work, an algorithm is proposed to solve the optimisation problem and achieve its

global optimality. More importantly, the authors reveal the reason for the effect of the quantisation levels on the

performance of cooperative system. Lower and upper bounds of quantisation levels are derived u nder the given signal

to interference noise ratio (SINR) requirements. The lower and upper bounds are then demonstrated to be rather close

to the numerical results. It is also numerically shown that the proposed algorithm can achieve the global optimality

and is robust with respect to different multi-user situations.

1 Introduction

In modern cellular systems, network capacity is mainly limited by

inter-cell interference. The limitation is particularly severe near the

cell edge where the quality of service deteriorates sharply due to

strong interference from the nearby cells. To address this issue,

joint multicell processing (MCP) or cooperation of multi-point

(CoMP) is adopted as a superior approach to eliminate inter-cell

interference [1]. In the cooperation among BSs, joint decoding in

the uplink and joint transmission in the downlink are employed to

overcome the interference effect. Theoretically, the interference

can be eliminated entirely when BSs share all the data and perfect

channel state information (CSI) with each other. In the uplink

scenarios, MCP and CoMP are also called as network

multiple-input and multiple-output (MIMO).

The inchoate concept of network MIMO is mentioned by

the authors in [2]. The capacity region of network MIMO can be

easily obtained with inﬁnite backhaul link capacity, because the

downlink scenario can be degraded to a broadcast channel (BC) and

the uplink network MIMO can be degraded to a multiple access

channel (MAC). However, in practical uplink scenarios, the effect of

ﬁnite backhaul capacity must be taken into consideration. Moreover,

owing to the ﬁnite backhaul links, the BSs need to compress

their received signals and then share the quantised signals with each

other via the ﬁnite-capacity backhaul links. Thus the quantisation

levels motivate us to explore their effect to the achievable rate

region of uplink network MIMO model with limited backhaul.

Researchers have studied uplink network MIMO with

ﬁnite-capacity backhaul in some of the latest research proposals. In

these researches, there are two major kinds of situations. One is

that the BSs are connected with each other for cooperation. While,

the other one is that the BSs are connected to a central processor

(CP) for cooperation. In the former situation, distributed

interference subtraction scheme is applied to acquire an achievable

data rate in [3]. Then in [4], a comprehensive analysis of rate

region under different cooperative schemes and different

quantisation scheme provides new insight into the value of

network MIMO. However, about the second situation, an

achievable rate from user to the CP is given based on a single-user

scenario in [5], and whether the BSs are capable of decoding or

not is also considered. In [6], the situation that two users

communicate with a CP via two BSs is considered. The author

also derives the upper and lower bounds of the average achievable

throughput. Further, under the Wyner model, the achievable

throughput of the multi-user situations are taken into consideration

in [1, 7]. While in [8], the performance of various multiuser

detection scheme is compared under a Gaussian interference

channel. Nevertheless, these works do not study the effect of the

quantisation levels to the performance of the system.

Some authors have also looked at the effect of quantisation levels

in [9–13]. In [9], the authors analysed the performance of the

cooperative system where complex distributed Wyner–Ziv (D-WZ)

compression was used. Further, a robust and efﬁcient distributed

compression for cloud radio access network is proposed to cope

with uncertainties on the correlation of the received signals in

[12]. In [11, 13], the quantisation levels of D-WZ are studied and

optimised to maximise the sum rate under the ﬁxed transmitted

power. However, the distributed compression requires each BS to

have the information about the joint statics of the received signals

across other BSs, and is difﬁcult to be implemented in practice.

Thus, in [10], the authors design simple receiver structures where

a single-user quantiser is deployed on the BSs and successive

interference cancellation (SIC) is applied at the CP. However, all

the works only consider the separated optimisations of transmit

power or quantisation levels and the works about joint

optimisation of transmit power and quantisation levels are very few.

Summary of contributions. In this paper, we focus on the

uplink network MIMO scenario in which each BS is connected

to a CP via a noiseless and rate-limited backhaul link (see Fig. 1).

To implement the compression scheme practically for multicell

processing, the BSs compress the signals using a single-user

quantiser after receiving the signals. Finally, the BSs send the

IET Communications

Research Article

IET Commun., 2015, Vol. 9, Iss. 16, pp. 2041–2047

2041

The Institution of Engineering and Technology 2015

quantised signals to the CP. In the CP, the SIC scheme is applied for

joint decoding. The contributions are organised as follows:

† We extend the results in [10, Theorem 2] to a weighted sum-rate

(WSR) problem of jointly optimising quantisation levels and

transmit power. However this WSR optimised problem is not a

convex problem with respect to the power values and the

quantisation levels due to the coupled interference.

† By analysing property of the quantisation levels to the WSR

optimised problem and referring to the solution of obtaining the

boundary of the achievable rate region in [14–17], we propose an

algorithm to solve the complex optimised problem and achieve the

global optimality. The convergence of the proposed algorithm is

proved.

† Next, in [18], although we have derived the theoretical lower and

upper bounds of the quantised levels based on two-users and

two-BSs scenario when each user has its own SINR requirement,

the theoretical results are expanded to multi-user and multi-BS

scenario in this paper. The analyses reveal that the quantised levels

not only affect the rate of users, but also save the power of users

to achieve the SINR requirement. In our simulation results, the

global optimality of our proposed algorithm is able to be achieved.

Besides, the results also show that the upper bound and lower

bound are also very close to the theoretical results.

The paper is organised as follows. In Section 2, we brieﬂy

introduce the model of uplink network MIMO system and the

quantised model. In Section 3, the effect of quantisation levels to

the achievable rate region is analysed, and an algorithm is

proposed to achieve the global optimality of the formulated WSR

optimised problem in this section. Then in Section 4, we derive

the theoretical lower and upper bounds of the quantised levels

under the given SINR requirements. The reason why the lower

bound and the upper bound exist is explained. The numerical

simulations are presented in Section 5, and the ﬁnal conclusions

are drawn in Section 6.

2 System model

In this section, the uplink model considered in our work is depicted

in Fig. 1, where there are K single-antenna users and L

single-antenna base stations (BSs) in our scenarios. Each BS is

connected to the CP via a noiseless backhaul link with capacity C

for joint decoding. All the data X

of users follow Gaussian

distributions, that is, X

[ CN(0, 1). Y

denotes the signal received

by BS l and

the signal quantised by BS l. The coefﬁcient H

∈

ℂ states the channel gain from user j to BS l. n

is the background

noise which is also Gaussian as n

[ CN(0,

Hence the signals received by the BS l can be expressed as

= H



√



i=1,i=l



√

+ n

, l = 1, 2, ..., L. (1)

where



√

is the power divided to the data of user i. We assume

individual power constraints per user as

≤ P

imax

, i = 1, 2, ..., K (2)

where P

imax

is the maximised transmitted power of user i.

The BSs are assumed to be oblivious to the codebooks of users

and forward quantised

of their received signal Y

to the central

processor (CP) via orthogonal backhaul links, each of which has

capacity C

. Here a single-user quantiser is used for the

compression of each sequence Y

, based on the Gaussian ‘test

channel’ deﬁned by

= Y

+ q

, for l = 1, 2, ..., L, (3)

where q

is Gaussian quantisation noise q

[ CN(0, Q

)[19]. The

detail description about the quantisation model can be found in

[10, 16], hence we omit for briefty.

3 Problem formulation and propose d solution

In this section, we will review some results in [10, Theorem 2], and

then extend the results to a WSR problem of jointly optimising

quantisation levels and transmit power. Finally, the effect of the

quantisation noise on the performance of our model is explored

and the WSR problem is solved by our proposed algorithm.

3.1 Achievable rate region and formulated WSR

optimised problem

To render the performance of multicell joint processing more

tractable in [10], we assume K = L and a ﬁxed-order SIC scheme

is applied to the CP, which results in much simpler rate

expressions. Next, we deﬁne the achievable rate region for the

ﬁxed-order SIC scheme.

Deﬁnition 1: The rate region of the ﬁxed-order SIC scheme is

deﬁned as

SIC



,..., p

, ..., r

), (4)

and the constraint of r

is expressed as

≤ log 1 +

||H



i=k+1

||H

+ Q



, k = 1, 2, ..., L.

(5)

The detail proof of the rate constraint r

can be found in [10]. It is

worth mentioning that the single-user quantisation noise Q

constraint as

log 1 +



i=1

||H



≤ C

, k = 1, 2, ..., L. (6)

It is obvious that the quantisation noise is related to the feasibility of

the power region from the constraint (6). Under the higher

quantisation levels, the power region becomes much bigger.

Therefore, higher power levels will resist higher quantisation noise

to raise the data rate (5). However, the available maximum power

may be constrained by the maximum power P

kmax

when the

Fig. 1 Uplink transmission model via a central processor

IET Commun., 2015, Vol. 9, Iss. 16, pp. 2041–2047

2042

The Institution of Engineering and Technology 2015

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