distributed cell configuration strategy for macro/micro overlaid ...€¦ · the hot spot is...

International Journal of Software Engineering and Its Applications

Vol. 9, No. 9 (2015), pp. 177-188

http://dx.doi.org/10.14257/ijseia.2015.9.9.15

ISSN: 1738-9984 IJSEIA

Copyright ⓒ 2015 SERSC

Distributed Cell Configuration Strategy for Macro/Micro

Overlaid Hierarchical Cellular Systems

Eunsung Oh

Department of Electronics Engineering, Hanseo University,

Chungcheongnam-do, Korea, 360-706

[email protected]

Abstract

This paper presents cell configuration strategies for orthogonal frequency division

multiple access (OFDMA) based hierarchical cellular systems (HCS). We consider two

cases: the symmetric case that HCS is used to extend the data rate coverage and the

asymmetric case that HCS is applied to cover the hot spot. We formulate the cell

configuration strategy problem with spectral reuse planning and channel allocation

constraints, and suggest solutions for each case. The numerical results show that HCS

can improve the system stability in the symmetric case and enhance the system

performance about two times rather than that of the conventional cellular system, when

the hot spot is created at the macro-cell edge in the asymmetric case. In addition, we

describe that the co-channel interference from macro-cell base stations (BSs) are the

dominant factor of system performance, but that from microcell, BSs can be negligible.

Keywords: Cell configuration, radio resource allocation, hierarchical cellular system,

orthogonal frequency division multiple access, co-channel interference, quality of service

1. Introduction

Because of the increasing the mobile multimedia service e.g., gaming, video streaming,

and high-speed Internet access, the required data rate has been rapidly growing. However,

the macro-cell data rate coverage is less economically viable with an increasing demand

of high data rate services. To reduce this problem, the cellular structure of micro-cells

work overlaying existing macro-cells, called the overlaid cellular systems or hierarchical

cellular systems (HCS) [1, 2]. In HCS, two or more hierarchical cells are considered.

They consist of pico-cells to serve indoor user equipments (UEs), and micro-cells to

provide services to indoor or outdoor UEs. Both are overlaid by macro-cells. Small cells

provide greater spectral reuse and larger capacity, and allow the use of low power. They

also extend the data rate coverage that larger cells cannot serve. Large cells are used to

cover larger areas with low-cost implementation and to provide overflow groups of

channels for clusters of small cells when heavily loaded.

For enhancing the performance of HCS, the efficient cell configuration strategy is

required. The cell configuration algorithms have been proposed based on load balancing

[3–5]. In [3], it is introduced that load balancing can improve the system capacity in

CDMA based HCS systems. Jeong et al., presented a load sharing strategy controlled by

the serving cell selection [4]. The serving cell is selected based on measurement of the

channel quality and the load condition. It is shown that the macro-cell backs up the micro-

cell well in unusual heavy traffic load condition. Kwon and Cho proposed the resource

management algorithm in CDMA systems [5]. The proposed algorithm solves the

resource shortage in micro-cells by increasing the resource usage, and the resource

shortage is resolved by decreasing traffic in macro-cells. The computer simulation shows

that HCS systems can improve utilization of resource compared with conventional

systems.


Vol. 9, No. 9 (2015)

178 Copyright ⓒ 2015 SERSC

Also, the frequency planning in HCS systems has been researched [6]–[8]. It presented

a frequency planning between macro-cells and micro-cells in [6]. They compared the per-

cell capacity to share the frequency, and showed that the capacity of the frequency sharing

system is poor because of the large amount of the co-channel interference (CCI) between

the macro-cell and the micro-cell. Similar results are shown in [7]. Kim et al. showed that

the cell capacity is maximized by co-locating macro-cell and micro-cell sites with

different frequencies in CDMA systems [7]. However, if the interference avoidance

technique is considered, the frequency split does not maximize the system capacity [8].

Chandrasekhar and Andrews illustrated that, considering the worst-case interference at a

corner micro-cell, interference avoidance through a time-hopped CDMA and sector

antennas allows about a 7x higher micro-cell BS density, relative to a split spectrum

network with omnidirectional micro-cell antennas. These results provide guidelines for

the design of robust shared spectrum in HCS systems.

In this paper, we establish the cell configuration strategy in HCS downlink systems.

The goal of the strategy is to maximize the total transmitted data rate. The cell

configuration strategy in HCS environments is introduced considering the uniform traffic

case only [9]. This paper considers two HCS usage models: First, HCS systems are used

for the coverage extension. In this case, it is assumed that the traffic is uniformly

distributed. We define it as the symmetric case. HCS systems are also applied to the

asymmetric case such as the hot-spot case. In the hot-spot case, micro-cells must serve

small regions of high demand traffic with in the macro-cell coverage area. To handle

various cases, orthogonal frequency division multiple access (OFDMA) is considered [10].

To solve the problem, the optimization problem for maximizing the total transmitted data

rate is formulated. From the second-order condition for convexity, it is shown that the

problem has a global optimum point. Using some assumptions, the optimal cell

configuration strategy is proposed for the total transmitted data rate maximization.

This paper is organized as follows: In Section II, system models used in this study are

explained and the optimization problem for the total transmitted data rate maximization is

formulated. Section III presents the optimal cell configuration strategies. Section IV

details the simulation results of proposed cell configuration strategies, and discusses the

performance of HCS systems. Our conclusions are summarized in Section V.

2. System Model and Problem Formulation

2.1. System Model

Figure 1. A Macro/Micro-Cell HCS System Model. This Figure Illustrates that Three Microcell BSs Subsists in One Macro-Cell BS Service Area. Micro-cell

BSs are Posited with the Equal Distance

We consider a system where its service area is divided into hexagonal macro-cells of

equal size with the base station (BS) at the center of each macro-cell, ,


Vol. 9, No. 9 (2015)

Copyright ⓒ 2015 SERSC 179

and micro-cells are overlaid on each macro-cell service area, , as shown

in Figure 1. The 3-sector antenna for macro-cell BSs and the omni-directional antenna for

micro-cell BSs are assumed, respectively. Macro/micro-cells use same frequency

assignment (FA). In other words, the same radio channel is reused in every cell.

Subchannelized OFDMA with Nt subcarriers is used for the multiple access

schemes. The subcarrier space is divided into a number Ng of successive groups.

Each group contains Ns subcarriers. A subchannel has one element from each group

allocated, so N is the number of subchannel elements, N = Ng [11]. Subchannels are

randomly allocated to each UE. We assume partial CSI at the BS and per fect CSI at

the UE. This means that BSs only know the average channel gain of each

subchannel. The BS with the maximum signal strength, which then considers the

best serving cell selection, serves each UE.

A full buffer case is assumed for each UE. It means that the serving UEs are

always in the active state. The sets of UEs served by macro-cells and microcells are

defined as U1 and U2

, and represent the sets of UEs as for the

macro-cell and for the micro-cell, respectively. It is assumed that

the overall system is homogeneous in statistical equilibrium. In a homogeneous

system, one cell is statistically the same as any other cell. Using this observation,

the problem can be decoupled as a cell from the rest of the system, and the system

performance can be evaluated by analyzing the performance of the cell.

2.2. Problem Formulation

The goal of this work is to maximize the total transmitted data rate. The objective

function is formulated as

f Ru( ) = RuuÎU1

å + RuuÎU2

å , (1)

where Ru [bits/sec] is the transmitted data rate of a UE u. Using the Shannon

capacity, it is calculated as,

Ru

=BW

Nnulog

21+g

u

Rx( ). (2)

As shown in (2), the transmitted data rate is determined by the amount of

allocated channel resource to a UE u, nu , and the unit data rate constructed as the

transmitted signal to interference ratio (SIR) of a UE u, gu,

gu

Tx =Gubpi

ai1

Gub

1

p1

b1ÎB

1

å +ai2

Gub

2

p2

b2ÎB

2

å for uÎ U1,U2{ } and iÎ 1,2{ }, (3)

where Gub is the channel gain from BS b to UE u including the path loss and

shadowing impact, p1 and p2

are the transmitted power at macro/micro-cell.

Macro/micro-cells use the same FA; therefore the co-channel interference is

affected by both macro-cells and micro-cells. aij is the channel orthogonal factor

between cell j and cell i [6]. Because the subchannel is constructed as an interleaved

type in subchannelized OFDMA systems, the SIR of a UE u needs not be calculated

in each subcarrier [12]

We firstly consider the minimum required data rate as the quality of service

(QoS) guarantee constraint,


Vol. 9, No. 9 (2015)


Ru

³hu for uÎ U1,U2{ }, (4)

where hu [bits/sec] is the minimum required data rate of UE u.

Constraints for the cell configuration are added. The spectral reuse planning, ri ,

is considered. The spectral reuse planning is related to the traffic load and CCI,

because aij of (3) can be calculated as ri ´ r j

when random allocation is assumed

[13]. The constraint is expressed as

0 £ ri£1 for iÎ 1,2{ }, (5)

where the lower index 1 and 2 are presented for the macro-cell and the micro-cell,

respectively. In (5), ri =1 means that all channels are used at the cell, and the cell is

shut down if ri = 0.

And, the channel allocation constraint, nu, for each user is inserted for the link

performance,

nu

uÎUi

å / N £ ri

for iÎ 1,2{ }, (6)

Using the constraints explained above, the optimization problem is formulated as

maxr ,n

Ru

uÎU1

å + Ru

uÎU2

åìíï

îï

üýï

þï

s.t. Ru

³hu, "uÎ U

1,U

2{ }

0 £ ri£1, i Î 1,2{ }

nu

uÎUi

å / N £ ri, i Î 1,2{ }

(7)

The optimization problem in (7) means that the total transmitted data rate is

maximized by the cell configuration strategy of the spectral reuse planning and the

channel allocation considering the minimum required data rate.

3. Distributed Cell Configuration Strategy

In this section, the cell configuration strategies of HCS downlink systems are

determined. We firstly reformulate the optimization problem considering the signal

model. Based on that, we propose the cell configuration strategy for the total transmitted

data rate maximization.

3.1. Symmetric Case

The first usage of HCS is to increase the transmitted data rate by enhancing the

coverage. In this case, it is assumed that UEs are uniformly distributed, which is defined

as the symmetric case, and the spectral reuse planning for macro-cell and micro-cell are

equally controlled, r1 = r2.

Based on the above assumption, the transmitted SIRs of (3) are calculated as


Vol. 9, No. 9 (2015)


gu

1

Rx =Gubp

1

r1r

1Gub

1

p1

b1ÎB

1

å + r1r

2Gub

2

p2

b2ÎB

2

å=

1

r1

2gu

1

Tx for uÎU1

gu

2

Rx =Gubp

2

r2r

1Gub

1

p1

b1ÎB

1

å + r2r

2Gub

2

p2

b2ÎB

2

å=

1

r2

2gu

2

Tx for uÎU2

(8)

And the problem in (7) is reformulated as

maxr ,n

R̂u

uÎU1

å + R̂u

uÎU2

åìíï

îï

üýï

þï

s .t. R̂u

³hu, "uÎ U

1,U

2{ }

0 £ x £1,

x £ ri, i Î 1,2{ }

nu

uÎUi

å / N £ ri, i Î 1,2{ }

(9)

where R̂u

=BW

Nnulog

21+g

u

Tx / ri

2( ) . The object function is monotonic decreasing in ri . Thus,

the second constraint for the spectral reuse planning in (7) is modified as the second and

third constraints in (9).

In (9), the constraints satisfy the convexity, and the objective function is a concave

function, so the modified problem of (9) becomes a convex optimization problem. A

convex optimization problem can achieve a global optimized solution through Lagrangian

relaxation [14].

To solve the problem, the second and third constraints are relaxed using the Lagrangian

relaxation,

L n,r,x,l,m( ) = Ru

uÎUi

å + l 1- x( ) +m1

r1- x( ) +m

2r

2- x( )

(10)

The relaxed problem is decomposed into two parts. The first part is the problem of the

global spectral reuse planning, x,

maxx

- l +m1+m

2( ) x+ l (11)

Considering the slackness condition and the dual values, the solution of (8) is

determined as

x = min 1,r1,r

2( ) (12)

It is said that the system is not limited by CCI when x =1. However, if r1 =1 or r2 =1

then the system is restricted by CCI effected to the macro- or the micro-cell.

The problem of the second part is constructed by the residual part of (10) with the first

and fourth constraints. It is decomposed to the independent problem per each cell.

Therefore, we can do the distributed cell configure. In this paper, the way to solve the

problem of the second part for the macro-cell configuration is presented. Without loss of

generality, the micro-cell configuration can be gotten in the same way.

Similar to solving the first part, the first and fourth constraints in (7) is relaxed using

the Lagrangian relaxation,

L n,r,m,n ,w( ) = Ru

uÎU1

å +m1r

1+ n

uRu-h

u( )uÎU

1

å +w1Nr

1- n

u

uÎU1

åæ

è

çç

ö

ø

÷÷ (13)

From KKT and slackness condition, it is calculated as


Vol. 9, No. 9 (2015)


2 12

1

1 lo g 1 0

T x

u

u

u

L B W

n N

1

1 13

1 1 1

120

lo g 2

T x

u u u

T x

u U u

nL B WN

N

1

1 10

u

u U

N n

1

0u u u

u U

R

(14)

Under the characteristic of dual variables, nu,w

1> 0 , the first equation of (14) is

expressed as

nu

=w1

N

BW

log2

log 1+gu

Tx

r1

2

æ

èçç

ö

ø÷÷

-1³ 0 w

1³BW

Nlog

21+

gu

Tx

r1

2

æ

èçç

ö

ø÷÷, "u ÎU

1

(15)

Considering the dual problem, w1 is calculated as

w1=BW

Nlog

21+

gu*

Tx

r1

2

æ

è

çç

ö

ø

÷÷ (16)

where u* = arg maxuÎU

1

gu

Tx( ) . Using (14) and (16), the channel for each UE except UE u*

is

allocated to

2 2

1

lo g 1

u

u T x

u

n

N

B W

(17)

And, the UE u*

is residually allocated to satisfying the condition,

nu

gu

Tx / r1

2

1+gu

Tx / r1

2

1

log 1+gu

Tx / r1

2( )-

1

2

æ

è

çç

ö

ø

÷÷

uÎU1

å = 0 (18)

From results, the cell configuration strategy is summarized as follows:

[The cell configuration strategy at the symmetric case]

1) At each cell, the local spectral reuse planning, ri , is calculated by (17) and (18).

2) The information of the local spectral reuse planning is exchanged, and the global

spectral reuse planning is decided from (12).

3) The channel is allocated based on the global spectral reuse planning using (17) and

(18) at each cell.

3.2. Asymmetric Case

HCS can be applied at the asymmetric case such as covering hot spots. In this case, the

micro-cell operation is restricted because the power of the micro-cell has a very low value

compared with that of the macro-cell, p2 ≪ p1. Therefore, we assume that the spectral

reuse is only planned at the macro-cell, r1, and the spectral reuse factor for the micro-cell

is fixed to one.

Under the environments, the optimization problem of (7) is reformulated as


Vol. 9, No. 9 (2015)


maxr ,n

Ru

uÎU1

å + Ru

uÎU2

åìíï

îï

üýï

þï

s.t. Ru

³hu, "uÎ U

1,U

2{ }

0 £ r

1£1,

nu

uÎU1

å / N £ r1,

n

u

uÎU2

å / N £1

(19)

Similar to the symmetric case, the optimization problem of (19) is also the convex

optimization problem

Applying the Lagrangian relaxation, (19) can be expressed as

L nu,r

1,m

1,nu,w

i( ) = Ru

uÎ U1,U

2{ }

å + nuRu-h

u( )uÎ U

1,U

2{ }

å +m1

1- r1( )

+w1Nr

1- n

u

uÎU1

åæ

è

çç

ö

ø

÷÷+w

2N - n

u

uÎU2

åæ

è

çç

ö

ø

÷÷

(20)

From KKT and slackness conditions, the channel for each UE is allocated as

2 2

1

lo g 1

u

u T x

u

n

N

B W

for uÎU1

2 2

1

lo g 1

u

u T x

u

n

N

B W

for uÎU1 /u2

*

nu

2* = N - n

u

uÎU2/u

2*

å .

(21)

The spectral reuse planning of macro-cell is obtained to satisfying the follow condition,

nu

gu

Tx / r1

2

1+gu

Tx / r1

2

log 1+gu

1*

Tx / r1

2( )log 1+g

u

Tx / r1

2( )-

1

2

æ

è

ççç

ö

ø

÷÷÷+

uÎU1

ånu

2

gu

Tx / r1

2

1+gu

Tx / r1

2

log 1+gu

2*

Tx / r1( )

log 1+gu

Tx / r1( )uÎU 2

å = 0 (22)

Comparing to (18), equation (22) is shown that, at the asymmetric case, the spectral

reuse can be less than that at the symmetric case because of the micro-cell. At the

asymmetric case, the micro-cell is dependent on the macro-cell, thus the cell

configuration is processed at the macro-cell.

The cell configuration strategy at the asymmetric case is summarized as follows:

[The cell configuration strategy at the asymmetric case]

1) The spectral reuse planning, ri , is initialized.

2) The channel is allocated based on the spectral reuse planning using (21).

3) The spectral reuse planning is determined through (26).

4) The step 2) and 3) is repeated until the value is converged.

4. Simulation Results


Vol. 9, No. 9 (2015)


In our simulation, we considered the subchannelized OFDMA with 1024

subcarriers. The number of subchannel sets is 30 subchannels, and each data channel

set has 24 subcarriers [15]. The cellular system being simulated consists of 19 two-

tier hexagonal cells. In order to avoid the boundary effect, the results from the

center hexagonal cell are used.

4.1. System Throughput

To fairly compare, we calculated the spectral efficiency per a macro-cell area,

i.e., one macro-cell plus micro-cells. In figures, d means the distance from a macro-

cell BS to a micro-cell BS at symmetric case and a hot spot at asymmetric case,

respectively.

2 6 10 14 18 22 26 301

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

Number of user equipment

Spe

ctra

l eff

icie

ncy

[b

its/s

ec/

Hz]

without microcells

with 5 microcells at d=200m




d=600m

d=200m

Figure 2. Spectral Efficiency versus the Number of Micro-Cell and UE at the Symmetric Case with hu = 256[kbps / sec]

Figure 2 shows spectral efficiencies when the number of UE and the distance

between a macro-cell BS and a micro-cell BS are varying at symmetric case. At the

symmetric case, spectral efficiency without micro-cells is increased in low traffic

region, but is decreased in medium and high traffic regions. That is why in low

traffic cases, the system can obtain the multi-user diversity when the number of UEs

is increased, but CCI constraints the spectral efficiency in medium and high traffic

regions. However, spectral efficiencies with micro-cells are maintained in medium

and high traffic regions. This means that HCS systems can enhance the system

stability in high traffic region. Also, the spectral efficiency is improved when the

number of micro-cell is increasing and the distance between the macro-cell BS and

the micro-cell BS becomes far off. It is shown that HCS systems obtain performance

enhancement by spreading the traffic. Without loss of generality, when the micro-

cell is posited at the macro-cell edge, the enhancement is maximized in medium and

high traffic regions. Switching off BS without serving UE occurs in the low traffic

region. Therefore, the spectral efficiency has the maximum value when the

microcell is posited near the macro-cell BS.


Vol. 9, No. 9 (2015)


Figure 3. Spectral Efficiency versus the Number of Micro-Cell and UE at the Asymmetric Case with hu = 256[kbps / sec]

Figure 3 illustrates spectral efficiencies versus the number of UEs at asymmetric

case. Hot spot is modeled that 20 UEs are randomly generated in a circular region

within 150m, and a micro-cell is posited at the center of circle. In this case, the

spectral efficiency without micro-cells has a similar value to the symmetric case, but

that with micro-cells are enhanced in all traffic regions. This means that micro-cells

support all UEs in hot-spot area, and the spectral efficiency is dependent on that in

HCS systems.

As a result, the HCS system can improve the system stability at high traffic and

high-required data rate at the symmetric case, and can dramatically enhanced the

spectral efficiency at asymmetric case.

4.2. Optimum Spectral Reuse Planning

Figure 4 shows the optimum spectral reuse planning at symmetric case. If the

minimum required data rate case is lower than the optimum, spectral reuse planning

without micro-cells is one at the most traffic region. It means that CCI does not

limit the system performance in the low requirement case. However, increasing the

traffic in the high requirement case decreases the optimum spectral reuse planning.

That is why CCI constraints the system performance. On the contrary, the effect of

traffic can be neglected by the optimum spectral reuse planning with micro-cells.

The optimum spectral reuse planning with micro-cells depends on the distance

between the macro-cell BS and the micro-cell BS. The longer distance case has a

larger optimum spectral reuse planning. It means that the amount of CCI from the

macro-cell BS is seriously affected in HCS systems. Because the optimum spectral

reuse planning has a similar value at 3 and 5 microcell cases, it is said that the effect

of CCI from the microcell BS is neglectful.


Vol. 9, No. 9 (2015)


2 6 10 14 18 22 26 300.7

0.75

0.8

0.85

0.9

0.95

1

1.05


Op

tim

um

rh

o, r

*

without microcells





d=600m

d=200m

Figure 4. Optimum Spectral Reuse Planning versus the Number of Micro-Cell and UE at Symmetric Case with hu = 256[kbps / sec]

2 6 10 14 18 22 26 300.75

0.8

0.85

0.9

0.95

1

1.05


Op

tim

um

rh

o, r

*

without microcells at d=200m



Figure 5. Optimum Spectral Reuse Planning versus the Number of Micro-Cell and UE at the Asymmetric Case with hu = 256[kbps / sec]

At the asymmetric case, the optimum spectral reuse planning without micro-cells

is illustrated in Figure 5. That has the similar value at symmetric case. It means that

the distribution of UE’s position doesn’t affect the system performance. It is also

shown in results of the spectral efficiency. However, the optimum spectral reuse

planning with micro-cells at asymmetric case has the value of minimum spectral

reuse planning. It is said that the system performance is decided by the performance

of micro-cell.

As a result, it is said that all spectral resource must be used to obtain the optimum

performance in low requirement regions, but resource partitioning is optimum in

high requirement region without micro-cells. However, because HCS systems can


Vol. 9, No. 9 (2015)


separate the traffic, the optimum spectral reuse planning with microcells is

dependent on CCI from macro-cell BSs at symmetric case. This has the minimum

spectral reuse planning because the microcell performance constraints the system

performance at asymmetric case.

5. Conclusions

In this paper, we proposed cell configuration strategies for OFDMA based HCS

downlink systems at symmetric case and asymmetric case. First, we formulated the

optimization problem with spectral reuse planning and channel allocation

constraints, and obtained the optimum solution using the Lagrangian relaxation

because the optimization problem is the convex problem. The proposed solutions are

only required partial CSI and are able to be distributed cell configuration. Results

showed that HCS systems can enhance the system stability at symmetric case and

improve the system performance at asymmetric case, and verified that the CCI from

macro-cells is the important parameter in HSC systems. Furthermore, we outlined

the relationship among resource parameters. Further research is needed to consider

the dynamic resource management, i.e. power control, MIMO.

Acknowledgements

This work was supported by 2014 Research Grant of Hanseo University.

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Vol. 9, No. 9 (2015)


[15] Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems Amendment for

Physical and Medium Access Control Layers for Combined Fixed and Mobile Operation in Licensed

Bands, IEEE Standard 802.16 (2006).

Author

Eunsung Oh, received his B.S., M.S. and Ph.D. degrees in

Electrical Engineering at Yonsei University, Seoul, Korea, in 2003,

2006 and 2009, respectively. From 2009 to 2011, he was a post-

doctoral researcher in the Department of Electrical Engineering at the

University of Southern California's Viterbi School of Engineering.

From 2011 to 2012, he was a senior researcher at Korea Institute of

Energy Technology Evaluation and Planning, Korea. From 2012 to

2013, he was a research professor in the Department of Electrical

Engineering at Konkuk University, Korea. He is currently an assistant

professor in the Department of Electrical and Computer Engineering

at Hanseo University, Korea. His main research interests include the

design and analysis of algorithms for green communication networks

and smart grid.

distributed cell configuration strategy for macro/micro overlaid ...€¦ · the hot spot is...

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