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98 IEEE TRANSACTIONS ON BROADCASTING, VOL. 56, NO. 1, MARCH 2010
Adaptive Resource Allocation for MIMO-OFDM Based
Wireless Multicast Systems
Jian Xu, Member, IEEE, Sang-Jin Lee, Member, IEEE, Woo-Seok Kang, Member, IEEE, and
Jong-Soo Seo, Member, IEEE
Abstract—Multiple antenna orthogonal frequency division
multiple access (OFDMA) is a promising technique for the high
downlink capacity in the next generation wireless systems, in
which adaptive resource allocation would be an important re-
search issue that can significantly improve the performance with
guaranteed QoS for users. Moreover, most of the current resource
allocation algorithms are limited to the unicast system. In this
paper, dynamic resource allocation is studied for multiple antenna
OFDMA based systems which provide multicast service. The
performance of multicast system is simulated and compared with
that of the unicast system. Numerical results also show that the
proposed algorithms improve the system capacity significantly
compared with the conventional scheme.
Index Terms—Adaptive resource allocation, MIMO, multicast
service, OFDM, water-filling.
I. INTRODUCTION
THE next-generation wireless networks are expected to
provide broadband multimedia services such as voice,
web browsing, video conference, etc. with diverse Quality
of Service (QoS) requirements [1]–[4]. Multicast service
over wireless networks as in Fig. 1 is an important and chal-
lenging goal oriented to many multimedia applications such
as audio/video clips, mobile TV and interactive game [1]–[5].
There are two key traffics, namely, unicast traffics and multi-
cast traffics, in wireless multimedia communications. Current
studies mainly focus on unicast traffics. In particular, dynamic
resource allocation has been identified as one of the most
efficient techniques to achieve better QoS and higher system
Manuscript received March 17, 2009; revised December 04, 2009. First pub-
lished February 05, 2010; current version published February 24, 2010. This
work was supported by the IT R and D program of MKE/KEIT (2009-S-032-01,
Research on Multiple Antenna and Multi-hop Relay Transmission Technologies
for Next Generation Mobile Broadcasting Service).
J. Xu was with the Center for Advanced Broadcasting Technology and the
Digital Transmission Laboratory, Department of Electrical and Electronic En-
gineering, Yonsei University, Seoul 120-749, Korea. He is now with the Mobile
Communication Technology Research Lab, LG Electronics, Anyang 431-080,
Korea (e-mail: james.xu@lge.com).
S. J. Lee is with the Center for Advanced Broadcasting Technology and
the Digital Transmission Laboratory, Department of Electrical and Electronic
Engineering, Yonsei University, Seoul 120-749, Korea, and also with the
Research and Development planning team of Korea Radio Promotion Agency
for next generation broadcasting, Seoul, Korea (e-mail: acejin@yonsei.ac.kr;
acejin@korpa.or.kr).
W.-S. Kang and J.-S. Seo are with the Center for Advanced Broadcasting
Technology and the Digital Transmission Laboratory, Department of Electrical
and Electronic Engineering, Yonsei University, Seoul 120-749, Korea (e-mail:
wooseok@yonsei.ac.kr; jsseo@yonsei.ac.kr).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TBC.2009.2039691
Fig. 1. Cellular structure of multicast transmission system.
spectral efficiency in unicast wireless networks. Furthermore,
more attention is paid to the unicast OFDM systems.
Orthogonal Frequency Division Multiplexing (OFDM) is re-
garded as one of the promising techniques for future broadband
wireless networks due to its ability to provide very high data
rates in the multi-path fading environment [6]. Orthogonal Fre-
quency Division Multiple Access (OFDMA) is a multiuser ver-
sion of the popular OFDM scheme and it is also referred as mul-
tiuser OFDM.
Multiple input multiple output (MIMO) technologies have
also received increasing attentions in the past decades. Many
broadband wireless networks have now included MIMO tech-
nology in their protocols including the multicast system [1].
Compared to single input single output (SISO) system, MIMO
offers the higher diversity which can potentially lead to a mul-
tiplicative increase in capacity.
In multiuser OFDM or MIMO-OFDM systems, dynamic re-
source allocation always exploits multiuser diversity gain to im-
prove the system performance [7]–[11] and it is divided into
two types of optimization problems: 1) to maximize the system
throughput with the total transmission power constraint [9]; and
2) to minimize the overall transmit power with constraints on
data rates or Bit Error Rates (BER) [10]. To the best of our
knowledge, most dynamic resource allocation algorithms, how-
ever, only consider unicast multiuser OFDM systems.
In wireless networks, many multimedia applications adapt to
the multicast transmission from the base station (BS) to a group
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IEEE TRANSACTIONS ON BROADCASTING, VOL. 56, NO. 1, MARCH 2010 99
Fig. 2. Block diagram of multiple antenna OFDM multicast system.
of users. These targeted users consist of a multicast group which
receives the data packets of the same traffic flow. The simulta-
neously achievable transmission rates to these users were inves-
tigated in [12] and [13]. Recently scientific researches of multi-
cast transmission in the wireless networks have been paid more
attention. For example, proportional fair scheduling algorithms
were developed to deal with multiple multicast groups in each
time slot in cellular data networks [14].
The dynamic resource allocation for OFDM based multicast
system was researched in [15], however it focused on SISO
system and can not be applied to MIMO system directly. On
the other hand, the conventional scheme in current standards
such as IEEE 802.16 or 3GPP LTE for multicast service con-
siders the worst user very much, which may waste the resource.
In this paper, we propose dynamic subcarrier and power allo-
cation algorithms for MIMO OFDMA-based wireless multicast
systems. In the proposed algorithms, the subcarriers and powers
are dynamically allocated to the multicast groups. Our aim is
to maximize the system throughput given the total power con-
straint. Let us assume that there are multiple multicast groups in
a cell and each multicast group may contain a different number
of users. The users included in the same multicast group are
called co-group users and these can be located in different places
in the cell.
This paper is organized as follows. Section II introduces the
multiple antenna OFDMA based multicast system model and
presents the optimization objective function. In Section III, the
proposed resource allocation algorithm is described. Simulation
results are illustrated in Section IV and conclusions are drawn
in Section V.
II. SYSTEM MODEL
The block diagram of multiuser MIMO-OFDM downlink
system model is shown in Fig. 2. It shows that in the base
station channel state information of each couple of transmit
and receive antennas are sent to the block of subcarrier and
power algorithm through the feedback channels. The resource
allocation information is forwarded to the MIMO-OFDM trans-
mitter. The transmitter then selects the allocated number of bits
from different users to form OFDMA symbols and transmits
via the multiple transmit antennas. The spatial multiplexing
mode of MIMO is considered. The resource allocation scheme
is updated as soon as the channel information is collected and
also the subcarrier and bit allocation information are sent to
each user for detection.
The following assumptions are used in this paper. The trans-
mitted signals experience slowly time-varying fading channel,
therefore the channel coefficients can be regarded as constants
during the subcarrier allocation and power loading period.
Throughout this paper, let the number of transmit antennas be
and the number of receive antennas be for all users. Denote
the number of traffic flows as , the number of user as and
the number of subcarriers as . Thus in this model downlink
traffic flows are transmitted to users over subcarriers. Assume
that the base station has total transmit power constraint . The
objective is to maximize the system sum capacity with the total
power constraint. We use the equally weighted sum capacity as
the objective function.
The system capacity optimization problem for muticast
MIMO-OFDM system can be formulated to determine the
optimal subcarrier allocation and power distribution:
(1)
where is the system sum capacity which can be derived based
on [16] and the above assumptions; is the total available
power; is the power assigned to user in the subcarrier ;
can only be the value of 1 or 0 indicating whether subcar-
rier is used by user or not. is the rank of which
denotes the MIMO channel gain matrix on subcarrier
for user and are the eigenvalues of ;
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100 IEEE TRANSACTIONS ON BROADCASTING, VOL. 56, NO. 1, MARCH 2010
is the allocated user index on subcarrier ; is the noise
power in the frequency band of one subcarrier.
The different point of muticast optimization problem in (1)
compared to the general unicast system is that there is no con-
straint of for all , which means that many users
can share the same subcarrier in multicast system because they
may need the same multimedia contents.
The capacity for user , denoted as , is defined as
(2)
III. PROPOSED SUBOPTIMAL SUBCARRIER ALLOCATION AND
POWER DISTRIBUTION
The optimization problem in (1) is generally very hard to
solve. It involves both continuous variables and binary variables.
Such an optimization problem is called a mixed binary integer
programming problem. Furthermore, since the feasible set is not
convex the nonlinear constraints in (1) increase the difficulty in
finding the optimal solution.
Ideally, subcarriers and power should be allocated jointly to
achieve the optimal solution in (1). However, this poses a pro-
hibitive computational burden at the base station in order to
reach the optimal allocation. Furthermore, the base station has
to rapidly allocate the optimal subcarrier and power in the time
varying wireless channel. Hence, low-complexity suboptimal
algorithms are preferred for practical implementations. Sepa-
rating the subcarrier and power allocation is a way to reduce
the complexity, because the number of variables in the objec-
tive function is almost reduced by half.
In an attempt to avoid the full search algorithm in the pre-
ceding section, we devise a suboptimum two-step approach.
In the first step, the subcarriers are assigned assuming the
constant transmit power of each subcarrier. This assumption
is used only for subcarrier allocation. Next, power is allocated
to the subcarriers assigned in the first step. Although such a
two-step process would cause suboptimality of the algorithm, it
makes the complexity significantly low. In fact, such a concept
has been already employed in OFDMA systems and also its
efficacy has been verified in terms of both performance and
complexity. However, the algorithm proposed in this paper is
unique in dealing with MIMO-OFDM based multicast resource
allocation.
Before we describe the proposed suboptimal resource allo-
cation algorithm, we firstly show mathematical simplifications
for the following subcarrier allocation. It is noticed that in
large SNR region, i.e., , we get the following
approximation:
(3)
where is named as product-criterion which
tends to be more accurate when the SNR is high. On the other
hand, in small SNR region, i.e., , using
, we get
(4)
where is named as sum-criterion which
is more accurate when the SNR is low. These two approxima-
tions will be used in the suboptimal algorithm for the high SNR
and low SNR cases, respectively. In this way, we can reduce
the complexity significantly with minimal performance degra-
dation.
The steps of the proposed suboptimal algorithm are as fol-
lows:
• Step 1 Assign the subcarriers to the users in a way that
maximizes the overall system capacity;
• Step 2 Assign the total power to the allocated subcarriers
using the multi-dimension water-filling algorithm.
A. Step 1—Subcarrier Assignment
For a given power allocation vector for
each subcarrier, RA optimization problem of (1) is separable
with respect to each subcarrier. The subcarrier problem with
respect to subcarrier is
(5)
Then the multicast subcarrier allocation algorithm based on
(3) for each subcarrier is given as follows.
1) For the th subcarrier, calculate the current total data rate
when the th user is selected as the user who has lowest
eigenvalue product
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IEEE TRANSACTIONS ON BROADCASTING, VOL. 56, NO. 1, MARCH 2010 101
(6)
2) For the th subcarrier, select the user index which can
maximize
(7)
Then we have
otherwise
(8)
For the low SNR case, the product-criterion (3) is changed
into the sum-criterion (4) for this step’s subcarrier allocation.
B. Step 2 Power Allocation
The subcarrier algorithm in step 1 is not optimum because
equal power distribution for the subcarriers is assumed. In this
step, we propose an efficient power allocation algorithm based
on the subcarrier allocation in step 2. Corresponding to each
subcarrier, there may be several users to share it for the multi-
cast service. In this case, the lowest user’s channel gain on that
subcarrier among the selected users in step 1 will be used for the
power allocation. The multi-dimension water-filling method is
applied to find the optimal power allocation as follows.
The power distribution over subcarriers is
where means the power assigned to each antenna of subcar-
rier and it is the root of the following equation,
(9)
where is the allocated user index on subcarrier ; is the
water-filling level which satisfies where
and are the total power and the number of subcarriers,
respectively.
In case of , that is, a single antenna system,
the optimal power distribution for the subcarriers is transformed
into the standard water-filling solution:
(10)
where and is the same as for a
single antenna.
The multi-dimension water-filling algorithm is an iterative
method, by which we can find the optimal power distribution
to realize the maximum of system capacity.
IV. SIMULATION RESULTS
In this section, simulation results are presented to demon-
strate the performance of the proposed algorithm. The simula-
tion parameters of the proposed system are given in Table I. The
TABLE I
SIMULATION PARAMETERS FOR THE MIMO-OFDM SYSTEM
Fig. 3. Sum capacity comparison of multicast and unicast systems.
wireless channel is modeled as a frequency selective channel
consisting of six independent Rayleigh multipaths. Each multi-
path component is modeled by Clarke’s flat fading model. The
number of users is 4 and the number of antennas is .
Each couple of transmit antenna and receive antenna is assumed
to be independent to the other couples. Total transmit power is 1
W and AWGN power spectral density varies from 85 dBW/Hz
to 60 dBw/Hz. The total bandwidth B is 1 MHz, which is di-
vided into 64 subcarriers. The capacities in the following figures
are averaged over 10000 channel realizations.
A. Comparison of Multicast and Unicast Systems
In Fig. 3, the sum capacities of multicast and unicast schemes
are shown for multiple antenna OFDM systems. Here it is sup-
posed that there is no channel power difference between the
users. In the multicast system, it is supposed that 4 users re-
ceive the same contents, while in the unicast system the con-
tents of users are different from each other. 3 by 1 multicast
and unicast system means that 3 users receive the same con-
tents as one group and the left one user receives different con-
tent. And 2 by 2 multicast and unicast system means that 2 users
receive the same contents as one group and the left two users
are unicast users. It is noticed that the multicast scheme with
the proposed method can achieve higher capacity than the uni-
cast scheme or the mixed cases. The more multicast users exit,
the higher system capacities can be achieved. For the fairness of
comparison, on each subcarrier the user with the highest eigen-
value product is selected to use it in the unicast system.
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102 IEEE TRANSACTIONS ON BROADCASTING, VOL. 56, NO. 1, MARCH 2010
Fig. 4. Sum capacity comparison of proposed scheme and conventional one in
multicast system when the SNR is high.
Fig. 5. Sum capacity comparison of proposed scheme and conventional one in
multicast system when the SNR is low.
B. Comparison of Proposed Scheme and Conventional One
for the Multicast System
In this subsection, the sum capacities of the proposed scheme
and conventional scheme for the multicast system are shown in
Figs. 4 and 5 for the high SNR and low SNR cases, respectively.
It is supposed that 4 users receive the same contents and there
is 5 dB or 10 dB average channel power difference between the
users. In the conventional scheme, on each subcarrier the user
with the lowest eigenvalue product is selected as the baseline to
transmit the information. From both Figs. 4 and 5, it is noticed
that the proposed method can achieve higher capacity than the
conventional one. The more average channel power difference
between the users, the larger gains can be obtained. This means
that the proposed adaptive subcarrier and power allocation algo-
rithm is more effective in the presence of higher channel or link
difference. This is because the drawback of the conventional
scheme is more evident in the case of higher channel or link
difference.
V. C ONCLUSION
This paper presented a new method to solve the subcarrier and
power allocation problem for multi-user MIMO-OFDM based
multicast system. The optimization problem was formulated to
maximize the system capacity with a total transmit power con-
straint. Due to the complexity of optimal algorithm, two step
suboptimal algorithm was proposed. The proposed subcarrier
allocation algorithm determined the number of users for each
subcarrier based on the maximization criteria, in which the ca-
pacity of each subcarrier can be maximized. Then the proposed
power allocation scheme adopted multi-dimension water-filling
method in order to maximize the system capacity. Simulation re-
sults showed that the system capacity of the proposed scheme is
significantly improved as compared with the conventional one.
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