Joint Downlink and Uplink Tilt-Based Self-Organization of Coverage and Capacity Under Sparse System Knowledge

1 Joint Downlink and Uplink Tilt-Baed Self-Organization of Coverage and Capacity Under Spare Sytem Knowledge Sacha Berger, Meryem Simek, Albrecht Fehke, Paolo Zanier, Ingo Viering, and Gerhard Fettwei Abtract Concurrent elf-organization of coverage and capacity in both downlink and uplink i an ambitiou tak ince (i) coverage and capacity are conflicting Key Performance Indicator (KPI) and becaue (ii) an adequate downlink performance doe not necearily entail an adequate uplink performance ince the downlink and uplink interference cenario are fundamentally different. However, alo conidering the uplink when elforganizing the network i crucial, becaue the uplink tranmiion i becoming more important due to the arie of new application and ervice, uch a ocial networking, video call or enor network, which require either a parity between downlink and uplink traffic or even more uplink than downlink traffic. In thi article, we propoe a general concept for the elforganization of multiple KPI while having only very pare knowledge about the network. Uing thi concept, we propoe an effective tilt-baed algorithm that manage to jointly optimize coverage and capacity in downlink and uplink. In an urban cenario with real LTE ite location we were able to increae the cell-edge uer throughput by 70 % (downlink) and 24 % (uplink) while concurrently decreaing the number of uncovered uer by 21 % (downlink) and 25 % (uplink) compared to a well-choen reference tilt etting. Index Term Self-Organizing Network, Joint Optimization, Coordinated Optimization, Uplink and Downlink, Antenna Tilt, Coverage and Capacity Optimization. I. INTODUCTION A major challenge that mobile network are facing i that they have to cope with a highly inhomogeneou traffic demand. Often uer are concentrated in relatively mall area, e.g. on central plaza or quare (ee, e.g., [1], [2]). Such trong uer concentration, called Hot Spot (HS), are likely to overload the network locally, which in turn can lead to a low quality of ervice for the uer affected. In addition to the inhomogeneou traffic demand, the capacity offered by the network i alo not homogeneou in pace, which i, among other, caued by an irregular bae tation ditribution and ignal fading. Combining the inhomogeneity of both, the traffic demand and the network, lead to a highly inefficient ytem. Hereby, a Self-Organizing Network (SON) i treated a a promiing olution for increaing the network efficiency and, hence, for maintaining and/or increaing the network quality of ervice while aving capital and operational cot at the ame time. Among a multitude of poible parameter to be modified, the antenna tilt i treated to be a highly efficient parameter for the network elf-organization (ee, e.g. [3], [4]) and, therefore, alo of interet in thi work. The variety of ue cae relevant for elf-organization, uch a automatic neighbor relation, load balancing, or Coverage and Capacity Optimization (CCO), i alo large (ee, e.g. [5], [6]). Among the aortment of SON ue cae, the tilt-baed CCO i one of the focu topic ince network operator often conider the Key Performance Indicator (KPI) coverage and capacity a ome of the mot relevant KPI. eearcher in academia and indutry categorize procedure and algorithm dedicated for a elf-organization of coverage and capacity uually by mean of the ytem architecture (centralized, ditributed or hybrid), by mean of the temporal granularity, and alo by mean of the organization or optimization approach ued (e.g. learning-baed, rule-baed, or baed on claical optimization). In the majority of the contribution, however, reearcher do not comment on the type and amount of input data that i required for the operation of the SON procedure invetigated. Neverthele, pecifying the input required for operation i crucial a it dictate the technical and financial effort to be overcome when applying the algorithm propoed into practical network. Often an extenive amount of input data i required for the operation of tilt-baed elf-organization procedure, e.g. the uer receive power of all cell and tilt value conidered or the uer location. Obtaining thi data for the network to be optimized uually require ubtantial technical and financial effort, even if minimization of drive tet procedure are ued [7]. For that reaon, thi paper propoe a tilt-baed olution approach to the CCO ue cae which require only very pare input data, i.e., pare ytem knowledge. Another important property of SON procedure i, whether they elf-organize the Downlink (DL) only, the Uplink (UL) only or the DL and UL jointly. Until now, the network DL performance wa aumed to be of much higher importance than the UL performance. The reaon i that the traffic on the DL part of the network ued to have a much higher hare than the UL tranmiion [8], [9]. However, due to new application and ervice ariing, uch a enor network, video call, and ocial networking, to name but a few, the UL i becoming more and more important. Hence, when performing reearch in the field of elf-organization of coverage and capacity, reearcher hould not only conider the DL but rather the DL and UL jointly ince (i) both DL and UL are crucial for the network performance and (ii) an increaed DL capacity doe not imply an increaed UL capacity and vice vera. A major reaon for the latter i that, the UL interference i dictated by the uer location while the DL interference i given by the Bae Station (BS) location. However, other propertie, uch a the tranmit power, the tranmiion cheme, and maybe alo the cheduler deviate between DL and UL, which further decouple their performance. In the following, we preent an overview on exiting work in Copyright (c) 2015 IEEE. Peronal ue of thi material i permitted. However, permiion to ue thi material for any 0018-9545 other purpoe (c) 2015 mut IEEE. be Peronal obtained ue i from permitted, the IEEE but republication/reditribution by ending a requet torequire pub-permiion@ieee.org. IEEE permiion. See

2 the field of tilt-baed elf-organization of capacity and coverage. We will focu our evaluation on the input data required for operation and on the fact whether the UL tranmiion i alo conidered. A. elated Work Solution for tilt-baed elf-organization of coverage and capacity are typically baed on learning method, rule-baed procedure, or claic optimization method. The mot important contribution uing learning technique have been publihed by Ul Ilam et al. [10], [11] and azavi et al. [12]. All three cited publication employ fuzzy Q-learning which i a reinforcement learning technique [13]. In Q-Learning the goal i to ucceively learn the bet action (that can be elected from a predefined action et) to take given a current tate (whoe propertie are alo predefined). einforcement learning ha the advantage that in general no prior knowledge about the ytem behavior i required. That i why the category of learning baed SON approache can truly be conidered a requiring very pare knowledge about the network to be optimized. However, the main diadvantage of learning baed olution i the convergence guarantee if they are applied to multi-agent ytem. Additionally, a very precie and uually application baed parameter etting i required, which mean they need to be deigned for each ytem individually. The contribution from Engel et al. [14], Karvouna et al. [15], Kleig et al. [16], and Partov et al. [17] can be merged into another category. Thi category employ either claic optimization approache and / or rule-baed approache in order to improve the network coverage and capacity condition. For example, Engel contribution combine a traffic-lightrelated approach, that i actually a rule-baed acce, with a mixed-integer linear program, which can be conidered a a claical optimization approach. Thee contribution have in common that they conider the procedure propoed for earching a new tilt value to run in an offline imulation, i.e., during the earch the actual tilt value applied in the network tay contant. Only the tilt etting that i the olution of the offline optimization i then applied to the real network. The approache of thi category are highly effective, however, they require the operator to accurately model the network to be optimized. To do o, the uer location and their receive power for all cell and tilt value are required. If thi extenive data i not available the algorithm propoed cannot be applied. Another diadvantage of thi olution category i that they entail a certain delay, which i caued by the time required for the offline optimization, until an action can be taken. Pleae ee [18] for more detail on offline elforganization. Another category can be formed by contribution that do neither require extenive ytem knowledge (i.e., that they operate under pare ytem knowledge) nor addre the elf-organization via learning method. Under pare ytem knowledge we conider the fact that it i not poible to model or predict the network to be elf-organized given the input at hand. For example, we are incapable to model or predict the network at hand a oon we do not know where the uer are located or which receive power they have for certain tilt value. Due to thi pare ytem knowledge aumption, thee contribution apply every tilt etting propoed in the real network and, hence, they do not require a imulation of the network to be optimized. We claify uch olution approache a online elf-organization. Except of our previou contribution [19], [20], and [18], we could find only two other publication in thi category: [21] and [22]. Both publication propoe a elf-organization procedure that doe not require a imulation of the network to be optimized and, therefore, propoe trategie that earch for new tilt value locally around the current tilt etting a they expect no dramatic performance degradation for mall tilt variation. The latter publication propoe a rule-baed elf-organization procedure while the prior contribution utilize a coordinate acent earch. Diadvantage of the approach publihed by Eckhardt et al. [21] i that they only optimize the pectral efficiency but not the data throughput and do not evaluate in detail whether the earch method propoed i adequate for an optimization taking place in real network. However, analyzing the earch method feaibility for an optimization in the real network i eential a the network operator alo ha to avoid trong performance degradation during the elf-organization procedure. Furthermore, [22] doe not explain how to choe the cell to be optimized and alo doe not tate how to obtain the coverage and capacity objective that are related to an area covering multiple cell with local meaurement only. Pleae note, that all the contribution mentioned above have in common that they only conider the DL. To the bet knowledge of the author, there i no publihed work propoing a joint DL and UL elf-organization of coverage and capacity. Concluding, we can tate that there exit only little work on tilt-baed elf-organization of coverage and capacity that doe not require extenive knowledge on the network to be optimized and that there exit, to the bet knowledge of the author, no contribution conidering DL and UL jointly. B. Contribution Thi work aim to overcome the aforementioned hortcoming of the tate of the art. A major contribution of thi work i a general concept applicable for the concurrent elforganization of multiple KPI under the aumption that the impact of a change of a network parameter on the KPI cannot be imulated or predicted, i.e., under pare ytem knowledge aumption. The concept propoed i not pecific to a certain network parameter. The main propertie of the concept, which i baed on pare ytem knowledge, are that we utilize KPI-pecific cot function that repreent the operator optimization goal and KPI prioritization. The accumulation of the cot function output, which are denoted a cot, facilitate to evaluate the network uing a joint cot value which hall be decreaed. operate the elf-organizing network in an online manner, i.e., we apply every parameter etting propoed to the real network and obtain the KPI value of interet via meaurement only. In thi way, no imulation of the network i included in the elf-organization procedure.

3 decreae the joint cot by utilizing a coordinate decentlike earch approach. The earch approach i appropriate for an online operation a at mot one network parameter i adjuted and only mall parameter modification are allowed. Furthermore, thi work applie the concept propoed to a tiltbaed joint DL and UL elf-organization of coverage and capacity. We preent the algorithm, evaluate it performance in term of coverage, capacity, and convergence peed uing a real-world urban LTE deployment cenario, and elaborate on the algorithm feaibility in practice. Pleae note that, thi work focue on SON procedure having a high feaibility to be applied in practice rather than on SON procedure finding the globally bet parameter etting. We would like to point out that thi work i a continuation of our previou work in the field of tilt-baed CCO (ee [19], [20], and [18]). On the one hand thi paper ummarize our previou effort for the firt time and on the other hand thi paper alo goe beyond what ha been addreed in our previou work. The major noveltie are that (i) we preent a general concept for the elf-organization of multiple KPI rather than only an algorithm for tilt-baed coverage and capacity optimization, (ii) we conider the DL and UL jointly, (iii) we thoroughly motivate the propertie of our cot function ued, and (iv) we employ imulated annealing to obtain an upper bound of the KPI performance. The remainder of thi paper i tructured a follow. In Section II we introduce the general concept for multi-kpi elf-organization under pare ytem knowledge. Section III i dedicated to introduce the DL and UL ytem model ued in thi work. Thereafter, we apply the concept propoed: The algorithm, which we et up, i preented in Section IV and the ytem level imulation reult are reported in Section VI. We elaborate on the algorithm feaibility in Section V and conclude our work in Section VII. II. A CONCEPT FO SELF-OGANIZATION OF MUTLIPLE KPIS UNDE SPASE SYSTEM KNOWLEDGE SON are dedicated to upport multiple, o-called elf-x function, including but not limited to elf-optimization, elfhealing, elf-configuration, and elf-protection. Thi work focue on the apect of elf-optimization and i, for the mot part, alo applicable to elf-healing. Ideally a elf-optimizing network maximize the network quality of ervice while minimizing the capital and operational expene. However, nowaday mobile network are highly complex involving a multitude of network parameter (e.g., antenna tilt, antenna azimuth, and handover margin) and KPI (e.g. cell edge uer throughput, coverage, and call dropped rate) to be et and conidered, repectively. Therefore, we view the tak of elfoptimization not a an optimization in the ene that the globally bet parameter etting hall be found but rather a a tak that require to balance multiple KPI within a deired value range. For example, the network coverage hall be held in a value range between 98 % and 100 %, but a maximization to the highet poible value i not required. Hence, we addre the o-called elf-optimization ue cae alo imply a a elforganization ince it i not about an optimization in the ene of finding the bet etting poible. Therefore, we ue the term elf-optimization and elf-organization interchangeably in thi work. Thi ection i dedicated to preent a concept for the elforganization of a cellular network that i neither pecific to a certain parameter type nor to certain KPI. Our elf-appointed goal are that the concept 1) i applicable even though the dependency between the network parameter() to be adjuted and the KPI() to be conidered i unknown, i.e., the concept hall addre a cenario in which we have pare knowledge about the network to be optimized. We further elaborate on thi topic in the Subection II-A and preent how the concept propoed manage to elf-organize the network under uch retrictive aumption in Subection II-B. 2) i capable of handling multiple KPI. Adding a KPI to an exiting et of KPI that are elf-organized hall not require major change in the elf-organization procedure. We addre thi goal in the Subection II-A. 3) i capable of including operator-pecific elforganization goal. Thee goal hall include a deired value range for each KPI to be optimized and a prioritization among them. A. Introduction to Spare Sytem Knowledge In view of the elf-organization of a cellular network, we conider pare ytem knowledge to be the fact that the data available decribing the network i inufficient to preciely model or predict the KPI value of interet given a certain network parameter etting. In order to be capable of modeling or predicting the network KPI preciely, detailed knowledge about the network, uch a uer location and receive power ditribution, i required. Hence, we decribe the amount of ytem knowledge available a pare if we cannot model or predict our KPI given a certain network parameter etting and a extenive if thi i poible. However, we aume that we are alway able to meaure the KPI value of interet for the parameter etting that i currently applied in the network. In our tilt-baed application which i going to be preented in the Section IV to VI, pare ytem knowledge mean that we are neither able to predict nor able to model the network coverage and capacity value given a certain tilt etting. We aume that we are not in knowledge of the uer receive power for any cell and any tilt value and that we are not aware of the uer location. Due to lack of the aforementioned propertie, we are not able to model or predict any coverage and capacity change a a tilt change. However, we aume to be able to meaure the network coverage and capacity for the current tilt etting. B. Online Self-Organization The mot common way to operate a SON are online and offline operation [18]. Both term, online and offline operation, refer to the way how the SON earche for a more adequate parameter etting if the current parameter etting doe not lead to atifactory KPI value. A SON that operate online only relie on KPI meaurement and

4 refrain from utilizing a imulation model of the network, which would enable to predict the KPI value given a certain parameter etting. Hence, an online SON i forced to meaure the reulting KPI value for each parameter etting that i propoed by the elf-organization algorithm. In thi way, an online SON iterate in a loop coniting of (i) propoing a new parameter etting to the real network and (ii) meauring the KPI value for thi parameter etting. In contrat, an offline SON relie on an accurate imulation model of the network. Uing the imulation model, the offline SON can run a earch for an adequate parameter etting without actually applying any parameter change to the real network. The parameter etting found to be optimal in the offline imulation i then applied to the real network. Of coure, the deciion whether to employ an online or offline SON operation i dictated by the knowledge that i available about the network. We refer the intereted reader to [18] for more detail on online and offline operation of SON. Since we conider pare ytem knowledge, an offline SON operation i excluded (becaue we are unable to model the network under conideration) and, therefore, we propoe the uage of an online SON operation. Furthermore, we aume that the network operator want to (i) keep the time required for the optimization minimal and (ii) would like to avoid KPI performance degradation alo during the aforementioned optimization. Hence, both the number of parameter etting a well a the KPI performance of the parameter etting propoed matter becaue each parameter etting propoed i applied to the real network. Thee condition lead to eential limitation when chooing or creating an optimization method. Hence, an important quetion i which optimization method are adequate for an online SON operation? Let u aume that large parameter change are likely to affect the KPI performance largely. A we do not know whether a parameter change improve or degrade the performance of our KPI of interet, we have to avoid large parameter change, i.e., we can only propoe mall change to the current parameter etting. Even though the operator might tolerate mall KPI performance degradation during the parameter optimization, the optimization hould till be configured in a way that uch KPI performance degradation are of very limited duration. Therefore, we alo have to retrict the optimization method peritence, i.e., we cannot tolerate that the method earche through parameter etting decreaing the KPI performance for a very long time. Thi retriction will indeed limit the optimization method capability for ecaping from local optima, however, it i required due to the online SON operation. Furthermore, we hall retrict the amount of etting propoed a the overall duration required for finding a new parameter etting hall be limited. Concluding, we can tate that an online SON operation require an optimization method that propoe mall parameter change only, minimize the time pend in parameter etting that degrade the KPI performance, and minimize the number of parameter etting propoed. In [20] the author invetigated the uitability for variou tiltbaed earch method for online elf-organization of coverage and capacity in DL. A procedure imilar to a coordinate decent earch led to bet performance in term of the above lited condition. C. Cot Function Approach A already tated in the beginning of thi ection, the major goal of thi elf-organization concept are that the concept can handle a multitude of KPI and that we can include the operator goal, i.e., the deired KPI value range and a prioritization among the KPI. Let u firt outline how the concept propoed addree thee goal by the uage of KPIpecific cot function before we provide more detail on how to et up thee cot function: The idea i to et up KPI-pecific cot function whoe argument and value are the correponding KPI value and unit-le cot, repectively. Since the cot i dedicated to be a meaure of the neceity for improvement for thi KPI, the cot function are defined uch that they are zero for the deired KPI value range and increae the more the KPI i apart from thi value range. The elf-organization of the network i then realized by accumulating the cot of all KPI and trying to minimize thi joint cot by mean of a earch procedure adequate for online optimization. Following thi approach, we can implement the operator elf-organization goal for each KPI, by adjuting each KPI cot function. Alo, we can realize a KPI prioritization by caling the cot function among each other, uch that certain KPI are more cot-enitive than other, which will give them a higher importance during the elf-organization. Furthermore, it i eay to add a KPI to an exiting SON, a it require no change in the earch procedure but only to conider an additional cot function. Having thi outline in mind, the following et-up of cot function i conidered. Let u conider a et of KPI K to be elf-organized, where we addre the value of the i th KPI a K i K, and a et of parameter P available for modification, where we addre the value for the j th parameter a P j P. Pleae note that, each KPI K i i conidered to be of a different type, e.g. K 1 could be the value of the network coverage while K 2 i the value of the network capacity. In contrat, for the parameter we alway conider the ame type of parameter but refer to different cell or antenna, e.g. P 1 and P 2 could addre the value of the antenna tilt at cell 1 and 2, repectively. For each KPI K i to be conidered we et up a pecific cot function ϕ i. Each of thee cot function provide an unit-le meaure that rate the need for improvement for the KPI it i pecific to. Thi i achieved by making the cot function a function that map a KPI value to a cot value Φ i, i.e., ϕ i : K, K i Φ i i. Hence, neglecting the KPI-pecific ubcript i we can write Φ = ϕ(k). Now let u give a point by point decription how to et up the cot function: 1) Define the deired value range for all KPI conidered. When defining the threhold of the deired value range, one hall conider both the operator goal for the repective KPI and the network to be optimized. The reaon for alo conidering the latter are twofold. On the

5 one hand, we may give away potential for a performance increae if the threhold are et uch that the network KPI already lie within the deired value range. On the other hand, etting unattainable KPI threhold i advere a well becaue it might happen that even with an elf-organization the deired KPI value might not be reachable leading to endle long attempt of the SON to achieve it goal. Neverthele, the latter problem can be counteracted by control technique. 2) Set up the cot function of each KPI eparately. Define each cot function in a way that their cot value i zero for the deired value range of the KPI they are pecific to. Apart from the deired value range the cot function hall be (i) monotonou, (ii) convex, and (iii) of limited teepne. Monotonicity hould be applied in order to emphaize the increaing need for optimization a the deviation between the actual KPI value and the deired KPI value range increae. Thi cot increae hould be convex. The reaon i that concave function are unfavorable a they allow a KPI value to be driven far away from it deired value range without a dramatic cot increae. Moreover, property (iii) hould hold becaue very teep function are in the limit imilar to a tep function. Such function are diadvantageou ince they do not allow for a continuou cot weighting. Hence, we propoe defining a cot increae of type ak n, where a i a weighting factor and n an exponent. Conidering the above mentioned propertie (i) to (iii), we till have remaining freedom defining the cot function increae (in term of a and n). Without lo of generality, we propoe uing exponent in the range from n = 2... 4 a they meet all the requirement lited and are eay to handle. The weight a hall be et a follow. 3) Define the KPI prioritization among the KPI. We can realize a prioritization among KPI by defining the cot function uch that the hare of the cot from a KPI on the total cot i higher than the hare of another KPI. In thi way, the elf-organization will be more influenced by the former KPI than by the latter KPI, a more cot can be reduced by improving the former KPI. We propoe uing the remaining freedom in the weight a of the cot function in order to realize the deired cot ratio between the multiple KPI. Conidering the KPI value that are typically preent without a elforganization of the network, the cot function weight a can be decreaed or increae uch that the deired cot ratio are met. in the real network and the KPI value for a certain parameter etting are obtained via meaurement. By accumulating KPI-pecific cot function, which model the operator elforganization goal, we can obtain a joint cot function which conider all KPI concurrently. Thi joint cot function i then decreaed by uing a earch method that i adequate for online optimization. Following thi concept, we achieve our goal tated at the beginning of thi ection. Thee goal are imultaneouly the concept main contribution beyond tate of the art. III. SYSTEM MODEL Since we adopt the DL ytem model from [23] and the UL ytem model from [24], we only give a hort overview on both DL and UL ytem model. Pleae note that, we will perform pixel-baed imulation which require a perpixel formulation of the ytem model. However, for eaier undertanding we preent the ytem model in a per-uer perpective. The tranition to a pixel-baed decription can be done by conidering a uer denity λ(u p ) for each pixel u p which repreent the average number of uer located in thi pixel. A. Downlink Sytem Model We aume a LTE OFDMA network coniting of multiple ectorized macro BS which erve an area 2. Each ector erve a cell, which i defined a = {u = argmax v ˇPrx,v (u), ˇP rx, (u) ˇP rx,min }. (1) ˇP rx,v (u) and ˇP rx,min denote the received DL ignal power from ector v at location u and the minimal required receive power in DL, repectively. i the cell index. We define the cell territory a = {u = argmax v ˇPrx,v (u)}. Note that,. A uer belong to the territory which provide the highet DL ignal trength, i.e., the connection function can be defined a = X(u) = argmax v ˇPrx,v (u). Since we adopt a full buffer model, we lightly underetimate the Signal-to- Interference-and-Noie-atio (SIN) what we accept in view of the low computational complexity. We compute an uer data rate following a reource fair cheduler aumption and uing the Shannon formula with an upper limit of 6 bp /Hz. Let f (ř) be the Cumulative Ditribution Function (CDF) of all oberved average DL uer throughput ř in the area. The 5 th percentile of the DL uer throughput in i defined a: ˇQ 5 = inf{ř f (ř) 0.05}. (2) D. Summary We propoe a general concept for the elf-organization of multiple KPI under pare ytem knowledge. We define pare ytem knowledge to be the fact that we are incapable of modeling or predicting the KPI given a certain parameter etting. Due to thi retriction, the elf-organization can only take place following an online SON operation. In an online SON operation every parameter etting propoed i applied Uing thi general definition, we can refer to the 5 th percentile of the DL uer throughput in any arbitrary area by imply replacing by the area which i currently of interet, e.g., = for the 5 th percentile of the DL uer throughput in cell. Pleae note that we abbreviate the 5 th percentile of the DL uer throughput by the throughput percentile or imply the throughput. We define the coverage on a per-uer bai. The DL coverage Č in the area i defined a the ratio between all covered uer and the um of all covered and uncovered

6 uer, i.e., Č = Ň cov Ň cov + Ň uncov, (3) where Ň cov uncov and Ň denote the number of covered and uncovered uer in DL in, repectively. Pleae note that, we define the coverage on a per-uer bai rather than on an area bai ince we do not have knowledge on the uer location (ee pare ytem knowledge aumption in Sect. II-A). B. Uplink Sytem Model We model the LTE UL, i.e., a ingle carrier FDMA ytem. Each uer control it tranmit power according to the 3GPP Tranmit Power Control (TPC) [25], i.e., ˆP tx (u) = min{ ˆP max, P 0,X(u) + α X(u) L X(u) (u) +10 log 10 ( ˆM(u))}, (4) where ˆP tx (u), ˆPmax, L X(u) (u), and ˆM(u) denote the UL tranmit power of a uer located at u, the maximal UL tranmit power, the path lo between location u and the erving cell X(u), and the number of Phyical eource Block (PB) that are aigned to the uer located at u in UL, repectively. P 0,X(u) and α X(u) are cell pecific TPC parameter pecified in [25]. If we neglect the part 10 log 10 ( ˆM(u)) in Eq. (4) then ˆP PB tx we obtain the uer UL tranmit power per PB. Pleae note that we aume UL and DL path lo to be the ame, uch that we write in Eq. (4) ˆL X(u) (u) = ĽX(u)(u) = L X(u) (u). Alo, we would like to emphaize that the UL uer aignment i given by the DL receive power, i.e., by the connection function X(u). From [24], we choe the modified reource fair cheduler. Thi cheduler trie to allocate the frequency reource fairly among all uer. However, if the reource fair hare exceed the uer maximal amount of PB M max = min{1, floor( ˆP max PB / ˆP tx )} (5) that the uer can tranmit on following the TPC, the cheduler aign only M max PB to thi uer. We model the cheduling deciion a a random proce in which each uer ha a certain cheduling probability. Conequently, the UL SIN depend on the random cheduling deciion. We compute a uer UL data throughput uing the Shannon formula with an upper limit of 6 bp /Hz. In the Shannon formula we ue an uer average SIN, i.e., we average the interference from 1000 cheduling realization (Monte Carlo approach) in order to obtain an average SIN. eplacing the DL rate ř and the DL CDF f (ř) with the UL rate ˆr and the UL CDF f (ˆr) in Eq. (2) lead to the 5 th percentile of the UL uer throughput in : ˆQ5 = inf{ˆr f (ˆr) 0.05}. Similarly, replacing the number of covered and uncovered uer in the DL with the correponding UL metric lead to the UL coverage: ˆN cov ˆN cov uncov Ĉ = ˆN cov + ˆN uncov, where and ˆN denote the number of covered and uncovered uer in the UL, repectively. IV. ALGOITHMS FO A TILT-BASED SELF-OGANIZATION OF COVEAGE AND CAPACITY UNDE SPASE SYSTEM KNOWLEDGE In thi ection, we preent tilt-baed SON olution for the CCO ue cae baed on the general SON concept preented in Section II and uing the aumption and definition from Section III. At firt, we define our elf-organization goal. Thereafter, we propoe a elf-organization algorithm dedicated to addre the elf-organization goal by mean of antenna tilt adjutment. In order to better undertand the reult of the joint DL and UL elf-organization, we alo propoe elforganization algorithm which are dedicated to excluively addre the DL or UL, repectively. Moreover, we provide an Upper Bound (UB) for the performance of the joint DL and UL elf-organization, which applie the heuritic optimization method of Simulated Annealing (SA). A. Self-Organization Goal In thi work, we target for achieving the following goal. We target on jointly keeping the DL and UL coverage and capacity over a certain minimum level. We concentrate our effort on coverage if a certain minimal coverage level i not achieved. However, if thi minimal coverage level i provided we prioritize the capacity becaue aiming for very high coverage value typically caue high interference which entail low SIN. When applying approache for elf-organizing the capacity, we focu on the cell edge uer, i.e., on the 5 th percentile of the uer throughput, which we imply addre a the throughput or throughput percentile in the remainder of thi work. We concentrate on the cell edge uer a thee are the critical uer which uffer a low quality of ervice. Since the threhold to be choen for the coverage and throughput depend on the cenario to be optimized, we are defining them once we look at a pecific cenario a decribed in Section VI. Another requirement i that we have a light prioritization of the DL over the UL. A we focu on the throughput percentile when optimizing the network capacity, we ue the term throughput and capacity interchangeably. B. Algorithm The elf-organization algorithm propoed are baed on the concept preented in Section II and on our previou contribution [20] and [19]. The UB provided by a SA approach ha originally been propoed a an offline olution for the CCO ue cae in [26] 1. Pleae note that thi ection concentrate on preenting the algorithm. We comment on the algorithm propertie in Section V and invetigate their performance in Section VI. 1) Joint DL and UL Self-Organization: In order to addre the elf-organization goal mentioned in the beginning of thi Section, we ue a cot function for each KPI to be conidered: ˇϕ C for the DL coverage, ˆϕ C for the UL coverage, 1 Pleae note that all previou contribution mentioned ( [19], [20], [26]) addre the CCO ue cae excluively in DL.

7 Algorithm 1 Monitoring and Cluter Set Up equire: meaure f (ˆr) cell 1: Č Ň cov Ĉ Ň cov, Ň cov +Ň uncov cov ˆN ˆN cov + ˆN uncov Ň uncov, ˆN cov, ˆN uncov, f (ř), ˇQ 5 inf{ř f (ř) 0.05} ˆQ 5 inf{ˆr f (ˆr) 0.05} 2: Φ ˇϕ Q ( ˇQ 5 ) + ˆϕ Q ( ˆQ 5 ) + ˇϕ C (Č ) + ˆϕ C (Ĉ ) 3: if : Φ > 0 then 4: Set up a optimization cluter C around cell t 0 = argmax {Φ }; C conit of cell t 0 and 1 t and 2 nd tier neighbor of t 0 ; all cell in the cluter except of the 2 nd tier neighbor are ummarized in the et C; C and C denote the correponding area 5: Č C Ĉ C C Ň cov {Ň cov C +Ň uncov } cov C ˆN C { ˆN cov + ˆN uncov } ˇQ 5 C inf{ř C f C (ř) 0.05} ˆQ 5 C inf{ˆr C f C (ˆr) 0.05}, where f C and are obtained by accumulating the CDF from all f C C 6: Φ C ˇϕ Q ( ˇQ 5 C ) + ˆϕ Q ( ˆQ 5 C ) + ˇϕ C (Č C ) + ˆϕ C (Ĉ C ) 7: Apply Algorithm 2 for finding the et of tilt value of the cell C that minimize the joint cluter cot Φ C 8: end if 9: Go to tep 1. ˇϕ Q for the DL throughput percentile, ˆϕ Q for the UL throughput percentile. A tated in Section II, the cot function hall be created conidering both the operator elf-organization goal and the network at hand, i.e., the cot function are pecific to the network or in other word they are pecific to the imulation cenario. Hence, we accept to have the above mentioned cot function available without preenting their detailed definition for now. We will introduce the cot function together with the imulation cenario in Section VI. Uing the cot function, the algorithm can run the monitoring and cluter et up procedure preented in the peudo code of Algorithm 1. In Algorithm 1 each cell to be conidered for elforganization meaure it coverage and throughput tatitic (Ň cov, Ň uncov cov uncov, ˆN, ˆN, f (ř), f (ˆr)) and compute it cell-wie cot Φ. If a cell ha a cot unequal to zero, then the algorithm et up an optimization cluter C around the cell having the highet cot and compute the cot Φ C referring to the optimization cluter. Thereafter Algorithm 2 i triggered. Pleae note that, the earch for new tilt value in line number 7 in Algorithm 1 i retricted to the et C in order to avoid edge effect. Thi earch (line number 7 in Algorithm 1) can be repreented by the peudo code preented in Algorithm 2, where Pt w denote the tilt value of ector t during iteration w. Algorithm 2 realize the Coordinate Decent-like (CD) earch method. The algorithm pick one cell tilt (one coordinate) and optimize thi tilt before moving Algorithm 2 Coordinate Decent-like Tilt Search equire: t 0, k = 1, v = w = 0 and from Algorithm 1: C, C, Φ C, P w t 1: repeat 2: for t = t 0, t 1, t 2, t 3, t 4, where t 1,..., t 4 denote the four tronget neighbor of cell t 0 in C do 3: pick random earch direction δ from = {+1, 1 }. 4: while k 2 do 5: w w + 1, P w t P w t + δ, obtain Φ w C, k k + 1 6: end while 7: Φ w C = Φw C Φw 2 C 8: if Φ w C 0 then 9: invert earch direction: δ δ 10: w w + 1, Pt w Pt w 2 + δ, obtain Φ w C 11: w w + 1, Pt w Pt w + δ, obtain Φ w C 12: Φ w C = Φw C Φw 2 C 13: if Φ w C 0 then 14: end earch, pick Pt w where w = argmin w Φ w C 15: end if 16: end if 17: k 1 18: while k 2 do 19: w w + 1, Pt w Pt w + δ, obtain Φ w C, k k + 1 20: end while 21: Φ w C = Φw C Φw 2 C 22: if Φ w C 0 or w 10 then 23: end earch, pick Pk w where w = argmin w Φ w C 24: end if 25: Go to line 17. 26: end for 27: v v + 1 28: until v = 3 or Φ w C = 0 to a different cell (different coordinate), which i in general a CD-like procedure. In principle, any arbitrary earch for better tilt value could be applied in line 7 of Algorithm 1. However, ince we are following an online optimization (due to the pare ytem knowledge aumption) we are retricted in the choice of the earch method applied (ee Section II-B). In [20], we compared the performance and applicability a an online earch of the CD-like earch preented in Algorithm 2, a imultaneou perturbation tochatic approximation earch, and a Nelder-Mead earch. Baed on thi evaluation, we propoe the uage of the CD-like earch method ince it entail the bet performance (in term of improving the KPI value) while being applicable a an online earch (i.e., that the algorithm only rarely propoe etting which decreae the KPI performance ignificantly). Pleae note that, an update of Φ w C in Algorithm 2 (ee line 5, 10, 11, and 19) require to meaure the coverage and throughput tatitic Ň cov, Ň uncov, ˆN cov uncov, ˆN, f (ř), f (ˆr) for all cell C becaue we are performing an online optimization. In the following, we addre the algorithm which elforganize the coverage and capacity jointly in DL and UL, i.e., the combination of Algorithm 1 and 2, a DLUL-CD.

8 TABLE I SA PAAMETE SETTINGS Parameter 1 2 3 4 5 Initial Temperature T (0) 80 240 240 360 420 Temperature Schedule, T (w+1) = T (0) 0.95 w T (0) 0.95 w T (0) /ln w T (0) 0.95 w T (0) 0.95 w e-annealing Interval 100 80 80 80 80 2) Self-Organization in DL Only: The algorithm which elf-organize the coverage and capacity only in DL work exactly in the ame way a the algorithm DLUL-CD with the following difference. Intead of conidering the DL and UL cot function when computing the joint objective Φ and Φ 2 C, thi algorithm only employ the DL cot function ˇϕ C and ˇϕ Q for computing Φ and Φ C, repectively. In thi way, the algorithm only conider the DL performance of the coverage and capacity when elf-organizing the network antenna tilt. In the following, we addre thi algorithm a DL-CD. Pleae note that, thi algorithm i identical to the one propoed in [19] and i conidered a a reference algorithm. 3) Self-Organization in UL Only: The algorithm which elf-organize the coverage and capacity only in UL i identical with the algorithm DL-CD, with the difference that thi algorithm employ the UL cot function only, i.e., ˆϕ C and ˆϕ Q. In the following, we addre thi algorithm a UL-CD. C. Upper Bound Providing an UB in term of which KPI performance could have been achieved with the bet poible tilt configuration i of high interet, becaue it allow to better evaluate the performance of the algorithm DLUL-CD, DL-CD, and UL- CD. However, the complexity of typical elf-organization cenario i too large for a brute force earch. In a cenario with 50 ector and 10 poible tilt value available at each ector we already have 10 50 poible etting, which approximately equal the number of atom on earth [27]. Simulating all 10 50 poible tilt etting would certainly exceed our computational reource and, hence, we propoe to conider the SA approach a an UB. SA i a metaheuritic optimization method propoed by Kirkpatrick et al. in [28] which mimic the cooling proce of olid. An important feature of SA i that new parameter configuration are alo accepted if they are wore than the current parameter configuration. In thi way, SA can overcome local optima and, if it run for infinite time, can find the global optimum [29]. However, even with a limited amount of iteration, SA i capable of finding near globally optimal olution. Hence, we conider SA a an adequate method for providing an UB. We contruct our UB uing SA a follow. We employ Algorithm 1 but with two difference. Firt, we do not et up optimization cluter (line 4 in Algorithm 1) but rather ue the complete et of antenna tilt to be adjuted at once. Hence, the joint cot to be minimized can be written a Φ UB = ˇϕ Q ( ˇQ 5 TA ) + ˆϕ Q ( ˆQ 5 TA ) + ˇϕ C (Č TA ) + ˆϕ C (Ĉ TA ), (6) 2 See line number 2 and 6 in Algorithm 1. where Č TA = TA TA Ň cov TA cov {Ň TA + Ň uncov TA } (7) cov Ĉ TA = TA ˆN TA cov uncov TA { ˆN TA + ˆN TA } (8) ˇQ 5 TA = inf{ř TA f TA (ř) 0.05} (9) ˆQ 5 TA = inf{ˆr TA f TA (ˆr) 0.05}. (10) In the formula above, TA denote the Target Area (TA) which contain all cell that are conidered to be elforganized. Second, we do not apply Algorithm 2 (line 7 in Algorithm 1) for finding the et of tilt value that minimize the joint objective Φ UB but rather apply SA. Since the performance of SA depend on an adequate choice of the algorithm parameter, we conider five different parameter etting of the SA algorithm and ue the bet reult of all five verion a the UB, which we abbreviate a UB-SA. The parameter etting of the five different SA algorithm are preented in Table I. Pleae note that, the UB SA cannot be conidered a an applicable olution to our joint DL and UL CCO ue cae ince the SA algorithm doe not meet the requirement for an online optimization. Due to (i) the high number of tilt change performed per iteration, (ii) the randomne when earching for a new tilt configuration, and (iii) the poibility to accept alo tilt configuration which entail a high KPI performance degradation, the SA algorithm applied in thi work are very likely to ignificantly degrade the KPI performance during the elf-organization proce. V. PACTICAL ASPECTS OF IMPLEMENTATION Thi Section i dedicated to comment on the practical apect ariing when implementing the DLUL-CD algorithm. A. Temporal Granularity and Temporal Change of the Network We call the duration between two update of the antenna tilt configuration a the temporal granularity of the algorithm. Due to the online SON operation the temporal granularity of the algorithm propoed i lower bounded by the longet of the following duration: duration required to obtain reliable tatitic on the KPI to be elf-organized duration required to communicate the KPI tatitic duration required to compute the new tilt configuration given the current KPI duration required to change the antenna tilt. Since we conider the antenna tilt to be modified electrically, the correponding duration for modifying an antenna tilt value

9 i rather mall. Alo the computation time for obtaining the new tilt configuration i aumed to be in the range of milliecond or econd ince Algorithm 1 and 2 are rather hort and imple code. Furthermore, we conider the communication of the meaurement reult not to be limiting ince we aume the according communication channel to be of large bandwidth. Hence, the critical duration i the one required to obtain reliable coverage and throughput tatitic for each cell. In the following, let u etimate how long thi duration may be in an urban macro cell deployment. In order to etimate thi duration, we are required to know (i) how many ample we need to collect and (ii) what i the time required for collecting a ample. In [30], the author provide a method which allow u to compute the number of ample required for computing a percentile given a deired confidence and the ditribution function of the ample. However, the ditribution of the ample, i.e., the ditribution of the data rate within a cell, i highly dependent on the uer ditribution and, hence, in general unknown. That i why we cannot trictly compute the number of ample required. Neverthele, we can etimate thi number. In [31], the author evaluate the accuracy of a percentile etimation in a random experiment for variou ample ize and variou ample ditribution. Baed on their reult, we can etimate that a ample ize of 500 to 1000 uncorrelated ample 3 hall be ufficient for a proper computation of the 5 th percentile. We aume that we need approximately the ame number of ample for etimating the coverage. But what time do we need to obtain a ample? Auming a reource fair bandwidth haring and a cell load of ρ = 0.5, we can compute the number of uer imultaneouly active in a cell to be ρ /1 ρ = 1 [32]. If we take thi example and aume that each ample obtained i uncorrelated and the uer or BS tranfer 5000 kbit of data with an average data rate of 500 kbp, then it take on average 10 to obtain a ample. Hence, it would require 10 1000 = 10000 2.8 h to obtain enough ample for the computation of KPI value. Neverthele, thi duration change when conidering a different et of the above aumed number. For example, from [31] we can alo derive that it require much le ample to etimate a percentile if we can tolerate larger error. In uch cae, the amount of ample required could be in the range of a few hundred, leading to a minimal temporal granularity in the range below 1 h. However, a econd bottleneck dictate the temporal granularity of the algorithm. For bet performance of the algorithm propoed, the network mut be tationary for at leat a couple of iteration (e.g. for the time that the algorithm earche for a better tilt value a one ector; ee peudo code of Algorithm 2). A the network traffic demand i, epecially during day time, highly varying in the order of hour, we hould not choe a temporal granularity in thi range. Here, the bet choice depend on the minimal temporal granularity etimated above. If thi duration i in a range below 1 h, than the algorithm could follow the daily traffic change, however, if 3 In our application we could conider two ample to be uncorrelated if they are either obtained from different uer or if both ample are form the ame uer but the uer path lo changed ignificantly between the collection of the two ample. the minimal duration i in the range of multiple hour, then we are forced chooing a higher granularity. For example a daily update could be choen in the latter cae, if we conider that the network i approximately tationary between day (e.g. Tueday i imilar to Wedneday). B. Multiple SON Algorithm The algorithm propoed are deigned uch that in every iteration only one tilt i changed. Hence, given the teady tate aumption mentioned previouly, we can directly map the change in the KPI to the tilt modification. However, if multiple SON algorithm, which do not coordinate their action among each other, are working in the network imultaneouly, it can happen that the SON algorithm interfere with each other. For example, a hypothetic SON algorithm A could change a network parameter after another hypothetic SON algorithm B jut changed a different network parameter and i currently buy meauring the impact of thi change on the KPI value (aynchronou parameter change). In thi cae, the action of SON algorithm A would impact the KPI meaurement of SON algorithm B and, hence, would ditort the meaurement reult from SON algorithm B. A imple but effective approach to counteract uch interference between multiple SON algorithm could be to require, that the network parameter of cell belonging to the current optimization cluter C can only be modified by the SON algorithm which did et up thi optimization cluter. In thi way, we till have the poibility to run multiple SON algorithm in parallel but protect each SON algorithm action patially from the other SON algorithm. A the optimization cluter C conit of 2 tier of neighbor around the critical cell and a we only modify the tilt in the critical cell itelf and it 1 t tier of neighbor, parameter change from other SON algorithm outide of the optimization cluter C hall only have a mall impact. C. SON Architecture The algorithm DLUL-CD a well a the algorithm DL- CD and UL-CD can be implemented not only following a centralized but alo following a ditributed architecture. In the latter cae, each BS would be equipped with a SON functionality and the BS would communicate with each other via the X2 interface in order to exchange meaurement reult and to organize the proce of Algorithm 1 and 2. In the former cae, a ingle SON functionality would be located in the Network Management (NM). The BS would end the meaurement data required for the SON operation via the outhbound and northbound interface to the NM. Main advantage of a ditributed SON architecture over a centralized one i the poibility to operate on mall time cale (typically econd to minute). However, the temporal granularity of the online algorithm propoed in thi work i lower bounded by the time required to obtain the cell-wie coverage and throughput tatitic, which i expected to lat more than 1 minute. Hence, a centralized architecture eem more reaonable ince it entail a better calability with regard to larger number of cell. Neverthele, a ditributed SON architecture might be

10 the preferred olution in heavy loaded dene urban cenario, where we can expect to collect enough meaurement in le than 15 minute. D. Coverage and Throughput Meaurement In order to compute cell-wie cot Φ and the joint objective Φ C each ector need to meaure it coverage tatitic, which i conidered to conit of the number of covered and uncovered uer in DL and UL (Ň cov, Ň uncov cov uncov, ˆN, ˆN ), and it throughput tatitic, which i conidered to be the collection of all average data rate oberved in DL and UL (f (ř), f (ˆr)). In the ytem model ued in thi work, we conider imple coverage condition according to receive power: A uer located at u i covered in DL if v: ˇPrx,v (u) ˇP rx,min and i alo covered in UL if ˆP rx,v (u) ˆP rx,min, repectively. Hence, computing the number of covered and uncovered uer in the imulation i imple, however, in practice thi can be challenging. The number of covered uer in UL ˆN cov can be obtained by counting the number of different uer ID performing ucceful call releae and outgoing handover. The number of uer that are affected by an UL coverage problem, i.e., ˆN uncov may be etimated by counting both the number of detected adio Link Failure (LF) at the BS and the number of after-failure report end to the BS that indicate DL coverage but report no UL connection. The number of uer that are uncovered in DL may be etimated by counting the number of after-failure report that indicate no DL connection. The remaining meaure i the number of covered uer in DL Ň cov. Since we know that N = Ň cov + Ň uncov (11) cov uncov N = ˆN + ˆN we can compute the number of covered uer in DL a Ň cov = ˆN cov + ˆN uncov Ň uncov. (12) Pleae note that in Eq. (11) N denote the total number of uer that are located in the territory of cell. The DL and UL throughput CDF can imply be obtained by collecting the DL and UL data rate oberved for each call. The throughput CDF of a joint area, e.g. the cluter area, can be created by accumulating the oberved data rate from all cell belonging to the cluter. In order to limit the communication overhead caued by the SON algorithm each cell may end it oberved data rate in form of a hitogram. By accumulating the hitogram from all cell conidered we can obtain the joint hitogram from which we can derive the joint throughput CDF. E. Communication Overhead The communication overhead generated by the DLUL- CD algorithm depend on the SON architecture conidered. Since an additional communication overhead i uually unproblematic for the outh- and northbound interface but may be critical for the X2 interface, we are retricting u to a ditributed SON architecture for thi part. The DLUL- CD algorithm require each ite to communicate it ector etimated number of covered and uncovered uer in DL and UL a well a the throughput hitogram in DL and UL. However, a proven below, thi communication overhead i inignificant. The coverage information conit only of four number which are aumed to require each 8 bit. Each throughput hitogram could range from 0 kbp to 10 Mbp with a bin ize of 1 kbp. Hence, the throughput hitogram would include 10 4 bin. Auming each bin to require 8 bit lead to 80 kbit per hitogram. Therefore, a complete meaurement et of a three-ectorized ite can be aumed to require 3 (2 80000 bit + 4 8 bit) = 480096 bit 480 kbit. Auming a fully-mehed X2 interface, 100 threeectorized ite, and a temporal granularity of one day, the total communication overhead can be etimated to um up to 480 kbit 100 99/60 60 24 = 55 kbit /. Moreover, we would like to mention that reearch ha hown that thi communication overhead can be decreaed without diminihing the DLUL- CD algorithm performance by increaing the hitogram bin ize. Pleae note that, additional ignaling will be caued by (i) the et up of the optimization cluter, (ii) the requet of new meaurement data, and (iii) the organization of the CDlike earch method. However, each of thi meage will be in the ize of everal bit ince no meaurement data need to be tranferred. F. Optimization Cluter In line 4 of Algorithm 1 the optimization cluter need to be et up. For doing o the initiating cell need to know which are it 1 t and 2 nd tier neighbor. Thi knowledge may be taken from (i) cell neighbor lit, (ii) information on the ector location and their tranmit direction, and (iii) predefined neighbor relationhip. VI. SYSTEM LEVEL SIMULATIONS AND ESULTS Thi ection i dedicated to apply the algorithm propoed in a imulation and evaluate their performance. In Section VI-A we introduce the imulation cenario ued and then define the coverage and throughput cot function applied in Section VI-B. We preent the algorithm coverage and throughput performance and compare them to the UB-SA in Section VI-D and VI-C. Moreover, in Section VI-E we evaluate the convergence peed of the algorithm propoed. A. Scenario We invetigate a realitic dene urban cenario (European city center) with real LTE ite location and tilt-reolved ray tracing path lo data. The imulation cenario i hown in Fig. 1 and the imulation parameter are preented in Table II. In order to avoid that we evaluate the algorithm propoed uing only a ingle, very pecific, cenario, we are conidering 64 different traffic demand ditribution. Each traffic demand ditribution conit of a uniform uer denity of 60 uer /km 2 and one or two traffic demand HS which are 130 time dener populated than the urrounding area. The HS, which are not larger than 0.0165 km 2, are located at reaonable location, uch a at central quare or at the univerity. We aume

11 y [m] 3000 2500 2000 1500 1000 500 Simulation Parameter Carrier Frequency 2.6 GHz Bandwidth 10 MHz BS Antenna Gain 14 dbi Path Lo ay Tracing Penetration Lo 10 db + 0.6 db UE Height 1.5 m Thermal Noie 121 dbm PB Spatial eolution 5 5 m Poible Antenna Tilt 4 14 UL Min. eceive Power ˆP rx,min 124 dbm PB UL TPC Parameter α 0.8 UL TPC Parameter P 0 91 dbm UL Max. Tranmit Power P max 23 dbm DL Min. eceive Power ˇP rx,min 120 dbm PB BS Tranmit Power 29 dbm PB TABLE II SIMULATION PAAMETES CONSIDEED. 0 0 500 1000 1500 2000 x [m] dbm 150 100 50 Fig. 1. Map of bet received ignal trength for the imulation cenario under tudy. The point denote ite location and the arrow indicate the tranmit direction of the ite ector. Sector denoted by a thick arrow are conidered for the elf-organization. The other ite (thin arrow) have a fixed tilt of 6 and erve a interferer. The area hown i the TA TA. The tilt etting ued for thi plot i the reference tilt etting. that all traffic demand cenario are equiprobable. Since (i) the algorithm tilt modification focu on the BS around the HS 4 and ince (ii) the HS are located at very different place, we can aume that the 64 imulation cenario differ from each other coniderably. The antenna tilt can be modified from 4 to 14 in integer tep 5. The initial tilt etting are obtained uing two very imple initializing procedure which only conider the coverage. Starting with all tilt at the maximal (minimal) poible value, we ucceively decreae (increae) the tilt of all cell in a random order until the coverage increae le (decreae more) than 75 m 2. We take the tilt etting which perform better in term of both coverage and throughput a the initial tilt configuration. A thi procedure i dedicated to find an adequate initial tilt etting only and, therefore, repreent the network planning phae taking place before applying the SON algorithm propoed, we are auming full ytem knowledge at uniform traffic demand for thi initialization. That i why, we can ue a coverage metric related to an area rather than to uer. In contract, however, we elf-organize the network under the previouly mentioned pare ytem knowledge aumption. Pleae note that the ector not conidered for elf-organization (the thin arrow in Fig. 1) have a fixed tilt of 6. At the initial tilt etting we oberve an average DL and UL coverage in the TA of 97.7 % and 96.4 %, repectively. The average DL and UL throughput percentile i 47 kbp and 26 kbp, repectively. Pleae note that the average i conidered to be over the 64 different traffic demand cenario. 4 Becaue often the BS covering the HS have the highet cot Φ 5 Thi i value range i given by the ray tracing path lo data. B. Cot Function The cot function ued for the imulation are preented in Fig. 2. Let u motivate the choice of thee cot function. a) Cot Function Threhold: We ue the following threhold for the cot function 98 % for the DL coverage 97 % for the UL coverage 400 kbp for the DL throughput percentile 350 kbp for the UL throughput percentile A tated in Section II, we conider both the operator elforganization goal and the network at hand when etting the threhold. Pleae keep in mind that, the throughput definition ued in thi work alo conider uncovered uer with 0 kbp data rate (ee Section III). By electing the throughput threhold rather high compared to the initial throughput, we achieve two effect. Firt, we immediately create very high cot if the coverage fall below 95 % ince the throughput percentile mut then be 0 kbp (becaue 5 % of the uer have a data rate of 0 kbp). Thi high cot will avoid coverage below 95 % whenever it i poible. Once thi minimal coverage i achieved, we concentrate on the throughput optimization, ince the additional coverage cot are maller compared to the throughput cot. In cae we achieve high throughput, we till try to optimize the coverage by mean of the coverage cot function. The threhold of the coverage cot function are et jut above the initial value a we want to focu on throughput. b) Cot Function Exponent: All cot function are of quadratic type. Too teep cot function have the diadvantage, that they behave like a tep function in the limit and, hence, do not allow for a continuou weighting of the cot. Cot function that are linear have the diadvantage that the cot doe not increae coniderably a we move apart from the deired value range of our KPI. Hence, we chooe a quadratic increae of the cot with an increaing gap between the actual KPI and the KPI threhold. However, chooing cot function with a lightly higher teepne, e.g. cubic, would alo be an adequate approach. c) Cot Function Weighting: We cale the abolute cot between the different KPI by mean of a weighting factor of the quadratic cot function. The cot function are caled uch that the relation between DL and UL cot conidering

12 Cot [a.u.] 10 8 6 4 2 95 96 97 98 99 100 DL Coverage Cot UL Coverage Cot Cot [a.u.] 200 150 100 50 280 320 360 400 440 DL Throughput Cot UL Throughput Cot 0 0.97 0.98 0.99 1 1.01 1.02 Coverage / DL Coverage Threhold 0 0.7 0.8 0.9 1 1.1 Throughput / DL Throughput Threhold (a) DL and UL coverage cot function ued in thi work. The lower x-axi how the coverage divided by the DL coverage threhold ČTH = 98%. (b) DL and UL throughput cot function ued in thi work. The lower x- axi how the throughput percentile divided by the threhold of the DL 5,TH throughput percentile ˇQ = 400kbp. Fig. 2. Coverage and throughput cot function ued by the elf-organization algorithm. Pleae note that, we omit pecifying whether the KPI i related to DL or UL in the x-axie ince we preent both DL and UL cot in one plot. Since the algorithm ue thee cot function irrepective whether they compute a cell-wie cot or the cluter cot, we do not pecify to which area we relate to by imply writing. The cot i unit le, i.e., can be caled in arbitrary unit (a.u.). the average initial KPI value i 1.2 to 1, i.e., the DL i lightly The relative change in term of the DL and UL throughput more important than the UL. percentile i preented in Fig. 3. ˇQ5,opt 5,opt TA and ˆQ TA denote the optimized DL and UL throughput percentile in the TA. ˇQ5,ref TA C. Throughput eult 5,ref and ˆQ TA denote the DL and UL throughout percentile in the TA at the reference tilt etting. It i viible in Fig. 3(a) that the DL-CD algorithm perform better im term of the DL throughput than the UL-CD. Exactly the oppoite can be 3 oberved for the UL (ee Fig. 3(b)), i.e., the UL-CD algorithm perform better in term of the UL throughput than the DL-CD 2.5 algorithm. Thi reult wa expected becaue the DL-CD algorithm 2 conider the DL throughput but not the UL throughput (and the other way around for the UL-CD algorithm). The fact 1.5 that the DL-CD (UL-CD) algorithm can till achieve a notable performance gain in the UL (DL) throughput i caued by the 1 mutual coupling between DL and UL throughput. Both DL and UL performance depend on the path lo between the BS DL CD UL CD DLUL CD UB SA and the uer. A we are conidering DL and UL path lo to be (a) elative change in the target area throughput percentile in downlink ˇQ the ame, a tilt change that improve the DL throughput may 5 TA. alo improve the UL throughput. It i noteworthy that the DL throughput performance of the DLUL-CD algorithm i lightly 3 better (in the median) than the performance of the DL-CD algorithm. Thi can be explained a follow. In principle, we 2.5 are oberving two different effect when comparing the DL- 2 CD (UL-CD) with the DLUL-CD algorithm. Firt, we reduce the freedom in optimization if we add additional UL (DL) 1.5 cot ince a tilt etting that might be very favorable for the DL 1 (UL) may not be adequate for the UL (DL). Hence, we expect that the DLUL-CD algorithm perform better then UL-CD but DL CD UL CD DLUL CD UB SA wore than DL-CD in term of the DL throughput. Second, the UL throughput cot have an effect on the overall cot that i (b) elative change in the target area throughput percentile in uplink ˆQ 5 TA. imilar to a moother. When adjuting an antenna tilt, the DL throughput percentile i affected due to (i) a changed path lo ituation and due to (ii) a changed amount of uer in the cell. The latter can lead to high bandwidth gain if the number of ˇQ 5,opt ˆQ 5,opt TA / ˇQ 5,ref TA TA / ˆQ 5,ref TA Fig. 3. Box plot of the TA throughput percentile for both DL and UL for all algorithm invetigated. The red line denote the median over all 64 cenario and the blue box how the area where the middle 50 % of the reult are located. The antenna (whiker) extend to the mot extreme data value. The median of the throughput percentile at the reference etting wa 47 kbp in DL and 26 kbp in UL.

13 uer to be erved in a cell decreae 6. However, in the UL we conider a modified reource fair cheduler according to [24]. Thi cheduler never cheduler more than floor{ Pmax PB / ˆP tx } PB to a ingle uer in order to avoid that a uer i driven into power limitation due to a too high bandwidth. Since epecially the cell edge uer have to tranmit with high power per PB (ee Eq. (4)) thee uer are very unlikely to experience bandwidth gain. Hence, the UL throughput percentile i much le enitive to tilt change than the DL throughput percentile. That i why the UL throughput cot are much moother than the DL throughput cot and adding UL throughput cot to exiting DL cot moothen the joint cot. A a reult, the localized earch method applied in the algorithm (ee Algorithm 2) ha a higher change to overcome local optima and, therefore, the DL throughput performance may increae depite of the effect mentioned previouly if we add UL throughput cot to exiting DL throughput cot. Accordingly, the ame cannot hold true the other way around ince we are decreaing the moothne of the joint cot if we add DL cot to exiting UL cot. Hence, we oberve a performance improvement in the DL throughput percentile when moving from the DL-CD algorithm to the DLUL-CD algorithm (ee Fig. 3(a)) but a performance degradation in the UL throughput percentile when moving from the UL- CD algorithm to the DLUL-CD algorithm (ee Fig. 3(b)). Our jutification i alo upported by the fact that the UL throughput gain are in general maller than the DL throughput gain, which i caued by the maller enitivity of the UL throughput on antenna tilt modification. In term of the DL throughput percentile, the DLUL-CD algorithm achieve a median performance gain of 70 % while the UB-SA achieve 110 %. In the UL, the DLUL-CD algorithm increaed the throughput percentile in the median by about 24 % while the UB-SA can achieve 75 % gain. Hence, the algorithm propoed (DLUL-CD) accomplihe 2 /3 and 1 /3 of the poible gain in DL and UL, repectively. D. Coverage eult The abolute change in term of the TA coverage in DL and UL (Č TA and Ĉ TA ) i preented in Fig. 4. We denote the optimized coverage value a Čopt TA and Ĉopt TA in the DL and UL, repectively. The DL and UL coverage at the reference tilt etting are denoted a Čref TA and Ĉref TA, repectively. It i viible that the UL-CD algorithm perform better than the DL- CD algorithm in both DL and UL coverage. The reaon i that a UL coverage condition i tronger than a DL one. Adding DL cot to the UL-CD algorithm, i.e. moving from UL-CD to DLUL-CD, decreae the overall hare of the coverage cot which lead to the fact that the DLUL-CD algorithm perform wore than the UL-CD algorithm. Pleae note that the TA coverage at the reference etting wa 97.7 % in DL and 96.4 % in UL. Hence, the algorithm UL-CD decreaed the amount of uncovered uer by about 21 % in the DL and by about 25 % in the UL. We would like to emphaize that thi gain i regarded a being urpriingly high conidering that (i) the throughput wa the preferred KPI during the elf-organization and (ii) the 6 Pleae note that we conider a reource fair cheduler in the DL. Č opt TA Čref [%] TA Ĉ opt TA Ĉref [%] TA 2 1.5 1 0.5 0 4 3 2 1 0 DL CD UL CD DLUL CD UB SA (a) Abolute change in the DL TA coverage Č TA. DL CD UL CD DLUL CD UB SA (b) Abolute change in the UL TA coverage Ĉ TA. Fig. 4. Box plot of the TA coverage for both DL and UL for all algorithm invetigated. reference etting ha been obtained by conidering coverage a the only KPI. All algorithm manage to guarantee a minimal coverage of 95 % in every imulation cenario. E. Convergence eult Before we dicu the algorithm peed of convergence, let u comment on the general convergence propertie of the algorithm propoed. The CD earch method can only be proven to converge to the optimal point, if the objective function i convex, which i not the cae in our application. Hence, there i in general no guarantee that the CD-like earch method applied in thi work can find a local or the global optimum. However, ince the CD-like earch method applied in the algorithm DL-CD, UL-CD, and DLUL-CD jump to the bet etting found after it earch (ee line 23 in Algorithm 2), we can guarantee that the algorithm do not decreae the network performance in term of cot. In contrat, SA i proven to converge to the global optimum of a nonconvex objective function after infinite many iteration in [29]. However, a we cannot perform infinite many iteration, we cannot guarantee finding a local or the global optimum either. Neverthele, ince the algorithm propoed operate online, the peed of convergence to the KPI value preented above, i.e., the number of tilt etting that had to be propoed in order to achieve the gain preented above, i of interet. Let u introduce the et ˇQ5,w 5,ref 5,1 5,2 5,w TA = { ˇQ TA, ˇQ TA, ˇQ TA,..., ˇQ TA }, 5,w where ˇQ TA denote the TA throughput percentile in DL ˇQ 5 TA at the w th iteration of the algorithm. We ue the following

14 Q x (S(w)) 100 80 60 40 x = 90 x = 50 x = 10 DLUL CD 20 UB SA 0 0 20 40 60 80 100 Iteration w Fig. 5. 10 th, 50 th, and 90 th percentile of the convergence peed metric S(w) for the algorithm DLUL-CD and the UB SA. metric to evaluate the peed of convergence: 5,w 5,ref max( ˇQ S(w) = TA ) ˇQ TA ˇQ 5,opt 100. (13) 5,ref TA ˇQ TA Note that, S(w) alway tart at 0 for w = 0 (ince ˇQ 5,0 5,ref TA = { ˇQ TA }) and i upper limited by 100 (ince 5,w 5,opt max( ˇQ TA ) ˇQ TA ω). In Fig. 5 we preent the 10 th, 50 th, and 90 th percentile of S(w) for the algorithm DLUL-CD and the UB SA, where the percentile relate to the 64 traffic demand cenario. It i viible that the DLUL-CD algorithm require in the median (50 th percentile) over all cenario about 40 iteration to achieve 80 % of the maximal poible gain and 70 iteration of achieve the maximal gain poible. In 10 % of the cenario invetigated the algorithm could achieve 90 % of it maximal poible DL throughput performance already after 13 iteration. For the other KPI the convergence propertie are very imilar. Alo, we can conclude that the UB SA i much fater than the DLUL-CD algorithm. A the algorithm DL-CD and UL-CD employ the ame earch method a the algorithm DLUL-CD, they alo how an almot identical convergence behavior a the algorithm DLUL-CD. Hence, we refrain from howing their convergence reult in Fig. 5 for the ake of clarity. F. Concluion on Simulation eult We can conclude that the DLUL-CD algorithm outperform both the DL-CD algorithm and UL-CD algorithm in term of our elf-et goal from Section IV-A. All three algorithm manage to keep the coverage above the deired minimum value of 95 %, where the UL-CD algorithm can even achieve coverage gain. However, beide of guaranteeing the minimal coverage our focu i the throughput optimization where we want to improve both DL and UL but prioritize the DL. The DLUL-CD algorithm can meet thee requirement the bet a it increae the DL throughput percentile by 70 % but till achieve a UL throughput percentile gain of 24 %. The DL-CD and UL-CD algorithm increae the DL throughput percentile by 66 % and 55 %, repectively. In the UL the DL- CD algorithm achieve a throughput gain of 12 % and the UL- CD algorithm 43 %. Hence, in view of all our elf-organization goal and their prioritie, we conider the DLUL-CD algorithm to outperform the DL-CD and UL-CD algorithm. VII. SUMMAY AND CONCLUSIONS In thi paper we propoed a concept which i dedicated to elf-organize multiple key performance indicator under the retriction that the network at hand cannot be modeled. We denote thi retriction a pare ytem knowledge. Uing thi concept, we propoed an algorithm which modifie the network antenna tilt in order to olve the ue cae of concurrent coverage and capacity optimization in both downlink and uplink jointly. Simulation uing a realitic urban cenario how that a joint conideration of downlink and uplink outperform algorithm which only conider the one or the other. Thi reult i of particular interet ince the uplink i becoming more important due to the arie of new application and ervice uch a ocial networking, video call or enor network. The major diadvantage of the algorithm propoed i that it require a rather long duration for the elf-organization and, therefore, i mainly uited to adapt the network to long term change of the traffic demand ditribution. Thi diadvantage i caued by the pare ytem knowledge aumption which force u to follow an online elf-organization. An alternative SON algorithm, which could work under full ytem knowledge, would be able to adapt the network fater, a the optimization method can be executed offline. Neverthele, we can conclude that elf-organizing network can alo achieve adequate reult if the knowledge about the network i very limited. EFEENCES [1] D. Lee, S. Zhou, X. 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Berger, M. Sozka, A. Fehke, P. Zanier, I. Viering, and G. Fettwei, Joint throughput and coverage optimization under pare ytem knowledge in lte-a network, in International Conference on ICT Convergence (ICTC), Oct 2013, pp. 105 111. [21] H. Eckhardt, S. Klein, and M. Gruber, Vertical antenna tilt optimization for lte bae tation, in Vehicular Technology Conference (VTC Spring), May 2011, pp. 1 5. [22] everb Network, Antenna Baed Self Optimizing Network for Coverage and Capacity Optimization, Sterling, VA, Tech. ep., 2012. [23] I. Viering, M. Dottling, and A. Lobinger, A mathematical perpective of elf-optimizing wirele network, in International Conference on Communication (ICC), June 2009, pp. 1 6. [24] I. Viering, A. Lobinger, and S. Stefanki, Efficient Uplink Modeling for Dynamic Sytem-Level Simulation of Cellular and Mobile Network, EUASIP Journal on Wirele Communication and Networking, vol. 2010, no. 1, 2010. [25] Evolved univeral terretrial radio acce (e-utra); phyical layer procedure, 3GPP, Technical Specification TS 36.213. [26] S. Berger, P. Zanier, M. Sozka, A. Fehke, I. Viering, and G. Fettwei, What i the advantage of cooperation in elf-organizing network? in Wirele Day (WD) Conference, Nov 2013, pp. 1 6. [27] D. Weienberger, How many atom are there in the world? 2014. [Online]. Available: http://education.jlab.org/qa/mathatom\ 05.html [28] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by Simulated Annealing, Science, vol. 220, no. 4598, pp. 671 680, 1983. [29] D. Handeron, H. S. Jacobon and A. W. Johnon, The Theory and Practice of Simulated Annealing. Theory and Practice, 2003. [30] A. J. Gro and V. A. Clark, Survival ditribution, reliability application in the biomedical cience, Biometriche Zeitchrift, vol. 18, no. 8, pp. 671 671, 1976. [31] F. Schoonjan, D. De Bacquer, and P. Schmid, Etimation of population percentile, Epidemiology (Cambridge, Ma), vol. 22, no. 5, pp. 750 751, 2011. [32] S. B. Fredj, T. Bonald, A. Proutiere, G. e gnie, and J. W. obert, Statitical bandwidth haring: A tudy of congetion at flow level, in Conference on Application, Technologie, Architecture, and Protocol for Computer Communication. ACM, 2001, pp. 111 122. Sacha Berger (S 14) received hi diploma in phyic (equal to M.Sc.) with ditinction from the Univerity of Technology Dreden, Germany in 2011. During hi tudie, he worked a an intern with the Fraunhofer Intitute for Manufacturing Technology and Advanced Material in Dreden, Germany, with the digade GmbH in Zittau, Germany, and with Webato Product North America, Inc. in Fenton, Michigan, USA. He i currently working toward hi Ph.D. degree at the Vodafone Chair Mobile Communication Sytem at the Univerity of Technology Dreden, Germany. Hi current reearch interet include elforganizing network, non-convex optimization, adaptive antenna, and uplink power control. Meryem Simek (SM) received her Dipl.-Ing. degree in Electrical Engineering and Information Technology from Univerity of Duiburg-Een, Germany in 2008, holding a cholarhip from the German National Academic Foundation Studientiftung de deutchen Volke which i granted to the outtanding 0.5 % of all tudent in Germany. She obtained her Ph.D. degree on reinforcement learning baed inter-cell interference coordination in heterogeneou network from the ame univerity in 2013. In 2013, he wa a pot-doctoral viiting cientit at Florida International Univerity, where he wa working on mobility management in heterogeneou network and device-to-device communication. She i currently a pot-doctoral reearcher and group leader at the Vodafone Chair Mobile Communication Sytem at the Technical Univerity Dreden, Germany. Her main reearch interet include radio reource management in heterogeneou wirele network, 5G wirele ytem, and the tactile internet. Albrecht Fehke received hi diploma a well a Ph.D. in electrical engineering with highet honor from Technical Univerity of Dreden in 2007 and 2014, repectively. From 2010 to 2014 Albrecht ha been reponible for a reearch group at TU-Dreden and worked on variety of reearch project with key vendor and operator. He co-authored more than 40 reearch paper in the area of mobile network energy efficiency, elf-organizing network, queuing theory, and mathematical optimization. Among other, he wa awarded the 2014 Fred W. Ellerick prize of the IEEE Communication Society. In 2014 Albrecht co-founded Airray, a tartup company working on large cale antenna array for 5G mobile communication, where he i currently active. Paolo Zanier i a eearch Engineer at Nokia Network. He received hi mater degree in Electronic Engineering at Univerity of Triete, Italy. During hi career in Nokia, he worked in everal &D poition in the area of radio and M2M. He i currently part of a project exploring new concept for 5G architecture, focuing on ditributed cloud and control plane evolution.

16 Ingo Viering i co-founder and CEO of Nomor eearch GmbH located in Munich, Germany. Furthermore, ince 2007 he i alo enior lecturer at Munich Univerity of Technology. Hi reearch interet are the ytem apect of current and future communication ytem including the detailed interaction of the multitude of feature. Ingo got hi Dr.-Ing. from Univerity of Ulm in 2003. He pent a reearch tay with the Telecommunication eearch Center Vienna (FTW) in 2002, where he conducted early meaurement of the MIMO channel. He received hi Dipl.-Ing. degree from the Univerity of Technology Darmtadt in 1999. He ha filed around 100 patent, publihed more than 80 cientific paper, and he i actively contributing to 3GPP. In 2009, he wa awarded the VDE Award for the achievement of Nomor eearch. Gerhard Fettwei (F 09) earned hi Ph.D. under H. Meyr uperviion from WTH Aachen in 1990. After one year at IBM eearch in San Joe, CA, he moved to TCSI Inc., Berkeley, CA. Since 1994 he i Vodafone Chair Profeor at TU Dreden, Germany, with 20 companie from Aia/Europe/US ponoring hi reearch on wirele tranmiion and chip deign. He coordinate 2 DFG center at TU Dreden, namely cfaed and HAEC. Gerhard i IEEE Fellow, member of the German academy acatech, and hi mot recent award i the Stuart Meyer Memorial Award from IEEE VTS. In Dreden he ha pun-out eleven tartup, and etup funded project in volume of cloe to EU 1/2 billion. He ha helped organizing IEEE conference, mot notably a TPC Chair of ICC 2009 and of TTM 2012, and a General Chair of VTC Spring 2013 and DATE 2014.