SET COVER PROBLEM OF COVERAGE PLANNING IN LTE-ADVANCED RELAY NETWORKS Fan-Hsun Tseng1, Li-Der Chou1 1 National Central University, Taiwan [email protected], [email protected] Han-Chieh Chao2,3, Wei-Jen Yu2 2 National I-Lan University, Taiwan 3 National Dong Hwa University, Taiwan [email protected], [email protected]

ABSTRACT The various mobile devices nowadays are developed rapidly, such as the smart phones and tablet PCs. Users are able to acquire different multimedia services through wireless communication at anytime and anywhere. However, the great demand also results in the insufficient for bandwidth usage. Therefore, the fourth generation of mobile telecommunications (4G) technology is proposed and investigated widely. One of the popular technologies is Long Term Evolution Advanced (LTE-Advanced), which proposed by the Third Generation Project Partnership (3GPP). The Evolved NodeB (eNB) and Relay Node (RN) are the major components in LTE-Advanced networks. How to deploy these two components to enlarge the network coverage and performance is a vital issue. In this paper, we investigate into the coverage problem with a well-known Set Cover problem, and propose a heuristic algorithm named Set Covering algorithm to solve it. The ultimate object is achieving the highest network coverage and capacity with the least uncovered mobile user. In the simulation result, we use MATLAB to simulate network deployment, and evaluate the planning results. According to the simulation results, we accomplish the better network capacity and higher number of covered users. Keyword: 4G, LTE-Advanced, relay technology, network planning, set cover problem.

1. INTRODUCTION Long Term Evolution (LTE) is the mobile communication standard which was proposed by the Third Generation Project Partnership (3GPP) [1], and the further version towards LTE-Advanced in Release 10 [2]. It is able to satisfy the transmission data rates requirement with 1 gigabit per second in downlink and 500 megabit per second in uplink, which defined by International Telecommunication Union (ITU). There are two major enhancements of LTE-Advanced that are the carrier aggregation technology and relay technology. The carrier aggregation technology permits grouping several different channels into one logical channel, hence achieves the higher peak traffic channel data rate. On the other hand, the relay technology is introduced to economize on construction cost by deploying RN, and improves the network throughput and coverage. Since the relay technology makes a breakthrough 1

in LTE, some researchers start to investigate and analyze the performance of relay development for a realistic suburban environment in Germany [3]. In a developing country, network planning becomes a prerequisite step for deploying network infrastructure. In this paper, we focus on the relay technology in LTE-Advanced networks. The relay technique is considered as a cost-effective solution in 3GPP LTE-Advanced by way of coverage extension and throughput enhancement, which shown as Figure 1. For providing the higher cell capacity, the RN is deployed between the eNB and user who nears the cell edge. Therefore, the user is able to obtain the better signal-to-noise ratio (SNR) value. Besides, the RN could be placed around the shelter and bypasses it, and overcomes the defect of shadowing effect. Furthermore the RN is able to deploy nearby cell edge to extend the coverage of eNB, hence the users still can be served even then out of range. According to the previous statements, the transmission distance, coverage of eNB and network capacity can be improved by deploying RNs.

eNB

RN

RN Signal Enhancement

Shadowing Effect

RN Coverage Extension

Figure 1. The scenario of LTE-Advanced with relay This paper is organized as follows. In section II, we introduce the existing researches in LTE-Advanced networks, and compare different network planning approaches for relay networks. The section III introduces the Set Cover problem and states the proposed heuristic algorithm, viz Set Covering algorithm. In section IV, we firstly illustrate the planning result of Set Covering algorithm with a planning case, then discuss and compare the simulation results with other approaches. Finally, the conclusions and future works about this research are drawn in section V.

2. RELATED WORKS No matter what kind of network, network planning is a necessary process for environment construction, such as [4] and [5]. The relay technology has been widely studied in wireless communications including cost-efficiency, throughput enhancement and coverage extension, especially the IEEE 802.16j and LTE-Advanced mobile systems in recent years [6]. The primary goal of the network planning is not only low cost but also high capacity, many methods have been proposed. In [7], the researchers proposed a heuristic algorithm to solve the throughput maximization relay station placement (TM-RSP) problem in IEEE 802.16j WiMAX networks. To satisfy the limitation of budget, the proposed algorithm deploys relay stations (RSs) for the better gain. In [8], the researchers found a minimum number of RSs to satisfy the requests of subscribers via cooperative

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communication. Therefore, the lower cost is achieved and the network performance is improved. In [9], the researchers formulated a mixed integer linear programming (MILP) model, and used the Pareto front and multi-objective Tabu search as their solution. The same objective with ours is that the construction cost in LTE network is considered, but the researchers only consider the site selections of eNBs unlike both of eNBs and RSs in this work. The transmission power and resource block in uplink are considered in [10], but only the eNBs are deployed in their network environments. In [11], the authors formulated their cooperation game theory with the position selection and power allocation of eNBs. The difference between [11] and this work is that the researchers considered the eNB distribution and power assignment, and we desire to fulfill the requirements of users with the minimum construction cost. In [12], the proposed scheme optimized the cell load, which depends on the location selection of eNB and the tilt and azimuth of antenna. In [13], the authors investigated the relay node deployments on throughput and cell coverage area extension between pico eNB and RN, which is unlike the lowest cost for deploying eNB and RN in ours. The impact on site planning of relay networks in the LTE-Advanced was also investigated in [14]. The researchers considered the signal-to-noise-ratio (SNR) and signal-to-interference-plus-noise-ratio (SINR), and the same with this paper is that the SINR is considered in both literatures. However, the researchers only concerned the site selection of multiple RNs within the cell range of an eNB. It is worthy to mention that a multiple eNBs and RNs LTE-Advanced network is constructed by the proposed Set Covering algorithm in our work. There are still many related literatures about relay technology in LTE-Advanced networks. For example, some researchers concentrated on the analysis of relay performance [15], and some utilized RNs to extend network coverage, such as [16] and [17], and some dedicated to design the relay architecture in order to achieve cost efficiency [18]. The most similar works with ours are [19], [20] and [21], which are the previous works proposed by us. In [19], we proposed Tree algorithm for increasing reliability of IEEE 802.16j mobile multi-hop relay (MMR) networks. Then, the Supergraph Tree (S-Tree) algorithm and Interference-Aware Tree algorithm [20] was proposed to minimize the construction cost and communication interference in the MMR networks However, these proposed algorithms was designed for the MMR networks, which is different with two hop relaying limitation in LTE-Advanced network. Therefore, we investigated the characteristics of two hop relaying and proposed a study in [21]. In this paper, we proposed Set Covering algorithm based on Set Cover problem, and enhanced the network performance and coverage with the definitely acceptable construction cost than previous works.

3. PROBLEM DEFINITION AND PROPOSED ALGORITHM In this section, the Set Cover problem is introduced and defined, and the design concept of Set Covering algorithm is also explained. We describe the problem that we defined first, there are two types of nodes in the topology. One is the candidate position (CP) for the eNB and RN deployment, the other one is the location of user equipment (UE). The ultimate goal is determining the eNB and RN numbers at the lowest cost and satisfying the user demands.

3.1 Set Cover Problem The Set Cover problem is a well-known problem in set theory, which is adopted to many research field. The brief introduction is described as follows. The definition of Set Cover problem is given an universal set with elements ,

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and find sets whose union comprises the universal set . Then, the Set Cover problem is to identify the smallest numbers of set whose union still contains all elements in the universe. For instance, given the universal set with five elements, and a set with five subsets. Clearly the union of all given subsets in contains all elements in the universal set . Therefore, we can cover the universal set with two subsets which are and as the smallest set numbers. As the above statement, we approach the concept of Set Cover problem to plan LTE-Advanced networks. Assume that the universal set is all UEs in network, and the each subset is regarded as a CP that can be deployed an eNB or RN to serve the UEs. An illustration , represents an eNB or RN which covers the UE1, UE2 and UE3. We desire to find the smallest number of subsets that implies the least number of constructed sites. Therefore, we will find the minimum construction cost and least uncovered UEs.

3.2 Set Covering Algorithm Based on Set Cover problem, we design a heuristic algorithm named Set Covering algorithm to solve the network planning in LTE-Advanced networks. The principle steps in Set Covering algorithm are stated as follows. First of all, we examine the user who served by the least CPs, and select the CP that serves the most UEs and deploy an eNB at this CP. In this way, the UEs can be ensured covering and serving by the deployed eNB, and the deployed eNB serves the most numbers of UEs. After that, we select the CPs to deploy RNs, which serve the UEs within the coverage range of the deployed eNB. Finally, repeat the above steps until all of the UEs are served. The difference between the previous methods with ours is that the consideration of the deployment order. In previous algorithms, the deployment priority of RN is higher than eNB thus the performance of capacity is worse. The Set Covering algorithm is contrary to previous algorithms, hence the better network performance and more UEs can be achieved and serviced. We introduce the Set Covering algorithm herein. Let a set of nodes as and a set of links between nodes as . Given an undirected graph , where and . Then, it can be known that and . Assume that a set of CP with | | , and a set of UE with | | . If an eNB (RN) is placed on the location corresponding to , then ( ). If there is no instrument placed on the location corresponding to , then . That is, . Denote and as subsets of nodes. Then, is used to generate a descendant ordered list of the elements in according to the adjacent number of nodes in based on the graph , and the ascendant ordered list vice versa. If the order of the nodes is in same degree, the sequence of the nodes can be arbitrary. Since is an ordered list, [ ] is denoted as the -th vertex in . Moreover, the utility rate of UE is defined as . In addition, the depth of routing tree should be limited within . The Set Covering algorithm is shown as Table 1, lines 2 to 6 are used to find CP for deploying eNB, which can serve most UEs. Lines 10 to 15 select CPs to deploy RNs until there is no uncovered UEs. In addition, lines 16 to 19 are used to guarantee that the required utility rate can be achieved, otherwise the eNB is deployed to replace the RN. Finally, the property that the hop count between the eNB and RN should be limited with two-hop relaying is guaranteed in lines 21 to 25. 4

Table 1. Set Covering algorithm Algorithm: Set Covering Algorithm ( , , , ) Input: : underlying graph : vector indicating the placement of eNB and RN : minimum required average utility : maximum depth of the routing tree 01 02 repeat 03 [ ] 04 05 06 [ ] [ ] [ ] 07 08 09 initial i=1 | | 10 while 11 if [ ] 12 [] [] [] 13 14 i++ 15 until 16 repeat 17 18 [ ] 19 until 20 repeat 21 22 if 23 24 [ ] 25 until

3.3 Evaluate of Network Planning In this subsection, we explain how to evaluate the results of planned network. As above-mentioned, we focus on the network coverage which implies the least uncovered UEs, and achieve the better network capacity. The detail definitions of measurement metrics are as follows. 1. Construction cost: we simply define the construction cost is related to the deployment cost of eNBs and RNs, rather than considering the recurring operational expenditure (i.e. Operation & Maintenance, site rent etc.) [22]. The construction cost of an eNB is 10 unit costs, and the RN is 2.5 units. 2. Communication interference: we consider that the UEs may receive multiple signals from various eNBs and RNs, hence the communication interference is existing. For instance, an UE receives three signal sources that one of the signals is the major signal and others are interferences. The represents the receive interference of , let . (1) ∑ The is the signal from CP , and the is between the and CP . 3. Uncovered users: we focus the coverage of planning network, thus the numbers of uncovered users are calculated. Each UE has the SINR value and represents the communication quality. If the communication quality is too low to communicate, 5

we define it belongs to uncovered user. The free space propagation model [7] is utilized to calculate the SINR value, which shown as . (2) ( ( ) ) The is the transmission power from the signal source, represents the interference, is the frequency band, is the speed of light, and is the distance. 4. Capacity of users: we obtain the SINR value of UEs are in equation (2). Then, the Shannon capacity theory is used to calculate the capacity of UEs. It is shown as follow. . (3) Where is the channel capacity in bits per second, and is the bandwidth of the channel in hertz.

4. EXPERIMENT RESULTS The simulation is performed by MATLAB [23], and the experimental computer CPU is core2 1.7GHz and the RAM is 3GB. The simulation is simulated with five different network scenarios (randomly allocate), and calculates the average to avoid the singular state. The major parameters used in the simulation are shown as Table 2. Table 2. The parameters of simulation Variables/parameters Value Topology size

25×25 (KM)

Number of CPs Number of UEs Radius of eNB Radius of RN Deployment cost of eNB Deployment cost of RN Transmission power of eNB Transmission power of RN

50 300 3400 (M) 1000 (M) 10 (units) 2.5 (units) 47 (dBm) 43 (dBm)

4.1 Development Case In this subsection, we illustrate the Set Covering algorithm with a deployment case. In the network planning case, there are 50 CPs marked and labeled as blue circles, and 300 UEs are marked as red stars in the 25 kilometers multiplies 25 kilometers network. The random network topology is shown as Figure 2. The planning result of Set Covering algorithm is shown as Figure 3. The dark blue solid points represent the CPs which are deployed with eNBs, and the light blue hollow points are the RNs deploy on CPs. The blue line represents the relay link form eNB to RN, and the red dotted line is the connection of UE. One thing should be mentioned again, all of nodes are randomly distributed. Because the proposed Set Covering algorithm is based on the Set Cover problem, the main object is to cover and serve the most UEs. Therefore, the UEs whom covered by the least number of CPs, it should be first and foremost served. Then, an eNB should be placed on the CP which covers the most UEs. Finally, we repeatedly deploy RNs to connect with eNB until all of UEs are covered. 6

Figure 2. Network topology

Figure 3. The deployment result by Set Covering algorithm As Figure 3 shows that there are 26 eNBs and 12 RNs, and the total construction cost is 272 unit costs. According to the 3.3 subsection, we evaluate the performance and result of planned network. There are 41 uncovered users, and the total capacities of UEs are 7519.66 bits per second. 7

4.2 Results and Analysis In the simulation results, we will show the comparisons between different factors, including the network planning time, construction cost, number of uncovered users and network capacity. Firstly, the computation efficiency of all algorithms is showed as Figure 4. We increase the number of CPs and calculate the planning time. As Figure 4 shows that the planning time of four algorithms is linear and less than two seconds. The Set Covering algorithm searches recursively for covering all UEs so that it spends more planning time. Although the planning time proposed Set Covering algorithm is slightly longer than others, the planning procedure still complete in two seconds. In other words, the proposed algorithm and previous algorithms are suitable for large scale planning area and complicate planning environment. Tree

S-Tree

IA-Tree

SetCover

Planning Time (sec)

4

3

2

1

0 40

50

60

70

80

90

100

Number of Candidate Positions Figure 4. Calculation time with varying the number of CPs The construction cost with different network topology is shown as Figure 5. The simulation parameters are same with Table 2 in this experiment, and we also calculate the average deployment cost of four algorithms. The Tree algorithm deploys eNBs in most parts of CPs, and only places seldom RNs. Therefore, the average construction cost of Tree algorithm is the highest. Then, the construction costs of S-Tree and IA-Tree algorithm are lower than Tree and Set Covering algorithm. The Tree algorithm was designed to minimize the construction cost by placing RNs principally, hence its construction cost is lower. On the other hand, the communication interference between eNBs is considered in IA-Tree algorithm, thus the near eNBs are replaced with RNs. The construction cost of IA-Tree algorithm is the lowest, but it also implies that the number of uncovered users will higher than other algorithms. Because the Set Covering algorithm was design to cover UEs as many as possible, it spends higher construction cost but still lower than the Tree algorithm.

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Tree avg. of Tree

S-Tree avg. of S-Tree

IA-Tree avg. of IA-Tree

SetCover avg. of SetCover

Construction Cost (Units)

300 250 200 150 100 50 0 scenario1

scenario2

scenario3

scenario4

scenario5

Different Network Topology Figure 5. Construction cost in five different network topologies The number of uncovered users in different network topology is shown as Figure 6. Both of S-Tree and IA-Tree algorithm were proposed based on deploying RNs, so the unserviceable UEs are more than Tree and Set Covering algorithm. Although the difference in construction cost between Tree and Set Covering algorithm is light, but the uncovered UEs of the proposed algorithm is much lower than the Tree algorithm. According to this result, it is obvious that the proposed Set Covering algorithm achieves the better network coverage. In other words, there are more UEs can be satisfied in the planning result of proposed Set Covering algorithm. Tree avg. of Tree

S-Tree avg. of S-Tree

IA-Tree avg. of IA-Tree

SetCover avg. of SetCover

120

Uncovered Users

100 80 60 40

20 0 scenario1

scenario2

scenario3

scenario4

scenario5

Different Network Topology Figure 6. Number of uncovered users in five different network topologies

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Finally, we evaluate the network capacity based on the equation 3 in subsection 3.3, and compare the four algorithms in five different network topologies, which is shown as Figure 7. One thing should be mentioned here, the network capacity is summed of all covered UEs in eNBs and RNs. Although the construction cost of S-Tree and IA-Tree is low, their uncovered UEs and network capacity is unideal. Unlike S-Tree and IA-Tree algorithm, the Tree and Set Covering algorithm achieve the higher network capacity. Furthermore, the proposed Set Covering algorithm accomplishes the better network capacity than Tree algorithm with the lower construction cost and uncovered UEs.

Network Capacity (MB)

Tree avg. of Tree 9000

S-Tree avg. of S-Tree

IA-Tree avg. of IA-Tree

SetCover avg. of SetCover

8000 7000 6000 5000 4000 3000 2000 1000 0 scenario1

scenario2

scenario3

scenario4

scenario5

Different Network Topology Figure 7. Network capacity in five different network topologies

5. CONCLUSIONS AND FUTURE WORKS For the large scale network planning, the cost efficiency is a vital issue. In this paper, we formulate the coverage problem based on a well-known Set Cover problem, and propose Set Covering algorithm to achieve the better network coverage and performance in LTE-Advanced relay networks. We have three major contributions in this research: 1) the network of multiple eNBs and RNs is considered and constructed; 2) the linear planning time of proposed algorithm is accomplished; 3) the best network coverage and capacity is achieved in four algorithms. According to the simulation results, the proposed Set Covering algorithm is suitable for planning the better network quality in a crowded city. In the future works, we will consider how to find the solution of an inevitable trade-off between these factors such as construction cost, communication quality and covered user. The multi-objective optimization problem will be defined, and an evolutionary algorithm will also be proposed. We expect the planning result could be more usable and adoptable for developing the LTE-Advanced networks.

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[14] O. Bulakci, S. Redana, B. Raaf, and J. Hamalainen, Performance enhancement in LTE-Advanced relay networks via relay site planning. IEEE 71st Vehicular Technology Conference (IEEE VTC 2010-Spring), Taipei, Taiwan, May 16-19, 2010, pp. 1-5. [15] L. Rong, S.E. Elayoubi, and O.B. Haddada, Impact of relays on LTE-Advanced performance. IEEE International Conference on Communications (IEEE ICC 2010), Cope Town, South Africa, May 23-27, 2010, pp. 1-6. [16] R. Irmer, and F. Diehm, On coverage and capacity of relaying in LTE-Advanced in example deployments. IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2008), Cannes, France, Sep. 15-18, 2008, pp. 1-5. [17] T. Beniero, S. Redana, J. Hamalainen, and B. Raaf, Effect of relaying on coverage in 3GPP LTE-Advanced. IEEE Vehicular Technology Conference (IEEE VTC 2009-Spring), Barcelona, Spain, Apr. 26-29, 2009, pp. 1-5. [18] X. Huang, F. Ulupinar, P. Agashe, D. Ho, and G. Bao, LTE relay architecture and its upper layer solutions. IEEE Global Telecommunications Conference (IEEE GLOBECOM 2010), Miami, Florida, USA, Dec. 6-10, 2010, pp. 1-6. [19] C.-Y. Chen, Y.-S. Liang, C.-M. Yu, C.-H. Ho, and S.-Y. Kuo, Increasing reliability for IEEE 802.16j mobile multi-hop relay networks planning. IEEE 15th Pacific Rim International Symposium on Dependable Computing (PRDC), Shanghai, China, Nov. 16-18, 2009, pp. 1-5. [20] F.-H. Tseng, C.-Y. Chen, and H.-C. Chao, Minimizing construction cost for IEEE 802.16j multi-hop relay networks. International Conference on Pervasive Computing and Application (ICPCA), Maribor, Slovenia, Dec. 1-3, 2010, pp. 1-6. [21] F.-H. Tseng, C.-Y. Chen, L.-D. Chou, T.-Y. Wu and H.-C. Chao, A study on coverage problem of network planning in LTE-Advanced relay networks. IEEE 26th International Conference on Advanced Information Networking and Applications (IEEE AINA 2012), Fukuoka, Japan, March 26-29, 2012, pp. 944-950. [22] E. Lang, S. Redana S., and B. Raaf, Business impact of relay deployment for coverage extension in 3GPP LTE-Advanced. IEEE International Conference on Communications Workshops (IEEE ICC Workshops 2009), Dresden, Germany, Jun. 14-18, 2009, pp. 1-5. [23] MATLAB. Available form : http://www.mathworks.com/products/matlab/

ACKNOWLEDGE This research was also partly funded by the IPv6 Upgrade and Promotion Program (1/4) under grants 102J2207001 and the National Science Council (NSC) of the Taiwan under grants NSC 101-2221-E-197-008-MY.

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