performance analysis of device-to-device communications in cellular networks under...

Performance Analysis of Device-to-DeviceCommunications in Cellular Networks Under VaryingLoad Conditions

Priyadarshi Ashok Dahat1• Suvra Sekhar Das1

� Springer Science+Business Media New York 2015

Abstract Device-to-device (D2D) communications is identified as potential technology

for future cellular networks. It is a promising concept to provide the high data rate re-

quirements for bandwidth hungry applications like social networking, multimedia services

etc. It facilitates better utilization of radio resources and shorter transmitter receiver delays

and therefore better user performance. In this paper framework for studying performance

of D2D communications in orthogonal frequency division multiple access based multi-

cellular scenario is developed using downlink cellular resources. The load condition of

D2D mode in addition to that of cellular mode plays an important role. The performance of

both modes for their respective load conditions have been analyzed. The key parameters

analysed are ratio of signal power to noise plus interference power (SINR), outage pro-

babilty, effect of variation in D2D transmitter power, capacity, mode selection and D2D

mode switching distance. The goal of the paper is to find the optimum distance for

switching to D2D mode from cellular mode for loads with different power ratios. The

results shows that D2D communications is beneficial for cellular edge UEs and improves

their capacity. It is seen that with increase in load in both the cellular and D2D modes the

corresponding link capacity falls. It is also seen that as the cellular load increases, the

switching distance moves away from BS while it moves towards the BS when the D2D

load increases.

Keywords Cellular load � Device-to-device communications � D2D load � Mode

selection � Multicellular system � Switching distance

& Priyadarshi Ashok [email protected]; [email protected]

Suvra Sekhar [email protected]

1 G. S. Sanyal School of Telecommunications, Indian Institute of Technology, Kharagpur, India

123

Wireless Pers CommunDOI 10.1007/s11277-015-2501-4

1 Introduction

Current cellular system are facing the challenge of accomodating the increasing number of

users and the bandwidth requirement of their high data rate applications within the limited

spectrum available. Device-to-device (D2D) communications is one of the promising

technique to cater to these needs. It is the process whereby two proximal user equipments

(UEs) communicate directly thereby bypassing the BS. The authors in [1] studied D2D

under LTE-Advanced and showed that D2D peers are able to use D2D opportunity if they

are close even though cellular network may be interference limited by itself. 3GPP pre-

sented plenary document on study on proximity based services [2] during september 2011.

Further 3GPP RAN held a workshop in 2012, to identify common requirements for future

3GPP radio access technologies. Device to device communications was proposed as one of

the technology for beyond release 12. In recent years there has been sharp increase in

mobile data traffic, particularly video traffic, usage of internet social networking sites like

facebook, orkut etc. due to appearance of tablets, smart phones and lot other new appli-

cations and device to device communications is seen to cater these needs.

Peer discovery, physical layer procedure and radio resource management (RRM) are the

major functions of D2D communications. Peer discovery is the procedure of finding

suitable UEs as D2D pair. RRM in D2D communications consists of mode selection,

resource allocation, power control, inter-cell and intra-cell interference mitigation [3]. In

cellular network assisted D2D communications, network plays key role in mode selection,

power control, scheduling, and selecting transmission format (modulation and coding rates,

multi-antenna transmission mode, etc.).

Mode selection is the process of finding whether to operate UE in cellular mode or D2D

mode. It depends on the proximity of devices, inter-cell and intra-cell interference con-

ditions, channel condition and instantaneous load condition on the network. Underlay and

overlay mode selection of D2D communication in LTE single cell scenario has been dealt

in [4]. But considering single cell means neglecting intercell interference, rather in mixed

cellular and D2D scenario intracell as well as intercell interference plays important role.

Mode selection based on minimum sum power has been studied by authors in [5] while

satisfying rate requirements using coaltion game approach. The authors in [6] considers

mode selection (three modes i.e reuse mode, dedicated mode and cellular mode) along with

resource allocation in intercell as well as intracell interference. But the authors have

considered taking only path loss for calculating power, whereas small scale fading and

shadow fading have not been considered.

Power control is an important RRM function. Joint mode selection, power and resource

allocation have been dealt in [7]. Distributed power control algorithm allocates power in

mixed cellular and D2D scenario so that overall throughput is maximized with minimum

overall power consumption [8]. With proper power control, the interference between

cellular and D2D can be coordinated for better overall performance [9]. The authors in [10]

shows that proper resource management leads to increase in total througput by using D2D

without generating interference to cellular network. But in their model the received power

calculation does not consider shadow fading. If shadowing not taken leads to wrong D2D

link length.

In [11] the authors have studied the performance when relay is used to facilitate the

communication between D2D whose receiver is at the outage. The link between one UE to

eNB is poor in condition and hence another UE in between acts as relay for completing the

transmission from UE to eNB [12]. Relay has been introduced to help in communication

P. A. Dahat, S. S. Das

123

between D2D in cognitive network [13]. It has been shown that performance is better with

relay as compared to direct transmission between D2D. System capacity and coverage of

cellular network can be enhanced by using D2D relays [14]. The authors have described

that helping UE facilitates in transmitting the signal to target UE. The study has been done

through simulation taking Manhattan grid model.

Cumulative distribution function (CDF) of transmit power and SINR using Poisson

point processes in D2D networks has been studied in [15]. D2D call admission control

followed by resource allocation using bipartite approach and power control using uplink

resources have been studied in [16]. The authors in [17] dealt with optimal D2D- cellular

user (CU) matching as well as their power coordination and proposes an algorithm to

jointly optimize all D2D links and CUs. In [18] distance constrained resource sharing

criteria with uplink has been proposed to reduce the outage probability. In [19] resource

sharing between cellular and D2D using uplink in mutliple user system have been studied.

The scenario considered is single cell only with the limitataion that atmost only one D2D

reuses the resource of the each cellular user. The authors have studied the performance

using auction based approach in [20] for maximizing the sum rate while considering more

than one D2Ds using the same resource. In [21] the authors have studied D2D-interference

limited area (ILA) control scheme to manage interference from cellular network to D2D

Rf

Macro BS 2

D2D2

Macro BS 3

D2D1

Rx

Rx

Rx

SignalInterfering

SignalIntended

Tx

Tx

Tx

D2D3

Macro BS 1

UE

UE c2

c1

x

Fig. 1 System model for mixed cellular and D2D communications

Performance Analysis of Device-to-Device Communications...

123

systems. The method shows improvement in ergodic capacity with their approach as

compared to conventional D2D approach. But in both the papers the scenario considered is

single isolated cell with no cellular loading into account.

In multicellular system load varies with the time of the day, hence cellular as well as

D2D communication performance also varies with time. When cellular network is fully

loaded, the D2D communication has to operate in the same cellular subchannels. On the

other hand, when network is less loaded D2Ds may be alloted the un-used subchannels. In

mixed cellular and D2D multicellular system not only subchannel allocation but also the

co-channel interference (CCI) from neighbouring cells depends on cellular and D2D load

of the neighbouring cells. In literaure authors have studied D2D performance as in- band

i.e., cellular band and out- of cellular band. However there is limited literature which deals

with how much cellular loading affects the cellular and D2D mode performance. Thus

there is a need to incorporate the effect of the temporal variations of load onto the

performance of mixed cellular and D2D scenario. Further there is also the need to study

cellular and D2D mode analysis under different load conditions. Our mode selection

criteria not only depends on the quality of the signal strength experienced by D2D but also

on the interference condition. As the intracell and intercell interference depends on the

distance/location of the users we have taken distance criteria along with SINR for mode

selection.

This paper presents the mode selection and capacity analysis of D2D enabled cellular

network in a multicellular-scenario. The results shows the SINR for cellular and D2D

mode for different loads at different locations from BS. The outage probability has been

obtained for both cellular and D2D modes. Further link capacity has been obtained for both

modes as a function of distance and also for different cellular and D2D loads. Then we

gave the optimum switching distance for D2D mode of operation from the cellular mode

with different cellular and D2D loads for different power ratios.

The rest of the paper is organized as follows: Sect. 2 presents the system model for

mixed D2D and cellular scenario. Section 3 deals with SINR, capacity and mode selection.

Section 4 describes the results and discussion, while the last Sect. 5 concludes the paper

(Fig. 1).

2 System Model

We consider downlink mixed D2D and cellular scenario, where D2Ds are underlaying

cellular network. The macrocell network consists of Nm number of hexagonal cells of

radius Rc equipped with omni directional antennas. N number of UEs are assumed to be

uniformly distributed inside the central macrocell with density q ¼ NpR2

c. We want to find the

distribution of UEs around UE of our interest located at reference position x to be em-

ployed as D2D transmitter. We also want to find the distance of UE from reference UE

which satisfies QoS criteria to make D2D pair.

Probability distribution function (PDF) of distance rd of nth nearest UE from the ref-

erence UE may be expressed as in [22]

fdðrd; nÞ ¼2ðpqÞn

ðn� 1Þ! r2n�1d e�pqr2

d ; rd [ ¼ 0; n ¼ 1; 2; :::N: ð1Þ

Hence the PDF of choosing most proximal UE to make D2D pair can be given by taking

n ¼1 in the above


123

fdðrd; 1Þ ¼ 2pqrde�pqr2d : ð2Þ

First we find D2D link length rd in meters from reference UE located at x as D2D

transmitter and other UE in the coverage area receiving the signal considering shadow

fading and distance. Due to shadowing even for the same distance the amout of received

power will vary and for the same required received power rd would vary. In log-normal

shadowing model logarithm of received power may be given by

10 log10 Prd¼ 10 log10 Prd

þ w; ð3Þ

where 10 log10 Prdis area mean power and w is a zero mean gaussian distributed random

variable with standard deviation r. Let Prminbe the minimum power to establish connection

as D2D pair. Received power Prdat UE from transmitter UE should be [Prmin

to make a

D2D pair. Hence normalized received power P̂ can be expressed in terms of Prminat

normalized distance r̂d ¼ rd

Rfas in [23] as

10 log10 P̂r̂d¼ 10 log10

�r̂d

��g þ w; ð4Þ

where g is path-loss exponent and Rf is distance corresponding to Prmin. Here Rf is related

to Prminby

Prmin¼ Prðd0Þ

Rf

d0

� ��g

; ð5Þ

where d0 is a reference distance and Prðd0Þ ¼ Ptd

ð4pd0k Þ

2 is the received power at distance d0.

Further Ptd is D2D transmit power in dBm and k is wavelength of operation. Thus Rf can

be expressed as

Rf ¼ do � 10Ptd�Prminþ20 log10ðk=ð4pdoÞ

10g

� �: ð6Þ

In order to make D2D pair ratio Prd=Prmin

should be[1 or in terms of logarithmic (in dB

domain), it should be more than zero. Thus probability that two proximal UEs operate in

D2D mode may be expressed as in [23]

pdðr̂dÞ ¼ Pr 10 log10

Prd

Prmin

� �[ 0

� : ð7Þ

From (4)

pdðr̂dÞ ¼1ffiffiffiffiffiffiffiffiffiffiffi2pr2p

Z 1

0

exp � 1

2

t � 10 log10^ðrdÞ�g

r

!22

4

3

5dt ð8Þ

¼ 1

21� erf a

lnðrd=Rf Þn

� �� ; ð9Þ

where n ¼ r=g and a ¼ 10=ðffiffiffi2p

lnð10ÞÞ.Next we find D2D link length rd in terms of Rf and pd. From (9)


123

ln� rd

Rf

�¼

n erf�1�1� 2pd

�

að10Þ

rd ¼Rf expn erf�1

�1� 2pd

�

a

" #

; ð11Þ

rd ¼ do � 10

�Ptd�Prminþ20 log10ðk=ð4pdoÞ

10g

�exp

�nerf�1

�1� 2pd

�

a

ð12Þ

as expn erf�1

�1�2pd

�

a

� ¼ eK and is constant for particular pd , r and g . Hence rd becomes

rd ¼ do � 10Ptd�Prminþ20 log10ðk=ð4pdoÞ

10g

� �� eK : ð13Þ

The above expression shows that D2D link length rd depends on Ptd , Prmin, k, pd, r and g.

Figure 2 shows rd for 95 % of time to be in coverage under without shadowing and with

shadowing for r ¼ 4, 6 and 8 dB taking d0 ¼ 1 m and Prmin¼ �104 dBm. It can be

observed that for a particular r, rd increases with Ptd . It is also seen that for particular Ptd ,

rd increases with r and this effect is less predominant at lower Ptd whereas it becomes

significant at higher values of Ptd .

2.1 UEs in D2D Transmitter Coverage Area

We next find number of UEs that lie in the coverage area of our reference UE acting as

D2D transmitter. The number of such UEs that fall in this D2D transmitter coverage area

may be expressed as

Ndmax¼ qpr2

d ¼ Npr2

d

pR2c

¼ Nrd

Rc

� �2

: ð14Þ

The above expression may be expressed using (12) as

−10 −5 0 5 10 15 20 250

50

100

150

200

250

300

350

Ptd

(dBm)

D2D

lin

k le

ng

th r

d (

m)

Without shadowingShadowing σ = 4 dBShadowing σ = 6 dBShadowing σ = 8 dB

Fig. 2 D2D link length versustransmit power


123

Ndmax¼ N

Rf

Rc

expn erf�1 1� 2pdð Þ

a

� �� 2

: ð15Þ

Figure 3 shows the maximum number of UEs (Ndmax) that lie in the coverage area of our

reference UE acting as a D2D transmitter. The coverage is for 95 % of time with varying

transmit power and total UEs in macro cellular area for r ¼ 6 dB and g ¼ 4. It is observed

that Ndmaxincreases linearly with N for fixed Ptd . It is also seen that for fixed N, Ndmax

increases exponentially with Ptd .

2.2 Expected Distance of Interfering D2Ds

The expected distance of the nth interfering D2D transmitter corresponding to selected

D2D receiver may be expressed as in [23]

E½rdn� ¼ �rdn

¼Z 1

0

rdfdðrd; nÞdr ¼C�nþ 1

2

�

ffiffiffiffiffiffipqp �

n� 1�!: ð16Þ

Figure 4 shows expected distance of interferers versus index of nth interferer with

Rc ¼ 288 m for N ¼ 100 and N ¼ 150. Under N ¼ 100 the observed expected distance of

the first inteferer is 23.3 m whereas under N ¼ 150 it is 20.84 m. It further shows that

expected distance of interfer decreases with N.

2.3 Bandwidth, Load and Activity of Cellular UEs and D2Ds

We consider OFDMA based cellular system having total bandwidth B Hz divided into

number of sub-channels. Occupancy of UE and nth interfering D2D in cellular area has

been modeled as active (ON) and inactive (OFF) as in [24, 25] and has been considered as

exponentially distributed. The amount of loading is represented as b and is defined as ratio

number of active UEs to total UEs. When a particular subchannel is selected for com-

munication by UE/eNB to other UE, SINR not only depends on received signal strenght

but on interference as well. In OFDMA based networks orthogonal allocation is done for

subchannels in a cell of interest, but neigbouring cells may be using same subchannel and

leads to CCI. CCI depends on load (bc) in neigbouring cells.

050

100150

200250

300

−10

0

10

20

0

50

100

150

200

N ( Number of UEs in celllular area)Ptd

in dBm

Nd

max

Fig. 3 Number of UEs that canbe broadcasted


123

In mixed cellular and D2D scenario, allocation of subchannels to D2Ds needs to be

done in such a way that QoS of primary cellular UEs are less affected by D2Ds presence.

When bc is\100 %, subchannels not been utilized may be alloted to D2Ds. But when bc is

equal to 100 %, subchannel allocation can be done carefully without or with less affecting

QoS of primary UEs. Under this case orthogonality preserved gets lost and CCI is there

from within the cell itself. In order to enhance system capacity further a single subchannel

may be alloted to more than one D2D in the cell. This may lead to further CCI within the

cell. Thus a tradeoff is there between the number of D2Ds using the same sub-channel

versus CCI to be less.

3 SINR, Capacity and Mode Selection

In mixed D2D and cellular scenario receiver UE having communication in subband k will

receive signal from intended transmitter and from iterfering D2D transmitters as well as

CCI from neigbouring cells based on their load (bc). Here we find received SINR at UE

placed at arbitary location in macrocell (r,h).

The received SINR in a UE under cellular mode at a location ðr; hÞ on a subband k using

downlink resources may be expressed as

cDLk;cðbc; bd;Ptkd

;PtkcÞ ¼ Ptkc0

Gkc0PNdmax

j¼1 PtkdjGkdj

vj þPNM�1

i¼1 PtkciGkci

vi þ BsbN0

ð17Þ

where Ptkc0is BS transmitted power, Gkc ¼ Lkczkcvkc is the channel gain, Lkc ¼ d

�gkc is path

loss component, zkc ¼ jhkcj2 is small scale fading component and follows Gamma distri-

bution and vkc ¼ expðwÞ is shadowing component for subband k. D2D transmitters loca-

tions are given by E½rdn� and vk is activity factor of UE acting as D2D transmitter on

subband k. First order probability mass function is given by Pr½vj ¼ 1� ¼ bd , where bd is

load factor of D2D. Bsb is the bandwidth of subchannel k and N0 is one sided power

spectral density of additive white Gaussian noise.

5 10 15 20 25 30 35 40

50

100

150

200

250

Interfering D2D transmitter index

E[r

dn

] (m

)

AnalyticalSimulation

N = 100

N = 150

Fig. 4 Expected distance of interfering D2D transmitters with Rc ¼ 288 m


123

Similarly SINR under D2D mode may be expressed as

cDLk;dðbc; bd;Ptkd

;PtkcÞ ¼ Ptkd0

Gkd0PNdmax�1j¼1 Ptkdj

Gkdjvk þ

PNM

i¼1 PtkciGkci

vi þ BsbN0

; ð18Þ

where Ptkd is the D2D transmitter power. The above expression can rewritten as

cDLk;dðbc; bd;P

tk;d;P

tk;cÞ ¼

zk;d0

Iðbc; bd;Ptk;d;P

tk;cÞ

ð19Þ

The denominator term I in the above expression is approximated as log-normal random

variable as I ¼ expðXÞ [25] where X is gaussian random variable with mean lX ¼2lnðEfIgÞ � 1

2lnðEfI2gÞ and r2

X ¼ lnðEfI2gÞ � 2lnðEfIgÞ. The product zk;d0times

expð�XÞ can be approximated as overall log-normal random variable cDLk;d � expðYÞ, where

Y is gaussian random variable with mean lck¼ wð1Þ � lX and variance

r2ck¼ fð2; 1Þ þ r2

X , where w is Eulers’s psi function and fð2; 1Þ is Riemann’s zeta func-

tion. The PDF of SINR may be expressed as

pck¼ 1

ckrck

ffiffiffiffiffiffi2pp exp

�ðln ck � lckÞ2

2r2ck

" #

: ð20Þ

CDF of lognormally distributed SINR may be expressed under cellular mode as

Pr cDLk;c\Cc

� �¼Z Cc

0

pck;cdck;c ð21Þ

¼1� Q10 log10 Cc � lcDL

k;c

rcDLk;c

!

ð22Þ

and under D2D mode as

Pr cDLk;d\Cd

� �¼Z Cd

0

pck;ddck;d ð23Þ

¼1� Q10 log10 Cd � lcDL

k;d

rcDLk;d

!

ð24Þ

Outage probability of cellular mode on kth subband sharing the spectrum with D2Ds

may be expressed as

PCoutðbc; bd;Ptkd

;PtkcÞ ¼ Pr c\cC

min

� �ð25Þ

where cCmin is minimum required SINR for communication in cellular mode . Similarly the

outage probability of D2D mode on kth subband sharing the spectrum with cellular UE

may be expressed as

PDoutðbc; bd;Ptkd

;PtkcÞ ¼ Prðc\cD

minÞ ð26Þ

where cDmin is minimum required SINR for communication in D2D mode.


123

3.1 Capacity Analysis

Link capacity of cellular/D2D mode is the measure of maximum possible rate (bits/sec/Hz)

that can be supported by the link. Link adaptation process matches data rate with the

instantaneous channel condition by appropriately choosing the modulation level. Practi-

cally discrete modulation levels are there with discrete rate supported. For each discrete

level there is minimum SINR (clmin) and maximum SINR (clmax

), if the SINR falls between

clminand clmax

that particular modulation level is choosen and bl bits are pumped. The

probability of choosing a particular lth level can be expressed as

pl ¼Z clmax

clmin

pcðcÞdc: ð27Þ

The bits to be pumped for a level can be given by

blðciÞ ¼ log2

� ci

cth

�; ð28Þ

where cth is the cutoff value for power policy. From the practical point of view there is

upper limit on number of constellation size. Let the maximum number of levels be NL.

Thus the normalized link capacity of cellular mode CNk;cðbc; bd;Ptkd

;PtkcÞ and D2D mode

CNk;dðbc; bd;Ptkd

;PtkcÞ on an average may be expressed as

¼XNL

l¼1

blpl ðbits=sec=HzÞ

Long term average throughput over the bandwidth B may be expressed under given load

condition bc for cellular mode as

Tk;cðbc; bd;Ptkd;PtkcÞ ¼ BðbcÞ � CN

k;cðbc; bd;Ptkd;PtkcÞ ðbits=secÞ

for D2D mode as

Tk;dðbc; bd;Ptkd;PtkcÞ ¼ BðbcÞ � CN

k;dðbc; bd;Ptkd;PtkcÞ ðbits=secÞ

As with a particular subband k one cellular UE and N � bd active D2Ds can be served

and hence system throughput per subband k can be expressed as

Tk;sysðbc; bd;Ptkd;PtkcÞ ¼ Tk;cðbc; bd;Ptkd

;PtkcÞ

þ NbdTk;dðbc; bd;Ptkd;PtkcÞ ðbits=secÞ:

ð29Þ

3.2 Mode Selection

Mode selection is to select the cellular mode of operation or D2D mode of operation and

may be based on SINR and depends on parameters inter-cell interference plus intra-cell

interference, distance, shadowing, channel condition and cellular and D2D load. The eNB

estimates the capacity of each mode at the receiver UE for both cellular and D2D mode and

selects the mode with better capacity. As the capacity in multicellular scenario depends on

the interference condition i.e the position of the D2D receiver UE with respect to NB while

using downlink resources. The distance where the capacity of D2D mode becomes better


123

than cellular mode can be said to be D2D mode switching distance. Let us represent this

D2D mode swithching distance in terms of the cell radius as RNsw. As the capacity of both

modes depends on bc; bd;Ptkdand Ptkc

and hence RNsw. Thus bc and bd plays a crucial role in

mode selection.

As the intra-cell plus inter-cell interference depends on the distance/location we have

taken distance criteria along with SINR for mode selection. Further in this work while

dealing mode selection, we considered that more than one D2D (bd %) plus cellular UE is

active at an instant of time per subchannel. The mode selection problem is modeled as

maxðCNk;d;C

Nk;cÞ ð30Þ

subject to Pcout �P

c=D2Dout �Pc

out þ �, where Pcout and P

c=D2Dout are the outage probability of

cellular UE located at Rf without and with D2Ds presence and � is tolerable offset. The

offset � is calculated based on the upper bound when system is fully loaded i.e.

bc ¼ 100 %.

3.3 Scheduling and Bandwidth Requirement

We consider round robin scheduling which is based on equal weightage to each user and is

passive to fading charactersitics. For the UEs near to the BS positive effect of fading does

not cancel with negative with the result that they achieve near to peak rate whereas for UEs

near to the edge it gets cancelled out and hence they never achieve the peak rate. This

reveals that UEs near to BS needs less bandwidth and are fair to operate in cellular mode.

But the UEs at the cell edge if operated in cellular mode needs large bandwidth along with

lesser througput offered by them. Thus if these edge UEs are switched to D2D mode, the

bandwidth requirement by these edge UEs becomes less. Now these edge UEs are able to

deliver higher througput as well. The overall effect of these consideration is that system

througput increases appreciably along with offloading facilitation of BS.

4 Results and Discussion

The analysis has been done taking parameters as mentioned in Table 1. It is assumed that

all cells are loaded with same loading factor.

Table 1 System parametersParameter Value

Number of macrocells 36

Macrocell radius 288 m

Carrier frequency 2.4 GHz

Path loss exponent 3

Shadow fading (r) 4 dB

Bandwidth (B) 10 MHz

Subchannel bandwidth 200 KHz

Thermal noise level (N0) -174 dBm

Modulation and coding levels 8

Number of UEs in central macrocell 100


123

−40 −20 0 20 400

0.2

0.4

0.6

0.8

1

γDLk

(βc, β

d, P

tkd

) (dB)

Pr(

γ <=

γth

)

βc =100 %, β

d = 4 %,

D2D mode

βc =100 %, β

d = 10 %,

βc =50 %, β

d = 4 %,

at 100 m

Cellular mode

−40 −20 0 20 400

0.2

0.4

0.6

0.8

1

Pr(

γ <=

γth

)

γDLk

(βc, β

d, P

tkd

) (dB)

βc =100 %, β

d = 10 %, D2D mode

βc =50 %, β

d = 4 %,

βc =100 %, β

d = 4 %,

at 175 m

Cellular mode

−40 −20 0 20 400

0.2

0.4

0.6

0.8

1

Pr(

γ <=

γth

)

γDLk

(βc, β

d, P

tkd

) (dB)

D2D mode

at 270 m

βc =100 %, β

d = 10 %

βc =100 %, β

d = 4 %

βc =50 %, β

d = 4 %

Cellular mode

Fig. 5 CDF of SINR of cellularand D2D UEs


123

Figure 5 shows CDF of SINR of UE under cellular and D2D mode. In analysis trans-

mitter power of each D2D transmitter Ptkd¼ 24 dBm and cellular BS (BS) Ptkc0

¼ 41 dBm.

The comparative analysis of the three plots shows that at 100 m the cellular mode is

having higher SINR as compared to D2D mode but when the distance changes to 270 m the

conditions becomes invert and rather D2D mode becomes prefferable. The performance of

the two modes are nearly same at 175 m. Thus it can be said that there is a swithching

distance from BS below which the cellular SINR is better than D2D mode and above which

D2D mode SINR is better than cellular mode.

Figure 6 shows outage probability of UE with respect to distance with Ptkd¼ 24 dBm

and Ptkc0= 41 dBm and the cmin taken is 0 dB. It shows that outage probabality of cellular

and D2D modes depends not only on distance but on number of active D2Ds in cellular

area as well. It is observed that higher the number of active D2Ds the outage probabality of

both cellular and D2D mode increases.

Figure 7 shows the outage probabality analysis with respect to distance for transmit

D2D power Ptkd¼ 24 and 15 dBm. It is observed when Ptkd

is changed from 24 dBm to 15

dBm, the outage probability of cellular mode decreases and that of D2D mode increases. It

further shows transition in switching distance from 134 to 255 m. Thus we can say that by

varying power the outage probabilities of cellular and D2D mode can be varied. If we want

to decrease the outage porobability of cellular mode BS power has to be increased or D2D

transmit power has to be decreased which leads to decrease in intracell interference due to

D2D onto cellular and hence improvement in cellular performance. Similarly if we want to

improve D2D performance BS power has to be decreased or D2D transmit power has to be

increased.

Figure 8 shows normalized link capacity in bits/sec/Hz for cellular and D2D mode of

operation. It shows that there is a swithching distance from BS below which the cellular

normalized link capacity is better than D2D mode and above which D2D mode normalized

link capacity is better than cellular mode. It is also seen that for a fixed distance with less

bc better normalized link capacity is achieved whereas with increase in bc there is fall in

normalized link capacity for both cellular as well as D2D modes.

0 50 100 150 200 250 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance (m)

Ou

tag

e p

rob

abili

ty P

r(γ

< γ m

in)

βc = 100 %, β

d = 4 %

βc = 50 %, β

d = 4 %

D2D mode

cellular mode

βc = 100 %, β

d = 10 %

Fig. 6 Outage probability versusdistance


123

Figure 9 shows normalized link capacity versus bc versus distance plot for 17 dB power

ratio. It is seen that distance criteria is appropriate for mode selection whereas bc affects

within the the particular mode only. It is seen that the distance where D2D mode capacity

is better than cellular mode is having range. In the figure this range is 89 m to 188 m.

Figure 10 shows RNsw for D2D mode from cellular mode versus bc. In this power ratio is

the ratio of BS power to D2D transmitter power. It is based on when normalized link

capacity of D2D mode becomes better than cellular mode it is better to switch to D2D

mode. It is observed that with lower bc, RNsw is towards the BS but there is distance gap

between BS and RNsw whereas when bc becomes higher RN

sw is farther from BS. The figure

also shows that by increasing power ratio RNsw can be shifted to larger distance and can be

brought towards BS by decreasing power ratio.

Figure 11 shows normalized link capacity versus bd versus distance for 17 dB power

ratio. It is seen that with increase in bd both the cellular and D2D mode normalized link

0 50 100 150 200 250 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance (m)

Ou

tag

e p

rob

abili

ty P

r(γ

< γ m

in)

cellular mode

Ptd

= 15 dBm, βc = 100 %,

βd = 4 %

D2D mode

Ptd

= 24 dBm, βc = 100 %,

βd = 4 %

Fig. 7 Effect of variation inpower on outage probability

0 50 100 150 200 250 3000

1

2

3

4

5

6

7

8

Distance from eNB (m)

Cm

an

d C

d (

bit

s/se

c/H

z)

Cellular mode

βc = 50, β

d=4 %,

Ptd

= 24 dBm βc = 100, β

d=4 %,

Ptd

= 24 dBm

βc = 100, β

d=10 %,

Ptd

= 24 dBm

D2D mode

Fig. 8 Normalized capacity ofcellular mode and D2D modeversus distance


123

020

4060

80100

0501001502002503000

1

2

3

4

5

6

7

8

βc

Distance (m)

No

rmal

ized

cap

acit

y (b

its/

sec/

Hz)

Cellular mode

D2D mode

Fig. 9 Normalized link capacityof cellular and D2D mode versusbc versus distance

10 20 30 40 50 60 70 80 90 1000.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

Cellular load βc (%)

RN sw

Power ratio = 17 dBPower ratio = 14 dBPower ratio = 11 dB

Fig. 10 Normalized thresholddistance obtained for switching toD2D mode versus bc

0

5

10

15

0501001502002503000

2

4

6

8

βd

Distance (m)

No

rmal

ized

cap

acit

y (b

its/

sec/

Hz)

Cellular mode

D2D mode

Fig. 11 Normalized capacity ofcellular and D2D mode versus bd

versus distance


123

capacity falls. It is also observed that with increase in bd the distance where the D2D mode

capacity becomes better than cellular mode gets nearer to BS.

Figure 12 shows RNsw for D2D mode from cellular mode versus bd when 100 D2Ds are

there in total in the cell of interest.It is seen that with increase in bd , RNsw tends towards BS

but not very near to BS.

Figure 13 shows bandwidth required by UEs in D2D mode with respect to cell load for

throughput of 1 Mbps. It is seen that D2Ds towards the cellular edge needs less bandwidth

whereas the bandwidth requirement becomes larger when D2Ds are near the BS. It is also

observed that with cell load the effect on bandwidth for the D2Ds at the cellular edge is

less whereas for those at nearby to BS it jumps to higher requirement.

5 Conclusions

In this paper, we have analyzed when and how to optimally exploit D2D mode to enhance

the cellular capacity. We observed that with increase in cellular and D2D load link capacity

of both modes falls, but the switching distance for D2D mode recedes away from BS with

0 5 10 15

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

D2D load βd (%)

RN sw

Power ratio = 17 dBPower ratio = 14 dBPower ratio = 11 dB

Fig. 12 Normalized thresholddistance obtained for switching toD2D mode versus bd

020

4060

80100

50100

150200

250300

0

0.5

1

1.5

2

2.5

3

3.5x 106

βcDistance (m)

Ban

dwid

th R

equi

red

(Hz)

Fig. 13 Bandwidth required for1 Mbps versus bc


123

cellular load whereas it tends towards BS with increase in D2D load. It is also seen that

bandwidth required for D2D mode is almost flat with the exception of locations near the

BS and for higher cell load where the the bandwith required for D2D mode becomes very

large. Thus we do say by observing capacity of both modes and the bandwidth required by

D2D mode that D2D communication enhance the system performance by improving the

system capacity if they are employed within certain range from the BS. Under the case of

17 dB power ratio this range varies from 0.39 of cell radius at 10 % cell load to 0.64 at

100 % load. It is also seen that if these UEs are switched to D2D mode, the bandwidth

requirement by these edge UEs becomes less. The reason is that due to proximity of

transmitter and receiver, the signal strength is better as compared to cellular link. Now

these UEs are able to deliver higher througput as well. The overall effect of these con-

sideration is that system througput increases appreciably along with offloading facilitation

of BS.

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Priyadarshi Ashok Dahat received his B.E. degree in Electronics andCommunications Engineering in 1999 from the Malaviya NationalInstitute of Technology, Jaipur - India and M.E. degree in ElectronicsEngineering (spl. Digital Communication) from Devi Ahilya Univer-sity Indore in 2008. He has been Assistant Professor at Devi AhilyaUniversity Indore. He is currently a Ph.D. scholar at G.S.Sanyal Schoolof Telecommunications, Indian Institute of Technology Kharagpur -India since 2011. His research interests is wireless communication andincludes OFDM based systems, adhoc networks and device-to-devicecommunications (D2D) in cellular systems.


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Dr. Suvra Sekhar Das obtained his B.Eng. degree in Electronics andCommunication Engineering from Birla Institute of Technology,Mesra, Ranchi, India in the year 2000. He completed PhD at AalborgUniversity in 2007. He worked as senior scientist at Innovation Lab ofTata Consultancy Services (TCS), from 2000 to 2008. He is currentlyAssistant Professor in the Department of Electronics and ElectricalCommunication Engineering as well as in the G. S. Sanyal School ofTelecommunications at IIT Kharagpur. His research interest is in crosslayer optimization of mobile broadband cellular networks.


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