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A Dynamic Programming based Technique for Optimal Allocation of
Radio Resource in Multi-user Cellular Long-Term Evolution (LTE)
Downlink
ABAYOMI M. AJOFOYINBO and KEHINDE OROLU Department of Systems
Engineering
Faculty of Engineering Complex University of Lagos, Lagos,
Nigeria
Email: [email protected];
[email protected]
Abstract: In recent time, researchers have investigated the
problems of radio resource allocation in Long-Term Evolution (LTE)
Downlink and have made useful contributions. In the current work, a
deterministic dynamic programming based technique is proposed for
optimal allocation of radio resource in the downlink of a
multi-user LTE Cellular Systems. The objective is to maximise
instantaneous channel throughput through optimal allocation of
radio resource. The proposed model was simulated on a Personal
Computer using C# programming language. It is shown that the
proposed technique maximises instantaneous channel throughput
through optimal allocation of Resource Blocks (RBs).
Key-Words: Subcarrier, Dynamic, Optimal, Radio, Resource, Block,
Throughput
1 Introduction In the downlink of the Long-Term Evolution (LTE)
Cellular Systems, radio resources are partitioned in both the
frequency and time domains. Access to radio resources is controlled
in terms of frames and frequency channels. These frames and
frequency channels are referred to as the Orthogonal Frequency
Division Multiplexing (OFDM) Resource Blocks (RBs). Each sub-frame
(i.e.,1 millisecond in the time domain) consisting of two (2) RBs
is divided into fourteen (14) symbols of which up to three symbols
at the start of the sub-frame can be used for controlling channel
signaling. In recent time, researchers have investigated the
problems of radio resource allocation in LTE Downlink and have made
useful contributions. For example, Huang et al [1] investigated the
problem of gradient-based scheduling and resource allocation for a
downlink of a Cellular OFDM system, which reduces to solving a
convex optimisation problem in each time slot. The work considered
scheduling and resource allocation for the downlink of a Cellular
OFDM system, with various practical considerations including
integer tone allocations, different sub-channelization schemes,
maximum signal-to-noise ratio constraint per tone, and self-noise
due to channel estimation errors and phase noise. The authors
proposed an algorithm that automatically yields an integer carrier
allocation. Kasier and Ahmed [2] proposed a priority based
resource
allocation algorithm for heterogeneous services in the relay
enhanced Orthogonal Frequency Division Multiple Access (OFDMA)
downlink systems. The aim of the research was to maximise the
system throughput while satisfying the Quality of Service (QoS) of
the heterogeneous services comprising Real Time (RT) and
Non-Real-Time (NRT) services. The proposed algorithm reduces the
outage probability of the system and increases the system
throughput. An-ding et al [3] presented an adaptive sub-carrier and
power allocation scheme for OFDMA systems according to their
different Quality of Service (QoS) requirement and traffic type.
The proposed algorithm maximised the transmission data rate while
satisfying total power constraint and a certain Bit Error Rate
(BER) requirement. The algorithm first allocates sub-carriers and
bits to high priority users according to their rates and Bit Error
Rate (BER) requirement, and then distributes the residual resources
to the ordinary users in terms of the proportional fairness
principle. Simulation results show that the proposed method has
better performance than the existing algorithms. In [4], Kumar et
al proposed new heuristic algorithms to solve the sub-carrier, bit,
and power allocation problem in polynomial computational
complexity. The two-stage allocation algorithms include the initial
sub-carrier assignment and the iterative improvement two-steps.
Simulation results show that the performance of the proposed
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heuristic algorithm is close to that of the optimum solution. Li
and Liu [5] proposed a two-level resource allocation scheme, where
the first level coordinates cells while the second level performs
per-cell optimisation. Moreover, Koutsopoulos and Tassiulas [6]
presented two classes of centralised heuristic algorithms. The
first one considers each sub-carrier in each cell. The results
obtained show that the first class of heuristics performs better
and quantify the input of different parameters on system
performance. Thonabalasingham et al [7] worked on joint allocation
of various radio resources and concluded that joint allocation of
various radio resources has a clear potential over methodologies
that allocate single resource. In an interesting contribution,
Koutsimanis and Fodor [8] worked on the elastic nature of data
applications. In this research work, each user is associated with a
minimum and maximum resource block requirements and the resource
allocation problem consists of maximising the overall throughput
such that these requirements are met. Wong and Evans [9] developed
optimal resource allocation algorithms for OFDMA systems assuming
the availability of only partial (imperfect) Channel State
Information (CSI). They considered both continuous and discrete
weighted sum rate maximisation subject to total power constraints,
and average bit error rate constraints for the discrete rate case.
The work of Hosein [10] focused on the optimal allocation of power
and bandwidth (number of subcarriers) with the objective of
maximising the sector-wide throughput. The research worked
determined the regions within which (a) a frequency reuse factor of
unity is optimal, (b) orthogonal frequency allocations is optimal
and (c) joint processing of signals from both sectors is optimal.
Zhou, Zhu and Huang [11] proposed a Genetic Algorithm (GA) based
cross-layer resource allocation for the downlink multiuser wireless
OFDM system with heterogeneous traffic. The GA was used to maximise
the sum of weighted capacities of multiple traffic queues at the
Physical layer, where the weights are determined by the Medium
Access Control (MAC) layer. In the current work, a deterministic
dynamic programming based technique is proposed for optimal
allocation of radio resource in the downlink of a multi-user LTE
Cellular Systems. The remainder of the paper is organized as
follows: Problem formulation is presented in Section 2. This
includes systems modelling and allocation policy. The Simulation of
the proposed model is presented in Section 3 followed by a
discussion of Simulation results in Section 4. Section 5 concludes
the paper. This
paper contributes to knowledge in the field of optimal
allocation of RBs to achieve maximum throughput in the downlink of
multi-user LTE Cellular Systems. This is a novel contribution.
2 Problem Formulation Even though some network state information
are readily accessible to the Base Station (BS), other parameters,
for example channel state information, are communicated as feedback
from the User Equipment (UE) or Mobile Station (MS) to the BS. When
required parameters or state information are received, the BS then
takes scheduling decision to maximise the utility function chosen
by the Network Operator. It is assumed in the current work that the
Channel Quality Information (CQI) is available. Thus, the BS is
able to take informed decision on applicable modulation technique.
We model allocation of RBs to users as a deterministic dynamic
programming problem. The essential feature of the dynamic
programming approach is the structuring of optimisation problems
into multiple stages, which are then solved sequentially one stage
at a time [12]. Moreover, each of the stages is associated with the
states of the process. These states reflect the information
required to fully assess the consequences that the current decision
has upon future actions. The specification of the states of the
system is a critical design parameter of the dynamic programming
model.
2.1 Systems Modelling The proposed dynamic programming model is
assumed to consist of six (6) states, namely: 0, 2, 4, 6, 8, and
10. These states represent the number of allocated RBs. Moreover,
the model consists of n stages, which represent the users on the
LTE downlink. In developing the recursive optimisation procedure,
we obtained a solution of the overall n-stage problem by first
solving a one-stage problem, and sequentially including one stage
at a time, and solving one-stage problem until the overall optimum
is reached. The applicable dynamic programming procedure in this
work is the Back Induction (BI) process wherein the first stage to
be analysed is the final stage of the problem and the n-stage
problem is solved moving backwards one stage at a time until all
stages are included to obtain optimal solution. The problem
requires making n interrelated decisions with respect to the number
of RBs to be allocated to each of the users at every scheduling
instant. We define the following variables:
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jx
= Number of RBs allocated to user j ;
nj ,.....,2,1
kx
= Possible allocation of RBs;
50,.....,2,1,0k
100,.....,4,2,0kx )( jj xp = Throughput obtainable from
allocation of jx RBs to user j . q
= Maximum number of RBs that can be allocated to a user (q =10
)
osN = Number of OFDM symbols j
osN = Number of OFDM symbols for user j modN = Number of bits
per OFDM Symbol jN mod = Number of bits per OFDM Symbol for
user j REN = Number of Resource Elements (RE)
m
= Total number of RBs n
= Total number of users. s = Number of RBs still available for
allocation
The objective is to choose jx so as to
Maximize nj jj xpZ 1 )( (1) Subject to nj j mx1 (2) where
qx j 0 (3) qx j ,...,2,0
(4) nj ,...,2,1 (5)
We note that j
jjosjj xNNxp ***12)( mod
(6)
2.2 Allocation Policy In this proposed model, the computation
leading to the allocation of RBs follows a recursive procedure. The
recursive procedure and tracking policy are presented in the
following sub-sections.
2.2.1 Recursion We define ),( jj xsf as the cumulative
contribution of user j to the objective function given s
available
RBs and jx allocation to user j . For the last user (i.e., nj ),
0)(* 1 jj xsf .
Thus, )(),( jjjj xpxsf (7)
From the next to the last user to the first user (i.e.,
1,.....,1 nj ), equation (8) applies: )()(),( * 1 jjjjjj
xsfxpxsf (8)
The optimal decision for user j is the maximum of the respective
cumulative contribution to the total throughput. This is given by:
),(max)(
,...,2,0
*
jjsx
j xsfsfj (9)
The corresponding allocation of RBs is given by: ),(maxarg
,...,2,0* jjsxj xsfx j (10) 2.2.2 Allocation tracking Starting with
user j=1, and s available RBs, we invoke equation (10) to compute
the optimal resource allocation, **jx , to each user.
For the first user (i.e., j = 1) ),(maxarg 11,...,2,0**1 1 xsfx
sx (11) where ms
Equations (12) and (13) give subsequent optimal allocation to
other users (i.e., j =2,3,.....,n).
**
1 jxss (12)
)(*** sxx jj (13)
Table 6 shows RBs allocation to all users.
3 Simulation Results The proposed dynamic programming based
technique was simulated on Personal Computer using C# programming
language. The simulation and user parameters are presented in
Tables 1 and 2 respectively. The results of the simulation are
presented in Tables 3, 4, 5 and 6.
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Table 1: Simulation Parameters Transmission bandwidth 20MHz
Total number of RBs 100
Number of subcarriers per RB 12
Modulation technique QPSK(2), 16QAM(4), 6AQAM(6) Maximum number
of RB for a user 10
Number of users 20 Number of states in the dynamic programming
model 6 (i.e.,0,2,4,6,8, and 10)
Table 2: User parameters
User
Nmod (QPSK=2, 16QAM=4, 64QAM=6)
Nos (per sub-frame)
NRE = 12 *Nos (Per sub-frame)
Nmod * NRE Total bits per sub-frame (2 RBs)
1 2 7 84 168
2 6 11 132 792
3 4 9 108 432
4 4 9 108 432
5 6 11 132 792
6 4 9 108 432
7 4 9 108 432
8 6 11 132 792
9 6 11 132 792
10 4 9 108 432
11 2 7 84 168
12 2 7 84 168
13 6 11 132 792
14 2 7 84 168
15 4 9 108 432
16 2 7 84 168
17 6 11 132 792
18 6 11 132 792
19 4 9 108 432
20 4 9 108 432
Table 3: Throughput of each user (i.e., )( jj xp ) User j
RBs 1 2 3 4 5 ... 18 19 20
0 0 0 0 0 0
... 0 0 0
2 168 792 432 432 792 ... 792 432 432
4 336 1584 864 864 1584 ... 1584 864 864
6 504 2000 1296 1296 2000 ... 2000 1296 1296
8 672 2000 1728 1728 2000 ... 2000 1728 1728
10 840 2000 2000 2000 2000 ... 2000 2000 2000
12 840 2000 2000 2000 2000 ... 2000 2000 2000
14 840 2000 2000 2000 2000 ... 2000 2000 2000
16 840 2000 2000 2000 2000 ... 2000 2000 2000
18 840 2000 2000 2000 2000 ... 2000 2000 2000
20 840 2000 2000 2000 2000 ... 2000 2000 2000 ... ... ... ...
... ... ... ... ... ...
88 840 2000 2000 2000 2000 ... 2000 2000 2000
90 840 2000 2000 2000 2000 ... 2000 2000 2000
92 840 2000 2000 2000 2000 ... 2000 2000 2000
94 840 2000 2000 2000 2000 ... 2000 2000 2000
96 840 2000 2000 2000 2000 ... 2000 2000 2000
98 840 2000 2000 2000 2000 ... 2000 2000 2000
100 840 2000 2000 2000 2000 ... 2000 2000 2000
Table 4: Throughput and optimal RBs allocation to the last user
(i.e. user j = n)
S
)( 2020 xp
20x
*
20 ( )f s *20x 0 0 0 0 0
2 432 2 432 2
4 864 4 864 4
6 1296 6 1296 6
8 1728 8 1728 8
10 2000 10 2000 10
12 2000 10 2000 10
14 2000 10 2000 10
16 2000 10 2000 10
18 2000 10 2000 10
20 2000 10 2000 10 ... ... ... ... ...
88 2000 10 2000 10
90 2000 10 2000 10
92 2000 10 2000 10
94 2000 10 2000 10
96 2000 10 2000 10
98 2000 10 2000 10
100 2000 10 2000 10
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Table 5: Throughput and optimal RBs allocation to the next to
the last user (i.e., j = n-1)
xk s 0 2 4 6
:
100 *
19( )f s *19x 0 0
0 0 2 432 432
432 0 4 864 864 864
864 0 6 1296 1296 1296 1296
1296 0 8 1728 1728 1728 1728
1728 0 10 2000 2160 2160 2160
2160 2 12 2000 2432 2592 2592
2592 4 14 2000 2432 2864 3024
3024 6 16 2000 2432 2864 3296
3456 8 18 2000 2432 2864 3296 : 3728 8 20 2000 2432 2864 3296 :
4000 10 : : : : : : : :
88 2000 2432 2864 3296 : 4000 10 90 2000 2432 2864 3296 : 4000
10 92 2000 2432 2864 3296 : 4000 10 94 2000 2432 2864 3296 : 4000
10 96 2000 2432 2864 3296 : 4000 10 98 2000 2432 2864 3296 : 4000
10
100 2000 2432 2864 3296 : 2000 4000 10
Similarly, equations (8), (9) and (10) are invoked to obtain
throughput and optimal RBs allocation to other users (i.e., j =
n-2,...,1).
Table 6: RBs allocation to users
User j s 1 2 3 4 5 6 7 8 ... 19 20
0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 2
4 0 0 0 0 0 0 0 0 0 4
6 0 0 0 0 0 0 0 0 0 6
8 0 0 0 0 0 0 0 0 0 8
10 0 0 0 0 0 0 0 0 2 10
12 0 0 0 0 0 0 0 0 4 10
14 0 0 0 0 0 0 0 0 6 10
16 0 0 0 0 0 0 0 0 8 10
18 0 0 0 0 0 0 0 2 8 10
20 0 0 0 0 0 0 0 4 10 10 ...
88 0 4 8 8 6 8 10 6 10 10
90 0 4 8 8 6 10 10 6 10 10
92 0 4 8 8 6 10 10 6 10 10
94 0 4 8 8 6 10 10 6 10 10 96 0 4 8 8 6 10 10 6 10 10 98 0 4 8 8
6 10 10 6 10 10
100 0 4 8 8 6 10 10 6 10 10
Starting with user j = n = 20, we invoke equation (7), (8), and
(9) in relation to the data in Tables 2 and 3, to obtain throughput
for all users as presented in Tables 4 and 5. The corresponding RBs
allocation to users j=1,2,...,n is given by equation (10). The
overall optimal allocation of RBs that maximises the channel
throughput for all users is presented in Table 7. Two cases are
presented, namely: allocation of RBs using (a) dynamic programming
and (b) fair allocation techniques.
Table 7: Optimal RBs allocation
User
Allocated RBs, **jx Dynamic
programming based technique
Fair allocation technique
1 0 4 2 4 6 3 8 4 4 8 4 5 4 6 6 8 4 7 8 4 8 4 6 9 6 6
10 8 4 11 0 4 12 0 4 13 6 6 14 0 4 15 8 6 16 0 4 17 6 6 18 6 6
19 8 6 20 8 6
Fig. 1:RBs Allocation to each user (Proposed Dynamic Programming
(DP) and Fair Allocation
(Fair Alloc) Techniques)
2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
16
18
20
USER
RESO
URCE
BL
OCK
S
RESOURCE BLOCKS ALLOCATION PER USER
DPFair Alloc
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By using data in Tables 1, 2, 3 and 7, we compare the channel
performance of the proposed dynamic programming based technique for
optimal allocation of RBs with the Fair allocation approach. For
the Fair allocation technique, fixed RBs (i.e., minimum=4 and
maximum=6) are allocated to users based on the applicable
modulation technique (i.e., 64QAM=6RBs, QPSK=4RBs and 16QAM=4RBs).
The results are presented in Tables 8 below.
Table 8: Comparison (Dynamic Programming Vs Fair Allocation)
User
Bits per Sub-frame
(2 RBs)
Dynamic Programming (DP)
Technique
Fair Allocation (FA)
Technique ORA TP CT ORA TP CT
1 168 0 0 0 4 336 336
2 792 4 1584 1584 6 2000 2336
3 432 8 1728 3312 4 864 3200
4 432 8 1728 5040 4 864 4064
5 792 4 1584 6624 6 2000 6064
6 432 8 1728 8352 4 864 6928
7 432 8 1728 10080 4 864 7792
8 792 4 1584 11664 6 2000 9792
9 792 6 2000 13664 6 2000 11792
10 432 8 1728 15392 4 864 12656
11 168 0 0 15392 4 336 12992
12 168 0 0 15392 4 336 13328
13 792 6 2000 17392 6 2000 15328
14 168 0 0 17392 4 336 15664
15 432 8 1728 19120 6 1296 16960
16 168 0 0 19120 4 336 17296
17 792 6 2000 21120 6 2000 19296
18 792 6 2000 23120 6 2000 21296
19 432 8 1728 24848 6 1296 22592
20 432 8 1728 26576 6 1296 23888 Legend to Table 8:
ORA - Optimum RB Allocation TP - Throughput CT - Cumulative
Throughput
4 Discussion of the Simulation Results In this paper, we assumed
20 users and allocation of maximum of 10 RBs to each user.
Instantaneous throughput for each user is presented in Table 3.
Throughput and optimal allocation of RBs to users are presented in
Tables 4 and 5. Based on available RBs, Table 6 shows optimal
allocation of RBs to users. Furthermore, Table 7 shows optimal
allocation
Fig. 2: Cumulative throughput for all users. (Proposed Dynamic
Programming Model)
Fig. 3: Cumulative Throughput for all users. (Fair Allocation
Approach)
Fig. 4: Cumulative throughput for all users. (Comparison:
Dynamic Programming based Technique versus
Fair Allocation Approach)
2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3x 104
USER
THR
OUG
HPU
T
Cumulative Throughput (DYNAMIC PROGRAMMING)
2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3x 104
USER
THRO
UGHP
UT
Cumulative Throughput (FAIR ALLOCATION)
2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3x 104
USER
THR
OUG
HPUT
Cumulative Throughput (COMPARISON)
DPFair Alloc
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of RBs to each user corresponding to maximum overall
instantaneous throughput. The graphs of optimal RBs allocation to
users, for both the dynamic programming and fair allocation
techniques, are presented in Figure 1. Figure 2 shows the
cumulative throughput for users using the dynamic programming based
technique for optimal RB allocation. Similarly, cumulative
throughput for users using the fair allocation technique is
presented in Figure 3. To demonstrate the efficacy of the proposed
methodology, we present the comparative graphs for cumulative
throughput in Figure 4.
5 Conclusion In Cellular Systems, the aim of dynamic allocation
techniques is maximisation of utility function that represents
network system-wide requirement through optimal allocation of radio
resources. In this paper, the primary resource is a set of
time-frequency blocks referred to as Resource Blocks (RBs). We have
proposed a dynamic programming based technique for optimal
allocation of RBs in a multi-user Cellular LTE downlink. This is a
novel contribution to the field of radio resource allocation in
cellular LTE. The objective is to maximise network throughput
through optimal RBs allocation, given availability of required
channel quality information. The proposed technique was simulated
on a Personal Computer using C# programming language. We also
compared results obtained using the proposed technique with the
fair allocation methodology. Comparatively, the proposed dynamic
programming based technique for optimal allocation of RBs yields
better instantaneous throughput than the fair allocation technique.
It is shown by the results obtained that the proposed model can,
indeed, maximise instantaneous channel throughput through optimal
allocation of RBs to users.
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