cell configuration strategy for ofdma based hierarchical cell...

Cell Configuration Strategy for OFDMA Based

Hierarchical Cell Structure

Eunsung Oh

Department of Electronics Engineering, Hanseo University, Korea, 360-706

(e-mail: [email protected])

Abstract. This paper presents cell configuration strategies for orthogonal

frequency division multiple access (OFDMA) based hierarchical cell structure

(HCS) downlink systems. It is considered that HCS systems are used to extend

the data rate coverage. The cell configuration strategy problem is formulated

with spectral reuse planning and channel allocation constraints, and is proposed

the solution. The numerical results show that the proposed algorithm can

enhance the system performance of HCS systems.

Keywords: Cell configuration, hierarchical cell structure, orthogonal frequency

division multiple access, resource allocation.

1 Introduction

Wireless communication systems recently provide multimedia services such as voice,

video streaming and high-speed Internet access, etc. These services require high data

rate wireless communications. To provide various high data rates services in the same

location, it is preferable that some macro-cells overlay other microcells [1]. This

cellular structure is called the overlaid cell structure or hierarchical cell structure

(HCS) [2].

In HCS systems, UEs with different characteristics (i.e., mobility, required traffic,

etc.) are initialized at different cells. Therefore, to enhance the system performance,

the efficient cell configuration strategy is required in HCS systems [3].

It has been researched about the cell configuration algorithms [4] and the

frequency planning [5] in HCS systems. Prior works have shown that the HCS system

can enhance the system capacity. However, proposed strategies are based on the

heuristic approach. In addition, most of the schemes are proposed based on the

coordinated cell configuration across cells with several practical challenges.

In this paper, the cell configuration strategy is established for the total transmitted

data rate maximization in HCS downlink systems. Firstly, the optimization problem

for maximizing the total transmitted data rate is formulated. Using some assumptions,

the optimal cell configuration strategy is proposed for the total transmitted data rate

maximization. The control strategy is researched with partial channel state

information (CSI).

Advanced Science and Technology Letters Vol.108 (Mechanical Engineering 2015), pp.80-85

http://dx.doi.org/10.14257/astl.2015.108.18

ISSN: 2287-1233 ASTL Copyright © 2015 SERSC

2 System Model and Problem Formulation

2.1 System model

It is considered a system that its service area is divided into hexagonal macro-cells

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

cells are overlaid on each macro-cell service area. Macro/micro-cells use same

frequency assignment (FA). The subcarrier space is divided into successive groups. A

subchannel has one element from each group allocated. Subchannels are randomly

allocated to each UE. It is assumed partial CSI at the BS and perfect CSI at the UE.

The best serving cell selection is considered that each UE is served by the BS which

has the maximum signal strength. Let the sets of macro/micro BSs be B1 and B2

,

and the UEs served by macro-cells and micro-cells is presented as U1 and U2

,

respectively.

2.1 Problem formulation

Assuming the homogeneous system, the objective function for the total transmitted

data rate is calculated as

f Ru( ) = RuuÎU1

å + RuuÎU2

å (1)

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

modeled by the Shannon capacity as,

Ru

=BW

Nnulog

21+g

u

Rx( ) (2)

where nu is the number of subchannel allocated to a UE u, BW is the system

bandwidth, and gu is the transmitted SIR of a UE u, which is calculated as

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 power from BS b to UE u, p1 and p2

are the transmitted

power at macro/micro BS, and aij is the channel orthogonal factor between cell j

and cell i [6].

The optimization problem for maximizing the total transmitted data rate is

formulated as

Advanced Science and Technology Letters Vol.108 (Mechanical Engineering 2015)

Copyright © 2015 SERSC 81

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{ }

(4)

3 Cell Configuration Strategy

One of the important usage models of HCS is the coverage extension. In this case, it

is assumed that UEs are uniformly distributed. Therefore, we assume that the spectral

reuse planning for macro-cell and micro-cell are equally controlled.

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

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

(5)

Using this model, the optimization problem of (4) 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{ }

(6)

where R̂u

=BW

Nnulog

21+g

u

Tx / ri

2( ) . The object function with R̂u is monotonic

decreasing in ri . Thus, the second constraint for the spectral reuse planning in (4) is

modified as the second and third constraints in (6). The optimization problem of (6) is

the convex optimization problem because the constraints are satisfied the convexity

and the object function is concave [7].

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

Lagrangian relaxation,


82 Copyright © 2015 SERSC

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

uÎUi

å + l 1- x( ) +m1

r1- x( ) +m

2r

2- x( )

(7)

From (7), the 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 (8)

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

determined as

x = min 1,r1,r

2( ) (9)

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 (7) with the

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

Similar to solve 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

÷÷ (10)

From KKT, slackness condition and the characteristic of dual variables, nu,w

1> 0,

it 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

(11)

Considering the dual problem, w1 is calculated as

w1=BW

Nlog

21+

gu*

Tx

r1

2

æ

è

çç

ö

ø

÷÷ (12)

where u* = arg maxuÎU

1

gu

Tx( ).

The channel for each UE except UE u* is allocated as

2 2

1

lo g 1

u

u T x

u

n

N

B W

(13)

It means that the minimum channel satisfied the minimum required data rate is

allocated to UEs without UE, which has the best CSI. For the best CSI UE the

channel is allocated to satisfying the follow 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 (14)



4 Simulation results

In our simulation, the system considered subchannelized OFDMA with 1024

subcarriers. The number of subchannel sets is 30 subchannels. 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. The simulation

values were chosen for urban environments [8]. To fairly compare, it is calculated the

spectral efficiency per a macro-cell area, i.e, one macro-cell plus microcells. In

figures, d means the distance from a macro-cell BS to a micro-cell BS.

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

ctr

al effic

iency [bits/s

ec/H

z]

without microcells

with 5 microcells at d=200m




d=600m

d=200m

Fig. 1. Spectral efficiency versus number of micro-cell and UE with hu = 256[kbps / sec]

Spectral efficiencies verse number of UEs is shown in Fig. 2. Spectral efficiency

without micro-cells is increased in low traffic region, but that is decreased in medium

and high traffic region. That is why in low traffic case the system can be obtained the

multi-user diversity when the number of UEs are increased, but CCI constraints the

spectral efficiency in medium and high traffic region [12]. However, spectral

efficiencies with micro-cells are maintained in medium and high traffic region. It

means that HCS systems can be enhanced the system stability in high traffic region.

And, 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 are obtained the 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 region. In low traffic

region, the switching-off BS without serving UE is occurred. Therefore, the spectral

efficiency has the maximum value when the micro-cell is posited near the macro-cell

BS.


84 Copyright © 2015 SERSC

4 Conclusions

In this paper, it is proposed a cell configuration strategies for OFDMA based HCS

downlink systems. First, the optimization problem is formulated 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 shown that HCS systems can enhance the system stability and

improve the system performance.

Acknowledgment. This research was supported by Basic Science Research

Program through the National Research Foundation of Korea (NRF) funded by the

Ministry of Science, ICT & Future Planning (No. 2013R1A1A1009526).

References

1. H. Claussen, L. T. W. Ho, and L. G. Samuel, “Financial analysis of a pico-cellular home

network deployment,” in Proc. IEEE Int. Conf. Communications, Jun. 24-28, 2007, pp.

5604–5609.

2. K. Son, E. Oh, and B. Krishnamachari. "Energy-efficient design of heterogeneous cellular

networks from deployment to operation." Com. Networks vol.78, pp. 95-106, 2015.

3. L. Ortigoza-Guerrero and A. H. Aghvami, Resource Allocation in Hierarchical Cellular

Systems. London, UK: Artech House, 1999.

4. D. G. Jeong and W. S. Jeon, “Load sharing in hierarchical cell structure for high speed

downlink packet transmission,” in Proc. IEEE Global Telecommunications Conf., vol. 2,

Nov. 17-21, 2002, pp. 1815–1819.

5. S. Kim, D. Hong, and J. Cho, “Hierarchical cell deployment for high speed data cdma

systems,” in Proc. IEsEE Wireless Communications and Networking Conf., Mar. 17-21,

2002, pp. 7–10.

6. E. Oh, M.-G. Cho, S. Han, C. Woo, and D. Hong, “Performance analysis of reuse-

partitioning-based subchannelized OFDMA uplink systems in multicell environments,”

IEEE Trans. Veh. Technol., vol. 57, no. 5, pp. 2617–2621, Jul. 2008.

7. G. Li and H. Liu, “On the optimality of the OFDMA network,” IEEE Commun. Lett., vol. 9,

no. 5, pp. 438–440, May 2005.

8. IEEE 802.16m Evaluation Methodology Document (EMD), IEEE Std. 802.16m, 2009.

9. E. Oh, S. Han, C. Woo, and D. Hong, “Call admission control strategy for system throughput

maximization considering both call- and packet-level QoSs,” IEEE Trans. Commun., vol.

56, no. 10, pp. 1591–1595, Oct. 2008.



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