Novel Resource Allocation Algorithm for Improving Reuse One Scheme Performance in LTE Networks

Transcription

1 Novel Resource Allocation Algorithm for Improving Reuse One Scheme Performance in LTE Networks Mohamed A. AboulHassan, Essam A. Sourour Pharos University, Faculty of Engineering, Electrical Engineering Department, Alexandria, Egypt Alexandria University, Department of Electrical Engineering, Alexandria, 2544 Egypt Abstract The main challenge of LTE networks is to use unitary frequency reuse factor to achieve highest possible data throughput, however it leads to a severe interference affecting active users. Several interference mitigation techniques focus on bandwidth partitioning methods to avoid cell edge interference, although they improve user s average SINR, such techniques reduce maximum achievable data rate. In this work, we introduce a novel resource allocation algorithm utilizing reuse one scheme whereas users are scheduled so that interference between adjacent cells users served at same time in same RBs is minimized. Furthermore to meet LTE networks low latency target, a novel algorithm is designed to obtain the optimum allocation of users with better complexity compared to wellknown combinatorial optimization algorithms. Simulation results show that new proposed resource allocation algorithm improves both cell edge users throughput and total average throughput, and also achieves improved user s average SINR than classic reuse one scheme. I. INTRODUCTION Long Term Evolution (LTE) [], is a mobile network technology, is expected to substantially improve end-user throughputs to meet rapid growth in demanded mobile applications. To achieve highest throughputs through LTE networks, unitary frequency reuse factor must be used in the network i.e. all the available Bandwidth must be utilized by all cells. However, frequency reuse factor one leads to severe interference affecting strongly the Signal to Interference-plus-Noise-Ratio (SINR) of active users, especially cell edge users, which leads to a significant degradation in total cell s throughput. Static and dynamic interference mitigation and resource allocation techniques have been investigated to reduce Inter Cell Interference (ICI). Bandwidth partitioning methods have been widely studied to avoid ICI such as fractional frequency reuse schemes in [2] and [3] or focusing on partial frequency reuse scheme [4], soft frequency reuse scheme [5] and [6], and dynamic fractional frequency reuse scheme [7]. Although fractional frequency reuse schemes have enhanced cell edge users SINR, partitioning the available bandwidth still affects the target of LTE system to utilize the entire bandwidth and thus, achieves target peak data rates. To overcome bandwidth partitioning drawbacks, other resource allocation algorithms have focused on resource allocation stage as in [8] and [9], where maximizing cell edge users SINR is modeled as a global optimization problem, however finding the optimal solution is shown to be very complex procedure. Centralized schemes have been proposed such as schemes depending on central controllers as in [], nevertheless centralized schemes cannot achieve small latency target of LTE networks. Other work category focused on power assignment stage as in [] and [2], yet high complexity stills a main factor preventing the implementation of such algorithms in multicell scenario. In [3] and [4], the techniques focusing on the two resource allocations stages have been addressed where user scheduling problem and power assignment problem are considered as two distinct stages, however such techniques focused mainly on power assignment stage as a main area of research. In this work, we focus on the Resource Allocation (RA) stage where a new Resource Allocation Algorithm (RAA) for LTE networks is proposed. Our new proposed algorithm improves both average total cell throughput and average cell edge throughput rather than focusing on cell edge throughput. We also design a new efficient algorithm to reduce the complexity of scheduling optimization problem to meet global targets of smaller latency time and facilitate the implementation of proposed RA algorithm in a cellular environment. This work is organized as follows, section II presents an overview for the system model and problem formulation, in section III the algorithm designed to reduce complexity of the optimization problem is proposed, the novel resource allocation algorithm is described in section IV, simulation results are provided in section V and finally section VI concludes this work. II. PROBLEM FORMULATION Consider a LTE Network consisting of hexagonal cells layout. In LTE, the smallest element can be assigned to a user is the Resource Block (RB) with duration ms and occupies 8 KHz. Each Transmission Time Interval (TTI), the enb schedules active users within available RBs where the duration of each TTI is ms. The target of the proposed algorithm is to schedule users in a pattern where summation of values of the difference between the downlink power levels of same band RBs between adjacent cells is maximized i.e. center users are scheduled in same RB s IDs as edge users between adjacent cells. Let A and B are two adjacent cells, having m RBs per TTI, let Γ i (a) and Γ i (b) are set of values of SINR measured by users to be scheduled within current TTI, of cells A and B,

2 respectively where i =, 2,.., m. Proportional Fair algorithm [5] is considered the main scheduling algorithm in our work. Let P A = [P A... Pm] A T and P B = [P B... Pm] B T are two vectors representing power levels assigned to RBs scheduled in cells A and B, respectively. For simplicity we assume perfect SINR feedback and a naïve power assignment algorithm where values of power levels assigned to each resource block are inversely proportional to SINR level, with a total sum of power levels equals to P t. Therefore the utility function can be expressed as U = arg max J { m [ Pi A Pj B i= ]}, () i =, 2,..., m and J is set of m values of j for each value of U where j = f(i), f(i) is bijective function representing one-to-one mappings f : {, 2,...m} {, 2,...m} i.e. the pair (i, j) is not repeated between terms of summation of m terms to obtain the value of U i, j =, 2,..., m. It can be easily shown that we have m! possible values for utility function U, thus finding optimal solution is extremely hard unless exhaustive search method is used which is considered not applicable especially for large numbers of m. III. PROPOSED ASSIGNMENT ALGORITHM A. Mathematical modeling In this section, we propose a new and efficient algorithm to find the optimum solution of the utility function U in () with reduced complexity. Let G be a bipartite graph where G = (V, E) with bipartition (A, B) and weight function w : E R matching achieves maximum U, where the weight of matching is given by w = a i b j, (2) where a i and b j denote random variables uniformaly distributed over [SL,SU], SL and SU are the lower and upper bound values of a i and b i, respectively, a i A and b j B, i =,..., m and j = f(i). Let D be m m matrix containing all possible values of w, where a b a b 2... a b m a 2 b a 2 b m D = (3) a m b a m b 2... a m b m Therefore the utility function in () can be expressed as U = max d ij x ij, (4) subject to i= j= x ij =, j =,..., m i= x ij =, i =,..., m, j= where x {, }. This problem is considered as an assignment problem. We propose a novel algorithm that reduces the complexity of the assignment problem and can be efficiently implemented in a cellular environment. Define MD = {MD y MD y MD}, y = {,..., m!}, where MD is a m vector and MD y = {md yl }, where l =,..., m and md yl = d ij. Therefore we can define the U as follows U = max y { MD y }. (5) To maximize utility function, we need to calculate the value of L-norm of all vectors MD y, thus elements of MD y with maximum L-norm represent the optimal assignment. Our first step is to sort entries of vectors A and B in a descending order where a i > a i + and b i > b i + i =,..., m. Let a s and b t positive values a s = a i a i+ (6) b t = b i b i+, (7) where s and t =,..., m. Moreover let d ij be the entires of D and defined as j i d ij = a b + b l a p. (8) We aim to search for the optimal vector that has the maximum mean value. L-norm of MD y can be expressed as f(k) k MD y = a b + b l a p, (9) k= where y =,..., m!. Recalling that Γ γ= x γ = δ= x δ Θ θ= x θ, x δ >, x θ < and Γ = + Θ, equation (9) can be separated into two parts as follows g(λ) h(λ) Λ a b a l + + λ= φ= ĝ(φ) ĥ(φ) Φ a b a l +, () where Λ is the number of terms of (9) with values greater than zero and Φ is the number of terms with values less than zero, Λ + Φ = m. g(λ) takes random discrete values from the interval [, m] according to the bijection mapping f : λ f(λ) and the same mapping occurs for h(λ), ĝ(φ) and ĥ(φ). Let G, H, Ĝ and Ĥ be the sets containing values of g(λ), h(λ), ĝ(λ) and ĥ(λ), respectively. It can be proved that G Ĝ =, H Ĥ = and G + Ĝ = H + Ĥ = m. Accordingly the utility function can be expressed as U = max Λ,Φ + g(λ) Λ a b λ= φ= h(λ) a l + ĝ(φ) ĥ(φ) Φ a b a l +. ()

3 The term a b is constant and can be ignored. Therefore the maximization problem can be solved w.r.t a i and b j. To maximize U the following conditions have to be fulfilled ) To maximize the first part of (), it must include the terms g(λ) a l and h(λ) b l having minimum and maximum absolute values, respectively. 2) To maximize the second part, it must include the term ĝ(φ) ĥ(φ) and b l a l having maximum and minimum absolute values, respectively. 3) Elements of G and H must be in sequence, for example for m = 6 and Λ = 3 then G = {3, 2, 4} or {5, 6, 4} or any 3 numbers in sequence and the same condition is applied on Ĝ and Ĥ. Since the utility function is maximized for a sequenced values of G, G, H and Ĥ then elements of these sets can be rearranged to obtain the maximum value of U at one of the m diagonals of the matrix D. The selected vector MD y has entries md ij, i =,..., m and j can be obtained from the following equation { i + sh i + sh < m j = (2) i + sh m i + sh m, where sh + is the ID of the diagonal of D at which U is maximized and can be considered as a circular shift applied for the set B where, sh =,..., m, while set A s order remains unchanged. Therefore we can present two main lemmas ) For two sets A and B, where a i A and b j B, i and j =,..., m, D is a m m matrix where d ij = a i b j there exists m vectors MD y, where y =,... m!, md ij = {d ij }, i =,... m, and j = f(i) where f(i) is a bijective function whose range takes values over {,..., m} for each vector MD y. To maximize the utility function U where U = max y { MD y }, one or more of MD y vectors achieve maximum value of utility function U but there must be at least one vector MD y representing the elements of one of the m diagonals of D achieves the maximum value. 2) The index of the diagonal having second maximum value for U can be calculated as i = i max ±, where i max is the index of diagonal at which U is maximized. B. Complexity analysis To check the validity of applying proposed algorithm, we compare its complexity with two well-known combinatorial optimization algorithms, the first one is a brute force algorithm utilizing exhaustive research method and the other one is the Hungarian algorithm which is considered as one of most famous algorithms in solving assignment problems. The complexity of new proposed algorithm can be estimated by calculating the number of operations needed. Adding all the m elements of all m diagonals of D then finding the maximum value, we obtain a complexity of O(n 2 ). It can be easily shown that complexity of brute force algorithm is O(n n!). Complexity of Hungarian algorithm is implemented with O(n 4 ) as stated in [6] or can be simplified to O(n 3 ) as in [7]. Table I summarizes the values of operations needed for all possible values of RB numbers in LTE networks. RB (n) TABLE I OPERATIONS NEEDED FOR EACH RB CONFIGURATION no. Brute force alg. O(n! n 4 ) Hungarian alg. O(n 4 ) Hungarian alg. O(n 3 ) Proposed Alg. O(n 2 ) * * * * IV. PROPSOED RESOUCRE ALLOCATION ALGORITHM (RAA) In this section, we introduce the implementation of the proposed (RAA) in a realistic cellular network. As proved in the previous section, the optimal allocation between adjacent cells users is analogous to a circular shift applied to the sorted downlink power values over the RBs of one of the adjacent cells while the downlink power values of the other cell levels order remain unchanged. Therefore the output of the RAA is a circular shift applied to one of the adjacent cells. Without loss of generality, we assume flat fading channel model, hence changing RBs order assigned to users doesn t affect SINR values. A. RAA Summary The proposed scheduling algorithm procedure is given as follows ) RBs within current TTI are allocated to users according to Proportional Fair (PF) scheduling algorithm [5]. 2) For two adjacent cells A and B where P A = [P A... Pm] A T and P B = [P B... Pm] B T are the values of downlink power levels assigned to each resource block, the values of P A and P B are inversely proportional to SINR level, with a total sum equals to P t. 3) Downlink power values are sorted in descending order to obtain P A sorted and PB sorted. 4) Proposed algorithm in section II is implemented between P A sorted and PB sorted to determine the circular shift maximizing U given by (4). 5) The circular shift is applied to one of the two sorted downlink power levels in one of adjacent cells while the another cell s order remains unchanged. B. RAA implementation In this section, we present the implementation of RAA in LTE network. One of the main advantages of the new proposed assignment algorithm is converting the scheduling problem into a circular shift assignment problem. This circular shift can be assigned in various schemes centralized, hybrid or distributed schemes. In this work, two implementation schemes of RAA will be proposed, other implementation schemes can be discussed in future work.

4 ) Scheme one: The RAA is implemented within the three sectors of the same cell. The first, second and third sectors are sectors fulfilling the equation (CI MOD 3 =, 2 and zero, respectively) as shown in Fig., where CI is the cell ID. The circular shift values achieving maximum utility function in (4) resulting from implementing the RAA between first and second sectors, and the first and third sectors are assigned to the second and third sectors, respectively, while the first sector remains unshifted. 2) Scheme two: The same as scheme one for the first and second sectors while the second maximum shift is assigned between first sector and third sector. Fig.. Cells layout. V. SIMULATION RESULTS In this section, we evaluate the performance of RAA through performance comparison with variety of interference mitigation techniques existing in the literature. A. Scenario We consider a hexagonal LTE network with 7 cells, 3 sectors/cell, as shown in Fig.. A system level simulation is implemented using Matlab. Users are assumed to be located randomly within the cell coverage area. A flat fading channel model is assumed in our simulation. We select SINR threshold criteria for differentiating between edge users and center users, the SINR threshold value is set to db. The mapping between SINR values and achievable data rate are shown in [8]. Simulation parameters are stated in Table II. Techniques used for comparison are shown in Table III. B. System Level Performance evaluation In this section, the performance of the RAA in terms of average cell throughput, and cell edge average throughput, average throughput per user and average throughput per edge user is investigated. The average cell throughput is presented in Fig. 2, it can be shown that first scheme achieves best average cell throughput. The proposed scheme outperforms by approximately 2% improvement in average cell throughput. Note that achieves worst cell throughput due to the division of the total bandwidth. Bandwidth division affects also the performance of and. It can also be noticed that scheme achieves better throughput than, still achieves a slightly higher average cell throughput than. In Fig. 3, the average throughput of cell edge users is investigated, scheme achieves 4% improvement than which is considered the best performance in the simulation. Scheme 2 achieves almost the same performance as scheme, due to different criteria for applied circular shift for second and third sectors, which provides a virtual shift between the two sectors and consequently adjacent sectors, thus improving cell edge SINR. Although achieves worst cell edge throughput, this results due to the criteria of differentiating edge users and center users in our simulation, which considers almost all users in scheme 4 as center users due to high SINR. Still achieves better performance than. Investigating the average user throughput and edge user average throughput, the same performance is shown as in Fig. 4 and Fig. 5, respectively. These results indicate that the performance of our proposed resource allocation algorithm is independent of cell load. Due to the dependency of the value of data rate on SINR, values of data rates may differ according to SINR-to-Data rate mapping algorithm used. In Table IV, the average percentage of users below a certain SINR threshold (set to 4 db in our simulation) is presented. It can be shown that scheme and have improved SINR values than by 2% and 4%, respectively. Although SINR values are much improved for other addressed schemes, still bandwidth partitioning affects the peak data rate. Parameter System bandwidth Carrier frequency No. of RBs per half TTI 25 TABLE II SIMULATION PARAMETERS Setting.2 MHz 2GHz Cell layout see Fig. Number of sites Macrocell transmit power Inter-site distance Antenna Pattern Max no. of users per sector 35 Antenna gain 7 (=2 cells) with wrap-around 46 dbm 5 m θ A(θ) = min[2( ) theta 2, 2]dB 3dB where 8 < θ < 8 θ 3dB is the beamwidth(= 7 ) 4 dbi Dependent path loss (PL) log (D in m) White noise power density Shadowing fading (SHL) SHL standard deviation User velocity -74 dbm/hz Log-normal distribution 8 db 3 Km/s TABLE III SIMULATION SCENARIOS Sch. no. Sch. type Sch. no. Sch. type Scheme st scheme Scheme 4 Reuse three Scheme 2 2nd scheme Scheme 5 PFR [6] Scheme 3 Reuse one Scheme 6 SFR [4] VI. CONCLUSION In this work, we proposed a new Resource Allocation Algorithm (RAA) that improves the performance of reuse one

5 .3.2. scheme Fig. 2. Average cell throughput..3 scheme Fig. 3. Average cell edge users throughput..3 scheme Fig. 4. Average user s throughput per cell..3 scheme Fig. 5. Average cell edge user s throughput. scheme. The RAA is considered flexible to be implemented within any power assignment algorithm, robust to any SINRto-Data rate mapping algorithm and also suitable for multicellular environment by converting the resource allocation problem into a circular shift assignment operation. In order to obtain the optimum allocation, we designed a novel algorithm to reduce the complexity of the assignment problem to meet low latency target. Numerical results have shown that a TABLE IV AVERAGE PERCENTAGE OF USERS WITH SINR < 4 db Scheme ID average perc.(%) Scheme ID Scheme 72.3 Scheme Scheme 2 7 Scheme 5 69 Scheme Scheme average perc.(%) proposed hybrid scheme of new RAA achieves better average cell throughput and average cell edge throughput. It has also been shown that average values of throughput per user have been improved which implies that the new proposed algorithm is independent of cell load. REFERENCES [] 3GPP, [2] Porjazoski, Marko ; Popovski, Borislav, Analysis of Intercell interference coordination by Fractional frequency reuse in LTE, international conference on Software, Telecommunications and Computer Networks, 2, pp [3] Amer, Muhieddin, Optimal Configuration of Fractional Frequency Reuse System for LTE Cellular Networks, IEEE (VTC Fall), 22, pp. -5 [4] Siemens, R-635, Interference Mitigation by Partial FrequencyReuse, 3GPP RAN WG#42, London, UK, January 26. [5] E Krasniqi, Bujar ; Wrulich, Martin ; Mecklenbruker, Christoph F., Network-load dependent Partial Frequency Reuse for LTE International Symposium on Communications and Information Technology, 29., pp [6] Huawei, Soft frequency reuse scheme for UTRAN LTE, 3GPP TSG RAN WG #4, R- 557, May 25. [7] Wu, Weiwei ; Gitlits, Maxim ; Sakurai, Taka Dynamic resource allocation with inter-cell interference coordination for 3GPP LTE, Asia-Pacific Microwave Conference, 28,pp. - 4 [8] Fraimis, Ioannis G. ; Papoutsis, Vasileios D. ; Kotsopoulos, Stavros A., A distributed radio resource allocation algorithm with interference coordination for multi-cell OFDMA systems,ieee 2st (PIMRC), 2 pp [9] N. Ksairi, P. Bianchi, P. Ciblat, and W. Hachem, Resource allocation for downlink cellular OFDMA systemspart I: optimal allocation, IEEE Trans. Signal Process., vol. 58, no. 2, pp , 2. [] G. Li and H. Liu, Downlink radio resource allocation for multi-cell OFDMA system, IEEE Trans. Wireless Commun., vol. 5, no. 2, pp , 26. [] I. Kim, I. Park, and Y. H. Lee, Use of linear programming for dynamic subcarrier and bit allocation in multiuser OFDM, IEEE Trans. Veh. Technol., vol. 55, no. 4, pp , 26. [2] K. Illanko, A. Anpalagan, and D. Androutsos, Convex structure of the sum rate on the boundary of the feasible set for coexisting radios, in Proc. 2 IEEE International Conference on Communications, pp [3] Poulkov, Vladimir ; Koleva, Pavlina H. ; Asenov, Oleg ; Iliev, Georgi, Combined power and inter-cell interference control for LTE based on role game approach 34th International Conference on Telecommunications and Signal Processing(TSP),2, pp [4] Yiwei Yu ; Dutkiewicz, E. ; Xiaojing Huang ; Mueck, M. Downlink Resource Allocation for Next Generation Wireless Networks with Inter- Cell Interference, IEEE Trans. on Wireless Communications, pp , 23 [5] A. Jalali, R. Padovani, and R. Pankaj, Data Throughput of CDMAHDR a High Efficiency-High Data Rate Personal Communication Wireless System, in IEEE 5st (VTC) Proceedings, Tokyo, 2, pp [6] Kuhn H.W, The Hungarian method for the assignment problem.naval Research Logistics Quarterly 2(955), pp [7] J. Edmonds and R.M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, J. ACM, 9 (972),pp [8] Ramli, H.A.M.; Basukala, R.; Sandrasegaran, K.; Patachaianand, R. Performance of Well Known Packet Scheduling Algorithms in the Downlink 3GPP LTE System, IEEE 9th Malaysia International Conference on Communications (MICC),29,pp