A Mathematical Model for Joint Optimization of Coverage and Capacity in Self-Organizing Network in Centralized Manner

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1 2012 7th International ICST Conference on Commnications and Networking in China (CHINACOM) A Mathematical Model for Joint Optimization of Coverage and Capacity in Self-Organizing Network in Centralized Manner Wei Lo, Jie Zeng, Member, IEEE, Xin S, Member, IEEE, Jingy Li, Limin Xiao, Member, IEEE Tsingha National Laboratory for Information Science and Technology Tsingha University, Beijing, China, zengjie@mail.tsingha.ed.cn Abstract In this paper we introdce a mathematical model in the framework of long term evoltion (LTE) to solve the problem of coverage and capacity optimization by employing mlti-level random Tagchi s Method. The optimization process rns in a centralized manner with no hman intervention reqired and interacts with environment sitation atomatically. Under the mathematical model which combines coverage and capacity optimization by a coefficient factor, conventional Tagchi s Method transcends traditional trial-and-error approach in convergence speed and simple implementation, to offer even more search capacity, Gassian shrink coefficient and random optimization offset are applied to the level-to-tilts mapping fnction. Antenna tilt is an effective interference redction techniqe, which has been adopted as the tning parameter. The simlation reslts trn ot to be better than traditional Tagchi s Method and trial-and-error approach. The system model presented and evalated also gives an insight to the mathematical model especially the trade-off between coverage and capacity in homogeneos scenario. Keywords-SON; mathematical model; self-optimization; coverage; capacity; Tagchi s Method; I. INTRODUCTION Self-Organizing Network is introdced as part of Third Generation Partnership Project Long Term Evoltion to redce operation expenditres (OPEX), capital expenditres (CAPEX) and improve ser experience at the same time in standardization [1] and research [2]. Self-configration, selfoptimization and self-healing make p the three main SON fnctions, while the self-optimization part pts emphasizing on atomatically optimizing the networks when the celllar network enconters coverage or capacity degradation in order to improve ser experience, self-configration focs on redcing CAPEX by atomatic planning and deployment [3]. This paper examines hybrid optimization scheme of coverage and capacity nder the introdced mathematical model. Tning pilot power, antenna tilt and antenna azimth are the most effective approach in dealing with coverage and capacity optimization, enhancing signal strength while sppressing interference between neighbor cells. Electrical mechanism (opposing from mechanical mechanism, which reqire often site visits when optimization process starts) effectates tning antenna tilts remotely and rnning optimization in an online manner, here in this paper we carry ot or optimization process by tning the tilt. In the optimization scheme, we employ Tagchi s Method [4], which was widely sed in manfactring processes, and now being sed in many other fields. The essence of Tagchi s Method is OA which has a profond backgrond in statistics [5]. In the optimization process, the rows in OA table make p the total search capacity which is far smaller than the trial-anderror optimization approach s especially in the case of plenty of parameters to be tned. The athor adopts Tagchi s Method in electromagnetics problems with reslts showing Tagchi s Method s good properties of fast convergence speed in paper [6], easy implementation and near global optimm. In paper [7], the athor compares Simlated Annealing and Tagchi s Method in the metrics of performance and comptational complexity, SA optimization algorithm highly depends on the definition of the inpt parameters and has good possibility of getting stck in local optimm, while Tagchi s Method can refer to possible candidates far away from the original ones in the search space. In this paper, we stdy the joint optimization of coverage and capacity with a centralized architectre [8] sing modified Tagchi s Method, the centralized management entity collects the antenna down tilts in concerned cells in a celllar network, to offer even wider search capacity, we se mlti-level OA table and apply random optimization offset to the level-to-tilts mapping fnction. The optimization mathematical model is set as the linear relationship of 5%-tile of the UE throghpt and 50%-tile of the UE throghpt. In the simlation, we compare the original Tagchi s Method [7] and modified Tagchi s Method, the modified Tagchi s Method with wider search capacity improves coverage and capacity by a remarkable amont. The remainder of the paper is organized as followed: section II introdces system model and definitions, section III describes mathematical model for join optimization of capacity and coverage, section IV deals with simlation model and simlation environment, we have conclsions in section V. This work was spported by Beijing Natral Science Fondation Fnded Project (No ), National Science and Technology Major Project (No.2011ZX ), 973 Project (No.2012CB31600) and Samsng Company /12/$ IEEE

2 II. SYSTEM MODEL AND DEFINITIONS A. System Model The SON system model is defined as [9]: 21 cells in networks, shown in Fig. 1, along with six copies of the same layot distribte symmetrically on six sides. Each cell is served by a BS with a threedimensional antenna, each antenna in the networks is monted as the same height H. height A connection fnction c X ( ) decides the ser in networks connecting to a single a cell according to signal strength constraint. The path loss L is defined by the position of the ser and the serving cell. The overall signal attenation also incldes shadowing fading and antenna gain [9]. We have antenna gain A(, ) min ( A ( ) A ( )), A m, with path loss and shadowing map Mc( q ), the overall signal attenation L for ser with respect to cell X ( ) is X ( ), calclated as: LX ( ), LPL A(, ) Mc( q ) (1) With the framework defined above some additional parameters i.e. P as transmit power in cell X( ) X ( ) connecting to ser and N as the thermal noise. The signalto-interference ration of each ser in a cell can be defined as PX ( ) LX ( ), SINR N P L c X ( ) c c, The spectrm efficiency is derived from SINR by a step fnction. B. OA OA ( N, s, k, t ) is the essence of Tagchi s Method. s stands for s levels in the OA table. An OA table consists of k colmns and N rows with vales from s levels. t stands for the strength. The Orthogonal means in every sb-array of A with N row and t colmns, each row appears exactly the same times. Fig. 1 Cell layot (2) The Tagchi s Method optimization is based on OA concept, let X ( x1, x2, x m ) denotes the antenna down tilts to be tned, where m 21 in this paper. We constrct an OA(125,21,5,3) consists of 125 rows, 21 colmns and 5 levels ranging from 1 to 5 which offers more search capacity than original 3 levels [7]. C. Mathmatical Model for joint optimization Average throghpt and edge throghpt in a cell can be sed to respectively represent coverage and capacity, when the edge throghpt, more specifically the less than 5%-tile of the UE throghpt distribtion, sffers considerable degradation, the coverage deteriorates. Similarly, if 50%-tile of the UE throghpt distribtion enconters great drop, the capacity sffers deterioration. To jointly optimize coverage and capacity in the networks, we define mathematical model for joint optimization as follow: Where 1 1 OT r (1 r) (0 r 1) k k 1 1 c1 c,5% c1 c,50% k: the nmber of cells taken into consideration; c: the cell index; r: the compromise coefficient; : p%-tile of the UE throghpt distribtion in a single cp, % cell; With the mathematical model define in Eq. 6, we can prevent several cells from encontering a sharp coverage or capacity degradation. r is the compromise coefficient sed to emphasize the optimization target, the optimization process becomes more flexible in emphasizing on coverage optimization or capacity optimization. III. OPTIMIZATION SCHEME The algorithm is rn in O&M while the BS station for each cell is responsible for collecting the UE feedback parameters, optimization process is triggered when the ser in the cells experience poor signal strength or high drop rate. Here in this docment we assme the toggle condition for activating selfoptimization process when the SE in smmed in the concerned cells degrades to less than a threshold. The OA table in this docment consists of 125 rows and 21 colmns with 5 entries ranging from 1 to 5. Therefore, in each iteration, there are 125 experiments, the tilt in each iteration for each tning parameter, as described in Eq. 4. BT max( OT, OT, OT, OT, OT ) ix, m s1, xm s2, xm s3, xm s4, xm s5, xm (3) (4) When each iteration is finished, we pick ot the BT for each tning parameter and set the relevant tilt as the tilt in the crrent iteration and map it as the centered level tilt for next iteration as depicted in Best Picking part in flow chart Fig

3 Iterations Starts IV. SIMULATION CONFIGURATION AND RESULTS SON Coordinating Entity Mapping Level To Tilt OA Table Traversal Starts Compte OT LoopCont<126 Best OT Picking si, xm Update the Tilts Table Termination Met? End Fig. 2 Implementation of Tagchi s Method In paper [7], the search capability is determined by 3-level OA table. Moreover, in the mapping fnction, the tilt is picked ot in the previos iteration and set as the centered level for next iteration; the other two levels are designed by sbtracting or adding initial optimization range mltiplying a constant shrink coefficient. In this paper, we expand search capability and improve convergence speed by applying Gassian shrink coefficient and random fnction to the levels except the centered one, as described in Eq. 5. i Tx ( m), ( s / 2 l ) * *( ), 1 l s / 2 1 i1 i Tl, x( m) Tx ( m),, l s / 2 i Tx ( m), s / 2 l * *( ), s / 2 1 l s Where: i: Index of iteration 10 : Gassian shrink coefficient, here assigned e, : Initial optimization range, here 1. : Random vale offset YES YES NO NO i 2 ( ) In Eq. 5, the Gassian shrink coefficient decreases the level difference slowly dring the first several iterations to offer more freedom to find global optimm while speeds p redcing the level difference for greater convergence speed. The random optimization range offset offers more search capacity while keeps the mean vale of five levels homogeneosly distribte between optimization range for that iteration. After each iteration, we pdate the antenna tilts while shrink the optimization. If the termination condition is met in the optimization process, the algorithm stops, we assme if the Gassian shrink coefficient becomes less than a predefined vale, the optimization stops. (5) A. Scenario Configration A hexagonal 21 cells layot with assmption of 500m inner-site distance and wrap-arond which eliminate bondary effects is defined. Every single BS serves 3 sectors which represent 3 cells. The LTE-based system level simlation environment is set according to [10] [11] [12] [13], some crcial parameters are showed in Table II. The sers are distribted in the cells normally. We apply antenna tilt to the optimization process while assming pilot power and antenna azimth stay nchanged in the optimization process. In or simlation, the tilt starts with initial optimization ranging from 9degree to 15 degree and pdate the tilts by the mapping fnction defined in the previos session. B. Reslts Average throghpt and Edge throghpt are displayed in Fig. 3, as can be seen from the figre, average throghpt and edge throghpt converge qickly to a constant which only take almost two iterations. This shows the good convergence performance of Tagchi s Method nder the mathematical model introdced previosly. TABLE I. Parameters Cell Layot SCENARIO CONFIGURATION Vale 7 sites/3 sectors Active sers per sector 20 Carrier freqency Inter-site distance Minimm distance to base station Shadowing standard deviation Shadowing correlation distance Penetration loss Receive noise figre Thermal noise density Channel bandwidth BS maximm transmission power BS antenna gain (boresight) 2.0GHz 500m 35m 8dB 50m 20dB 7dB -174dBm/Hz 10MHz 43dBm 17dBi 3 db BS antenna beamwidth 70 deg BS antenna front-to-back ratio BS antenna height UE antenna gain 20dB 32m 0dBi UE antenna height 1.5m User movement Traffic Model Schedling Algorithm Random walk: 3km/h Fll Bffer Rond-robin 624

4 Fig. 3 Average thpt and Edge thpt Improvement Fig 4 shows OT will converge to a constant vale and optimized gradally. The optimization process is triggered when the UE receive signal strength degrades to the threshold and stopped when the termination is met. The compromise coefficient is r=0.5, from the crve we can see with the modified Tagchi s Method, the OT improves by 18.5% while with original Tagchi s Method, the OT improves by 16.5%, bt the convergence of the modified Tagchi s Method deteriorates becase of random optimization range offset. The iteration nmber and OA table row nmber make p the total comptation times which is arond 2500 and abot 10ms for each comptation, so the optimization process last abot 25 mintes which is minte scale. So it s fast enogh to adapt to the changes to the real environment. Fig. 5 shows the Cmlative Distribtion (CDF) Fnction of UE throghpt in the cells, it shows that the average throghpt and edge throghpt improves tremendosly after the optimization is done. Fig. 4 OT improvement Using Original Tagchi s Method and Modified Tagchi s Method Fig. 5 CDF for UE Throghpt before and after optimization sing original and modified Tagchi s Method Fig. 6 Trade-off between coverage and capacity Fig. 6 shows the trade-off between edge throghpt and average throghpt, when r<0.5, the optimization scheme pt emphasis on optimizing edge throghpt, or coverage, otherwise, it pts emphasis on optimizing average throghpt, or capacity, this optimization scheme possess three-fold optimization tasks, coverage optimization; capacity optimization; hybrid optimization of coverage and capacity. If the networks experience coverage deterioration, we need to set compromise coefficient less than 0.5, otherwise the networks enconter capacity degradation, we need to set the compromise coefficient more than 0.5, if both is reqired, the vale for r is 0.5, which is the case in this paper. V. CONCLUSION In this paper, nder the framework of centralized SON architectre, we propose a mathematical model to optimize coverage and capacity jointly with Tagchi s Method by tning antenna tilts, to offer more search capability and near normal distribtion optimization range, Gassian shrink coefficient is applied and random optimization range offset to the level-to-tilt mapping fnction. The optimization flow chart has been proposed according to OA table. Tagchi s Method can tremendosly redce the nmber of experiments, compared to traditional trial-and-error optimization approach. From the reslts, nder the mathematical model we can have the conclsion that Tagchi s Method has a good property of fast convergence and near global optimm search. Moreover, modified Tagchi s Method otrns original Tagchi s Method in optimization performance. REFERENCES [1] 3GPP, TR , E-UTRA: Self-configring and self-optimizing network se cases and soltions(release 9), V9.3.1, Mar [2] SOCRATES, Self-optimisation and self-configration in wireless networks, Eropean Research Project, [3] NEC, Self Organizing Network, NEC s proposals for next-generation radio network management, Febrary 2009, NEC Corporation. [4] Wei-Chng Weng, Fan Yang, A. Z. Elsherbeni, Electromagnetics and antenna optimization sing tagchi s method, Morgan and Claypool Pblishers. [5] A. S. Hedayat, N. J. A. Sloane, and J. Stfken, Orthogonal arrays: theory and applications. Springer-Verlag: New York, [6] Wei-Chng Weng, Fang Yang, A. Z. Elsherbeni, Linear antenna array synthesis sing tagchi s method: a novel optimization techniqe in electromagnetics, IEEE Transactions on Antenns and propagation, Vol. 55, No.3, March

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