Communications and Network, 2013, 5, 211-216
http://dx.doi.org/10.4236/cn.2013.53B2040 Published Online September 2013 (http://www.scirp.org/journal/cn)
Component Carrier Selection and Beamforming on
Carrier Aggregated Channels in Hetero geneous Networks
Changyin Sun1, Hongfeng Qing2, Shaopeng Wang2, Guangyue Lu1
1Department of Communication and Information Engineering, University of Xi’an Posts and Telecommunications,
Xi’an, China
2ZTE Cooperation, Xi’an, China
Received June, 2013
ABSTRACT
In this paper, component carrier selection and beamforming on carrier aggregated channels in Heterogeneous Networks
are proposed. The scheme jointly selects the component carrier and precoding (i.e. beamforming) vectors with the co-
operation of the other cells to deal with the interference between Macro cell and Pico cell. The component carrier selec-
tion and beamforming is achieved by optimizing the multi-cell downlink throughput. This optimization results in shut-
ting down a subset of the component carrier in order to allow for a perfect interference removal at the receive side in the
dense low power node deployment scenario. Additionally, algorithm based on Branch and Bound Method is used to
reduce the search complexity of the algorithm. Simulation results show that the proposed scheme can achieve high
cell-average and cell-edge throughput for the Pico cell in the Heterogeneous Networks.
Keywords: Heterogeneous Network; Inter-cell Interference Coordination; Beamforming; Carrier Aggregation
1. Introduction
The concept of Heterogeneous networks has attracted a
lot of interests recently to optimize the performance of
the network[1]. In Heterogeneous networks(HetNet), the
network topology is improved by overlaying the planned
network of high power Macro base stations with smaller
low power Pico base stations that are distributed in an
unplanned manner or simply in hotspots where a lot of
traffic is generated. These deployments can improve the
overall capacity and the cell edge user performance [2].
With HetNet deployment in same spectrum, users can
experience severe interference. This effect is due to the
often geographically random low power node deploy-
ment as well as the near-far problem arising from the
imbalance in path-gains and transmission powers be-
tween the macro cell and low power nodes. 3GPP-LTE
has devoted significant standardization effort towards
devising inter-cell interference coordination (ICIC)
schemes for minimizing interference, culminating in the
so-called “enhanced” ICIC (eICIC) in LTE-Advanced.
The eICIC is one of the most important features of
LTE Advanced, without it the range extension concept [3]
loses its advantage and efficiency. The eICIC solutions
are mainly divided into frequency domain solutions such
as carrier aggregation and time domain solutions such as
almost blank subframes (ABS) [2]. The main frequency
domain multiplexing inter-cell interference coordination
scheme used in LTE-Advanced is carrier aggregation,
which basically enables a LTE-Advanced user equipment
(UE) to be connected to several carriers simultane-
ously[2].
Carrier aggregation (CA) not only allows resource al-
location across carriers but also allows scheduler based
fast switching between carriers without time consuming
handovers, which means that a node can schedule its
control information on a carrier and its data information
on another carrier. So by scheduling control and data
information for both Macro and Pico layers on different
component carriers, interference on control and data can
be avoided. It is also possible to schedule center
Pico-eNodeB(eNB) user data information on the same
carrier that the Macro layer schedules its users, as the
interference from the Macro layer on center Pico-eNB
users can be tolerated, while Pico-eNB users in the range
extension areas are still scheduled in the other carrier
where the Macro-eNB users are not scheduled[4-6] .
In case of eICIC, only loose coordination among mac-
ros and picos is needed, which is advantageous from a
deployment perspective. Coordinated multipoint trans-
mission (CoMP) aims to achieve additional gains on top
of eICIC by tightening the coordination among cells. For
example, considering the practical constraints for joint
transmission, paper [7] focuses on Coordinated schedul-
ing/beamforming (CS/CB) based CoMP schemes in
C
opyright © 2013 SciRes. CN

C. Y. SUN ET AL.
212
which the concept of resource partitioning and almost
blank subframes is used firstly as an effective way of
mitigating the interference between the pico cell and
macro cell, and then on shared subframes, CS/CB is ap-
plied for improved interference coordination. As a result,
scheduling and beam selection gains can be achieved.
However, as the number of picos grows, it becomes
much harder to choose a beam good for every pico, if
possible at all, so the beam selection gain will vanish.
Paper [8] also employ multiple antennas in two-tier fem-
tocell networks to provide additional degrees of freedom
that can be used to help coordinate the cross-tier inter-
ference, it propose a beamforming codebook restriction
strategy. Although restricting the beamforming codebook
increases the quantization error for the macrocell users,
proportional fair scheduler compensate for the increased
quantization error by exploiting the channel selection
diversity gain and the multiuser diversity gain. As the
number of femtocell grows, the opportunistic channel
selection strategy will loose the limited additional de-
grees of freedom.
In this paper, component carrier selection and Beam-
forming on carrier aggregated channels in Heterogeneous
Networks is addressed. The Heterogeneous Networks
consists of complementing the Macro layer with low
power nodes such as Pico base stations, and solution
such as Range Extension is assumed to extend the cov-
erage area of the Pico nodes. The scheme jointly selects
the component carrier and precoding (i.e. beamforming)
vectors with the cooperation of the other cells to deal
with the interference between Macro cell and Pico cell.
The component carrier and beamforming selection is
optimized not only to exploit additional degrees of free-
dom provided by multiple antennas and component car-
riers, but also to restore the feasibility of the CS/CB
when the number of low power nodes grows. As a result,
the design will shut down a subset of the component car-
rier in order to allow for a perfect interference removal at
the receive side in the large dense low power node de-
ployment scenario. Additionally, algorithm based on
Branch and Bound Method is used to reduce the search
complexity of the algorithm. The proposed approach is
confirmed by simulation results compared with the per-
formance of the baseline approach.
2. System Model
We consider Hetnet network with the following features:
1) a certain number of Pico-eNBs are deployed through-
out one Macro cell layout; 2) The Pico-eNBs are ran-
domly distributed; 3) The users are randomly distributed
throughout the cell area.
Now consider the downlink transmission with M users
and K carriers in the network. The BSs and the users are
assumed to have N transmit antenna and one receive an-
tenna, respectively. For simplicity, the transmit power is
kept the same in each carrier per cell q, i.e. q. Let the
binary matrix ,,
P
{a| a{0,1}}
kmkmK M

A describes the
carrier selection among the users, where ,1
km
a

de-
notes that carrier k is assigned to user m, otherwise,
,0 km
a

.
Now, denote by ,,,, ,kmikmiki S

hb the channel power
gain to the selected mobile user m in cell q from the cell i
base station, in resource slot t, where
12
,,,, ,,,,
[,,
N
kmikmikmikmi
hh hh]
denotes the channel vector of the user m in cell q from
the cell i base station, 1
,
N
ki 
bC is the beamforming
vectors used to map the user in cell i data symbols to the
transmit signals. The channel gains are assumed to be
constant over each such resource slot, i.e., we have a
block fading scenario. Note that the gain ,,kmq corre-
sponds to the desired communication link, whereas the
gains ,,kmi for i
S
Sq

correspond to the unwanted in-
terference links. Assuming the transmitted symbols to be
independent random variables with zero mean and a
variance q, the signal to noise-plus-interference ratio
(SINR) for each user is given by:
P
2
,,,
,, 22
,,,,
1,
||
||
qkmqkq
kmq N
ki ikmikiq
iiq
P
SINR aP




hb
hb (1)
where

is the variance of the independent zero-mean
AWGN.
Then the achievable rate for user m is given by:
,2,,
11
log (1)
KK
mqkmq kmq
kk
RSINR



,,
R
(2)
Assume at time slot t, only one user ()mSq

is
scheduled at each base-station q, so we will not distin-
guish cell q and the user served by cell q for simplicity,
then from (1) and (2) the total achievable throughput
(sum rate) is then found as
,
1
Q
mq
q
RR


2
,,,,
2
11 22
,,,,
1,
||
log (1)
||
QK kq qkqqkq
N
qk
ki ikqikiq
iiq
aP
RaP



 
 
hb
hb
(3)
The component carrier selection and interference coor-
dination problems are to find the matrix A and ,kq
such that the objective function is optimized. Assuming
the goal is to achieve the highest system throughput while
ensuring proportional fairness among different users, the
following utility function needs to be maximized:
b
,
11
,
1
,
..1)
2) ||1
QK
qkq
qk
K
kq q
k
kq
RR
s
ta








b
C (4)

C. Y. SUN ET AL. 213
The constrained problem (4) is a mixed binary-non-
convex problem. To find the global optimum, one has to
exhaustively search through all possible ,ki (real val-
ues) and ,kq (binary values). Here, we shall first de-
compose it into the K independent per-carrier objective
function, then adopt the method of alternatingly optimiz-
ing antenna vectors and the component carrier selection.
b
a
The Lagrangian of problem (4), dualized with respect
to the constraint 1) is defined as:
,,
11
{}
K
qkq qkqqq
kqq q
J
Ra 


 C
 (5)
This Lagrangian can be decomposed into the K inde-
pendent per-carrier objective function. For a particularq

the optimization problem (5) can be solved in a per-car-
rier fashion:
,
,
{,}argmin{ }
..1)|| 1
2) 0
3) {0,1}
opt
kk k
kq
q
kq
J
st
a





Ba
b (6)
where ,,kqkqqkq
J
Ra   

.
To solve (4) by (6), q

should be tuned to enforce the
constraints as in [9], where an efficient Lagrange multi-
plier search procedure is presented. This procedure for
the Lagrange multipliers is assumed in the following
update formula:
1
,
1
(
K
tt
qq qkq
k
Ca




 
)

(7)
1, 2,,qQ
where ()
x
 means max(0, x), t is the iteration number,


is a step size parameter and q is the number of
carrier selected corresponding to the Lagrange multipli-
ers at hand.
C
Assume q

is fixed and ,kq is selected on carrier k,
the transmit beamforming vector q of cell q in carrier
k which maximizes the sum rate in (6) is given by the
following dominant eigenvector problem [10]:
ab
,
1,
()
Q
iq b
iiq




qi,qq
EAb 
q
b
q
(8)
where , and the real values H
qq,qq,
Ehh H
i,qi,q i,q
Ahh
,iq

is defined as following:
22 2
,22 2
|| ||
||
qq i
iq
iq q
PP
P



 

qq,qq i,i i
ii,ii i
Ihb hb
IhbI (9)
And is the received interference power of user q:
q
I
2
1, ||
Q
i
iiq P


qq,i
Ihb
i
With fixed we denote
(10)
The optimum point are the eigenvector corre-
sponding to the largest (resp. smallest) eigenvalue of (8).
*
q
b
*
,ki q
bb 2
,,,, ,
||
kqqkqqkq
hhb,
2
,,,, ,
||
qikqi qi
hbne can get a
k
h Thus, ofrom (6) with :
,kq
2
,
,,,
||
qq
kqi
,,
||
(1)
kq q k
aPh
2,
11 22
1,
log
QK
kqkq
N qk
ki iq
iiq
J
a   

aP N


 
 
(11)
2.1. Linear Convex Relaxation Approach
hese de-
h
Unfortunately, for given Lagrange multipliers, t
coupled optimization problems (11) are themselves dif-
ficult nonconvex problems. So a novel low-complexity
optimization algorithm is presented. The algorithm is
based on a relaxation of the nonconvex per-carrier opti-
mization problem (11) leading to a more direct and con-
ceptually simple procedure.
The convex relaxation starts with rewriting the objec-
tive function of (11) in the following form:
22
2,,,
1
{log (||)
Q
kkiikqiq
qi
JaPh 

 
 ,
22
2,
1,
}
log(|)
qkq
Q
ki ikqq
qiiq
a
aPh


 (12)
which consists of a convex part A (trst part ) and a
,,
|
i
 
he fi
concave part B. This objective function is a difference of
convex (d.c.) functions which is known to correspond to
a hard optimization problem [9]. The crucial step is now
to relax the nonconvex part B by hyperplane overestima-
tors, leading to the following relaxed objective:
,, ,
1,
()
Q
rel
kkikiki
qiiq
J
Auav

 
 (13)
where ,, ,
1,
()
Q
ki kiki
iiq
ua v
 

22
2,,
1,
log (||
ki
h)
Q
ki iq
iiq
aP


 (14)
This is tight with equality at approximtion

apoint ,ki
a.
The obtained relaxed objective function is a convex
fu
solved by the
Branch and bound. Branch and bo11] is a general
nction. The constraints are also convex leading to a
convex optimization problem which can be solved effi-
ciently.
The solution of this convex relaxation forms an upper
bound for the global minimum. Using the obtained upper
bound as a new point of approximation (see algorithm 1)
it can be proven that the sequence of relaxations pro-
duces a monotonically decreasing objective value and
will always converge. The proof is trivial and omitted
due to space limitations. Upon convergence it can be
proven that the obtained solution is a local optimum.
Although there is no theoretical proof for global optimal-
ity, simulation results are very promising showing global
optimality for very different scenarios.
2.2. Branch and Bound Method
The binary convex problems (11) are
und [

C. Y. SUN ET AL.
214
Table 2. Algorithm 2.
m 2 Branch and bound method
technique for finding optimal solutions of various opti-
mization problems. A branch and bound procedure has
two ingredients. The first ingredient is a smart way of
covering the feasible region by several smaller subre-
gions. This leads to a branching operation. The second
ingredient is bounding, which is a way of finding upper
and lower bounds for the optimal solution within a feasi-
ble subregion. The core of the approach is the simple
observation that (for a maximization task) if the upper
bound of a subregion A is smaller than the lower bound
for some other subregion B, then subregion A may be
safely discarded from the search.
To efficiently solve this problem by branch and bound
method, the problem is convex relaxed as:
S ubject to:
{} argmin{}
opt relk
J
k
a (15)
0
q


,ki
a
Which is convex with c
[0,1]
ontvariable , if we
denote as its optimal value, and the optimue of
th
nan
thod: round each
bi
inues k a
al val
is
1
e original problem is denoted * p, then 1 L a lower
bound ohe optimal value of (11).
An upper bound (denoted 1
U) o *
p c be fund by
several ways, one more sophisticated
L
n t
me
isnary variable k a then we'ltain th upper bound. If
11
UL l ob

, we can quit.
In the branchinoperation, we pick any index {q}, and
ubproblems: th
g
form two se first problem and the second
problem. The first and the second problem is the relaxed
problems with ,0
kq
a and ,1
kq
a respectively. Solving
the first and the second problem, we obtain the {lower,
upper} bounds } an{L
, U d{L,U} for ,0
mk
a

and
,1 mk
a respectively, thus the new bounds on *
p:
*
22
min{ ,}min{,)LLLpUUU

(16) }
The Branch and bound algorithm continue to
nary tree by splitting, relaxing, calculating bo
su
Algorithm 1 Successive linear CC k
form bi-
unds on
bproblems. The common strategy to select the leaf
node for further split operation is to pick a node with
smallest L, while that to select the variable for further
split operation is either the‘least ambivalent’ or the‘most
ambivalent’ way. The ‘least ambivalent’ way will choose
{q} for which *{0,1}q, with largest Lagrange multi-
plier, while the ‘most ambivalent’ way will choose {q}
for which |*
q− 1imum.
Table 1. Algotithm1.
/2| is min
convex relaxation for
1: Repeat l
2: Fo
3: ti
4: End For.
5: minimize: solve problem (12) with Relaxed (
r i=1 to Q.
ghten: compute
,() ki
ul ,()
ki
vl
rel
k
J
)
Algorith
Branching:
1: choose one of the carrier selection index{q};
2: solve two convex relaxed problems (11): set ,0
kq
a and
,1 kq
a

respectively
Bounding:
3: take the optimal value of the two convex relaxed problems as the
=
.
lower bounds{ L
,L};
4: take the solution of the two convex relaxed p
= {
roblems as the upper
bounds,UU
}when round all the relaxed binary variables to 0 or
1;
5: take minimum of the lower bounds as the current lower bound
2min{ ,}LLL on the optimal value of the optimization problem;
6: take minimum othe f upper bounds as the current upper bound
2min{ ,)UUUon the optimal value of the optimization problem;
Pruning:
7: If 22
UL


then quit the algorithm.
sub-tree (sub-pr
h
the‘ment;
to step 2.
8:else select the leaf node for further split operation :select the
oblem) with the smallest lower bound to be split;
9: end if
10: select te variable for further split operation :select another
as not been so far used while meet the ‘most am-index{q} which h
bivalent’ orost ambivalent’ requirem
11: go
3
I
a
astem. For comparison purpose, the per-
formances of the network with all the carriers fully re-
o station are also given. For
. Simulation Results
n this section, simulation results are presented to evalu-
te the performances of the proposed scheme in a carrier
ggregation sy
used between macro and pic
simplicity, we only consider one cell network which
contains 1 Macro-eNB and 2 Pico-eNBs. The radius of
Macro cell is 1000m. And the total number of users is 40.
The range extension threshold is 10dB. Detailed simula-
tion parameters including channel model and system as-
sumptions are summarized in Table 3. Most of them are
set according to the LTE-A simulation assumptions.
First , equal cell specific weight in the system sum rate
is used, and none uniform user distribution across the
macro cell is assumed, in this case, the users are dropped
at the dense area which overlay both the pico cells and is
about 12% of the Macro cell area. The cumulative dis-
tribution function (CDF) performances of the networks
with the new joint carrier selection and beamforming
scheme and frequency reuse 1 with beamforming scheme
are compared in Figure 1. Compared to the networks
where carriers are fully reused (‘Reuse 1’) between
Macro cell and pico cell, the throughput performance of
the macro cell with the proposed interference coordina-
tion scheme is significantly improved when equal cell
specific weight is applied. On the contrary, the through-
put performance of the Pico cell with the proposed
scheme is a little improved compared with that of the 6:End Loop until convergence

C. Y. SUN ET AL. 215
baseline scheme. Moreover, in order to clearly verify the
effects of the proposed scheme, we also present the per-
formance of the network throughput. Compared to the
baseline scheme where carriers are fully reused (‘Reuse
1’) between Macro cell and pico cell, the system through
put performance with the proposed interference coordi-
nation scheme is significantly improved. In this case, we
see gains beyond simple beamforming coordination gain.
Table 3. Simulation Assumption.
Parameters Value
Carrier bandwidth 10MHz
Number of Carriers 2
Path loss model Pico (R), R in km
Path loss model Macro (dB) 128.1+37.6log10(R), R in km
Shadowingition (dB)
cro (dBm)
(dBm)
dB) 140.7+36.7log10(
standard dev8
Transmit power Ma43
Transmit power Pico 20
Number of Tx Antenna 2
Number of Re Antenna 1
0100 200 300
0
0.2
0.4
0.6
0.8
1
Cell throughput(Mbit/s)
on with beamforming
CDF
CC seleti
Macro
Pico1
Pico2
System
0100 200 300
0
0.2
0.4
0.6
0.8
1
Cell throughput(Mbit/s)
CDF
Reuse 1 with beamforming
Macro
Pico1
Pico2
System
Figure 1. Performances with equal weight.
Next, the CDF performances of the networks with
none uniform user distribution and with cell specific
weight 12
{,,}{1/5,2/5,2/5}
MPP

 
2. Compared with the uniform
are compared
in Figure cells weight
{1,1,1} in the
Pico cen
sc
e of the Macro cell is a little im
m provided by
m
for mitigating the interference
ell and macro cell, then component
o restore the feasibility of CB in the
Figure 1, the throughput performance of
ll with the proposed interference coordinatio
heme is significantly improved when cell specific
weight is applied. On the contrary, the throughput per-
formancprovment com-
pared with that of the reuse one scheme.
In general we see there is both cell and system per-
formance improvement in throughput in using joint car-
rier selection and beamforming for interference coordi-
nation over the baseline scheme in both the scenarios.
The results suggest that the interference coordination not
only exploit additional degrees of freedo
ultiple antennas and component carriers, but also to
restore the feasibility of the CS/CB when the number of
low power nodes grows, which is achieved by shutting
down a subset of the component carrier in order to allow
for a perfect interference removal at the receive side in
the large dense low power node deployment scenario.
More over, with different cell specific weight in sum rate,
further load offset effect is observed beyond simple
range extension scheme.
4. Conclusions
In this paper, we consider joint component carrier selec-
tion and beamforming for carrier aggregation system in
Heterogeneous Networks. In the proposed scheme,
CS/CB is firstly applied
between the pico c
carrier is selected t
0100 200 300
0
0.2
0.4
0.6
0.8
1
CDF
CC seletion with beamforming
Macro
Pico1
Pico2
System
Cell throughput(Mbit/s)
0100 200300
0
0.2
0.4
0.6
0.8
1
Cell throughput(Mbit/s)
CDF
Reuse 1 with beamforming
Macro
Pico1
Pico2
System
Figure 2. Performances with un-equal weight.
dense low power node scenario. The component carrier
and beamforming selection is optimized not only to ex-
ploit additional degrees of freedom provided by multiple
antennas and component carriers, but also t restore the
feasibi ower
nodes wn a
o
lity of the CS/CB when the number of low p
grows. As a result, the design will shut do
subset of the component carrier in order to allow for a
perfect interference removal at the receive side in the

C. Y. SUN ET AL.
216
undation of Education department of Shaanxi
dation of ZTE Forum.
large dense low power node deployment scenario. Addi-
tionally, algorithm based on Branch and Bound Method
is used to reduce the search complexity of the algorithm.
The proposed approach is confirmed by simulation re-
sults compared with the performance of the baseline ap-
proach.
5. Acknowledgements
This work was supported in part by National Natural
Science Foundation of China (61102047, 61271276);
Key project (2012ZX03001025) of China, Natural Sci-
ence Fo
Province(2013JK1045); Foun
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