A Dynamic Programming Based Technique for Optimal Allocation of Radio Resource in Multi-user Cellular Long-term Evolution (LTE) Downlink

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:


ISBN: 978-1-61804-005-3 108

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.

References: 1. J. Huang, V.G. Subramanian, R. Agrawal, and

R.A. Berry, Downlink Scheduling and Resource Allocation for OFDM Systems, IEEE Transactions on Wireless Communications, Vol. 8, No.1, Jan. 2009

2. M. S. Kaiser and K.M. Ahmed, Radio Resource Allocation for Heterogeneous Services in Relay Enhanced OFDMA Systems, Journal of Communications, vol. 5, No.6, June 2010

3. W. An-ding, W. Xiu-ping, Q. Yu-yang, L. Li-Li and L. Shi-ju, An Adaptive sub-carrier and power allocation algorithm with QoS guarantee for OFDMA System, Journal of Communication and Computers, Vol. 5, No. 12 (Serial No: 49), Dec. 2008

4. G.H. Kumar, P.H. Krishnarao, K.S.R. Krishna, Two-stage Algorithm for sub-carrier, Bit and Power Allocation in OFDMA Systems, International Journal of Computer Science and Communications, vol. 1, No.2, July-Dec. 2010, pp. 51-54

5. G. Li and H. Liu, Downlink Radio Resource Allocation for Multi-cell OFDMA System, IEEE Transactions on Wireless Communications, Vol. 5, No.12, pp. 3451-3459, December 2006

6. I. Koutsopoulos and L. Tassiulas, Cross-Layer Adaptive Techniques for Throughput Enhancement in Wireless OFDM-Based Networks, IEEE/ACM Transactions on Networking, Vol. 14, No.5, pp. 1056-1066, October 2006

7. T. Thonabalasinghan, S. Hanley, L.L.H. Andrew and J. Papandripoulos, Joint Allocation of sub-carriers and Transmit Powers in a Multi-user OFDM Cellular Network, IEEE International Conference on Communications, pp. 269-274, 2006

8. C. Koutsimanis and G. Fodor, A Dynamic Resource Allocation Scheme for GBR Services in OFDMA Networks, Proceedings of the IEEE Conference of Communications, 2008, pp. 2524-2530.

9. I. C. Wong and B.L. Evans, Optimal Resource Allocation in OFDMA Systems with Imperfect Channel Knowledge, IEEE Transactions on Communications

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11. N. Zhou, X. Zhu and Y. Huang, Genetic Algorithm Based Cross-Layer Resource Allocation for Wireless OFDM Networks with Heterogeneous Traffic, 17th European Signal Processing Conference (EUSIPCO), 2009, pp. 1656-1659

12. F.S. Hillier and G.J. Lieberman, Introduction to Mathematical Programming, 2nd Edition, McGraw-Hill inc., 1995.


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A Dynamic Programming Based Technique for Optimal Allocation of Radio Resource in Multi-user Cellular Long-term Evolution (LTE) Downlink