Communications and Network, 2013, 5, 15-19
doi:10.4236/cn.2013.52B003 Published Online May 2013 (http://www.scirp.org/journal/cn)
Optimal Power Allocation Scheme for Downlink CoMP
Systems
Jun Li1, Han Hai1, Ying Guo2, Moon Ho Lee1
1Department of Electronic and Information Engineering, Chonbuk National University, Jeonju, Korea
2School of Information Science & Engineering Central South University, Changsha, China
Email: lijun52018@jbnu.ac.kr, hhhtgy@jbnu.ac.kr, yingguo@mail.csu.edu.cn, moonho@jbnu.ac.kr
Received 2013
ABSTRACT
Coordinated multi-point transmission and reception (CoMP) scheme enable LTE-Advanced systems to achieve their
higher spectral efficiency. Allowing base stations to cooperate one another is one of the solutions to mitigate the inter-
cell interference (ICI). In this paper, we propose an iterative power allocation scheme with MMSE procoding based on
a modified water-filling for downlink CoMP systems, which achieves the optimal performance. The simulation results
show that our proposed system can achieve its optimal rate according to its antenna configuration. Comparing them
with a block diagonalization (BD) shows the advantages of MMSE precoding, in particular at a low SNR region.
Keywords: CoMP; Precoding; Power Allocation; Waterfilling
1. Introduction
Coordinated multi-point transmission and reception (CoMP)
scheme has been widely used for LTE-Advanced system
to enhance cell average and cell edge throughput. Accord-
ing to a coordinating fashion, CoMP scheme is classified
into two strategies [1]: Joint processing (JP) and coordi-
nated scheduing/beamforming (CS/CB). In the JP strategy
as shown in Figure 1, each user equipment (UE) simul-
taneously receives data from multiple base stations (BSs)
with joint multi-user precoding, which is required to
share both user data and channel state information (CSI)
between base stations (BSs) and user equipments (UEs).
Stemming from that, this JP strategy could be used to
contribute to not only improving the strength of the receive
signal but also cancelling interference. However, it is re-
quired to exchange the significant amount of data among
links participating in its coordination. Besides, substan-
tial overheads should be taken into account in the network.
Compared with JP, CS/CB can avoid inter-cell inter-
ference (ICI) by applying precoding to each BS on an in-
dividual basis, which is required to share only CSI without
holding user data in common. As depicted in Figure 2,
the solid lines denote the desired signals and the dashed
lines denote the interference from other BSs locating in
other cells. Since sharing CSI requires much lower ca-
pacity than sharing data [2], CS/CB needs much lower
backhaul capacity than JP. A lot of studies have been
done on CS/CB [3-5]. However, an effective algorithm to
eliminate the interference for downlink CoMP and network
MIMO is still not sufficient. If the interference is known
at the transmitters, cooperative encoding using dirty paper
coding (DPC) could mitigate the inter-cell interference
(ICI) [6]. Apart from DPC, a zero-forcing (ZF) scheme
based on block diagonalization (BD) is proposed in [7].
In [8], BD is applied to a multi-cell scenario with an ICI
reduction scheme. However, as pointed out in [9], per-
formance of BD is suboptimal at a low SNR. In this paper,
we use the MMSE precoding to compensate the noise with
the interference, with the goal of maximizing the weighted
sum rate (WSR).
BS 1BS 2
BS 3
UE 3
UE 1UE 2
Figure 1. Joint processing (JP).
Copyright © 2013 SciRes. CN
J. Li ET AL.
16
BS 1BS 2
BS 3
UE 3
UE 1UE 2
Figure 2. Coordinated scheding/bea mfor ming (CS/CB
A solution to maximizing the WSR is proposed in [10]
on
s organized as follows. In Section 2, we
sh
2. System Model
e cluster which is comprised of
).
the condition that each UE is equipped with a single
antenna and the precoding matrix is chosen in order to
maximize the signal-noise-plus-interference ratios (SINR)
for each user. Aside from this, a power allocation scheme
is also proposed. In [11], non-iterative water-filling
scheme is proposed to solve the problem occurring when
applying BD.
This paper i
ow a proposed system model. In Section 3, we over-
view conventional power allocation schemes and propose
a modified optimal power selection scheme. In Section 4,
we show that our proposed system outperforms conven-
tional systems using computer simulation. In Section 5,
we come to some conclusions.
Consider a cooperativ
both N BSs and N UEs on the condition that each BS is
equipped with
N
t antennas while each UE is equipped
with a single anna. In addition, each cell has both a
single BS and UE, under the situation that each UE re-
gards the nearest BS as its local BS.
Figure 3 illustrates our system mo
ten
del. Each BS is de-
noted by each circle, which is represented by the (i),
where 1 i N. Aside from this,
N
1
,
t
ji
h´
Î indicates
the channel vector from a coordinateEi, while
N
1
[v ,,v]
t
ii i
v= indicates a beamforming vector used to
rference between BSi and UEi. In addi-
tion, the solid lines denote the desired signals while
dashed lines denote the interference from the coordinated
BSs.
Our p
d BSj to a U
mitigate the inte
roposed system is represented as follow. The re-
ceived signal of UEi, i
y is given by BSi with power i
P
(2)
(1)
(
N
)
1
2
N
1
v
2
v
N
v
BSs UEs
1
x
2
x
N
x
1,1
h
1,2
h
1,N
h
2,1
h
2,2
h
2,N
h
,1N
h
,2N
h
,NN
h
Figure 3. Downlink Multi-user beamforming of the CoMP.
nder CoMP transmission mode where
i
z (1)
Besides,
u1,, ,iN=
,,
1,
.
HH
ii
iii jijj
jji
yx xhv hv
=+ +
å
N
j
x
Sj
is the inter-cell interference signal trans-
mitted by B. The desired signal i
x
of UEi is only
transmitted by BSi. u
z denotes the noise at UEi, which
is a white Gaussian radom variable with zero mean and
variance 2
s.
n
3. Power Allocation Scheme
The design of the precoding matrix
[
]
1,,,
iN
Vv vv=
are chosen in
INR
(2)
where SINR is the signal to noise-plus-interference ratio
and the optimization of the powers i
P
order to maximize a WSR:
N
()
2
1
log 1.
ii
i
RSa
=
=+
å
i
at each receive antenna. The value [0,1]
i
aÎ indicates
the priority of each user, in particular ual prior-
ity,
case of eq
1
iNa=, for all i.
In this section, the received SINR for UEi is
2
H
,
2
2
,
1,
,
ii i i
iN
H
j
ij j
jji
iSINR
Phvs
=
+å
(3)
where
Phv
represents the norm, 2
,
H
iii
hv.is the desired
signal power of UEi, and 2
,
1,
N
H
j
ij j
jji
Phv
åindicates the
interference signal power from the other BSs. It should
satisfy the condition of power constraint max
B
S
P:
2
max
1
.
N
ii BS
i
PPv
=
£
å (4)
Copyright © 2013 SciRes. CN
J. Li ET AL. 17
The beamforming matrix is chose
MMSE criterion [12], which maximizes
receiver. Therefore, the beamforming matrix is repre-
se
V n according to
the SINR at the
nted as
1
1,
HH
N
VHHH I
-
æö
÷
ç÷
=+
ç÷
ç (5)
r÷
ç
èø
where , is the sign
ratio (S a possibl
power is an N by N identity
where ).
For simplicity without loss of generality, we can ap-
ate the equation (6) as
1
[]
T
iM
Hhhh=
NR), defined as a rat
and noise power 2
s.
r
io of
N
I
al-to-noise
e maximum
matrix.
The general problem is to find the powers i
P to sat-
isfy
()
2
maxlog 1,
N
ii
SINRa
ìü
ïï
ïï
+
íý
å (6)
1
i=
ïï
ïï
îþ
[0,1]
i
aÎ (11
N
i
ia
==
å
proxim
2
2
log 1
H
N
i
Phv
a
æö
÷
ç÷
ç÷
ç÷
ç
ç+
ç
å,
2
1
,
1,
.
ii i i
N
H
iji jj
jji
Phv
=
÷
÷
÷
÷
ç÷
ç÷
ç÷
ç÷
÷
ç
èø
å
(7)
Since the powers of different users are cou
an optimization approach. We assume that all the powers
except are set, that is . Therefore, two sub-
op
cation of waterfilling scheme is given by
pled, we set
i j
timum procedures are proposed to derive a closed-
form solution.
3.1. Waterfilling Scheme
The power allo
P ,Pj i¹
22
,
2,
ij
ii H
pK hv
a¹
êú
=-
êú
(8)
,
H
ji j j
iii
Ps
+
ù
+ú
êú
ëû
where
hv
é
ê
å
]
+
ent. The
denotes the maximum between ze
argum constant K can be found in [12]. In par-
ticular,
ro and the
1
i
aN= is chosen for a standard waterfilling.
um sum
3.2. Modified Waterfilling Scheme
The maxim of squared weights is defined as:
()
2
max .
BS
ik
kN
vW=
1, ,=
Therefore, we have to find a constant value K for
(9)
all
the power , the following equatio
i
Pn holds:
22
,
2.
H
ji jj
ij
i
iBS H
i
P
pK hv
hv
s
a¹
éù
+
êú
êú
=-
êú
W
å (10)
,iii
+
êú
ëû
This corresponds to a watrefilling distribution with
variable water level.
In block diagonalization, the SINR is given by [13]
2
2,
ii
i
P
SINRl
= (11)
s
w
precodg matrix is chosen from [13]fore, the
weighted sum rate is
here i
l are the diagonal elements of HV where the
in. There
2
22
1
log 1.
Nii
i
i
P
Rl
as
=
æö
÷
ç÷
ç
=+
÷
ç÷
ç÷
ç
èø
å (12)
The solution is given as [11]:
2
2,
ii
i
PK s
al
+
é
ù
ê
ú
=-
ê
ú
ê
ú
ë
û
(13)
which is also a waterfilling distribution with equal prior-
ity.
In fact, the procedures of itera
presented before are based on the fact that the powers
ihould be found. There, we should re-
e
r the proposed iterative waterfilling
aterfilling (MMSE PMWF)
found by exhaustive search
set to 0 dB. We can see that the optimum MMSE pre-
co
tive optimization as
j
P for ji¹ are known to obtain i
P. For this, a joint
optimzation s
resul
efor
pe
un
at the aforementioned waterfilling procedures to find
each i
P by adjusting j
P values of the preceding step
til the ting rate converges after setting arbitrary
initial values for j
P.
4. Simulation Results
In this section, wanalyze the performance in terms of
achievable rates fo
(MMSE PWF), modified w
and the optimum solution
(MMSE ES). We also compare these performances to
those of block-diagonalization using a waterfilling scheme
(BD WF).
For these numerical results, the channel matrix entries
are assumed to be independent identically distributed zero-
mean complex Gaussian random variables with variance
of 0.5 per dimension. The initial powers for the iterative
WF and MWF have been set equal to the i
P of the uni-
form power distribution and the final power allocations
are obtained after 5 iterations in all the simulations. For a
fair comparison, SNR is defined as the ratio in dB of
2
max /
BS
Ps.
In Figure 4, we compare the different solutions in
terms of mean achievable rate for each user on the condi-
tion that each user has the same priority and the SNR is
ding found by ES outperforms BD WF for all the val-
ues of the number of transmit antennas t
N, and MMSE
PMWF also outperforms MMSE PWF. Interestingly, the
simple solution of MMSE PMWF outperforms BD WF
Copyright © 2013 SciRes. CN
J. Li ET AL.
18
that requires a lengthy numerical optimization, in par-
ticular at the low SNR.
In addition, we obtain the region of achievable rates
for SNR=0 dB in Figure 5, where we show the effect of
the different power allocation schemes with MMSE pre-
coding. We can see that MMSE PMWF obtains higher
ac
e optimum power distribution can be ob-
ta
hievable rates than MMSE PWF. As the number of
transmit antennas increases, the difference between
MMSE ES and MMSE MWF is larger. However, even if
suboptimal, MMSE MWF outperforms BD WF as shown
in Figure 1, without resorting to a lengthy numerical
optimization.
The main difference in terms of complexity between
MMSE and BD approaches is coming from the power
optimization procedure. From the simulation results, we
can see that th
ined through a lengthy exhaustive search while water-
filling approaches allow a highly reduced complexity at
11.5 22.5 33.5 4
0.5
1
1.5
2
2.5
3
Number of transmit antennas N
t
Mean Rat e per user [bits/sec /
Hz]
MMSE E S
MMSE P MW F
MMSE P W F
BD WF
Figure 4. Mean achievable rate for each user with equal
probability, N=2 and SNR=0 dB.
00.5 11.5 22.5 3
0
0. 5
1
1. 5
2
2. 5
3
3. 5
mean Rat e us er 1 [ bi t s/sec/Hz]
Mean Rat e ues r 2 [ bit s/s ec/
Hz ]
MMSE ES
MMSE PMWF
MMSE PWF
N
t
=3
N
t
=2
N
t
=1
Figure 5. Region of mean achievable rates with N=2 and
SNR=0 dB.
the expense of some performance degradation. Since
waterfilling is performed over N user transmissions, it
does not depend on the number of transmit antennas.
Therefore, the complexity of PWF and PMWF is irre-
spective of the number of antennas per BS. In addition,
MMSE PMWF is a good choice in terms of the balance
between complexity and achievable rates.
5. Conclusions
In this paper, we present feasible combinations of MMSE-
based beamforming and iterative waterfilling power al-
location schemes that can be applied to the downlink of a
CBST system while they are required to take a tradeoff
between complexity and achievable rates into considera-
ed with MMSE beamforming outperforms a
R regime.
ments
tion. In addition, we show that the iterative MWF alloca-
tion combin
BD scheme that requires a lengthy numerical optimiza-
tion in the low and moderate SNR regimes under a
two-base station/two-user simplified scenario. Further-
more, we show that our proposed iterative MWF scheme
obtains a performance close to that of MMSE by exhaus-
tive search at a high SNR regime as well as MMSE and
BD have the same performance at a high SN
6. Acknowledge
This work was supported by the National Research
Foundation of Korea (NRF) grant funded by the World
Class University R32-2012-000-20014-0, the Korean
government (MEST) 2012-002521, and BSRP 2010-
0020942 Korea.
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