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IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 64, NO. 10, OCTOBER 2016 4181

Wireless Power Transfer in Massive MIMO-Aided

HetNets With User Association

Yongxu Zhu, Lifeng Wang, Member, IEEE, Kai-Kit Wong, Fellow, IEEE,

Shi Jin, Member, IEEE, and Zhongbin Zheng

Abstract—This paper explores the potential of wireless

power transfer (WPT) in massive multiple-input multiple-

output (MIMO)-aided heterogeneous networks (HetNets), where

massive MIMO is applied in the macrocells, and users aim to

harvest as much energy as possible and reduce the uplink path

loss for enhancing their information transfer. By addressing the

impact of massive MIMO on the user association, we compare

and analyze user association schemes: 1) downlink received

signal power (DRSP)-based approach for maximizing the har-

vested energy and 2) uplink received signal power (URSP)-based

approach for minimizing the uplink path loss. We adopt the linear

maximal-ratio transmission beamforming for massive MIMO

power transfer to recharge users. By deriving new statistical

properties, we obtain the exact and asymptotic expressions for

the average harvested energy. Then, we derive the average uplink

achievable rate under the harvested energy constraint. Numerical

results demonstrate that the use of massive MIMO antennas can

improve both the users’ harvested energy and uplink achievable

rate in the HetNets; however, it has negligible effect on the

ambient RF energy harvesting. Serving more users in the massive

MIMO macrocells will deteriorate the uplink information trans-

fer because of less harvested energy and more uplink interfer-

ence. Moreover, although DRSP-based user association harvests

more energy to provide larger uplink transmit power than the

URSP-based one in the massive MIMO HetNets, URSP-based

user association could achieve better performance in the uplink

information transmission.

Index Terms—Energy harvesting, heterogeneous network

(HetNet), massive MIMO, user association, wireless power

transfer.

I. INTRODUCTION

RADITIONAL energy harvesting sources such as solar,

wind, and hydroelectric power highly depend upon time

and locations, as well as the conditions of the environ-

ments. Wireless power transfer (WPT) in contrast is a much

Manuscript received February 9, 2016; revised May 30, 2016 and

July 9, 2016; accepted July 14, 2016. Date of publication July 27, 2016;

date of current version October 14, 2016. This work was supported by the

U.K. Engineering and Physical Sciences Research Council (EPSRC) under

Grant EP/M016005/1. The work of S. Jin was supported by the National

Natural Science Foundation of China under Grant 61531011. The associate

editor coordinating the review of this paper and approving it for publication

was S. Durrani. (Corresponding author: Lifeng Wang.)

Y. Zhu, L. Wang, and K.-K. Wong are with the Department of Electronic

and Electrical Engineering, University College London, London WC1E

6BT, U.K. (e-mail: yongxu.zhu.13@ucl.ac.uk; lifeng.wang@ucl.ac.uk;

kai-kit.wong@ucl.ac.uk).

S. Jin is with the National Mobile Communications Research Laboratory,

Southeast University, Nanjing 210096, China (e-mail: jinshi@seu.edu.cn).

Z. Zheng is with the East China Institute of Telecommunications, China

Academy of Information and Communications Technology, Shanghai 200001,

China (e-mail: ben@ecit.org.cn).

Color versions of one or more of the ﬁgures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TCOMM.2016.2594794

more controllable approach to prolong the lifetime of mobile

devices [1]–[3]. Additionally, the potentially harmful interfer-

ence received by the energy harvester can actually become a

useful energy source. Recently, the potential of harvesting the

ambient energy in the ﬁfth-generation (5G) networks has been

studied in [4]–[6].

Heterogeneous networks (HetNets) are identiﬁed as one of

the key enablers for 5G, e.g., [4], [7]. In HetNets, small cells

are densely deployed [7], [8], which shortens the distances

between the mobile devices and the base stations (BSs).

Recently, there is an interesting integration between WPT

and HetNets, suggesting that stations, referred to as power

beacons (PBs), can be deployed in cellular networks for

powering users via WPT [2]. In [9] and [10], the optimal

placement of power beacons in the cellular networks has been

investigated.

Recent attempts have been to understand the feasibility of

WPT in cellular networks, device-to-device (D2D) commu-

nications and sensor networks. In particular, both picocell

BSs and energy towers (or PBs) were considered in [11]

to transfer energy to the users, and their problem was to

jointly maximize the received energy and minimize the number

of active picocell BSs and PBs. Subsequently in [12], user

selection policies in dedicated RF-powered uplink cellular

networks were investigated, where the BSs acted as dedi-

cated power sources. Further, [13] studied a K -tier uplink

cellular network with energy harvesting, where the cellular

users harvested the RF energy from the concurrent downlink

transmissions in all network tiers. Then [14] studied the

D2D scenario in which the cognitive transmitters harvested

energy from the interference to support the communica-

tion. As mentioned in [15], however, ambient RF energy

harvesting is sufﬁcient only for powering low-power sen-

sors with sporadic activities, and dedicated energy source is

required for powering mobile devices such as smartphones.

As such, [16] turned the attention to the case, where D2D

transmitters harvested energy from the PBs, and proposed

several power transfer policies. In [17], battery-free sensor

node harvested energy from the access point and ambient

RF transmitters based on the power splitting architecture,

and the locations of RF transmitters were modeled using

Ginibre α-DPP.

On the other hand, massive multiple-input multiple-

output (MIMO) systems, using a large number of antennas at

the BSs, achieve ultra-high spectral efﬁciency by accommo-

dating a large number of users in the same radio channel [18].

For massive MIMO to become reality, there are still some

This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/

4182 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 64, NO. 10, OCTOBER 2016

issues such as high circuit power consumption [7], which

need to be addressed. The exceptional spatial selectivity of

massive MIMO means that very sharp signal beams can be

formed [19], [20] and of great importance to WPT. Motivated

by this, [21] studied the wireless information and power

transfer in a point-to-point (P2P) system including a single-

antenna user and its serving BS equipped with large antenna

array, where energy efﬁciency for uplink information transfer

was maximized under the quality-of-service (QoS) constraint.

Later in [22], a receiver with large number of antennas was

assumed to harvest energy from a single-antenna transmitter

and a single-antenna interferer, and an algorithm was proposed

to maximize the data rate while guaranteeing a minimum har-

vested energy with a large receive antenna array using antenna

partitioning. In contrast to [21]–[23] considered the uplink

throughput optimization in a single massive MIMO powered

cell, where an access point equipped with a large antenna

array transfers energy to multiple users. The opportunities and

challenges of deploying a massive number of distributed anten-

nas for WPT was discussed in [24]. In addition, the shorter

wavelengths at the mmWave frequencies enable mmWave BSs

to pack more antennas for achieving large array gains. Hence

recent research works such as [25] and [26] also studied

WPT in mmWave cellular networks. Particularly, in [25],

the mmWave antenna beam was characterized by using the

sectored antenna model and the energy coverage probability

was evaluated. In [26], uniform linear array (ULA) with analog

beamforming was considered for WPT in mmWave cellular

networks. Different from [25] and [26], this paper focuses on

massive MIMO enabled wireless power transfer with digital

beamforming in the conventional cellular bands, which will

be detailed later.

Regarded as a promising network architecture to meet the

increasing demand for mobile data, massive MIMO empow-

ered HetNets have recently attracted much attention [27]–[31].

In [27], downlink beamforming design for minimizing the

power consumption was investigated in a single massive

MIMO enabled macrocell overlaid with multiple small cells,

and it was shown that total power cost can be signiﬁ-

cantly reduced while satisfying the QoS constraints. Moti-

vated by these research efforts, in this paper, we explore

the potential beneﬁts of massive MIMO HetNets for wireless

information and power transfer (WPT and wireless infor-

mation transfer (WIT)), which is novel and has not been

conducted yet.

Different from the aforementioned literature such

as [21]–[23] where WPT and WIT were only considered

in a single cell, we study massive MIMO antennas being

harnessed in the macrocells, and employ a stochastic geometry

approach to model the K -tier HetNets. In particular, users

ﬁrst harvest energy from downlink WPT, and then use the

harvested energy for WIT in the uplink. In this scenario,

user association determines whether a user is associated

with a particular base station for downlink WPT in such

networks, and therefore it is crucial to study the effect of user

association on WPT. The work of [13] considered that users

relied on ambient RF energy harvesting, and only studied the

effect of user association on uplink information transmission.

User association in massive MIMO HetNets has been recently

investigated for optimizing the throughput [28]–[30] and

energy efﬁciency [31]. The effect of using different user

association methods on WPT in such networks is unknown.

Hence we examine the effect of user association on the

WPT and WIT in massive MIMO HetNets by considering

two user association methods: (1) downlink received signal

power (DRSP) based for maximum harvested energy, and

(2) uplink received signal power (URSP) based for minimum

uplink path loss. One of our aims is to ﬁnd out which scheme

is better for uplink WIT. In this paper, we have made the

following contributions:

• We develop an analytical framework to examine the

implementation of downlink WPT and uplink WIT in

massive MIMO aided HetNets with stochastic geomet-

ric model. As the intra-tier interference is the source

of energy, interference avoidance is not required and

maximal-ratio transmission (MRT) beamforming is used

for WPT for multiple users in the macrocells.

• We investigate the impacts of massive MIMO on the

user association of the HetNets, and examine both DRSP-

based and URSP-based algorithms by deriving the exact

and asymptotic expressions for the probability of a user

associated with a macrocell or a small cell in the HetNet.

• We derive the exact and asymptotic expressions for

the average harvested energy when users are equipped

with large energy storage. We show that the asymp-

totic expressions can well approximate the exact ones.

The implementation of massive MIMO can signiﬁcantly

increase the harvested energy in the HetNets, since it

provides larger power gain for users served in the macro-

cells, and enables that users with higher received power

are ofﬂoaded to the small cells.

In addition, DRSP-

based user association scheme outperforms URSP-based

in terms of harvested energy, which means that it sup-

ports higher user transmit power for uplink information

transmission.

• We derive the average uplink achievable rate supported

by the harvested energy. Our results demonstrate that the

uplink performance is enhanced by increasing the number

of antennas at the macrocell BS, but serving more users

in the macrocells decreases the average achievable rate

because of lower uplink transmit power and more severe

uplink interference. For the case of dense small cells,

it can still be interference-limited in the uplink. Fur-

thermore, although DRSP-based user association scheme

harvests more energy to provide larger uplink transmit

power, URSP-based can achieve better WIT performance

in the uplink.

The notation of this paper is shown in Table I.

II. N

ETWORK DESCRIPTION

This paper considers a K -tier time-division duplex (TDD)

HetNet including macrocells and small cells such as picocells

and relays, etc. Each user ﬁrst harvests the energy from its

serving BS (as a dedicated RF energy source) in the downlink,

Note that power gain is also referred to as array gain in the literature.

ZHU et al.: WPT IN MASSIVE MIMO-AIDED HetNets WITH USER ASSOCIATION 4183

TABLE I

OTATION

and uses the harvested energy for WIT in the uplink. Let

T be the duration of a communication block. The ﬁrst and

second sub-blocks of duration τ T and

(

1 − τ

)

T are allocated

to the downlink WPT and uplink WIT, respectively, where

(

0 ≤ τ ≤ 1

)

is the time allocation factor. We assume that

the ﬁrst tier represents the class of macrocell BSs (MBSs),

each of which is equipped with a large antenna array [32].

The locations of the MBSs are modelled using a homogeneous

Poisson point process (HPPP) 

with density λ

[33]. The

locations of the small-cell (such as micro/picocell, femtocell,

etc.) BSs (SBSs) in the i-th tier (i = 2,...,K ) are modelled

by an independent HPPP 

with density λ

. It is assumed

that the density of users is much greater than that of BSs so

that there always will be one active mobile user at each time

slot in every small cell and hence multiple active mobile users

in every macrocell.

In the macrocell, S single-antenna users

communicate with an N-antenna MBS (assuming N  S ≥ 1)

in the uplink over the same time slot and frequency band.

In the small cell, only one single-antenna user is allowed

to communicate with a single-antenna SBS at a time slot.

We assume that perfect channel state information (CSI) is

known at the BS,

and the effect of pilot contamination on

channel estimation is omitted. As mentioned in [7] and [35],

pilot contamination is a relatively secondary factor for all but

colossal numbers of antennas, and various methods to mitigate

pilot contamination via low-intensity base station coordination

have already been proposed in the literature such as [35].

In addition, universal frequency reuse is employed such that all

of the tiers share the same bandwidth and all the channels are

assumed to undergo independent identically distributed (i.i.d.)

quasi-static Rayleigh block fading.

In reality, there may be more than one active users in a small cell and this

can be dealt with using multiple access techniques.

We note that in [14], the probability mass function of the number of users

served by a generic BS was derived by approximating the area of a Voronoi

cell via a gamma-distributed random variable. However, the result in [14]

cannot be applied in this paper, since the Euclidean plane is not divided into

Voronoi cells based on the considered user association methods. We highlight

that it is an important work to study the case of the dynamic S following a

certain distribution in less-dense scenarios.

In the practical TDD massive MIMO systems, the downlink CSI can be

obtained through channel reciprocity based on uplink training.

A. User Association

We introduce two user association algorithms: (1) a user is

associated with the BS based on the maximum DRSP at the

user, which results in the largest average received power; and

(2) a user is associated with the BS based on the maximum

URSP at the BS, which will minimize the power loss of user’s

signal during the propagation.

Considering the effect of massive MIMO, the average

received power at a user that is connected with the -th MBS

( ∈ 

) can be expressed as

r,

= G





,M





, (1)

where G

denotes the power gain obtained by the user

associated with the MBS, P

is the MBS’s transmit power,





,M





= β



,M



−α

is the path loss function, β is

the frequency dependent constant value,



,M



denotes the

distance, and α

is the path loss exponent. In the small cell,

the average received power at a user that is connected with

the j-th SBS ( j ∈ 

)inthei-th tier is expressed as

r,i

= P





j,i





, (2)

where P

denotes the SBS’s transmit power in the i-th tier and

as above L





j,i





= β





j,i





−α

is the path loss function

with distance



j,i



and path loss exponent α

For DRSP-based user association, the aim is to maximize

the average received power. Thus, the serving BS for a typical

user is selected according to the following criterion:

BS : arg max

k∈

{

M,2,...,K

}

∗

r,k

, (3)

where

∗

r,M

= max

∈

r,

, and P

∗

r,i

= max

j∈

r,i

. (4)

By contrast, for URSP-based user association, the objective

is to minimize the uplink path loss, and as such, the serving

BS for a typical user is selected by

BS : arg max

k∈

{

M,2,...,K

}

∗

(

)

, (5)

where

∗

(

)

= G

max

∈





,M





, (6)

∗

(

)

= max

j∈



j,i



). (7)

Here, G

is the power gain of the serving MBS and L

∗

(

)

can be viewed as compensated path loss due to the power gain.

B. Downlink WPT Model

For wireless energy harvesting, the RF signals are inter-

preted as energy. Therefore, in the massive MIMO macrocell,

we adopt the simplest linear MRT beamforming

to direct the

Although user association for the downlink and uplink can be decoupled

to maximize both the DRSP and URSP, the main drawback for the decoupled

access is that channel reciprocity in massive MIMO systems will be lost [36].

Since there is no interference concern in the downlink power trans-

fer, other beamforming methods involving interference mitigation such as

zero-forcing (ZF) will reduce power gain and increase the power consumption

of the MBS.

参数B未提及

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