Communications and Network, 2013, 5, 74-79
http://dx.doi.org/10.4236/cn.2013.53B2015 Published Online September 2013 (http://www.scirp.org/journal/cn)
Copyright © 2013 SciRes. CN
Two-Step Resource Block Alloc at ion Algor ithm f or Data
Rate Maximization in LTE Downlink Systems*
Baorong Jiang1, Li Sun1,2, Pinyi Ren1
1School of Electronic and Information Engineering, Xi’an Jiaotong University, China
2National Mobile C ommunications Research Laboratory, Southeast University, China
Email: jbr123@stu.xjtu.edu.cn, lisun@mail.xjtu.edu.cn, pyren@mail.xjt u.edu.cn
Received June, 2013
ABSTRACT
This study focu ses on resourc e bloc k allocatio n issue in t he d ownlin k tr an s miss i o n s yste m s of the Long Term Evolution
(LTE). In existing LTE standa rds, all Allocation Units (AUs ) a lloca ted to any user must adopt the same Modulat io n and
Coding Scheme (MCS), which is determined by the AU with the worst channel condition. Despite its simplicity, this
strategy incurs significant performance degradation since the achi evable system throug hput is li mited b y the AUs hav-
ing the wor st channel quality. To address this issue, a two-step resource block allocation algorithm is proposed in this
paper. The algor ithm first allocates AUs to each user according to the users' priorities and the number of the ir required
AUs. Then, a re-allocation mechanism is introduced. Specifically, for any given user, the AUs with the worst channel
condition are removed. In this manner, the users may adopt a higher MCS level, and the achievable data rate can be
increased. Finally, all the unallocated AUs are assigned among users wit hout changing the chosen MCSs, and the total
thro ughput o f the s ys te m is f u rt her en ha nc ed . Si mul a ti on r e s ults s how t hat tha nk s to t he proposed algorithm, the system
gains higher throughput without adding too many complexities.
Keywords: Resource Block Allocatio n; Allocation Unit (AU); Two step; Re-allocation Mechanism
1. Introduction
Compared with 2G and 3G networks, The LTE systems
can provide higher data rates and better transmission
quality. Given limited radio resources, one challenge in
LTE systems is to support a large number of users and
satisfy differe nt users' data rate r equi reme nts. Ortho gona l
Freq uency Di vision Multiplex ing (OFDM) is used a s the
basic transmission scheme in LTE downlink systems,
which can achieve high system capacity. By using OFDM
technique multiple users can share OFDM sub-carriers in
a certain time slot [1-4]. In LT E syst em s, sub-carriers are
grouped into Resource Blocks (RBs), and each RB con-
sists of 12 adjacent sub-carriers. Two consecutive RBs
are called an Allocation Unit (AU) [5]. In practical sys-
tems, all AUs allocated to a given user should use the
same MCS, which is determined by the AU with the
worst channel co nd ition for this use r .
Resource block allocation has been extensively studied
in LTE systems. Proportional Fairness (PF) resource al-
location mechanisms were presented in [5] and [6],
which in reference [5] is composed of a priority adjust-
ment scheme and a resource block allocation scheme.
The prior ity a djustme nt scheme determines users’ priori-
ties according to channel conditions and average bit rate.
The resource block allocation scheme allocates resource
block to the user by PF mechanism, so t he user s fairness
is guaranteed. However, the usersdata rate requirements
are not taken into consideration in this allocation sche me.
Resource block allocation scheme for data rate maximi-
zation is proposed in [7-9], the algorithm i n reference [7]
allocates AUs to the users according to their priorities
determined by usersaverage channel conditions. In this
manner, the minimum rate requirement of each user is
satisfied. Nevertheless, for any user, the throughput is
limite d by t he wo r st channe l c onditio n, a nd the AUs with
better channel condition cannot be made full use of. In
addition, if the usersminimum data rate requirements
are too high, the users with lower prio rities will not meet
their minimum data rate requirements. It is not reasona-
ble that the remaining AUs are just assigned to the user
with the hi g hest prio rity. In order to solve those problems
presented above, a two-step resource block allocation
algorithm is proposed in this paper.
The proposed algorithm consists of initial allocation
The research reported in this paper was supported by
the National
Natural Science Foundation of China (No. 61201207),
the National
Science and Technology Major Project of China (No.
2012ZX03001005-004),
the Open Research Fund of National Mobile
Com
munications Research Laboratory, Southeast University (No.
2012D04), and the Fundamental Research Funds for the Central Uni-
versities of China.
B. R. JI ANG ET AL.
Copyright © 2013 SciRes. CN
75
scheme and re-allocation scheme. The initial allocation
scheme allocates AUs to each user based on the number
of AUs required by each user and its priority. The num-
ber of required AUs and the user's priority are deter-
mined by proportional fairness scheme. Next, for a cer-
tain user, the re -allocatio n sche me removes the AUs with
the worst channel condition if the users data rate is in-
creased by doing so. Those removed AUs are saved as
free AUs to re-allocate to the other users. If there are
some AUs remained after each user has reached its
minimum data rate requirement, the remaining AU is
assigned to the user whose M CS is not highe r than those
of AU. As a result, the capacity of the proposed alloca-
tion algorithm has a better performance than the Qos
algorithm a nd PF al gorithm, while its co mplexity ha s not
promoted so much.
The rest of this paper is organized as follows. Section
2 introduces the system model and presents the op timiza-
tion objective function of resource block allocation for
LTE systems. In section 3, the proposed resource block
allocation algorithm is described. The simulation results
are shown in Section 4. Finally, Section 5 makes a con-
clusion o f this p aper.
2. System Model
In LTE downlink transmission systems, we assume
that
K
active mobile users are distributed in a cell, and
the total number of AUs is denoted by N. T he c onsidered
system is sho wn in Figure 1. T here are five users in one
cell. Vector
,1 ,1,
[,, ]
T
kk kkN
cc c=c
indicates the Chan-
nel Quality Indicator (CQI) of user k for N AUs. The
boxes at the top of figure represent the total AUs in LTE
systems. The eNB allocates AUs to each user according
to the feedback of CQI. The numbers in the boxes a r e the
MCS indexes of corresponding AUs. We can see the
AUs allocated to the same user have different MCS in-
dexes, and the MCS of the user is determined by the AU
with wors t c hannel condition [10].
1
c
2
c
3
c
4
c
5
c
. . .
AUs
98
7 889
U1
MCS Index : 8
9
U2
MCS Index : 4
11
10
U3
MCS Index : 9
U4
MCS Index : 5
9
U5
MCS Index : 7
6
7
8
94
5
56789
Figure 1 . Sys tem model of reso urce bl ock all ocati on in L TE
downlink syst ems.
Let
,kn
c
denote the CQI of user k on AU n. The
minimum data tra nsmission ra te of the user k is i ndicated
by k
R.j
r
is the symbol transmission rate for a given
Mod ulati on and Cod ing Sc he me (M CS)
j
, and
J
is the
total number of MCS supported in the tra nsmissio n [11].
Define
au
N
as the number of symbols for data transmis-
sion in one AU. Set
s
T
as the OFDM symbol duration
time. Then, the bit rate transmitted in one AU can be
calculated by:
j
jau
au s
rN
rT
=
(1)
Variable
,kn
a
represents the resource allocation indi-
cator, with value 1 if AUn is allocated to user k and 0
otherwise. Furthermore, define the variable
,kj
b
as the
choice of MCS of user k, and
,
1
kj
b=
indicates that the
MCS
j
is chosen for user k. The data rate achieved by
user k can be described as:
,,
11
NJ j
kk nkjau
nj
rabr
= =
=∑∑
(2)
As the resource block allocation in this paper aims to
achieve maximum sum data rate, the optimization prob-
lem is formulated a s follows:
,, ,,
,11 1
max
knkj
NJ
Kj
k nkjau
abkn j
a br
= ==
∑∑ ∑
(3)
Subject to :
,
kk
rR k≥∀
(4)
,,
1
1,n, {0,1}
K
kn kn
k
aa
=
=∀∈
(5)
,,
11, , b{0,1}
J
kj kj
j
bk
=
=∀∈
(6)
Constraint (3) is the objective function stating the
achievable total rate, (4) ensures that each user can satis-
fy its mini mum data rate requ irement, (5) means that one
AU can only be allocated to one user, (6) presents the
fact that each user must use the same MCS, which i s de-
termined by the AU with the worst channel condition. It
should be pointed out that finding the optimal solution
would face high computational cost, so the suboptimal
algorithm with low complexity is preferable
3. Proposed Algorithm
The algorithm in this paper is proposed based the alloca-
tion regulatio ns of LT E do wnlink t rans miss io n. As user s
MCS is deter mined by the AU with the worst channel
condition, the data rate of each user is limited, and the
AUs with the better channel condition are wasted.
Therefore, a t wo-step resource block allocation algorithm
focus on those problems is proposed in this paper. The
B. R. JI ANG ET AL.
Copyright © 2013 SciRes. CN
76
first step of proposed algorithm initially alloca te s re-
source block by PF mechanis m. The next step
re-allocates the AUs with the worst channel condition of
each user.
3.1. Initial Allocation Scheme
1) Estimating the number of required AUs:
In thi s p ap e r, we calculate the number of AUs required
based on the ratio of users minimum data rate require-
ment to channel condition [4]. Let be the average
CQI of user k. is defined as the number of AUs
allocated to user k. should satisfy the following
conditions:
(7)
which means the number of AUs each user needs is pro-
portional to its minimum data rate requirement, and in-
versely proportional to the average channel condition.
The number of AUs allocated to user k is calculated by:
(8)
2) Calculati ng the prio rity of each user:
Reference [12] represents two methods to calculate the
priority. The one is stated in Eq. (9), which means that
the users with lower minimum rate requirements have
higher priorities. The next one is formulated in Eq. (10),
which indicates that the user with better channel condi-
tion could be first allocated. In this paper, we adopt a
new way to calculate users priority based on the va-
riance of channel conditions and minimum data rate re-
quirements simultaneously. The new method is given by
Eq. (11), which implies that the user with better channel
condition and lower data rate requirement has higher
priority.
The first one:
(9)
The second one:
(10)
The third one:
(11)
3) Allocating AUs to each user
The initial allocation scheme is described in Table 1,
which allocates AUs to the user k according to the
users’ priorities and the number of AUs each user needs.
Meanwhile, the minimum data rate requirement of each
user is guarante ed.
3.2. Re-allocation Scheme
In LTE systems, if AUs allocated to the same user have
different channel qualities in terms of CQI, the MCS is
determined by the lowest CQI to make sure that the data
transmitted by each AU can be correctly received. Ob-
viously, the usersdata rate is limited by the AUs with
the worst channel condition, and the AUs with better
channel condition cannot be made full use of. A solution
for above problem is proposed, which is explained in
Figure 2. The number of AUs allocated to each user in
Figure 2 is the same as Figure 1. Assuming that each
AU o nly consists of o ne symbol, the symbol transmission
rate can be found in Table 2. `Before' in Figure 2 is
MCS index and data rate obtained by the user without
removing any AUs. `DR' in Figure 2 is abbreviatio n of
data rate. Take user 2 for example, if the AU with the
worst channel condition is removed, MCS index of this
user turns into 5, and the data rate of this user is in-
creased. The dotted boxes indicate the removed AUs,
Which is saved as free AUs to allocate to other users,
such as the first AU adopted to user 3 is removed by user
2, and the MCS indexes of AUs allocated to user 3 turn
into higher level.
Table 1. The Initial Allocation Scheme.
Initial Allocation
01. Estimate the number of AUs required by according to
the Eqs. (8) and (9);
02. Calculate us e rs' pr iorit ies base d on the Eqs. (10), (11)
or (12), and sort them in descending order;
03. Find out the fir stAUs with better channel condition
from av a il ab l e AUs for user;
04. Calculate the data rate of user by Eq. (1), if it is les s
than its minimum d at a rate requirement, alloca te one more
AU to this user until the minimum requirement is met.
B. R. JI ANG ET AL.
Copyright © 2013 SciRes. CN
77
Figure 2 . The example to illustrate p roposed scheme.
Moreover, there are several AUs remaining in practic-
al applications after users have reached their minimum
data rate requirements. Those remaining AUs should be
assigned without changing the MCS of each user, that is
to say, we allocate the remaining AUs to users, whose
MCS are not hi gher t han tho se of remaining AU. By t his
way, the total number of AUs allocated to some users is
added, so the data rates achieved by these users are im-
proved. The re-allocation scheme is stated in Table 2.
4. Simulation Results
This section compares the performance of the proposed
scheme, Qos algorithm [7], and PF algorithm [5] and
max-rate algorithm. The simulation parameters are
shown in Table 4. All simulations are obtained by aver-
aging o ver 1000 channel realizations [13-14].
Table 2. MCS Table in LTE Systems.
MCS Index
1
2
3
4
5
r
(bit/symbo l) 0.1523 0.2344 0.3770 0.6010 0.8770
MCS Index 6 7 8 9 10
r
(bit/symbo l) 1.1758 1.4766 1.9141 2.4063 2.7305
MCS Index 11 12 13 14 15
r
(bit/symbo l) 3.3223 3.9023 4.5234 5.1152 5.5547
Table 3. The Re-allocation Scheme.
Re-allo ca tion schem e
01. For k=1:K
02. Allocate k
NAUs to us er
k
, and calculate
k
r
of this user;
03. While
kk
rR<
04. allocate one more AU to the user;
05. End While
06. Calculate data rate
'
k
r
without allocation of AUs with
07. the worst channel condition;
08. If
'
k
k
rr
09. Remove AUs with the worst channel condition.
10. Then
1kk= +
, go to s te p 1;
11. End If
12. End For
13. Allocate the remaining AUs to users, whose MCS are not
higher than those of remaining AU.
Table 4. Simulation Parameters.
Simulation Parameters Values
System bandwidth
Carrier frequency
Sampling frequency
Channel model
Number of AUs
Number of users
Cha n nel feedba ck
OFDM symbols per fra m e
TTI duration
20MHZ
2GHZ
30.72MHZ
SCM
50
6-18
Full
14
1ms
QPSK:1/3,1/2,2/3,3/4,4/5
Simulation Parameters Values
Modulation and coding
16QAM:1/2,2/3,3/4,4/5
64QAM:2/3,3/4,4/5
To illustrate users fairness achieved by each algo-
rithm, the fairness factor is introduced [2], which is
stated as:
2
2
11
( )/
KK
kk
kk
IT KT
= =
=
∑∑
(12)
where I is the fairness factor. k
T is the aver a ge data rate
of user k. The closer the fairness factor obtained by algo-
rithm approximates to 1, the better the fairness of the
algorithm is.
Figure 3 compares fairness index of the proposed
scheme, Qos algorithm, PF algorithm and max-rate algo-
rithm. As the max-rate algorithm aims to maximize the
system throughput without considering users' require-
ments, it di splays the worst in ter ms of fairness. With the
increasing of the number of users, the fairness factor of
max-rate algorithm is decreased sharply. The fairness
factors of the other three algorithms are close. Their
fairness factors are all more than 0.9 when the number of
users is less than 14. The proposed algorithm exhibits the
best fairness in these three algorithms, and Qos and PF
algorithm are slightly lower t han it.
The throughput of the system is shown in Figure 4.
Because the users' requirements and remaining AUs are
not considered, the throughput of PF algorithm is the
lowest of all. From the point of throughput, the proposed
algorithm is superior to the Qos and PF algorithm, bene-
fiting from higher MCS of some users, free AUs, and the
appropriate allocation of remaining AUs. Max-rate algo-
rithm displays the best performance of the four algo-
rithms. The curve of proposed algorithm is close to that
of the max-rate algorithm. When the number of users is
small, the curve of proposed algorithm is highe r t ha n t ha t
of max-rate algorithm. Because of the MCS selection
mechanism in LTE systems, max-rate algorithm cannot
always provide the best performance.
B. R. JI ANG ET AL.
Copyright © 2013 SciRes. CN
78
678910 11 12 13 14
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
The numbe r of users
F airn es s facto r
Proposed algorithm
Qos algorithm
PF algorithm
Max-rate algorithm
Figure 3. The fairness fa ct ors of four algorithms.
The unreached rate is used to illustrate the Qos guar-
anteed of each algorithm. The smaller the unreached
rates gained by the algorithm, the better the users Qos
guaranteed is. The unreached rate can be calculated by:
1
,
, 0, otherwise
Kkkk k
u kk
k
Rr Rr
r PP
=
−>
==
(13)
where
u
r
is the total unreached rate in the system.
k
r
is the data rate achieved by user k. k
P is the unreached
rate of user k.
Figure 5 demonstrates the unreached rate of the users
among the proposed algorithm, Qos algorithm, and PF
algorithm. The PF algorithm allocates AUs without con-
sidering the requirements of users, so unreached rates
gained by P F algorithm rapid ly increase as the number of
users increases. It can be found that Qos algorithm guar-
antees users' requirements well, and the unreached rate
achieved b y Qos algorithm is not too high. The proposed
algorithm keeps the unreached rate at the lowest level,
678910 1112 13 14
9.5
10
10.5
11
11.5
12
The numbe r of users
System Throughput (Mbit/s)
PF algorithm
Qos algorithm
Proposed algorithm
Max-rate algorithm
Figure 4. System throughput of four a lgorithms.
10 11 12 13 14 15 16 1718
0
0.2
0.4
0.6
0.8
1
1.2
1.4
The number of users
U nrea ched Rate (Mbit/s)
PF algorithm
Qos algorithm
Proposed algorithm
Figure 5. The unreached rate of three algorithms.
678910 11 12 13 14
10.4
10.6
10.8
11
11.2
11.4
11.6
11.8
12
The number of user s
System Throughput (Mbit/s)
P ri ority 1
P ri ority 2
P ri ority 3
Figure 6. System throughput of proposed algorithm with
different methods for determining the priorit ies.
Table 5. Compu tational complexity of four alg or ithms.
Algorithms Max-ra te PF Qos Proposed
Initial allocation
Qos gua rantee
Re-allocation
Total complexity
()OKN
\
\
()OKN
2
()O KN
\
\
2
()O KN
2
()O KN
()OKN
\
2
()O KN
2
()O KN
()OKN
()OKN
2
()O KN
close to zero. The unreached rate attained by proposed
algorithm is not more than 0.1 Mbit/s when the number
of users is les s t han 18 .
Figure 6 shows the throughput of proposed algorithm
with different methods for determining priorities. Ob-
viously, the priority considered users’ requirements and
channel conditions simultaneously presents the best per-
formance of all. The performance gained by the priority
determined by the channel condition is superior to that
gained by the priority determined by minimum data rate
require ment.
B. R. JI ANG ET AL.
Copyright © 2013 SciRes. CN
79
Table 5 shows the computational complexity of the
four algorithms. We can easily learn that the complexity
of ma x-rate algorith m is
()
O KN, and the complexity of
PF and Qos algo rithm a r e all
2
()O KN
. For the proposed
algorithm , th e c ompl exity of initial allocation is
2
()O KN
,
and the complexity of re-allocation scheme is
()
O KN,
Therefore, the overall complexity of proposed algorithm
is
22
()()()
O KNOKNO KN+= . It is observed that, the
proposed algorithm gains the quadratic complexity,
which is the same as that of PF and Qos algorithm. The
last column of Tabl e 5 explains that the max-rate algo-
rithm gets the lowest computational complexity, and the
other three algorithms have the same computational
complexity.
5. Conclusions
In this paper, we propose a two-step resource block allo-
cation algorithm for LTE downlink systems. The first
step of pro posed algorithm initiall y allocates AUs to each
user based on the proportional fairne ss sc he me. The n, t h e
proposed scheme re-allocates the AUs with the worst
channel condition of each user to improve the perfor-
mance restriction by those AUs. The algorithm can pro-
vide us with a higher data rate and a flexible allocation
scheme, and ensures the user's fairness. Simulation re-
sults show that the proposed algorithm provides higher
thro ughput and ens ures the fairness of each user.
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