Optimal Resource Allocation for Macro Cell-edge User in
Heterogeneous Macro-Femto Network
Yanwei Li, Zhenyu Zhou, Martin Macuha, Takuro Sato

Graduate School of Global Information and Telecommunication Study, Waseda University
Nishiwaseda 1-3-10, Shinjuku,Tokyo, Japan
1Introduction

Femtocell [1] has gained great attention in industry due tothe benefits for high data rate provision, low power consumption
in indoor environment. However, these benefits are greatly
limited by the challenges of interference between macrocell andfemtocell. In this paper, we emphatically analyse the resource
allocation for macro cell-edge users which location is far awayfrom Macro Base Station (MBS) but near Femtocell Base
Station (FBS). We develop a distributed optimal resource
allocation scheme to maximize the capacity of these macro celledge users. In this scheme, the macro cell-edge user is allowed
to use the unoccupied femtocell resources without affect theQoS of the original users in FBS. Firstly, the subchannels areallocated with the assumption of equal power distribution. Then
optimal power allocation is performed to maximize the totaltransmission rate of all the macro cell-edge users based on theLagrange optimal algorithm. Simulation results demonstrate ourproposed scheme can effectively allocate power and frequency
resource to these user devices, and achieve higher transmission
rate than equal power allocation.
2

FBS1

FUE

FUE11SFUEMUE

FBS 2

MUE

FUE21SFUEMBS
FBS 3
13

FUEFig. 1. System Model.
Here, we introduce a fairness index which is defined asbelow. It is used to ensure that each macro cell-edge user is able
to achieve its capacity requirement.
( R )(2)
K2k 1KkK  ( Rk ) 2
k 1

Then the optimization problem we considered can beformulated as follow:

System ModelIn this system, we consider one MBS with K Macro Users(UEs) that are uniformly located in its coverage area.
Meanwhile, there are several FBSs randomly deployed aroundthese MUEs. The system model is shown in Fig.1. We assume
that time is slotted and focus on the channel allocation problem
across these macro cell-edge users for a given time slot. It isreasonable to assume that the channel conditions do not changeover the duration of a time slot. In the certain time interval, theFBS sends the number and the ID of its unoccupied subchannel
to the MBS through the backhaul internet connection betweenthem. And the MBS can broadcast these subchannels to its celledge user devices. Then these users can selectively join the FBS
without exceed the resource constraint of the FBS. The originalusers of an FBS are defined as Primary Users (PFUEs), and thenewly joining cell-edge MUE is known as Secondary Users(SFUEs). If the channel is occupied by PFUE, then SFUE canonly transmit information in the channel with power constraintin order to guarantee the QoS requirement of PFUE.
Assume there are N unoccupied channels in nearby
femtocells which can be used by the macro cell-edge user
devices to improve its transmission rate. The object of this paper
is to maximize the transmission rate of cell-edge MUEs by
allocating them with optimal unoccupied FBS subchannels,
which means the macro cell-edge user is allowed to join theFBS temporally. Then these users will use the orthogonal
subchannel with the original FUEs and the transmission rate canbe formulated as below:
KNRk  Bc (k , n log 2 (1 k 1 n 1p F ,n g F ,n2))(1)

KNmax Bc ( k , n log 2 (1 k 1 n 1subject toR1 : R2 :N

pn 1F ,nk

pkF , n g kF , n

2Rk  1 : 2 :  k

 Ptotal , p

 k , n  {0,1},F ,nk 0Kk 1k ,n))(3)

for all k , n
 1 for all k , n

Where Bc is the constant bandwidth which is assigned toeach SFUE. pkF , n is the transmission power of FBS for MUE
F ,nk in nth subchannel. g k is the interference channel link gainfrom the FBS to MUE k , and  2 is the noise variance. Here, weconsider the transmission channel model which includes thedistance-dependent path loss, log-normal shadowing, andchannel variations due to frequency selection fading [2].
g  h210(  L( d ))/10(4)Where h is an exponential random variable with unit meanand variance. L(d ) is the distance-dependent path loss (in dB).
 k , n is defined to indicate the subchannel allocation statusof the i th MUE. If  k , n  1 , the k th MUE is allowed to use
the nth subchannel. Otherwise, if  k , n  0 , the k th MUE isrejected by the nth subchannel. The first constraint ensures thetransmission rate of each macro cell-edge user device. Assume
the transmission power in each subchannel is constraint. With
the knowledge of the total unoccupied channels, the total power
constraint can be known and we define it as Ptotal here. The third

3

Adaptive Resource Allocation

The objective of optimization problem we proposed in lastsection is a mix integer programming problem. We use lowcomplexity suboptimal algorithm to solve this problem [3]. The
algorithm concludes two steps, suboptimal subchannel
association and suboptimal power allocation.
In the suboptimal subchannel association scheme, we
assume that FBS distributes equal transmission power in each
subchannel for SFUE which wants to join its area. Different
subchannel will generate different channel gain for different UE.
With equal transmission power, to maximize its transmissionrate, the macro cell-edge user device will choose the subchannel
with highest channel gain. We define k as the set of subchannel

has the same capacity constraint. We compare our result with
the normal equal power control transmission. That is, theseunoccupied subchannels and power are equally allocated to all
the macro cell-edge user devices.
From Fig.2, it can be easily seen the total transmission rateof the macro cell-edge users is improved using our proposed
method. The resource is optimally assigned for each user. And
the total capacity of these users is increased. The fluctuation of
the blue bar is caused by the location of different user and thechannel gain in each subchannel.
total transmission rate under 64 unoccupied subchannels
25
proposed scheme
equal power allocation

total transmission rate (bit/s)

constraint shows that each subchannel can only be used by one
macro cell-edge user.

which is associated with cell-edge MUE k .
Algorithm 1: Iterative algorithm for subchannel
allocation of macro cell-edge user devices
Initialize k   for k  1,2 , K and Q  {1,2, , N}
For each subchannel do
Compute g kF , n according to (3)201510506810

1214161820

number of macro cell-edge usersFig. 2. Transmission Rate versus Number ofMacro Cell-edge Users.

If g kF , n > g kF , j for all j  Q, j  ntotal transmission rate of the worst userk  k  {n}Q  Q  {n}EndendBased on the above subchannel allocation, the optimization
problem can be rewritten as below. Compared with (3), wesimplified Bc , as Bc is a constant value which has no affection
to the optimization problem. And  k is the set of unoccupied
subchannel which is assigned to the macro cell-edge user.
Kmax(  log 2 (1 NpF ,nkn 1))

2Rk  1 :  2 :  k

 Ptotal , pkF , n  0

1   2 (5)for all k , nk  N

Next, we will present the Lagrange’s dual algorithm for theoptimize power allocation problem in the case of instantaneousconstraint. The Lagrangian of the optimization problem isdefined as:
KL ({ p },{k },{})    log 2 (1 F ,nkk  (  log 2 (1 k  2 n1KN  ( pk 1 n 1pkF , n g kF , n2k 1 n kKF ,nkF ,n1pF ,n1g2)   log 2 (1 n kF ,nkpg2)

F ,nk(6)))

 Ptotal )Where k are the Lagrange multipliers for the transmission
rate constraint and  are the Lagrange multipliers for thetransmit power constraint. For fixed k , maximization of (6) canbe decomposed into K independent subproblems. The
suboptimal power allocation is reached iteratively according to
the calculation of (6).
4

Lw=10dB
Lw=15dB
2.5

21.5

10.5

68101214161820

number of marco cell-edge users

pkF , n g kF , nk 1 n ks.t. R1 : R2 :3

Simulation Resluts

In this section, to evaluate the proposed scheme we set asimulation platform in which the total bandwidth is 10MHz andthe number of unoccupied femtocell subchannels is 64. The
transmission radius of macrocell and femtocell are 300m and20m, respectively. The macro cell-edge user devices arerandomly located in the macrocell coverage area. Of course, thedistance between these UEs and FBS is much closer than theirdistance to MBS. To make it simplify, we assume1 :2 : k  1:1: :1 , which means each macro cell-edge user

Fig. 3. Capacity versus number of UE withdifferent Lw .
Fig.3 illustrates the total capacity of cell-edge UEs versus thenumber of UE under different wall loss. It is clear that when thewall loss increases, the pathloss will increase. Then thethroughputs of the entire cell-edge UEs will decrease.
5Conclusion

In this paper, an adaptive resource allocation scheme isproposed to maximize the total transmission rate of macro celledge UE while considering the rate fairness between different
user devices. In this framework, the macro cell-edge user device
which experiences lower SINR is allowed to use the resource ofnearby femtocell without cause interference to the original FUE
in the femtocell. A two-step procedure is taken to achieve themaximal transmission rate, i.e. subchannel allocation and power
allocation. The simulation result shows the optimal algorithm
achieve higher capacity compared with the equal power
allocation from MBS. In the future, we would like to study thetotal transmission rate with different rate fairness requirement.
References[1][2][3]V.Chandrasekhar, J.G.Andrews, and A.Gatherer, “Femtocell
Networks: A survey”, IEEE Communication Magazine, Vol 46,
No.9, pp:59-67,Sep.2008.
P.Tarasak and T.Q.S.Quek, “Throughput and Fairness ofFemtocell Users in OFDM Macrocell-Femtocell Networks”, inIEEE Personal Indoor and Mobile Radio Communications(PIMRC), Toronto, Canada, Sept. 2011
Z.Shen, J.G.Andrews and B.L.Evans, “Adaptive Resource
Allocation in Multiuser OFDM Systems with Proportional RateConstraints”, in IEEE Trans. On Wireless Communications,vol.4,no.6,Nov. 2005, pp:2726-2737