Energy Efficient Inter-Frequency Small Cell Discovery in ...arately allocated to the small cell and macro cell layers or co-channel deployment scenario, where the small cell and macro

0018-9545 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. Seehttp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/TVT.2015.2482818, IEEE Transactions on Vehicular Technology

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Energy Efficient Inter-Frequency Small CellDiscovery in Heterogeneous Networks

Oluwakayode Onireti,Member, IEEE,Ali Imran, Member, IEEE, Muhammad Ali Imran,Senior Member, IEEEand Rahim Tafazolli,Senior Member, IEEE

Abstract—In this paper, using stochastic geometry, we inves-tigate the average energy efficiency (AEE) of the user terminal(UT) in the uplink of a two-tier heterogeneous network (HetNet),where the two tiers are operated on separate carrier frequencies.In such a deployment, a typical UT must periodically performinter-frequency small cell discovery (ISCD) process in order todiscover small cells in its neighborhood and benefit from thehigh data rate and traffic offloading opportunity that small cellspresent. We assume that the base stations (BSs) of each tier andUTs are randomly located and we derive the average ergodic rateand UT power consumption, which are later used for our AEEevaluation. The AEE incorporates the percentage of time a typicalUT missed small cell offloading opportunity as a result of theperiodicity of the ISCD process. In addition to this, the additionalpower consumed by the UT due to the ISCD measurement is alsoincluded. Moreover, we derive the optimal ISCD periodicity basedon the UT’s average energy consumption (AEC) and AEE. Ourresults reveal that ISCD periodicity must be selected with theobjective of either minimizing UT’s AEC or maximizing UT’sAEE.

Index Terms—Heterogeneous cellular network, stochastic ge-ometry, fractional power control, small cell discovery, energyefficiency.

I. I NTRODUCTION

To meet the exponentially growing capacity demands, thefuture of cellular networks is marked by heterogeneous de-ployments consisting of legacy macro cells with overlaid orunderlaid small cells [1]–[7]. Small cell enhancement couldeither be a scenario where different frequency bands are sep-arately allocated to the small cell and macro cell layers or co-channel deployment scenario, where the small cell and macrocell layers share the same carrier [2]–[4], [8]. It is expectedthat in the future, small cells will operate on dedicated higherfrequency bands, such as3.5, 5 and beyond5 GHz bands,where new licensed spectrum is expected to be available [1],[4], [8]. Since small cells have smaller coverage footprint, theydo not suffer from the high propagation loss which such bandcauses to macro cells. Furthermore, cross-tier interference isavoided by operating the small cells on the dedicated higher

Copyright (c) 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

O. Onireti, M. A. Imran and R. Tafazolli are with the Institute forCommunication Systems (ICS), University of Surrey, Guildford GU2 7XH,UK (e-mail: {o.s.onireti, m.imran, r.tafazolli}@surrey.ac.uk).

A. Imran is with Telecommunications Engineering, University of Okla-homa, Tulsa, OK, USA (e-mail: [email protected]).

This work was made possible by NPRP grant No. 5-1047-2437 from theQatar National Research Fund (a member of The Qatar Foundation). Thestatement made herein are solely the responsibility of the authors. Moreinformation about this project can be found at www.qson.org.

frequency bands, thus leading to an improvement in spectralefficiency [4]. The use of such bands for small cell canalso lead to a significant increase in capacity, since they canoffer larger bandwidths. Hence, small cells can provide highdata rate to hot spots while also offering traffic offloadingopportunity, which can be boosted by incorporating rangeexpansion bias [5], [6].

In the deployments where different frequency bands are sep-arately allocated to the small cell and macro cell layers, userterminals (UTs) connected to the macro cell must periodicallyscan for suitable small cells in their neighborhood in orderto benefit from the high data rate and the traffic offloadingopportunity which such offers. This can result in significantenergy consumption to the UT. The power limited nature of theUTs is major challenge in enabling truly broadband networks,hence; energy efficient discovery of small cells has beenidentified by3GPP as an important technical issue in carrier-frequency separated deployments [9]. Various inter-frequencysmall cell discovery (ISCD) mechanisms have been studiedin literature. Some of the proposed solutions for enhancingISCD include: UT speed based measurement triggering [10],[11], relaxed inter-frequency measurement gap [12], proximitybased ISCD [11], small cell signal based control measurementand small cell discovery signal in macro layer [3], [13]. Acommon feature in all the ISCD mechanisms is the periodicinter-frequency scanning and measurement by the UT, whichresults in significant UT energy consumption.

For a given small cell deployment density and UT speed,low ISCD periodicity (i.e. high scanning frequency) can resultin increased small cell offloading opportunity, thus enhancingthe capacity and coverage. However, this can also lead tohigher UT power consumption due to the high scanning fre-quency. Meanwhile, the UT’s transmit power can be reducedas a result of offloading to the small cells where lower transmitpower is required due to smaller cell radii. On the otherhand, high ISCD periodicity (i.e. low scanning frequency)can lead to the UT missing small cell offloading opportunity,thus resulting in a potential decrease in capacity. Most priorwork on ISCD in literature have focused only on the effectof ISCD periodicity on scanning power without evaluating theimpact of UT transmit power reduction when offloading to thesmall cells [10]–[12], [14]. In [14], a mobility aware handoverscheme for HetNets consisting of WiMAX and WiFi networkswas proposed. In their proposed scheme the UT intelligentlyselects a subset of the network to be scanned, thus savingUT energy consumption. Mobility based small-cell search hasbeen identified in [10], [11] as an approach that works well



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within the LTE-A deployment. It has also been shown in [11]that this approach can provide a savings of up to99% in UTbattery power consumption. Only recently, [15] considered UTtransmit power reduction as a result of offloading to the smallcell in their evaluation. However, the energy efficiency of thisscheme is yet to be investigated. Using stochastic geometry,an analytical framework was proposed in [16] to analyze thetrade-off between traffic offloading from the macro cells andthe energy consumption of cognitive small cell access points.

In this paper, we investigate the average energy efficiency(AEE) of a typical UT in the uplink of HetNet, where thesmall cells are deployed on carrier frequency other than thatof the serving macro cell and an ISCD scheme is utilized bythe UT. The AEE of a communication system is the averageamount of bits that can be delivered per joule consumedto do so, i.e. the ratio of the average ergodic rate to thetotal power consumed [17], [18]. The ergodic rate and thepower consumed by a typical UT depend on its association,which could be with either a macro cell or small cell. Hence,the AEE of a typical UT in a HetNet must be obtained bytaking the following into consideration: its average powerconsumption in the macro cell and small cell layers; its averageachievable rate in the macro cell or small cell layers; thepercentage of time it missed small cell offloading opportunityas a result of the ISCD periodicity and; the additional powerit consumes due to ISCD measurement. We model the BSlocations as random and drawn from spatial stochastic process,such as homogeneous Poison point process (PPP). In actualdeployment, small cells are usually unplanned; hence, theyare well modeled by the spatial random process [19]–[22].On the other hand, modeling macro cell BSs as PPP providelower bounds to the average rate and coverage probability ofreal deployment [23]. Repulsive point process such as Maternhard core point process (HCPP), which reflect the minimumseparation distance between BSs, provides a more realisticmodel but at the expense analytical tractability [24], [25].

In Section II, we first present the HetNet system model,which incorporates a range extension bias scheme to boost thesmall cell offloading potential. Next, we present the probabilityof UT’s association to a tier and the probability densityfunction (PDF) of the statistical distance between a typicalUT and it serving BS, which later serves as a basis for ourderivations. In Section III, we present the ISCD process andits implication in terms of the percentage of time a typical UTmissed small cell offloading opportunity. In Section IV, wederive the average UT power consumption and ergodic rate pertier, which are later used in Section V to evaluate its AEE. Wederive both the ideal and the realistic AEE of the typical UTin the uplink of the carrier frequency separated HetNet. Theideal AEE is based on an ideal UT association, where the UTassociates with the BS (small or macro cell) with the maximumbiased received power [6], [22], [26], [27]. On the otherhand, the realistic AEE is based on a realistic UT association,where UT association with the small cell is also dependenton the periodicity of the ISCD [11], [12], [15]. In Section VI,we first utilize a polynomial fitting method to approximatethe percentage of time the typical UT missed small celloffloading opportunity as a function of ISCD periodicity, for

a fixed UT speed and small cell density. Subsequently, byusing the approximated function, we derive the average energyconsumption (AEC) and AEE optimal ISCD periodicities, fora fixed UT speed and small density. Numerical results arepresented in Section VII. Results show that significant savingsin the UT’s AEC can be achieved by utilizing the optimalISCD periodicity. Furthermore, ISCD periodicity should be setbased on the target objective, which could be towards eitherAEC minimization or AEE maximization. Finally, conclusionsare drawn in Section VIII. A preliminary version of this workhas been reported in [28]. Herein, we have considered theinterference limited deployment with a cell range extensionbias scheme and UT power control.

II. SYSTEM MODEL

We consider a HetNet deployment which is made up of2tiers of BSs. The first tier represents macro cell layer whilethe second tier represents small cell layer. We consider thateach tier operates on a different carrier frequency and that eachtier is identified by its biasing factor, pathloss exponent and,its BSs transmit power and spatial density. The positions ofBSs in thejth tier are modeled according to a homogeneousPPPΦj with densityλj . Furthermore, a fully loaded networkwith one active uplink user per channel is assumed with theUTs locations approximated by a homogeneous PPPΦ(u)

with density λ(u), which is independent of{Φj}{j=1,2}. Itis also assumed that the density of the UTs is high enoughsuch that each BS in the network have a least one UTserved per channel. We consider that the received signals inthe jth tier are subject to pathloss, which we model usingthe pathloss exponentαj . The random channel variation ismodeled as Rayleigh fading with unit mean. We consider thatan orthogonal multiple access scheme is utilized within eachcell, such that there is no intra-cell interference. Furthermore,each of the BSs in thejth tier transmit the same power, i.e.Pj ,while the noise power is assumed to beσ2. In order to evaluatethe average UT transmit power, ergodic rate and AEE, weshift all point process such that a typical UT lies at the origin.Regardless of this shift, the homogeneous PPP distribution ofthe BSs remains preserved.

UT Association:Given thatk ∈ {1, 2} denotes the indexof the tier with which a typical user is associated and|Ski|is the distance between the typical UT, i.e., the origin andBS i ∈ Φk. Also the distance between the typical UT andthe nearest BS in thejth tier is denoted byDj . We considerthat the UT is associated with a cell based on the maximumbiased-received-power (BRP), i.e., the UT associates with thestrongest BS in terms of the long-term averaged BRP [22].The BRPs to the typical UT from the nearest BS in thejth

tier can be expressed as

Pr,j = PjL0

(Dj

d0

)−αjβj , (1)

whereL0 denotes the pathloss at a reference distanced0 andβj is the biasing factor, which is the same for all the BS in thejth tier. The biasing factor,βj , can be used to adjust the tier’sselection of UTs to allow for effective load balancing. Note



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that {βj}j=1,2 = 1 denotes the conventional cell association,where the UT connects to the BS that offers the highestaverage received power to the UT.

Distribution of the Distance between UT and Serving BS:Ithas been shown in [22, Lemma 3] that the probability densityfunction (PDF),fXk(x), of the distanceXk between a typicalUT and its serving BS in thekth tier based on the maximumBRP can be expressed as

fXk(x) =2πλkAkx exp

−π

2∑

j=1

λj

(Pj βj

)2/αjx2/αj

, (2)

whereAk, which is defined subsequently in (3), is the ideal-istic probability of the typical UT associating to thekth tier.

Idealistic Probability of UT Association to a Tier:In theideal settings, the UT associates with BSs based on themaximum BRP. In case of UT mobility, handover signalingoverhead and other mobility related overheads are not con-sidered. Furthermore, all handover associated time, such ashandover preparation time, handover execution time, time totrigger and the ISCD measurement time, are all equal to zero.Hence, in an ideal two-tier HetNet, the idealistic probabilitythat a typical UT is associated with a BS of thekth tier canbe expressed according to [22, Lemma 1] as

Ak = 2πλk

∫ ∞

0

r exp

−π

2∑

j=1

λj

(Pj βj

)2/αjr2/αj

dr, (3)

where Pj ,PjPk, βj ,

βjβk, αj ,

αjαk

. It follows that inan ideal UT association, the probability that a typical UTassociates with a tier is dependent on the BSs transmit powers,{Pj}j=1,2, densities{λj}j=1,2, and bias factors{βj}j=1,2.Moreover,Ak can be interpreted as the average fraction oftime that a typical UT is connected to the BSs belonging tothe kth tier [26]. Given the total timeT → ∞, the averagetime that the typical UT spends in the coverage of the macrocell (tier 1) and small cell (tier2) can be expressed as

T1 = A1T and

T2 = A2T , (4)

respectively, whereAk, ∀ k = {1, 2} is defined in (3).Realistic UT Association:In the realistic setting, a typical

UT that is connected to the macro cell must periodically scanfor suitable inter-frequency small cell (i.e. small cell withhigher BRP) before it can discover and offload its traffic (i.echange association) to such small cell. Hence, ISCD scanningand measurements are performed by UTs when associated withthe macro cell, at a network or UT specified periodicity. As aresult of the scanning periodicity and UT mobility, there existsa fraction of time,X , that the typical UT would miss small celloffloading opportunity. This implies that on the average, thetypical UT becomes connected to the macro cell forX morefraction of time that the small cell provides the maximum BRP.Hence, the average realistic time that the typical UT spendsin the macro cell coverage can be expressed from (4) as

T1 = A1T +A2TX = T (A1 +A2X ). (5)

Similarly, the average realistic time that the typical UT spendsin the small cell coverage can be expressed as

T2 = A2T −A2TX = (1−X )A2T. (6)

III. I NTER-FREQUENCYSMALL CELL DISCOVERY (ISCD)

A UT connected to the macro cell periodically scans itsneighbourhood to discover surrounding small cells. It alsoperforms inter-frequency measurements to ensure that it canconnect to another network when it finds a small cell witha higher BRP. The energy consumed for one inter-frequencysmall cell search can be expressed as

Et = PmTm, (7)

where Tm is the duration of the measurement andPm isthe power consumed by the UT for the measurement. Fora given deployment density,λj , having a high scanningfrequency results in a faster discovery of small cells andhence, increased small cell offloading opportunity, which leadsto increase in system level capacity. However, high scanningrate implies an increase in UT’s power consumption. On theother hand, reducing the scanning frequency results in the UTmissing small cell offloading opportunity, thus, leading to adecrease in system level capacity. Also, the typical UT cansignificantly reduce its transmit power when connected to thesmall cells. Consequently, there exists a scanning frequency,V ?, that achieves optimal performance in terms of averageUT energy consumption. If the scanning frequency is lessthan V ?, the small cells are not discovered on time, henceexcessive UT energy consumption as the UT spends moretime in macro cell coverage. On the other hand, excessiveenergy will be consumed in the search process if the scanningfrequency exceedV ?. The impact of the ISCD frequency,V ,or ISCD periodicity,V = 1

V, can be modelled in terms of

the percentage of time the UT missed small cell offloadingopportunity,X , as explained in the following.

Consider a typical UT moving according to a randomdirection mobility model with wrap around [29], [30]. Thetypical UT moves at a constant speedθ on [0, 1) according tothe following mobility pattern: A new direction or orientationis selected from(0, 2π] after the UT moves in a particulardirection or orientation for a durationς, hence, the selectionof the nth direction initializes thenth movement of the UT.The duration of each movementς is obtained as the timeduration for the UT to move (at a constant speedθ) betweentwo farthest points in the HetNet’s coverage. In order toobtainX , for a given UT speed, small cell density and ISCDperiodicity V = 1

V, we utilize the current3GPP standard

inter-frequency measurement of40 ms as our benchmark.For thenth movement with durationς, we estimate the timeduration that the UT spends in the coverage of the small cell,based on ISCD periodicityV and the standard inter-frequencymeasurement of40 ms, denoted byςnV andςn40ms, respectively.Hence, the average percentage of time the UT missed smallcell offloading opportunity,X , for a fixed UT speed,θ, andsmall cell densityλ2, can be expressed as

X = 1− E

[ςnVςn40ms

]

, (8)

whereE is the expectation operator.In Fig. 1, we plot the percentage of time the UT missed

small cell offloading opportunity,X , against the ISCD period-icity, V = 1

Vfor UT speed,θ = 3, 10, 20, 30 and 120 km/hr,



4

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

90

100

Fig. 1. Percentage of missed small cell offloading opportunity versussmall cell discovery periodicity for various UT speed,β1 = β2 =1, λ1 =

1π4002m2

, λ2 = 10λ1 and 20λ1, P1 = 46 dBm, P2 =26 dBm andα1 = α2 = 4 .

macro cell densityλ1 = 1π4002m2 , small cell densityλ2 =

10λ1 and20λ1, macro cell BS transmit powerP1 = 46 dBm,small cell BS transmit powerP2 = 26 dBm and pathlossexponentα1 = α2 = 4. It is obvious that if the scanningfrequency is increased, the UT would miss the small celloffloading opportunity for a lesser time since the discoveryprocess takes place more frequently at the time instance whenthe typical UT is in the coverage of the new small cell inits path. Also increasing the small cells density results in lesslikelihood for the typical UT to miss the small cell offloadingopportunity. In addition, as the UT speed increases, the UTmoves more quickly through the coverage of the small cell,hence an increase in the likelihood that the UT would missthe small cell offloading opportunity. Consequently, as the UTspeed increases, the percentage of time that the typical UTmissed the small cell offloading opportunity increases for anygiven ISCD periodicity, as illustrated in Fig. 1

IV. M ETRICS FORENERGY EFFICIENCY EVALUATION

Let R (bit/s) be the achievable rate andPT be thetotal power consumed for transmitting data at this rate, then,the AEE can be expressed in terms of the bit-per-Joule asCJ = R/PT . Hence both the power consumption model andthe achievable rate are essential in obtaining the AEE of acommunication system.

A. UT Power Consumption Model

The AEE of a communication system is closely related toits total power consumption. The power consumed by the UTis made up of the transmit power and the additional circuitpower incurred during transmission, which is independent ofthe transmission rate [31], [32]. If we denote the circuit power

asPc, the overall power consumption of the typical UT at adistancex from its serving BS can be expressed as

PTx = ΔPUx + Pc, (9)

where PUx is the transmission power of the typical UT,Δquantifies the UT power amplifier efficiency and it dependson the implementation and design of the transmitter [32].

Average UT Transmit Power in a Tier:Considering thatthe UT utilizes a distance-dependent fractional power control,hence the transmission power at a distancex to the BS inthe kth tier, PUx , is of the form P 0kx

αkτk , where P 0k is aparameter related to target mean received power (which isuser or network specific) in thekth tier, and τk ∈ [0, 1] isthe power control factor in thekth tier. Therefore, as thetypical UT moves closer to its associated BS, the transmitpower required to achieve the target received signal powerat the BS decreases. Hence, having smaller cells, where theUT can be closer to their serving BS as opposed to thetraditional macro deployment, is expected to yield a reductionin the transmission power. This is an important considerationin power limited devices such as the battery powered mobiledevices. The average transmit power of a typical UT in a tieris obtained by averagingPUx over the distancex (i.e., over thekth tier) and is thus expressed as

PUk = Ex[P 0kx

αkτk]

=

∫ ∞

0

P 0kxαkτkfXk(x)dx

(a)=2πλkP

0k

Ak

∫ ∞

0

x(1+αkτk)exp

−π

2∑

j=1

λj

(Pj βj

)2/αjx2/αj

dx(10)

where (a) follows from (2). If αj = α, ∀ {j = 1, 2}, theaverage transmit power of the typical UT over thekth tier issimplified according to [33, pp. 337] as

PUk =πλkP

0kΓ(1 + ατk2

)

Ak

πK∑

j=1

λj

(Pj βj

)2/α

(1+ατk2 )(11)

whereΓ denotes Gamma function. For the case without powercontrol, i.e.τk = 0, the average transmit power simplifies toP 0k in (10) and (11), respectively. Consequently, the averageoverall power consumption of the UT in thekth tier can beobtainedas

PTk = ΔPUk + Pc. (12)

B. Average Ergodic Rate of a Typical UT in a Tier

The associated signal-to-interference-plus-noise ratio(SINR) at the BS in thekth tier, which is at a randomdistancex from the typical UT can be expressed as

SINRk(x) =hk,0P

0kxαk(τk−1)

∑l hk,lP

0k |Yk,l|

αkτk |Vk,l|−αk + σ2, (13)

wherehk,0 is the exponentially distributed channel gain withmeanμ−1 from the typical UT, |Yk,l| is the distance fromeach interfering UT to their serving BS in thekth tier, |Vk,l|



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is the distance from the interfering UT to the BS serving thetypical UT in thekth tier, andhk,l represents the exponentiallydistributed channel power fromlth interfering UT. Note thatthere is no inter-tier interference since both tiers operateon separate carrier frequencies. In addition, an orthogonalmultiple access is also considered in each cell.

In order to derive the average ergodic rate of a randomlylocated UT in thekth tier, we consider that the UT isassociated with the BS with the maximum BRP. We thenfollow the same approach used in deriving the average UTtransmit power in a tier. Firstly, the ergodic uplink rate of atypical UT at a distancex from its serving BS in thekth tier isobtained. Thereafter, the ergodic uplink rate is then averagedover the distancex (i.e. over thekth tier). The average ergodicrate of thekth tier in the uplink channel is thus defined as

Rk , Ex [ESINRk [ln (1 + SINRk (x))]] . (14)

Contrarily to [34] where the average ergodic rate wasobtained based on a fixed minimum distance for the interferingUT, we define the average ergodic rate which is without suchlimitation in the following theorem.

Theorem IV.1:The average ergodic uplink rate of a typicalUT associated with thekth tier is

Rk=2πλkAk

∫ ∞

0

∫ ∞

0

x exp

−et−1SNR

− π2∑

j=1

λj

(Pj βj

)2/αjx2/αj

LIk(μP 0k

−1xαk(1−τk)

(et − 1

))dtdx, (15)

1whereSNR = P 0kxαk(τk−1)σ−2 and the Laplace transform

of the interference to thekth tier is given by

LIk(sk) = exp

(

−2πλk

∫ ∞

x

(

1−∫ ∞

0

μ

μ+ sP 0k yαkτkc−αk

2πλkAk

y exp

(

−π2∑

j=1

λj

(Pj βj

) 2αjy

2

αj

)

dy

)

cdc

)

.

Proof: See Section A of theAppendix.Note that the average ergodic rateRk is the average data rateof a typical UT in thekth tier with only one active UT ineach cell. Hence, it also denotes the average cell throughputof the kth tier when an orthogonal multiple access schemewith round robin scheduling is implemented. Furthermore, theaverage ergodic rate of a typical randomly located UT in theuplink of a two-tier HetNet can be expressed as

R =2∑

k=1

AkRk (16)

which simplifies as

R=2∑

k=1

2πλk

∫ ∞

0

∫ ∞

0

x exp

{

−et−1SNR

− π2∑

j=1

λj

(Pj βj

)2/αj(17)

x2/αj

}

LIk(μP 0k

−1xαk(1−τk)

(et − 1

))dtdx.

1The effect of the realistic association is captured by combining (15) withsome empirical formulas (e.g., [35], [36]).

The ergodic rate expression can be simplified for the noiselimited network (noise dominates the interference), which isstated as the following corollary of Theorem IV.1.

Corollary IV.2: The average ergodic rate in the uplink chan-nel of a typical UT associated with thekth tier for the noiselimited (σ2 � Ik) case is given by

Rk=2πλkAk

∫ ∞

0

−eξEi (−ξ)x exp

−π

2∑

j=1

λj

(Pj βj

)2/αjx2/αj

,

(18)where Ei denotes exponential integral function,ξ =xαk(1−τk)P 0k

−1σ2.

V. ENERGY EFFICIENCY OF CARRIER-SEPARATED

HETNET WITH INTER-FREQUENCYSMALL CELL

DISCOVERY

A. Ideal Average Energy Efficiency

In the previous section we derived generic expressionsfor the average ergodic rate,Rk, and the average powerconsumption,PTk , of the UT in each tier. The ideal AEE in theuplink of HetNet is the ratio of the average bit transmitted bythe typical UT to the average energy consumed by the typicalUT, while considering the ideal UT association. The averagebit transmitted by the typical UT in each tier is obtained fromthe average ergodic rate and the average time that the typicalUT spends in the coverage of each tier, as defined for the idealassociation in (4). Given that a typical UT spends an averagetime Tk in the coverage of BSs of thekth tier, hence the idealAEE in the uplink of two-tier HetNet can be expressed as

CJ =

∑2k=1 TkRk∑2k=1 TkPTk

(bit/J), (19)

where Tk, PTk and Rk are defined in (4), (12) and (15),respectively. Hence, the ideal AEE in the uplink of HetNetgiven in (19) can be simplified as

CJ =

∑2k=1AkRk∑2k=1AkPTk

=

2∑

k=1

AkRk

Δ2∑

k=1

(AkP

Uk

)+ Pc

. (20)

B. Realistic Average Energy Efficiency

As mentioned earlier in Section III, the typical UT con-sumes additional powerPm for each ISCD that it performswhen connected to the macro cell. Hence, this additionalpower must be incorporated into the power consumption modelin order to obtain the realistic AEE of the typical UT in thenetwork. It is important to note that apart from the ISCDperformed by the UT when connected to the macro cell, whichis for exploiting the traffic offloading opportunities availablein the small cell, the UT also performs a radio resourcemanagement (RRM) inter-frequency search when its receivedsignal strength falls below a certain threshold [15]. The RRM



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inter-frequency search is performed irrespective of the UTsassociation with either the macro or the small cell with theobjective to trigger a handover. This condition arises when theUT is in the cell edge region, where it typically has a lowersignal quality. In this work we focus on the additional powerconsumed by the UT when searching for the small cell withthe aim of benefiting from its traffic offloading opportunity,hence we do not consider the RRM inter-frequency searchpower consumption.

According to the realistic UT association expressions in(5) and (6), the typical UT is connected to the macro celland small cell for a durationT1 = T (A1 + A2X ), andT2 = (1−X )A2T , respectively, whereX is obtained em-pirically. Also, given a fixed ISCD measurement durationTm,with ISCD periodicityV , the average number of ISCDs that atypical UT experiences in the coverage of the macro cell canbe expressed as

NISCD =T1

Tm + V

=T (A1 + XA2)Tm + V

. (21)

Hence, the average additional energy consumed by the typicalUT as a result of the ISCD measurements in the macro cellcoverage can be expressed as

Eifm = NISCDTmPm (22)

=T (A1 + XA2)Tm + V

TmPm, (23)

based on the energy consumed for one ISCD measurement,which is given in (7). The AEC of a typical UT in a2−tierHetNet,Em, is thus the sum of the average energy consumedin the first tier (macro coverage), the average energy consumedin searching the small cells, and the average energy consumedin the second tier (small cell coverage). Therefore, the AECof a typical UT can be expressed as

Em =

2∑

k=1

TkPTk + Eifm. (24)

Consequently, the AEE of a typical UT in the uplink of a car-rier frequency separated two-tier HetNet, which incorporatesthe energy consumed for ISCD process, can be expressed as

CJC =

2∑

k=1

TkRk

Δ

2∑

k=1

(TkP

Uk

)+ TPc + Eifm

, (25)

which can be further expressed as

CJC = (26)R1 (A1 + XA2) +R2A2 (1−X )

PU1 (A1 + XA2) + PU2 A2 (1−X ) + Pc +

TmPm(A1+XA2)Tm+V

after substituting forTk andNISCD.

VI. OPTIMAL ISCD PERIODICITY

In this section, we investigate the optimal ISCD periodicityof a typical UT in the uplink of HetNet based on its AEC andAEE. As discussed earlier, there exists scanning frequencies,V ? and V ??, that achieves optimal performance in termsof average UT energy consumption and energy efficiency,respectively. If the scanning frequency is less thanV ?, thesmall cells will not be discovered on time hence excessiveUT energy consumption due to the time duration in macrocell coverage. On the other hand, excessive energy will beconsumed in the search process if the scanning frequencyexceedV ?. Similarly, scanning frequency that is less or greaterthan V ?? will not be energy efficient, since higher scanningfrequency means the small cells will be discovered early thus,high capacity at the expense of excessive UT AEC due toscanning. Whereas, a lower scanning frequency means lowercapacity, but with savings in UT AEC as a result of scanning.Hence, for scanning frequency higher thanV ??, the AEEdepreciates due to the excessive power consumption, whilethe AEE depreciates as a result of the lower rate when thescanning frequency lower thanV ??.

A. Approximation of the Percentage of Time a Typical UTMissed Small Cell Offloading Opportunity

In order to obtain the optimal ISCD periodicities in terms ofAEC and AEE, i.e,V ? = 1

V ?andV ?? = 1

V ??, respectively, we

must express the percentage of time that a typical UT missedsmall cell offloading opportunity, i.e.X , as a function of ISCDperiodicityV. It can be seen in Fig. 1 thatX is a function ofthe ISCD periodicity, the small cell density and the UT speed.Furthermore, it can be observed thatX can be approximatedas a linear function of ISCD periodicity for a fixed UT speedθ = 3 km/hr and small cell densitiesλ2 = 10λ1 and 20λ1.However, this is not the case for higher UT speed, hence,we generalize the approximation ofX as a function of ISCDperiodicity V via a polynomial curve fitting method, for afixed small cell density and UT speed, as follows

X (V ) ≈ X (V ) ≈N∑

f=0

afVf , (27)

whereN is the order of the polynomial,af is the f th poly-nomial coefficient. The parameterN can be chosen such thatthe following the mean square error equation is minimized, i.eε0 � 1,

∑

V

|X (V )−N∑

f=0

afVf |2

|V|� ε0, (28)

where|V| denotes the cardinality of the test vectorV. Table Igives the polynomial order and coefficient for the deploymentsettings withλ2 = 10λ1 and 20λ1, andθ = 3, 10, 20, 30, 120km/hr. Fig. 1 shows a tight match between the exact percentageof time the UT missed small cell offloading opportunity,X ,and its approximationX .



7

TABLE IPOLYNOMIAL ORDER AND COEFFICIENTSFOR VARIOUS DEPLOYMENT SETTINGS

Speed 3 km/hr 10 km/hr 20 km/hr 30 km/hr 120 km/hr

λ2 10λ1 20λ1 10λ1 20λ1 10λ1 20λ1 10λ1 20λ1 10λ1 20λ1N 1 1 2 2 2 2 3 3 4 4

a0 −1.27 × 10−4 −1.5 × 10−5 −2.38 × 10−4 −3.55 × 10−4 −1.5 × 10−3 −7.75 × 10−4 −2.440 × 10−3 −9.97 × 10−4 −4.1 × 10−3 −2.718 × 10−3

a1 2.148 × 10−3 1.737 × 10−3 6.987 × 10−3 5.378 × 10−3 1.39 × 10−2 1.156 × 10−2 2.1161 × 10−2 1.5566 × 10−2 8.54 × 10−2 6.633 × 10−2

a2 − − −1.28 × 10−5 −1.14 × 10−5 −7.2 × 10−5−5.71 × 10−5 −1.875 × 10−4 −1.193 × 10−4 −3.3 × 10−3 −2.255 × 10−3

a3 − − − − − − 4.8745 × 10−7 3.4865 × 10−7 5.9290 × 10−5 3.7217 × 10−5

a4 − − − − − − − − −3.836 × 10−7−2.3226 × 10−7

B. Optimal ISCD Based on Average Energy Consumption

The average EC expression in (24) can be expressed as afunction of the ISCD periodicity as follows

Em(V ) = TPU1 (A1 + X (V )A2) + TPU2 A2 (1−X (V ))

+TTmPm (A1 + X (V )A2)

Tm + V. (29)

By takingX (V ) ≈ X (V ) in (27), Em(V ) ≈ Em(V ), whichis clearly differentiable over its domain, such that∂Em(V )

∂Vcan

be expressed after simplification as

∂Em(V )

∂V=A2

(Δp(Tm+V )

2+TmPm(Tm+s)

)∂X (V )∂V

−TmPm(A1 +A2X (V )

), (30)

whereΔp = PU1 −PU2 . Let V ? be the solution to the equation

∂Em(V )∂V

= 0. Then ∂Em(V )∂V

≤ 0 and ∂Em(V )∂V

≥ 0 for anyV ∈ [0, V ?] and V ∈ [V ?,+∞], respectively, which in turnimplies that Em ≈ Em decreases overV ∈ [0, V ?] andthen increases overV ∈ [V ?,+∞]. Consequently,Em(V )has a unique minimum, which occurs atV = V ?. By setting∂Em(V=V

?)∂V

= 0 and using the approximation ofX (V ), fora given speed and small cell density given in Table I in (30),we can obtainV ?. For the case whereX (V ) is linear, i.e. thepolynomial orderN = 1 in (27), the optimal ISCD searchbased on the AEC can be simplified as

V ? = −Tm +

√TmPm [A2 (a0 − a1Tm) +A1]

A2a1Δp. (31)

However, for the case where the polynomial order,N > 1, wesimply use a linear search method such as Newton-Raphsonmethod.

C. Optimal ISCD Based on UT’s Average Energy Efficiency

The optimal ISCD periodicity in the previous subsectionwas based on the UT’s AEC. In this subsection, we derive theoptimal ISCD based on the AEE expression of (26), which canbe expressed as a function of the ISCD periodicity as follows

CJC (V ) = (32)R1 (A1 + X (V )A2) +R2A2 (1−X (V ))

PU1 (A1+X(V )A2)+TmPm(A1+X (V )A2)

Tm+V+PU2 A2(1−X (V ))

.

Similar to the AEC case, the AEE is differentiable over itsdomain and the ISCD periodicity that maximizes the AEE,

TABLE IISYSTEM PARAMETERS.

Parameter Symbol Value(units)Bandwidth pertier W 20 MHz

Macro cell BSdensity λ11

π4002m2

Small cell BSdensity λ2 5λ1, 10λ1, 20λ1UT density λ(u) 100λ1

Macro cell BS transmit power P1 46 dBmSmall cell BS transmit power P2 26 dBm

Small cell Bias factor β2 0, 2, 4, 6, 8, 10 dBUT pathloss compensation factor τ1 = τ2 = τ 0, 0.2, 0.4, 0.6, 0.8, 1.0

UT power controlparameter P 01 = P02 = P

0 −50 dBmReferencepathloss L0 −38.5 dBPathloss exponent αk 3, 3.5, 4

Thermal noisedensity N0 −174 dBm/Hz

V ??, can be obtained by setting∂CJC (V=V

??)

∂V= 0, which

simplifies as

∂CJC(V=V??)

∂V= 0 (33)

= Em(V )A2(R1 −R2)∂X (V )∂V

−

(2∑

k=1

AkRk+(R1−R2)A2X(V )

)∂Em(V )

∂V

Note that the optimal ISCD periodicity based on AEC, i.e.V ?, and AEE, i.e.V ??, are equivalent when the ergodic rate

in both tiers are equal, since∂CJC (V=V

??)

∂V= ∂Em(V )

∂Vin (33),

whenR1 = R2.

VII. N UMERICAL RESULTS AND DISCUSSIONS

In this section, we present numerical results on the ergodicrate, AEC, AEE and the optimal ISCD periodicity of a typicalUT in the uplink of a2−tier HetNet with both tiers operatingon separate carrier frequencies. The system parameters aregiven in Table II.

A. Achievable rate

We obtain numerical results for the average ergodic rate (inTheorem IV.1) with respect to the main system parameters;pathloss exponent, power control factor, BS density and biasfactor. In Fig. 2, we compare average ergodic rate obtainedvia simulation with the analytical results. We plot the averageergodic rate as a function of the small cell bias factor,β2,for small cell density values ofλ2 = 5, pathloss valuesα1 = α2 = 3.5 and power control factors,τ1 = τ2 = 0.8and τ1 = τ2 = 0. The results in Fig. 2 clearly show that theanalytical results provide lower bounds to the average ergodicrate. Furthermore, increasing the small cell bias factor,β2,leads to a reduction in the average ergodic rate of a typical



8

0 2 4 6 8 100.8

1

1.2

1.4

1.6

1.8

2

2.2

(a) τ = 0.8

0 2 4 6 8 10

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

(b) τ = 0

Fig. 2. Average ergodic rate for varying bias factor of small cells in a2−tier HetNet, β1 = 1, λ1 = 1π4002m2

, λ2 = 5λ1, P1 = 46 dBm, P2 =26 dBm

UT in the small cell whereas the average ergodic rate of thetypical UT in the macro cell increases. This is due to the factthat as the small cell bias factor increases, the coverage area ofthe small cells increases leading to increase in the interferencesuffered by the typical UT and consequently a reduction in theachievable ergodic rate. As the small cell bias factor increases,more macro UTs with low SINR become associated with thesmall cell, which degrades the average ergodic rate of thetypical UT in the small cell, but improve the rate in the macrocell.

In Fig. 3, using the analytical results, we plot the averageergodic rate of a typical UT as a function of the power controlfactor, τ1 = τ2 = τ , for pathloss exponents{α1 = 3.5, α2 =3.5}, {α1 = 3.5, α2 = 3} and{α1 = 3, α2 = 3.5}, small cellBS densityλ2 = 10λ1 and no bias, i.e,β1 = β2 = 1. Theresults show that the lowest ergodic rate in a tier is achievedby the tier with the lowest pathloss exponent, whereas thecontrary holds for the tier with the highest pathloss exponent.This is because the signal from the interfering cells will bestronger with lower pathloss exponent and weaker with higherpathloss exponent i.e., interference decays more slowly aspathloss exponent increases. It can be further observed thatthe ergodic rate of a typical UT over each tier and over theentire network reduces with increasing power control factorτ . Since the obtained rate is for typical UT in the network,the effect of the power control factor on all UTs (i.e., low,medium and high SINR UTs) is combined into a single value.Therefore, the decrease in the average rate asτ increases isdue to the loss in rate of some UTs whose transmit power isreduced, but the effect of this reduction is not overcome onaverage by the reduction in interference and increased rate byother UTs. Note that this observation was also made for thesingle tier network in [37].

0 0.2 0.4 0.6 0.8 1

100

Fig. 3. Average ergodic rate in a2−tier HetNet as a function offractional power control parameterτ, for bias factorβ1 = β2 =1, λ1 =

1π4002m2

, λ2 = 10λ1, P1 = 46 dBm and P2 = 26 dBm.

B. UT Power Consumption

In Fig. 4, we plot the average UT transmit powers in eachtier against the small cell bias factor,β2, for UT power control,τ = 1 and τ = 0.8. It can be observed that significantreduction in transmit power is achieved when the UT connectsto the small cell compared to when it connects to the macrocell, in the case with full power control, i.e.,τ = 1. This isas a result of the reduced distance to the BS when typical UTis in the coverage of the small cell, hence a lower transmitpower is required to achieve a desired received signal. Asthe power control factor reduces, the transmit power becomesmore independent of the distance between the nodes, hence



9

0 5 10 15 2010

-3

10-2

10-1

100

101

102

Fig. 4. Average user transmit power for varying bias factor ofsmall cells in a2−tier HetNet,β1 = 1, λ1 = 1

π4002m2, λ(u) =

100λ1, P1 = 46 dBm, P2 = 26 dBm, and α1 = α2 = 3.5.

a reduction in the ratio of the average UT transmit power inthe macro cell to that in the small cell. The result also showsthat as expected, the average transmit power in the small cellincreases as the small cell bias factor increase, whereas thecontrary holds in the macro cell.

C. Average Energy Efficiency

The results presented in Sections VII-A and VII-B clearlyshows the rate gain and transmit power reduction that isachieved when the UT connects to the small cell of an inter-frequency HetNet. This section presents numerical results onthe AEE while considering both the ideal and realistic UTassociation. Furthermore, the average ergodic rate used inevaluating the AEE is based on the analytical results.

1) Ideal Average Energy Efficiency:In Fig. 5, we plot theideal AEE, which is based on the ideal UT association againstthe small cell bias factor. It can be seen that increasing thedensity of small cells lead to an increase in the UT’s AEE inthe macro cell, small cell and overall network. Furthermorethe UT’s AEE performance in the small cell depreciate as thebias factor increases, since the average rate of the typical UTin the small cell decreases while its transmit power increasesas the small cell bias factor increases, as shown in Figs. 2and 4. On the other hand, the performance of the macro cellimproves since the contrary occurs. It can also be observedthat contrary to the overall average ergodic rate in Fig. 2, theoverall AEE in a fully loaded network improves with increasein bias factor.

2) Realistic Energy Efficiency:In Fig. 6, we plot therealistic AEE against the small cell discovery periodicity. Inthe upper graph, typical UT speed3 km/hr, 20 km/hr, and120 km/hr are considered for small cell densityλ2 = 10λ1.The results clearly show that there exists an ISCD periodicitythat maximizes the AEE. The lower graph shows the AEEperformance for small cell densities,λ2 = 10λ1, λ2 = 20λ1

0 2 4 6 8 10

101

102

Fig. 5. Ideal AEE for varying bias factor in a2−tier HetNet,β1 =β2 = 1, λ1 =

1π4002m2

, λ2 = 5λ1, 10λ1, P1 = 46 dBm, P2 =26 dBm τ = 0.8 andα1 = α2 = 3.5.

100.93

100.94

100.95

100.96

100.97

10-1

100

101

101

Fig. 6. Realistic AEE for varying small cell discovery periodicityand UT speed,β1 = β2 = 1, λ1 = 1

π4002m2, λ2 = 10λ1, P1 =

46 dBm, P2 = 26 dBm, τ = 0.8 andα1 = α2 = 4 . The starmarker indicates the ISCD periodicity that achieves the optimal AEE.

and typical UT speed of3 km/hr. As it is expected, increasingthe density of the small cells leads to an increase in AEE, sincethis results in a reduction in the average transmit power of thetypical UT coupled with an improvement in the small celltraffic offloading. Furthermore, it can be seen that the optimalISCD periodicity is dependent on the density of small cells andspeed of the typical UTs. For a fixed small cell density,λ2,a lower small cell discovery periodicity is required to achievethe maximum AEE as the typical UT speed increases. Whereasfor a fixed speed of the typical UT, as the small cell densityincreases, the optimal ISCD periodicity required to achieve themaximum AEE also increases.



10

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

Fig. 7. Optimal ISCD periodicity for various ISCD power con-sumption, small cell densities,λ2 = 10λ1, 20λ1, and UT speedof 3, 10, 120 km/hr, UT transmit powers,PU1 = 1.6114 W andPU2 = 1.14W .

Thus this analysis and subsequent determination of optimalISCD periodicity can pave the way towards the design of selforganizing network (SON) [38] functions that can adapt thecell discovery periodicity with respect to particular environ-ment (UT speed and small cell density) to achieve optimalAEE performance. Its worth noting that in future HetNets,small cell densities might change impromptu as cell may beswitched off and on in order to improve the networks energyefficiency. Hence, the need for such adaptive algorithms thatexploits the existence of optimal ISCD for given cell densitybecomes even stronger.

D. Optimal ISCD Periodicity

The results presented in this section are based on a fullpower control implementation in both tiers, i.e.τ1 = τ2 = 1. InFig. 7, we plot the optimal ISCD periodicity for ISCD powerconsumptionPm ranging from0.01 W to 2.5 W, average UTtransmit power in the macro cellPU1 = 1.6114 W, whichcorresponds toP 01 = −69dBm, UT speedθ = 3, 10 and120 km/hr, and small cell densityλ2 = 10λ1 and20λ1. Theaverage UT transmit power in the small cells with densityλ2 = 10λ1 and λ2 = 20λ1 at P 02 = −50.5 dBm are1.14 W and 0.5 W, respectively. The upper graph showsthe impact of varying of UT speed on the optimal ISCDperiodicity, while the lower graph shows the impact of varyingthe small cell density. The upper graph clearly shows thatas the UT speed increases, the ISCD periodicities requiredto achieve optimal AEC and AEE performances reduces. Onthe other hand, the lower graph shows that increasing thesmall cell density reduces the ISCD periodicities required toachieve optimal AEC and AEE performances. Furthermore,Fig. 7 clearly shows that increasing the ISCD power results

0.094

0.095

0.096

0.097

0.098

0.5 1 1.5 2 2.51.376

1.38

1.384

1.388

1.392

1.396

1.4

Fig. 8. Average power consumption and AEE based on optimalISCD periodicity, for small cell density,λ2 = 10λ1, and UT speedof 3, 10, 120 km/hr, UT transmit powers,PU1 = 1.6114 W andPU2 = 1.14W .

in an increase in the ISCD periodicity required to achieve theoptimal performance in terms of both AEC and AEE. ThoughUT power consumption is lower when UT is connected to thesmall cell, however, additional power is spent in searchingthe small cell. Hence increasing the ISCD power impliesan increase in the search periodicities required to achieveoptimal AEC and AEE performances. Fig. 7 further showsthat for a fixed UT transmit power in the small cell, the ISCDperiodicity required to achieve optimal AEC performanceexceeds the ISCD periodicity required to achieve optimal AEEperformance.

In Fig. 8, we plot the average UT power consumption (lowergraph) and AEE (upper graph) based on the optimal ISCDperiodicity against the ISCD power consumption,Pm, forsmall cell densityλ2 = 10λ1 and UT speedθ = 3, 10 and120 km/hr. As expected, increasing the ISCD power leads toan increase in the average power consumption and a reductionin the AEE. In addition, with the same network parameters, ahigh speed UT is less energy efficient since higher scanningfrequency (i.e., lower ISCD periodicity) is required to attainoptimal performance.

In Fig. 9, we plot the percentage reduction in AEC (lowergraph) and the percentage increase in AEE (upper graph),respectively, that are achieved from using the optimal ISCDperiodicity over using sub-optimal ISCD periodicityV =0.04, 0.1 10 and 60 s. We plot both graphs for average UTtransmit powerPU2 in the small cell ranging from0.01 W to1.44 W, which corresponds toP 02 ranging from−69.5 dBmto −49.5 dBm, and average UT transmit power in the macrocell PU1 = 1.6114 W, which corresponds toP 01 = −69dBm.Fig. 9 shows that significant amount of energy can be savedby adopting the optimal ISCD periodicity especially when



11

-54.1 -51.1 -49.3

0

5

10

15

20

25

30

0 0.5 1 1.5-12

-10

-8

-6

-4

-2

0

Fig. 9. Percentage reduction in AEC and percentage increase inAEE achieved by using optimal ISCD periodicity over sub-optimalISCD periodicity, for small cell densities,λ2 = 10λ1, UT speed,θ = 10 km/hr, ISCD power,Pm = 1 W and UT transmit power,PU1 = 1.6114W (P

01 = −69 dBm).

there is a large deviation between the optimal and sub-optimal values. For example, the optimal ISCD periodicity fordeployment setting withλ2 = 10λ1, Pm = 1 W, PU2 = 1.14and UT speed of10 km/hr used in Fig. 9 is such thatV ? ∧ V ?? ∈ [0.5 1.5] s (as shown in Fig. 7). However,using ISCD periodicityV = 0.04 and 60 s results in largerdifference compared withV = 0.1 and 10 s, which are morecloser to the optimal values.

Since, optimal ISCD periodicity can calculated as functionof statistical UT speeds and small cell density only, optimalISCD periodicity can be maintained in a spatio temporallyvarying environment of a HetNet by designing appropriateSON functions, without incurring major overheads in termsof hardware redesign or signaling overheads. As the energylimited nature of UT is one of the major challenges in futurebroadband networks such as 5G, the significant gain in theAEE of the UT through the implementation of optimal ISCDperiodicity can increase the battery life of UT significantly,particularly in ultra-dense HetNets that are being deemed asnecessity in 5G landscape.

VIII. C ONCLUSION

In this paper, we have investigated the energy efficiency ofthe user terminal in the uplink of a carrier frequency separatedtwo-tier heterogeneous network with flexible cell association,also known as biasing. Using Poison point process (PPP) oursystem model captured the network topology and the designparameters associated with each tier including base stationtransmit power, density, bias factor, and power control factor.We first derived generic expressions for the average transmitpower and average ergodic rate, which were later used in

energy efficiency derivation. The energy efficiency expressionsare based on the ideal and realistic user terminal associations.In the former, user terminals associate with the base stationwith the maximum biased received signal without consideringthe overheads required for such association. On the other hand,the latter further incorporates the percentage of time that atypical user terminal missed small cell offloading opportunityas a result of the periodicity of the measurement conducted forsmall cell discovery. In addition to this, the additional powerconsumed by the user terminal due to the inter-frequency smallcell discovery (ISCD) measurement was also included for thelater.

The main findings of this paper can be summarized asfollows: Firstly, there exists ISCD periodicity that maximizesthe energy efficiency and minimizes the energy consumptionwhen the realistic user terminal association is considered.Secondly, significant savings in the energy consumption ofthe user terminal can be achieved by using the optimal ISCDperiodicity. Lastly, the optimal ISCD periodicity for the userterminal based on energy efficiency always differs from thatwhich is based energy consumption, as long as the averageergodic rate in both tiers differs. Hence, the user terminalsISCD periodicity should be chosen based on the target ob-jectives such as energy consumption minimization or energyefficiency maximization. The findings of this paper can beimplemented in real network through self-organizing networkfunctions being already adapted by 3GPP for emerging cellularnetworks, where the periodicity of the ISCD process canbe selected based on the environmental setting to obtain theoptimal energy efficiency performance.

Note that randomly distributed network architecture hasbeen presented in this paper. However, future network ar-chitectures will be clustered and not randomly distributed.Since accurate modeling of network architecture is crucial,hence a better modeling such as Matern process with repulsiondeserves much attention in future study.

APPENDIX

A. Proof of Theorem IV.1

From (14), the average uplink ergodic rate in thekth tier is

Rk =

∫ ∞

0

ESINRk [ln (1 + SINRk (x))] fXk(x)dx

=2πλkAk

∫ ∞

0

ESINRk [ln (1 + SINRk (x))]

x exp

−π

K∑

j=1

λj

(Pj βj

)2/αjx2/αj

dx (34)

wherefXk(x) is defined in (2). Given thatE[X] =∫∞0P[X >

x]dx for X > 0 hence, we obtain

ESINRk [ln (1+SINRk (x))]=∫ ∞

0

P [ln (1+SINRk(x)) > t] dt

=

∫ ∞

0

P[SINRk(x)>e

t−1]dt (35)



12

The SINR in (13) can be rewritten asγ(x) = hkP−10 xαk(1−τk)Q

,

whereQ = Ik + σ2

L0. Hence,

ESINRk[ln (1 + SINRk (x))]

=

∫ ∞

0

P[hk > P

−10 x

αk(1−τk)Q(et − 1

)]dt (36)

However,

P[hk> P

−10 x

αk(1−τk)Q(et − 1

) ]

=

∫ ∞

0

exp[−μxαk(1−τk)P 0k

−1 (et − 1

)q]fQ(q)dq

= EQ[exp

(−μxαk(1−τk)P 0k

−1 (et − 1

)q)]

= exp

(

−et−1SNR

)

EIk[exp(−μxαk(1−τk)P 0k

−1(et−1

)Ik

)],

= exp

(

−et−1SNR

)

LIk(μxαk(1−τk)P 0k

−1 (et−1

))(37)

whereSNR = P 0kxαk(τk−1)

σ2andLIk (sk) = EIk

[e−sIk

]is the

laplace transform ofIk which simplifies as

LIk(sk)

= EIk

[

exp

(

−∑

z∈Zk

sP 0kYαkτkz V −αkz hz

)]

= EYz,Vz,hz

[∏

z∈Z

exp(sP 0kY

αkτkz V −αkz hz

)]

(a)= EYz,Vz

[∏

z∈Z

Ehz[exp

(sP 0kY

αkτkz V −αkz hz

)]]

(b)= EVz

[∏

z∈Z

EYz

[μ

μ+ sP 0kYαkτkz V −αkz

]]

(c)= exp

(

−2πλk

∫ ∞

x

(

1−EYz

[μ

μ+sP 0kYαkτkz c−αk

])

cdc

)

,(38)

where(a) is due to the independence ofhz, (b) follows fromthe fact that the interference fading powerhz ∼ exp(μ)and (c) is given in [23]. The limits of the integration arefrom x to ∞. Since x is the distance between the typicalUT and its serving BS, the closest interferer is at least adistancex from the serving BS of the typical UT. Similarto [37], considering that each BS is randomly located in theVoronoi cell of its corresponding active UT while assumingorthogonal multiple access within each cell. Hence, the PDF ofthe distance between an interfering UT to its serving BS, i.e.,Yz can be approximated by the PDFfXk(x) of the distanceXk between a typical UT and its serving BS in thekth tiergiven in (2). Hence by applying the density ofYz, the Laplacetransform of the interference in thekth tier given in (38) canbe further expressed as follows

LIk(s)= exp

(

− 2πλk

∫ ∞

x

(

1−∫ ∞

0

μ

μ+ sP 0k yαkτkc−αk

2πλk

Ak

y exp

(

−πK∑

j=1

λj

(Pj βj

) 2αjy

2

αj

)

dy

)

cdc

)

. (39)

Finally, the average ergodic rate expression in (15) is ob-tained by substituting (37) into (36) and thereafter substitutingthe later into (34).

ACKNOWLEDGMENT

We would also like to acknowledge the support of the Uni-versity of Surrey 5GIC (http://www.surrey.ac.uk/5gic) mem-bers for this work.

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Oluwakayode Onireti (S’11-M’13) received hisB.Eng. degree in Electrical Engineering from Uni-versity of Ilorin, Nigeria, in 2005. The M.Sc. in Mo-bile & Satellite Communications and Ph.D. degreesin Electronics Engineering from University of Sur-rey, UK, in 2009 and 2012, respectively. He secureda first class grade in his B.Eng. and a distinction inhis M.Sc. degree. He is currently a research fellow atthe Institute for Communication Systems (ICS), Uni-versity of Surrey, UK. He has been actively involvedin European Commission funded projects such as

ROCKET and EARTH. His main research interests include self-organizingcellular networks, energy efficiency, MIMO and cooperative communications.

Ali Imran (M’15) received his BSc in Elect En-gineering, in 2005 from University of Engineeringand Technology, Lahore, Pakistan. He received hisMSc in Mobile and Satellite Communications withdistinction, and PhD, both from university of Surrey,UK, in 2007 and 2011 respectively. He is an assistantprofessor in telecommunications at University ofOklahoma. He is currently leading a multinational$1.045 million research project on Self OrganizingCellular Networks, QSON (www.qson.org). His re-search interest include, self-organizing networks, ra-

dio resource management and big data analytics. He has authored over 40 peerreviewed articles and has presented number of tutorials at international forumssuch as IEEE ICC, IEEE WCNC, European Wireless and CrownCom on thesetopics. He is an Associate Fellow of Higher Education Academy (AFHEA),UK and Member of Advisory Board to Special Technical Community on BigData at IEEE Computer Society.

Muhammad Ali Imran (M03, SM’12) received hisM.Sc. (Distinction) and Ph.D. degrees from ImperialCollege London, UK, in 2002 and 2007, respec-tively. He is currently a Reader (Associate Professor)in the Institute for Communication Systems (ICS- formerly known as CCSR) at the University ofSurrey, UK. He has led a number of multimillioninternational research projects encompassing the ar-eas of energy efficiency, fundamental performancelimits, sensor networks and self-organising cellularnetworks. He is currently leading the new physical

layer work-area for 5G innovation centre and the curriculum design for theEngineering for Health program at Surrey. He has a global collaborative re-search network spanning both academia and key industrial players in the fieldof wireless communications. He has supervised 20 successful PhD graduatesand published over 200 peer-reviewed research papers including more than20 IEEE Transaction papers. He has delivered several keynotes, plenary talks,invited lectures and tutorials in many international conferences and seminars.He has been a guest editor for special issues in IEEE Communications,IEEE Wireless Communication Magazine, IET Communications and IEEEAccess. He is an associate Editor for IEEE Communications Letters andIET Communications Journal. He has been awarded IEEE Comsocs FredEllersick award 2014 and FEPS Learning and Teaching award 2014 and twicenominated for Tony Jeans Inspirational Teaching award. He was a shortlistedfinalist for The Wharton-QS Stars Awards 2014 for innovative teaching andVCs learning and teaching award in University of Surrey. He is a seniormember of IEEE and a Senior Fellow of Higher Education Academy (HEA),UK.

Rahim Tafazolli (M’02, SM’09) ) is a professor andthe Director of the Institute for Communication Sys-tems (ICS) and the 5G Innovation Center, Universityof Surrey, Surrey, UK. He is currently Chairmanof the EU Net!Works Technology Platform ExpertGroup and a board member of the U.K. Future In-ternet Strategy Group (UK-FISG). He has publishedmore than 500 research papers in refereed journals,international conferences and as invited speaker. Heis the editor of two books on “Technologies forWireless Future” published by Wiley’s Vol.1 in 2004

and Vol.2 2006. He was appointed as a Fellow of the WWRF (Wireless WorldResearch Forum) in April 2011 in recognition of his personal contribution tothe wireless world and for heading one of the Europe’s leading research groups

Documents

Energy Efficient Inter-Frequency Small Cell Discovery in ...arately allocated to the small cell and macro cell layers or co-channel deployment scenario, where the small cell and macro