Backhaul aware joint uplink and downlink user association

TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIESTrans. Emerging Tel. Tech. (2015)

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.2968

RESEARCH ARTICLE

Backhaul aware joint uplink and downlink userassociation for delay-power trade-offs in HetNets withhybrid energy sourcesDantong Liu1*, Yue Chen1, Kok Keong Chai1 and Tiankui Zhang2

1 School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, UK2 School of Information and Communications Engineering, Beijing University of Posts and Telecommunications, Beijing, China

ABSTRACT

In cellular networks, conventional user association algorithms are solely based on downlink (DL) performance, which maylead to inefficient transmission power and high interference in the uplink (UL) transmission. In addition, the backhauldata rate constraint has been neglected by the majority of the existing user association algorithms. However, the backhaulconstraint has become more severe in heterogeneous networks (HetNets) where small cells are densely deployed to meet theskyrocketing data traffic demand. In this paper, we propose an optimal backhaul-aware joint UL and DL user association fordelay-power trade-offs in HetNets with hybrid energy sources. In the considered HetNets, all the base stations are assumedto be powered by a combination of power grid and renewable energy sources, in order to achieve both uninterrupted andgreen communications. Taking both UL and DL transmissions into consideration, the proposed user association algorithmaims to improve network quality of service by minimising the sum of UL and DL average traffic delay, as well as to reducethe overall UL power consumption of users and DL on-grid power consumption by maximising the utilisation of greenpower harvested from renewable energy sources. To this end, a convex optimisation problem is formulated to minimisethe weighted sum of cost of average traffic delay and cost of power consumption. We have proved that the proposed userassociation algorithm converges to the global optimum, which enables a flexible trade-off between average traffic delayand power consumption. Simulation results validate the effectiveness of the proposed algorithm in adapting the trafficloads among base stations along with the distribution of green power and the backhaul data rate constraint. Simulationresults also demonstrate that the proposed user association algorithm achieves prominent improvement in UL averagetraffic delay reduction and effectively reduces both the DL on-grid power consumption and overall UL power consumptionof users, with limited sacrifice on DL average traffic delay, compared with the user association algorithm only based onDL performance. Copyright © 2015 John Wiley & Sons, Ltd.

*Correspondence

D. Liu, School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, UK.E-mail: [email protected]

Received 22 April 2015; Revised 12 June 2015; Accepted 27 June 2015

1. INTRODUCTION

The emerging fifth-generation (5G) mobile networksexpect significantly higher transmission rate and energyefficiency. Heterogeneous networks (HetNets), where var-ious low-power base stations (BSs) are underlaid in amacrocellular network, are able to achieve more spectrum-efficient and energy-efficient communications [1] to meetthe requirements of 5G networks.

Driven by environmental concerns and regulatorypressure, green communication has drawn tremendousattention from both industry and academia. Energy har-vesting is appealing because BSs are capable of harvesting

energy from the renewable energy sources, such as solarpanels and wind turbines, thereby substantially reducingthe overall energy consumption throughout the network.Yet, although the amount of renewable energy is poten-tially unlimited, the intermittent nature of the energy fromrenewable energy sources will result in highly randomenergy availability in BSs. Hence, in practice, BSs poweredby hybrid energy sources, a combination of power grid andrenewable energy sources, are much more practical thanthose solely powered by renewable energy sources in orderto provide uninterrupted service [2]. In the literature, powerallocation [3], coordinated multi-input multi-output [4],

Copyright © 2015 John Wiley & Sons, Ltd.

D. Liu et al.

network planning [5] and green energy allocation [6]have been studied in the hybrid energy sources-poweredscenario.

User association, which refers to associating user with aproper serving BS, has a great impact on the performanceof wireless networks. Most of the research works on userassociation investigate the problem from either the down-link (DL) [7–9] or uplink (UL) [10, 11] perspective. It isworth mentioning that HetNets introduce a major asym-metry between the UL and DL in terms of channel, trafficand hardware limitation. Because of the UL–DL asymme-try in HetNets, the user association for the optimal DL orUL performance only will not be effective to the oppositedirection. Specifically, we take the conventional user asso-ciation policy as an example, where a user is associatedwith the BS from which it receives the strongest DL ref-erence signal received power (RSRP) [12]. As illustratedin Figure 1, user A is located in the vicinity of a picoBS (PBS). Despite the distance from user A to the PBSis shorter than that from user A to the macro-BS (MBS),user A is associated with MBS due to the stronger receivedRSRP from the MBS. In the UL, user A needs to trans-mit with high power to ensure the target signal-to-noiseratio received by the MBS. This will introduce high ULinterference to users in the picocell, thereby degrading boththe spectrum and energy efficiencies and shortening usersbattery life.

In this sense, it is imperative to take both the UL and DLperformances into consideration when making user associ-ation decision in HetNets. To the best of our knowledge,only a limited number of existing works have consideredthe joint UL and DL user association in HetNets [13,14]. In [13], a user association algorithm was proposed tomaximise both UL and DL energy efficiencies via Nashbargain solution. In [14], a user association and beamform-ing design were proposed to coordinate the interference forenergy minimisation.

In addition, all the aforementioned discussions implythat the network has perfect backhaul between the BSand the network controller, and the wireless access linkbetween the BS and the user is the network bottleneck.

This implication is generally correct for the well-plannedMBS. However, in HetNets, the potentially dense deployedsmall BSs may incur overwhelming traffic over backhaullink. On the other hand, the current small cell backhaulsolutions, such as xDSL, non-line-of-sight microwave, arefar from the ideal backhaul solution with sufficiently largedata rate [15]. As such, the backhaul data rate constrainthas become far more stringent in HetNets.

To cope with the foregoing issues, we propose an opti-mal backhaul-aware joint UL and DL user associationfor delay-power trade-offs in HetNets with hybrid energysources in this paper. Average traffic delay is a critical met-ric for user association, which has been widely used inthe existing research [7, 16–19]. The delay that we con-sidered here includes not only the DL and UL averagetraffic delay over the wireless access link between the BSand the user but also the DL and UL average traffic delayover the backhaul link between the BS and the networkcontroller. The power grid operation is costly and non-environmentally friendly. In contrast, the harvested energyfrom renewable energy source is green, sustainable andfree of cost. Thus, instead of the overall DL network powerconsumption minimisation, we try to reduce DL on-gridpower consumption by maximising the utilisation of greenpower harvested from renewable energy sources. As such,for the power consumption, we take both the DL on-gridpower consumption and overall UL power consumptionof users into account. In wireless networks, power savingis often achieved at the price of degradation in networkquality of service (QoS) (i.e. higher latency and lowerthroughput) [20]. With this in mind, the proposed userassociation algorithm aims to achieve a flexible trade-offbetween UL/DL average traffic delay and UL/DL powerconsumption. To this end, a convex optimisation problemis formulated to minimise the weighted sum of cost of aver-age traffic delay and cost of power consumption. We provethat the proposed user association algorithm converges tothe global optimum.

This paper is organised as follows. Section 2 gives thesystem model. Section 3 formulates problem. Section 4presents the proposed user association algorithm and theproperties of the proposed algorithm. Sections 5 and 6 aresimulations and conclusions, respectively.

Figure 1. Downlink reference signal received power-based user association causes severe uplink interference. BS, base station; MBS,macro BS; PBS, pico BS.

Trans. Emerging Tel. Tech. (2015) © 2015 John Wiley & Sons, Ltd.DOI: 10.1002/ett

D. Liu et al.

2. SYSTEM MODEL

We focus on a two-tier HetNet where tier 1 is modelled asmacrocell and tier 2 as picocell. MBSs provide basic cov-erage, whereas PBSs are deployed in the coverage area ofeach MBS to enhance capacity. All the BSs are assumed tobe powered by both the power grid and renewable energysources. The proposed user association algorithm is car-ried out within a macrocell geographical area L � R2,which is served by a set of BSs B including one MBS andseveral PBSs, where all the BSs are assumed to share thesame frequency band with frequency reuse factor equallingto one. We investigate the backhaul-constrained HetNets inthis paper, and both the formulated UL and DL transmis-sions are composed of the wireless access link between theBS and the user, and the backhaul link between the net-work controller and the BS. Let x 2 L denote a locationand i 2 B an index ith BS, where i D 1 indicates theMBS and others are PBSs. Then the proposed user associa-tion algorithm is applied to decide which BS within L willserve which user at location x. Figure 2 details the systemmodel for the proposed backhaul-aware joint UL and DLuser association in HetNets with hybrid energy sources.

We assume that each user has both UL and DL trans-mission requests during the period when associated withcertain BS. There are two main techniques to separate ULand DL transmissions on the same physical transmissionmedium: the time-division duplex (TDD) and frequency-division duplex. TDD system, with the advantages toaccommodate UL and DL traffic asymmetrically, has beenregarded as a promising paradigm in 5G networks. Thus,in the paper, we use TDD to separate the DL and UL trans-missions with the synchronous operation across the entirenetwork to eliminate BS-to-BS and user-to-user interfer-ence [21]. As an inherit feature of TDD system, channelreciprocity is adopted here, where the UL and DL chan-nels between the same communicating pairs have the samechannel gain. We assume that the traffic requests arriveaccording to an inhomogeneous Poisson point process with

the arrival rate per unit area �.x/, and the UL and DL traf-fic sizes are independently distributed with mean �.x/ and�.x/, respectively.

In order to formulate the user association problem, wedefine the user association indicator as yi.x/. If the user atlocation x is associated with BS i, yi.x/ D 1; otherwise,yi.x/ D 0. We assume that at each time, one user can onlyassociate with one BS, and thus, we have

Pi2B yi.x/ D 1.

For the sake of decoupling the association and schedulingproblem, we assume that all the users associated with thesame BS are severed in a round robin fashion. To facilitatethe subsequent analysis, we define y D fyiji 2 Bg, whereyi D fyi.x/jyi.x/ D f0, 1g , x 2 Lg.

2.1. Traffic model

2.1.1. Uplink traffic model.

During the UL open-loop control, � is set as the targetsignal-to-noise ratio at BS. Thus, the desired transmissionpower of user at location x when associated with BS i isgiven by

pui .x/ D min

n��2

.gi.x/, pu

max.x/o

(1)

where �2 is the noise power level, pumax.x/ is user’s max-

imum transmission power and gi.x/ is the channel gainbetween the user at location x and BS i, which includespathloss and shadowing.

Assuming that a mobile user at location x is associ-ated with BS i, the UL transmission rate ru

i .x/ from thisuser to BS i can be generally expressed according toShannon–Hartley theorem [17], with W denoted as theoperating bandwidth:

rui .x/ D Wlog2

�1C �u

i .x/�

(2)

Figure 2. System model for the proposed backhaul-aware joint UL and DL user association in HetNets with hybrid energy sources.BS, base station; MBS, macro BS; PBS, pico BS.


D. Liu et al.

where

�ui .x/ D

pui .x/gi.x/

Ii.x/C �2(3)

here, Ii.x/ is the average interference to the UL transmis-sion of the user at location x from all the other users inneighbouring cells. Note that fast fading is not consideredhere because the time scale of user association is muchlarger than the time scale of fast fading. As such, ru

i .x/ canbe considered as a time-averaged transmission rate [16].In the UL, the co-channel interference for a certain usercomes from the users that simultaneously use the sameresource block in the neighbouring cells. In reality, theusers that cause interference change from one schedulingcycle to another due to scheduling dynamics. However,in terms of user association, the average interference toa user is more critical than the instantaneous interferenceat each scheduling cycle. Thus, we focus on the averageinterference to a user Ii.x/, which is given by [22]:

Ii.x/ DX

j2B,j¤i

ZLnx

pu

j .Ox/ yj .Ox/

Nj

!gi .Ox/ dOx (4)

where Nj DRLnx yj .Ox/ dOx is the number of users associated

with BS j.In order to guarantee the QoS of users in a sense that all

the users are served with the required traffic amount, thefraction of resource blocks used by the user at location xfor UL transmission, when associated with BS i, is

%ui .x/ D

�.x/�.x/yi.x/

rui .x/

(5)

where %ui .x/ also denotes the average UL traffic load

density at location x of BS i.Based on the UL traffic load density, the UL traffic load

of BS i is given by

�ui D

ZL%u

i .x/dx (6)

According to Burke’s theorem, the traffic request depar-ture process at BS’s wireless access link is a Poissonprocess with average departure rate equalling to the aver-age arrival rate. Thus, the average traffic arrival rate in BS’sbackhaul is �.x/.

We assume that the expected backhaul data rate is con-stant during the user association period [23]. With Ru

idenoted as the UL backhaul data rate of BS i, the averageUL backhaul traffic load density at location x of BS i isexpressed as follows:

Q%ui .x/ D

�.x/�.x/yi.x/

Rui

(7)

Then the UL backhaul traffic load of BS i is given by

Q�ui D

ZLQ%u

i .x/dx (8)

2.1.2. Downlink traffic model.

Assuming that a mobile user at location x is associatedwith BS i, the DL transmission rate from BS i to this userrd

i .x/ is

rdi .x/ D Wlog2

�1C �d

i .x/�

(9)

where

�di .x/ D

pigi.x/Pk2B,k¤i pkgk.x/C �2

(10)

here, pi is the transmission power of BS i and gi.x/ is thechannel gain between BS i and the user at location x.

Then the average DL traffic load density at location x ofBS i is derived as follows:

%di .x/ D

�.x/�.x/yi.x/

rdi .x/

(11)

Based on the DL traffic load density, the DL traffic loadof BS i is given by

�di D

ZL%d

i .x/dx (12)

Similarly, with Rdi denoted as the DL backhaul data rate

of BS i, the average DL backhaul traffic load density atlocation x of BS i is

Q%di .x/ D

�.x/�.x/yi.x/

Rdi

(13)

And then the DL backhaul traffic load of BS i is expressedas follows:

Q�di D

ZLQ%d

i .x/dx (14)

As such, the set F of the feasible user association y isgiven by

F D˚yj0 6 �d

i 6 1 � ", 0 6 Q�di 6 1 � ",

0 6 �ui 6 1 � ", 0 6 Q�u

i 6 1 � ",Pi2B yi.x/ D 1, yi.x/ 2 f0, 1g ,8i, 8x

o (15)

where " is an arbitrarily small positive constant to ensure�d

i < 1, Q�di < 1, �u

i < 1 and Q�ui < 1.

2.2. Power consumption model

The considered power consumption in this paper com-prises the on-grid power consumed by all the BSs in DLtransmission and the overall power consumption of users inUL transmission.

2.2.1. Downlink power consumption model.

We assume that both MBSs and PBSs in the HetNetsare powered by hybrid energy sources: power grid andrenewable energy sources. If the green power harvestedfrom renewable energy sources is not sufficient, BSs will


D. Liu et al.

consume the power from power grid. Because of the dis-advantage of ‘banking’ green power [24], here we assumethat the green power cannot be stored.

Generally, BSs consist of two types of power con-sumptions: static power consumption and adaptive powerconsumption. Adaptive power consumption is nearly lin-ear to the loads of BSs [25]. The static power consumptionis mainly caused by real-time A/D and D/A process-ing, air conditioning and so on, which is independentwith traffic load. For the sake of energy saving, someBSs can be switched into sleep mode with negligiblepower consumption †.

Here, we adopt the linear approximation in [25] to modelthe BS power consumption when this BS is switched intoactive mode, with Pi denoted as the total power consump-tion of BS i:

Pi D i�di pi C Ps

i (16)

where i is the slope of load-dependent power consump-tion of BS i, �d

i is the DL traffic load of BS i, andpi and Ps

i are the transmission power and static powerconsumption of BS i, respectively. It is worthwhile men-tioning that the small BSs such as PBSs and femto BSsmay have smaller static power consumptions than those ofMBSs because they have neither big power amplifiers norcooling equipments.

Then we denote Pgi as the green power of BS i harvested

from renewable energy sources, and the DL on-grid powerconsumption of BS i is expressed as follows:

Pgridi D max

�Pi � Pg

i , 0�

(17)

2.2.2. Uplink power consumption model.

The UL power consumption of user at location x isdetermined by

pu.x/ DX

i2Bpu

i .x/%ui .x/ (18)

Then the overall UL power consumption of users in theHetNets area is

Pu D

ZL

pu.x/dx (19)

3. PROBLEM FORMULATION

We formulate the user association problem as a con-vex optimisation problem, which aims to reduce overallUL power consumption of users, and achieve DL on-grid power saving by optimising the utilisation of greenpower harvested from renewable energy sources, as well asenhance network QoS by minimising UL and DL average

†It is assumed that when the BS is in sleep mode, it acts as a pas-

sive node and listens to the pilot transmission from users for channel

estimation, which consumes negligible power consumption compared

with being in active mode with data transmission. It is further assumed

that BS can switch between active and sleep modes frequently [14].

traffic delay. Our problem is to find optimal user asso-ciation y that minimises the total system cost, which isgiven by

miny

nf .y/ D ' .y/C !

�d .y/C !p

u .y/�jy 2 F

o(20)

where ' .y/ is the cost of average traffic delay, d .y/ isthe cost of DL on-grid power consumption and u .y/ isthe cost of overall UL power consumption of users. ! > 0is the relative weight to balance the trade-off between aver-age traffic delay and power consumption. Larger ! willlead to more emphasis on the power consumption to reduceboth the DL on-grid power consumption and UL powerconsumption of all users, while smaller ! will attach moreimportance to network QoS in order to decrease both ULand DL average traffic delays. !p is the relative weightbetween DL on-grid power consumption and UL powerconsumption of all users. Compared with the BS, the enduser generally has more limited power supply. As such, wenormally set !p > 1 to pay more attention on UL powersaving of all users.

3.1. Cost function of average traffic delay

We define the cost function of average traffic delay as thesum of DL wireless access delay �d

i , DL backhaul delayQ�di , UL wireless access delay �u

i and UL backhaul delay Q�ui ,

which is given by

' .y/ DXi2B

��d

i

��d

i

�C Q�d

i

�Q�di

�C �u

i

��u

i

�C Q�u

i

�Q�ui

��(21)

where �di

��d

i

�D �d

i

ı�1 � �d

i

�, Q�d

i

�Q�di

�D Q�d

i

.�1 � Q�d

i

�,

�ui

��u

i

�D �u

i

ı�1 � �u

i

�and Q�u

i

�Q�ui

�D Q�u

i

.�1 � Q�u

i

�.

Because users associated with the same BS are assumedto be served on a round robin fashion, when we considerthe system as M/GI/1 multi-class processor sharing sys-tem in [26], �d

i

ı�1 � �d

i

�is equal to the average number

of DL flows at BS i to be transmitted to users. Accord-ing to Little’s law, minimising the average number of flowsis equivalent to minimising the average delay experiencedby a typical traffic flow. Similarly, Q�d

i

�Q�di

�, �u

i

��u

i

�and

Q�ui

�Q�ui

�are modelled as average number of DL flows at

BS i’s backhaul, average number of UL flows at BS ifrom users and average number of UL flows at BS i’sbackhaul, respectively.

3.2. Cost function of power consumption

We define the green traffic load as the maximum DL trafficload that can be supported by the green power harvestedfrom renewable energy sources. Based on Equation (17),the green traffic load of BS i is derived as follows:


D. Liu et al.

Figure 3. Cost of downlink on-grid power consumption with different values of ˇ and ı.

�gi D max

", min

Pg

i � Psi

ipi, 1 � "

!!(22)

note that " is an arbitrarily small positive constant to ensure0 < �g

i < 1.According to Equation (17), DL on-grid power is only

consumed when green power is not sufficient. Thus, whenthe DL traffic load of BS i exceeds the amount of greentraffic load, that is, �d

i > �gi , DL on-grid power will be

consumed, which leads to the increase in the cost of DL on-grid power consumption. Otherwise, the cost of DL on-gridpower consumption will stay trivial. In doing so, the costfunction of DL on-grid power consumption is designed asfollows:

d .y/ DX

i2Bd

i .yi/ DX

i2Bı exp

ˇ�d

i

�gi

!(23)

where ˇ represents the network sensitivity towards DL on-grid power consumption (ˇ > 0) and ı aims to adjust thevalue of cost function (ı > 0). Figure 3 shows the curvesof cost function of DL on-grid power consumption ver-sus �d

i

ı�

gi with different values of ˇ and ı. It is shown

that with proper values of ˇ and ı, such as ˇ D 6 andı D 10�4, which we adopt in this paper, the cost func-tion of DL on-grid power consumption has the followingproperty: when �d

i

ı�

gi > 1, d

i .yi/ increases exponen-tially with the rise of �d

i and when 0 < �di

ı�

gi < 1, d

i .yi/

remains almost zero. Such a property encourages the gooduse of the green power harvested from renewable energysources, in order to reduce DL on-grid power consumption.Note that if the harvested green power of BS i is smallerthan its static power consumption, we will set �g

i D ". Inthis case, any traffic load will cause huge DL on-grid powerconsumption cost, thereby resulting in fewer users associ-ated with BS i and even turning BS i into sleep mode withno associated users.

Without loss of generality, for the cost of overall ULpower consumption of users, we just define u .y/ D Pu.

The larger overall UL power consumption of users willincur larger cost.

4. PROPOSED USER ASSOCIATIONALGORITHM

In this section, we propose the user association algorithm,which achieves the global optimum in minimising the totalsystem cost f .y/. The proposed user association algorithmis implemented in an iterative manner: BSs periodicallymeasure and advertise their loads, and then users make userassociation decision based on the advertised informationto minimise f .y/. The BS and user sides update itera-tively until convergence. The proposed user associationalgorithm is totally distributed. Through the interactionbetween BSs and users may incur overhead on controlinformation exchange, the proposed algorithm does notrequire any centralised computation, as such it will notincur algorithmic complexity issue here.

In order to guarantee convergence, we assume that spa-tial load distributions in the HetNets area are temporallystationary, and the time scale of users making user associ-ation decisions is faster than that of BSs advertising theirloads. In this case, BSs advertise their load conditions afterthe system remains stationary. We also assume that thegreen power of every BS is constant during the period ofdetermining user association. Such an assumption is feasi-ble. From statistics in real networks [27], the green powergeneration rate varies over time but could be assumedalmost constant during a certain period, for example, 1 h,which is definitely much larger than that of traffic requestarrival and departure process, for example, typically lessthan several minutes [16].

Because yi.x/ 2 f0, 1g, f .y/ is not continuously dif-ferentiable. In order to derive the optimal user associationalgorithm, we relax the feasible set by letting 0 6 yi.x/ 61; here, yi.x/ that specifies the probability of user at loca-tion x is associated with BS i. As such, the relaxed feasible


D. Liu et al.

set of user association is

_F D

nyj0 6 �d

i 6 1 � ", 0 6 Q�di 6 1 � ",

0 6 �ui 6 1 � ", 0 6 Q�u

i 6 1 � ",Pi2B yi.x/ D 1, 0 6 yi.x/ 6 1,8i, 8x

o (24)

Lemma 1. The relaxed feasible set of user association_F

is convex.

Proof. This lemma can be proved by the fact that_F is

composed of any convex combination of the user associa-tion y . �

Remark 1. Although we relax the original determinis-tic user association F to probabilistic user association QF ,the proposed user association algorithm determines theoptimal deterministic user association, where yi.x/ will beeither 0 or 1. This will be made clear in the proof ofTheorems 1 and 2.

We define the time interval between two consecutivetraffic load advertisements as an iteration. If the �d,.k/

i ,

Q�d,.k/i , �u,.k/

i and Q�u,.k/i represent the DL traffic load, DL

backhaul traffic load, UL traffic load and UL backhaul traf-fic load of BS i at kth iteration, respectively, and y.k/i .x/ isthe user association indicator of user at location x at kthiteration, we can obtain

df .y/

dy.k/i .x/D�.x/�.x/

rdi .x/

��

d,.k/i C rd

i .x/ Q�d,.k/i

�

C�.x/�.x/

rui .x/

��

u,.k/i C ru

i .x/ Q�u,.k/i

� (25)

where

�d,.k/i D

�1 � �d,.k/

i

��2C!ˇı

�gi

exp

ˇ�

d,.k/i

�gi

!(26)

Q�d,.k/i D

�1 � Q�d,.k/

i

��2�Rd

i

��1(27)

�u,.k/i D

�1 � �u,.k/

i

��2C !!ppu

i .x/ (28)

Q�u,.k/i D

�1 � Q�u,.k/

i

��2 �Ru

i

��1 (29)

4.1. Procedure of the proposed userassociation algorithm

The proposed user association algorithm consists of twoparts:

User side: During the kth iteration, users obtain the traf-

fic loads �d,.k/i , Q�d,.k/

i , �u,.k/i and Q�u,.k/

i , 8i 2 B of allthe BSs via the broadcast. And then the user at location x

chooses the optimal BS by

j.k/.x/ D arg maxi2B

rdi .x/r

ui .x/�

�d,.k/i Crd

i .x/ Q�d,.k/i

�ru

i .x/C˛.x/��

u,.k/i Cru

i .x/ Q�u,.k/i

�rd

i .x/

(30)

where ˛.x/ D �.x/=�.x/, which is the ratio of UL and DLmean traffic size.

Then the user association indicator is updated by

_y.k/

i .x/ D

�1, if i D j.k/.x/0, otherwise

(31)

Based on the updated user association indicator, usersbroadcast their user association indicators to all the BSsas follows:

y.kC1/i .x/ D .1 � &/

_y.k/

i .x/C &y.k/i .x/ (32)

where 0 6 & < 1 is the exponential averaging parameter.BS side: The updated advertising user association indi-

cators from the user side will change the loads of BSs,and then BS i updates the next advertising traffic loadas follows:

�d,.kC1/i D min

ZL

�.x/�.x/y.kC1/i .x/

rdi .x/

dx, 1 � "

!(33)

Q�d,.kC1/i D min

ZL

�.x/�.x/y.kC1/i .x/

Rdi

dx, 1 � "

!(34)

�u,.kC1/i D min

ZL

�.x/�.x/y.kC1/i .x/

rui .x/

dx, 1 � "

!(35)

Q�u,.kC1/i D min

ZL

�.x/�.x/y.kC1/i .x/

Rui

dx, 1 � "

!(36)

4.2. Existence of optimal solution

Lemma 2. A unique user association y� exists to min-imise f .y/ D ' .y/C !

�d .y/C u .y/

�.

Proof. The objective function f .y/ is a convex function

of y , when y is defined on_F , because r2f .y/ > 0, when

y 2_F . As such, there exists a unique optimal y� that

minimises f .y/. �

4.3. Convergence of the proposed userassociation algorithm

We denote_y.k/

D

�_y.k/

i ji 2 B�

, where_y.k/

i D�_y.k/

i .x/j_y.k/

i .x/ D f0, 1g , x 2 L�

, y.k/ D

�y.k/i ji 2 B

�,

where y.k/i Dny.k/i .x/j0 6 y.k/i .x/ 6 1, x 2 L

o.


D. Liu et al.

Lemma 3. When_y.k/¤ y�,

_y.k/� y.k/ is a descent

direction of f .y.k//.

Proof. This lemma can be proved by deriving�rf .y.k//,

_y.k/� y.k/

6 0.

�rf .y.k//,

_y.k/� y.k/

DRLP

i2Bh��.x/�.x/

ırd

i .x/��

d,.k/i C rd

i .x/ Q�d,.k/i

�C��.x/�.x/

ıru

i .x/� ��

u,.k/i C ru

i .x/ Q�u,.k/i

��

_y.k/i .x/ � y.k/i .x/

��dx

DRL �.x/�.x/

Pi2B

h��

d,.k/i C rd

i .x/ Q�d,.k/i

�.rd

i .x/

C˛.x/��

u,.k/i C ru

i .x/ Q�u,.k/i

�.ru

i .x/�

�

_y.k/i .x/ � y.k/i .x/

��dx

(37)

Note that Equation (38) holds, because_y.k/

i .x/derived from Equations (30) and (31) maximisesh��

d,.k/i C rd

i .x/ Q�d,.k/i

�rd

i .x/�1 C ˛.x/

��

u,.k/i C ru

i .x/

Q�u,.k/i

�ru

i .x/�1i�1

, for all i 2 B. Hence,

�rf .y.k//,

_y.k/

�y.k/E6 0. �

Pi2B

��

d,.k/i Crd

i .x/ Q�d,.k/i

�rd

i .x/C˛.x/

��

u,.k/i Cru

i .x/ Q�u,.k/i

�ru

i .x/

!_y.k/

i .x/ 6Pi2B

��

d,.k/i Crd

i .x/ Q�d,.k/i

�rd

i .x/C˛.x/

��

u,.k/i Cru

i .x/ Q�u,.k/i

�ru

i.x/

!y.k/i .x/

(38)

Theorem 1. The user association y converges to y� 2F that minimises f .y/.

Proof. Because of y.kC1/i .x/ � y.k/i .x/ D .1 � /

_y.k/

i .x/

C y.k/i .x/ � y.k/i .x/ D .1 � /

_y.k/

i .x/ � y.k/i .x/

�and

0 6 < 1, y.kC1/ � y.k/ is also a descent direc-tion of f

�y.k/

�according to Lemma 3. Based on

Lemma 2 where f�y.k/

�is a convex function and is

lower bounded by 0, we conclude that f�y.k/

�con-

verges. Suppose that f�y.k/

�converges to some point

other than f .y�/, then y.kC1/ produces a descentdirection again, which means that f

�y.k/

�can fur-

ther decrease in the next iteration. This contradicts theconvergence assumption. As such, y.k/ converges toy�. Because y.k/ is derived based on Equations (30)–

(36), where_y.k/

i .x/ D f0, 1g, y� is in the feasibleset F . �

4.4. Optimality of the proposed userassociation algorithm

Theorem 2. Suppose that the user association prob-lem is feasible, the deterministic user association y� D˚y�i ji 2 B

, where yi

� D fyi�.x/jyi

�.x/ D f0, 1g , x 2 Lg,is the optimal solution to the user association problem.

Proof. Because f .y/ is a convex function over a convex

set_F , if yi

� satisfies the following conditions,

˝rf�y��

, y � y�˛> 0 (39)

for all y 2_F ny�, then y� is the optimal solution for the

user association problem.Based on Equations (30)–(32) and Theorem 1, we can

conclude that the converged user association is determinis-tic, that is,

y�i .x/ D 1˚i D j�.x/

(40)

where

j�.x/ D arg maxi2B

rdi .x/r

ui .x/�

�d,�i Crd

i .x/ Q�d,�i

�ru

i .x/C˛.x/.�u,�i Cru

i .x/ Q�u,�i /rd

i .x/

(41)

And then the inner product can be computed as follows:

hrf .y�/ ,y � y�i

DRLP

i2Bh��.x/�.x/

ırd

i .x/��

d,�i C rd

i .x/ Q�d,�i

�C��.x/�.x/

ıru

i .x/� ��

u,�i C ru

i .x/ Q�u,�i

�� .yi.x/ � yi

�.x//� dx

DRL �.x/�.x/

Pi2B

h��

d,�i C rd

i .x/ Q�d,�i

�.rd

i .x/

C˛.x/��

u,�i C ru

i .x/ Q�u,�i

�ıru

i .x/�

� .yi.x/ � yi�.x//� dx

(42)Note that

Pi2B

��

d,�i Crd

i .x/ Q�d,�i

�rd

i .x/C˛.x/.�u,�

i Crui .x/ Q�

u,�i /

rui .x/

!yi.x/

>Pi2B

��

d,�i Crd

i .x/ Q�d,�i

�rd

i .x/C˛.x/.�u,�

i Crui .x/ Q�

u,�i /

rui .x/

!yi�.x/

(43)

holds, and thus, hrf .y�/ , y � y�i > 0. Therefore, thedeterministic user association y� is the optimal solution ofthe user association problem. �

Remark 2. The optimisation problem (20) is combina-tional because of the binary variable yi.x/. The complexity


D. Liu et al.

of the centralised brute-force algorithm is O�jBjjU j

�, with

jU j denoted as the total number of users in the HetNetsarea at one time. Such complexity is impossible even fora modest-sized network. Furthermore, centralised algo-rithm requires global network information and centralisedcontroller for coordination, and the amount of exchangedinformation is proportional to .jBj � jU j/. On the contrary,the computational complexity of the proposed distributeduser association algorithm for an individual user is O .jBj/in each iteration. As for the exchanged information, in

each iteration, each BS broadcasts �di , Q�d

i , �ui and Q�u

i ,and each user feedbacks its association request only tothe chosen BS. Thus, the exchanged information in theproposed distributed algorithm is .jBj C jU j/ for each iter-ation. According to [17], although the convergence speeddepends on the value of exponential averaging parame-ter & , fixed & close to 1 generally works well for theconvergence. However, how to optimise & is beyond thescope of this paper. In our simulation, we set & D 0.98;simulation results have shown that our proposed user asso-ciation algorithm converges quickly to the optimum, within150 iterations.

Remark 3. Up till now, we consider the condition wherethe optimisation problem (20) is feasible, that is, the fea-

sible set F is not empty with �di 6 1 � ", Q�d

i 6 1 �", �u

i 6 1 � ", Q�ui 6 1 � ", 8i 2 B. However, in the cir-

cumstance when the optimisation problem (20) is notfeasible because of high traffic load, the admission con-trol is required. In this case, the admission control with theobjective to minimise the sum cost of average traffic delay,power consumption and blocking traffic can be formu-lated with the similar approach in our previous work [18],where a threshold is used to determine whether a particu-lar user should be blocked or not, and the user associationalgorithm stays intact as the algorithm presented earlier inthis section.

5. SIMULATION RESULTS

To evaluate the performance of the proposed user associa-tion algorithm (proposed joint UL–DL UA), we simulate aHetNet composed of 19 macrocells. In each macrocell, sixPBSs are symmetrically located along a circle with radiusas 200 m and MBS in the centre. We assume that the greenpower of every BS is constant during a snapshot of simula-tion. As for the traffic model, for the sake of simplicity, wesimulate that the file transfer requests follow a homogenousPoisson point process where �.x/ D �, but note that ourmodel can still apply to the scenario with heterogeneoustraffic distributions. In the simulation, we assume that eachBS has the same UL and DL backhaul data rate. Withoutspecific indication, the backhaul data rates of MBS andPBS are defined as 100 and 60 Mbps, respectively [28].Each UL and DL request is assumed to have exactly onefile with mean file size � as 80 Kbits and � as 100 Kbits,as generally there is more traffic in DL than that in UL. Aswe adopt TDD to separate UL and DL transmissions, thereis channel reciprocity between UL and DL transmissions.

The other simulation parameters are shown in Table I.We first set the weight ! between cost of average traf-

fic delay and power consumption as 10�1, and the trafficarrival rate as 1.2. Figure 4 compares the snapshot of theresulting user association pattern in one macrocell areain different scenarios with different distributions of greenpower harvested from renewable energy sources as definedin Table II. In scenario 2, the green powers of all the PBSsare the same as those in scenario 1, except that the greenpower of MBS is lower than that in scenario 1. Figure 4shows that compared with scenario 2, more users are asso-ciated with MBS in scenario 1, where MBS has largergreen power. This figure indicates that the proposed algo-rithm is able to adapt the traffic loads among BSs alongwith the distribution of green power, in order to makegood use of the renewable energy and reduce DL on-gridpower consumption. In scenario 3, the green power of

Table I. Simulation parameters.

Parameter Value

Bandwidth 10 MHzInter-site distance 500 mTransmission power of MBS 46 dBmTransmission power of PBS 30 dBmMaximum transmission power of user 23 dBmNoise power �174 dBm/HzWeight of UL/DL power consumption !p 100Pathloss between MBS and user 128.1C 37.6log10d (km) [29]Pathloss between PBS and user 140.7C 36.7log10d (km) [29]Log-normal shadowing fading 10 dB [29]Static power consumption of MBS 780 W [25]Static power consumption of PBS 13.6 W [25]Slope of MBS load-dependent power 4.7 [25]Slope of PBS load-dependent power 4.0 [25]

DL, downlink; UL, uplink; BS, base station; MBS, macro-BS; PBS, pico BS.


D. Liu et al.

Figure 4. Snapshot of user association pattern: scenarios (a) 1, (b) 2 and (c) 3. BS, base station; MBS, macro BS; PBS, pico BS.

Table II. Green power distribution in different scenarios.

Scenario MBS (W) PBS1 (W) PBS2 (W) PBS3 (W) PBS4 (W) PBS5 (W) PBS6 (W)

1 974 33 32 33 31 32 332 870 33 32 33 31 32 333 870 33 32 10 31 32 33

BS, base station; MBS, macro BS; PBS, pico BS.

Figure 5. Cost of average traffic delay versus different numbers of iteration.

PBS3 is 10 W, which is lower than the static power con-sumption. We can observe from Figure 4(c) that there isno user associated with PBS3, leading to PBS3 switchedinto sleep mode. As such, our proposed algorithm is capa-ble of controlling the BS on/off dynamically according tothe available amount of green power, thereby undisputedlyreducing the DL on-grid power consumption effectively.

In the following simulation, we evaluate the perfor-mance of the proposed joint UL–DL UA in scenario 2.

Figures 5 and 6 demonstrate the cost of averagetraffic delay '.y/ and cost of power consumption�d.y/C u .y/

�with different values of weight !,

respectively. We can observe that with the increase ofweight !, the cost of average traffic delay rises and thecost of power consumption decreases. The larger weight !will lead to more emphasis on the power saving in orderto minimise DL on-grid power consumption and overall

UL power consumption of users, while the smaller weight! will attach more importance to the average traffic delayminimisation. This figure indicates that the weight ! inthe proposed joint UL–DL UA could adjust the trade-off between average traffic delay and power consumption.Note that such trade-off graph may also be used to choosethe value of ! in practice based on the maximum tolerabletraffic delay. From Figures 5 and 6, we can also obtain theconvergence of the proposed joint UL–DL UA. It is shownthat the proposed algorithm converges quickly to the globaloptimum within less than 150 iterations.

In the subsequent simulation, we set ! D 10�1. In orderto better benchmark the performance of the proposed jointUL–DL UA, we also implement two baseline algorithms:the max RSRP user association (max RSRP UA) and theuser association for DL delay-power trade-off (DL-onlyUA). Max RSRP UA is the conventional user association


D. Liu et al.

Figure 6. Cost of power consumption versus different numbers of iteration.

Figure 7. UL average traffic delay versus different pico BS backhaul data rates. UL, uplink; DL, downlink; RSRP, reference signalreceived power; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power trade-off; joint UL–DL

UA, proposed user association algorithm.

policy, where a user will associate with the BS from whichit receives the highest RSRP. In DL-only UA, user asso-ciation is determined to achieve the trade-off between DLaverage traffic delay and DL on-grid power consumptionwithout considering the UL transmission, or equivalently,the DL-only UA aims to minimise the system cost, whichis given by

f .y/ DX

i2B

��d

i .y/CQ�di .y/

�C !d.y/ (44)

Figures 7–10 compare the performance of these threealgorithms with different backhaul data rates of PBS.Figures 7 and 8 show the UL and DL average traffic delay,including both the wireless access and backhaul delays,and different backhaul data rates of PBS, respectively. Boththe UL and DL average traffic delays decrease with theincrease of PBS backhaul rate. When the backhaul data rateof PBS is very small, say 1 Mbps in our simulation, theaverage traffic delay differences of these three algorithmsare not distinct. This is because PBSs are easily congested

by relatively light traffic load, due to the low backhauldata rate. In this sense, because both the DL-only UA andproposed joint UL–DL UA are backhaul aware, they willassociate fewer users with PBSs in order to avoid PBS con-gestion, thereby achieving the similar effect with the maxRSRP UA, which associates most of users with the macro-cell due to the transmission power disparity between MBSand PBS. However, with the increase of PBS backhauldata rate, the backhaul data rate is no longer the bottle-neck. As such, both the backhaul-aware DL-only UA andproposed joint UL–DL UA are able to offload more usersfrom macrocells, achieving much less average traffic delaythan that of max RSRP UA. We can also observe fromFigures 7 and 8 that the proposed joint UL–DL UA issuperior to the DL-only UA in terms of UL average traf-fic delay but obtains inferior DL average traffic delay. Itcan be explained by the fact that with the consideration onboth UL and DL transmissions, the proposed joint UL–DLUA trades the DL average traffic delay for the UL averagetraffic delay, to achieve the optimal overall delay reduction.


D. Liu et al.

Figure 8. DL average traffic delay versus different pico BS backhaul data rates. UL, uplink; DL, downlink; RSRP, reference signalreceived power; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power trade-off; joint UL–DL


Figure 9. Overall UL power consumption of users versus different pico BS backhaul data rates. UL, uplink; DL, downlink; RSRP,reference signal received power; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power

trade-off; joint UL–DL UA, proposed user association algorithm.

Figure 10. DL on-grid power consumption versus different pico BS backhaul data rates. UL, uplink; DL, downlink; RSRP, referencesignal received power; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power trade-off; joint

UL–DL UA, proposed user association algorithm; SINR, signal-to-interference-plus-noise ratio.


D. Liu et al.

Figure 11. UL average traffic delay versus different traffic arrival rates. UL, uplink; DL, downlink; RSRP, reference signal receivedpower; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power trade-off; joint UL–DL UA,

proposed user association algorithm.

Figure 12. DL average traffic delay versus different traffic arrival rates. UL, uplink; DL, downlink; RSRP, reference signal receivedpower; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power trade-off; joint UL–DL UA,

proposed user association algorithm.

Figure 13. Overall UL power consumption of users versus different traffic arrival rates. UL, uplink; DL, downlink; RSRP, referencesignal received power; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power trade-off; joint

UL–DL UA, proposed user association algorithm.


D. Liu et al.

Figure 14. DL on-grid power consumption versus different traffic arrival rates. UL, uplink; DL, downlink; RSRP, reference signalreceived power; max RSRP UA, max RSRP user association; DL-only UA, user association for DL delay-power trade-off; joint UL–DL


Figures 9 and 10 show the overall UL power consump-tion of users and DL on-grid power consumption versusdifferent backhaul data rates of PBS, respectively. The DLon-grid power consumption that we plotted here is thesum DL on-grid power consumption of all the BSs in onemarcocell area. For max RSRP UA, both the overall ULpower consumption of users and DL on-grid power con-sumption do not change with the PBS backhaul data rate,because max RSRP UA does not take backhaul data rateas a metric when making the user association decision.For both the DL-only UA and proposed joint UL–DL UA,the overall UL power consumption of users and DL on-grid power consumption decrease with the increment ofthe backhaul data rate of PBS. With larger PBS backhauldata rate, more users will be offloaded from the con-gested macrocell, resulting in the load balancing and powersaving throughout the whole network. We also obtain aninteresting observation that the proposed joint UL–DLUA outperforms the DL-only UA in terms of both theoverall UL power consumption and DL on-grid powerconsumption reductions.

Figures 7–10 also demonstrate that when the PBS back-haul data rate exceeds some point (20 Mbps in our sim-ulation), the UL and DL average traffic delays changeslightly with the increase of PBS backhaul data rate, andthe DL on-gird power consumption and UL power con-sumption stay almost the same with the rise of PBSbackhaul data rate. This is because when the PBS back-haul data rate is large enough, it is no longer the bottle-neck for network performance. As such, the increase ofPBS backhaul data rate will not affect the resulting userassociation pattern.

Finally, Figures 11–14 compare the performance ofthese three algorithms with different traffic arrival rates.Figures 11, 12, 13 and 14 demonstrate the UL averagetraffic delay, DL average traffic delay, overall UL powerconsumption of users and DL on-grid power consumptionversus different traffic arrival rates, respectively. It is

easy to understand that the increasing traffic arrivalrate will bring in larger average traffic delay andmore power consumption. Whatever the traffic arrivalrate is, the proposed joint UL–DL UA achieves com-parable DL average traffic delay compared with theDL-only UA while effectively reducing the UL aver-age traffic delay, achieving DL on-grid power conser-vation and saving the overall UL power consumptionof users.

6. CONCLUSIONS

In this paper, we have proposed an optimal backhaul-aware joint UL and DL user association for delay-powertrade-offs in HetNets with hybrid energy sources, whereall the BSs are assumed to be powered by both thepower grid and renewable energy sources. With the con-vex optimisation problem formulation, we have provedthat the proposed user association algorithm converges tothe global optimum, which minimises the weighted sumof cost of average traffic delay and cost of power con-sumption. The proposed user association algorithm allowsfor a flexible trade-off between average traffic delay andpower consumption by adjusting the value of weight !.Simulation results demonstrate that the proposed algo-rithm is capable of adapting the loads of BSs along withthe distribution of green power and the PBS backhauldata rate, thereby effectively reacting to random greenpower availability in BSs and PBS backhaul constraints.Simulation results also validate the merits of the pro-posed user association algorithm in not only effectivelyreducing UL average traffic delay, overall UL power con-sumption of users and DL on-grid power consumption butalso achieving comparable DL average traffic delay, com-pared with the user association algorithm only based onDL performance.


D. Liu et al.

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Backhaul aware joint uplink and downlink user association