Joint Bandwidth Allocation and Small Cell Switching in ...

Joint Bandwidth Allocation and Small Cell Switching in Heterogeneous Networks Jens Bartelt, Albrecht Fehske, Henrik Klessig, and Gerhard Fettweis

Jens Voigt

Vodafone Chair Mobile Communications Systems Dresden University of Technology, Germany Email: {jens.bartelt, albrecht.fehske, henrik.klessig, fettweis}@ifn.et.tu-dresden.de

Actix GmbH Dresden, Germany Email: [email protected]

Abstract—One major topic of research into self-organizing network technology is the coordination of SON use cases. Network operators expect a coordinated handling of the parameter and configuration changes submitted to the operating network by closed-loop SON use case implementations. There are currently two basic approaches for SON use case coordination discussed in the literature: A so-called heading or tailing use case external coordination and the combination of separate use cases into one joint algorithm. In this paper, we extend a verified framework to combine mobility load balancing and inter-cell interference coordination use cases, especially for a heterogeneous network environment. Our approach results in a coordinated set of cell range expansion offsets, an efficient bandwidth allocation to support the (enhanced) inter-cell interference coordination use case, and an energy-efficient smart cell switching of the small capacity cells in a heterogeneous networks environment for a varying traffic demand during the course of a day, resulting in significant capacity enhancements while saving energy at the same time. Index Terms—SON, MLB, ICIC, ESM, network optimization, self-optimization, HetNet, small cells

I. I NTRODUCTION With self-organizing network (SON) technology widely regarded as the best way to make heterogeneous network (HetNet) deployment and management more efficient, there has been much focus on developing the necessary optimization algorithms to make this a reality. SON technology is typically categorized in so-called use cases. Popular examples of SON use cases for network selfoptimization are mobility load balancing (MLB), coverage and capacity optimization (CCO), or mobility robustness optimization (MRO). Each of these use cases is expected to run independently and to address issues related to imbalanced load among cells, coverage holes, or handover failures by changing parameters defined in the configuration management (CM) of the cellular network. These autonomously running SON use case implementations naturally run into problems of conflicting parameter changes. For that reason, a SON coordination is necessary for resolving possible parameter conflicts. This coordination is considered as one of the most critical challenges to meet during SON design. There are currently two basic approaches seen for SON use case coordination: First, a so-called heading or tailing coordination of conflicting parameters (separately before or after the independently determined parameter changes), which

was firstly introduced by the Socrates community, e.g., [1], or [2]. A second approach addresses separate use cases into one algorithm and optimize the cellular network towards a joint target. An example algorithm to combine CCO and MLB use cases into a joint algorithm was introduced in [3]. In this contribution we extend our framework of [3] to combine MLB and efficient bandwidth allocation (inter-cell interference coordination - ICIC/eICIC) optimization in a HetNet scenario, hereby, e.g., complementing the threshold-based MLB solution in [4]. As a surprising result, this combined optimization automatically suggests some small cells in the HetNet environment to have a very low or even zero bandwidth for some time periods of a varying traffic demand during the course of a day. This result suggests an automatic switch-off of some small cells while still providing sufficient network capacity for the current traffic demand and having a highly energyefficient operation of the complete HetNet deployment in the sense of the energy saving management (ESM) SON use case. This problem of combining MLB and ESM was also discussed in, e.g., [5], resulting in a heuristic approach. The already standardized ICIC/eICIC techniques of 3GPP LTE Rel. 10 are discussed in , e.g., [6]. We, however, present a combined optimization solution for MLB, ICIC/eICIC, and ESM in this contribution. This paper is further organized as follows: In Section II our system model is introduced, whereas in Section III the SON optimization problem is formulated and our joint algorithm is presented. In Section IV our verifying numerical studies are introduced and discussed, before we give our conclusions to this contribution in Section V. II. S YSTEM M ODEL The framework presented in this paper models the downlink of an LTE network. We extend our earlier framework in [3] by fractioning the overall bandwidth and introducing small cells. A. Network Layout and Traffic Distribution We consider sites to be deployed in an area L ∈ R2 with a location denoted by u ∈ L. At each site one or multiple base stations (BS) are deployed, being defined as either macro (mBS) or pico (pBS) BS. Then, the set

978-1-4673-6187-3/13/$31.00 ©2013 IEEE

N = {1, . . . , i, . . . , n}

(1)

comprises all BS indices. Further, the region L can be spatially partitioned into a set of non-overlapping areas P = {L1 , . . . , Li , . . . , Ln } ,

(2)

where each Li is the area served by a BS i. We call these areas cells. We further model the traffic demand as a Poisson point process characterized by the mean user arrival rate λ in s−1 and the exponentially distributed file size with mean Ω in bits. Considering the spatial user distribution δ(u) in km−2 with L δ(u)du = 1, the product σ(u) = λΩδ(u) yields the spatial traffic demand in

(3)

bps . km2

B. Bandwidth Fragmentation The overall frequency band is assumed to have a width of Btot in Hz. It is divided into a set of m non-overlapping and not necessarily equally spaced subbands1 , the width of which is denoted by bl and normalized by Btot . We collect the normalized widths of the subbands in the bandwidth vector B = (b1 , . . . , bl , . . . , bm ),

(4)

with B1 = 1 and B = {1, . . . , l, . . . , m} being the set of subband indices. Each BS i is either allowed or not allowed to transmit in each of the subbands, defining the column vector

ai,l

A = (ai,1 , . . . , ai,m )T with ⎧ i ⎪ ⎨1, if BS i is allowed to = transmit in the l-th subband ⎪ ⎩ 0, otherwise

(5) (6)

Each column vector Ai shall be called the ith BS’s admission vector. Applying these admission vectors Ai , we further define the matrix A = (A1 , . . . , Ai , . . . , An ). Each row vector of A then describes an interference situation as follows: A row l in A, representing a subband bl , reveals which BS i is allowed to transmit in the specific subband and which is not, protecting the allowed cells from all other cells’ interference. Assuming a fixed number of BSs, there is only a limited number of possible interference situations. This number is equal to the number of all combinations of {0, 1} of length n, which is 2n for n BSs. Further omitting the combination of only zeros (a subband which is not used by any BS), the maximum number of interference situations accounts for 2n − 1. We, however, reduce the number of interference situations by grouping pBSs based on the serving areas of mBSs and apply the same admission vector to each of the pBS belonging to one group. This is motivated by the fact that there is at least one mBS, which covers the pBS cell areas and therefore acts as 1 In

an LTE system, a subband consists of one or more Physical Resource Blocks (PRB). Then, a subband definition can be translated into an PRBbased ICIC scheme. The bandwidth fragmentation can also be interpreted as a time-based ICIC scheme, with A and B determining the ratio and position of almost blank subframes (ABS) for each cell.

the strongest interferer. Moreover, due to low transmit powers of the pBS, we assume only low interference among pBSs if they are deployed with reasonable inter-site distances. Thus, we conclude that the common admission vector of a pBS group does not harm the network performance dramatically. We denote the subband in which all BSs allowed to transmit the common band. In a case when some BSs are turned off, the common band is the subband in which the remaining BS are allowed to transmit. The special case when all BSs utilize the entire frequency band (i.e., bl = 1 for subband l | ai,l = 1 ∀ i) is the full frequency reuse (FFR) scheme. By using the maximum number of subbands for the given grouping and varying only B (i.e. the width of the subbands), we can vary continuously between any frequency reuse scheme, from orthogonal frequencies to FFR, and thus get a maximum degree of freedom for an ICIC scheme. C. Radio Link Performance Each BS i has a maximum transmit power of ptx,i with constant power spectral density (PSD) such that, if a BS is not allowed to transmit in all subbands, it will not transmit at full power. The constant PSD also leads to the fact that the SINR (signal-to-interference-and-noise ratio) in each subband can be calculated directly from the received powers. The power received by a mobile terminal at location u ∈ L is given by pi (u) = gi (u)ptx,i with gi (u) being the channel gain, comprising path loss, antenna patterns, and fast and slow fading effects. Depending on the admission matrix A, a user at location u experiences different SINRs in each subband bl . We consider cell-load-dependent SINRs as introduced in [7], where the interference power is weighted by the load, i. e., the probability of transmissions by the interfering BSs, resulting in time-average interference conditions. We assume that each allowed subband is equally utilized for data transmission by the BS, which results in equal loads in all utilized subbands of a BS. With the aforementioned assumptions, we propose the computation of the SINR experienced at location u, in subband bl , and with respect to BS i as γi,l (u, η) =

 j∈N ,j=i

pi (u) , aj,l ηj pj (u) + Btot N0

(7)

with N0 being the noise PSD. We use the well known Shannon formula to compute the achievable user rate in subband bl as2 ci,l (u, η) = ai,l bl Btot · log2 (1 + γi,l (u, η))

(8)

Since all subbands are used equally in the sense of resource occupation, the overall achievable rate of a BS i is estimated as the sum of all subband rates  ci (u, η) = ci,l (u, η) (9) l∈B

D. Resource Utilization of a Base Station We define the load density at location u as the ratio of traffic demand and deliverable rate. Then, the integral of the 2 See,

e.g., [3] for a discussion of extensions towards MIMO.

load density over a given cell area Li results in the cell load [3] σ(u) du (10) ηi = fi (η) = ci (u, η) Li

Defining the corresponding vector function f (·), the vector of cell loads η can be calculated by solving the system of equations η = f (η) (11) We solve the System (11) by the fixed point iteration

 η (k+1) := β (k) η (k) + (1 − β (k) )min f (η (k) ), 1 −  , (12) where β (k) is a vector iteration-dependent forgetting factor,  is an arbitrary small positive constant, and k is the iteration index. For the proof of convergence, we refer to [3]. III. J OINT MLB, ICIC, AND ESM O PTIMIZATION The more traffic has to be served by a BS, the higher is its load and the smaller is the fraction of resources that can be allocated for another user requesting a data file transfer. Hence, according to [8], the throughput regarding BS i at location u can be modeled as ti (u, η) = ci (u, η)(1 − ηi )

(13)

Since the user throughput is one of the most crucial performance indicators in mobile networks, its optimization is envisaged in this paper. A. Problem Formulation Defining our objective function (OF) as  ln (1 − ηi (P, B)) Φ (η) =

(14)

i∈N

and adopting principles from [3] and [9], we formally state our optimization problem as maximize P,B

Φ(η)

subject to 0  η  1, η = f (η), 0  B  1, B1 = 1

(15)

Note that we explicitly require the load vector η to be solved by the fixed-point iteration (12) and the 1-norm of B to be one, i. e., the entire frequency band to be utilized. Using our OF (14) and exploiting the two degrees of freedom P (2) and B (4), we maximize the geometric mean of the network’s available resources, which is suitable for enhancing the performance in terms of user throughput [9]. B. User Association and Bandwidth Allocation Algorithm Since the optimization of the partition P and the bandwidth vector B are differently structured optimization problems, we split the solution to Problem (15) into two separate optimization steps, which are performed in alternation. First, the partition is determined with the aid of a throughput-optimal user association rule (UAR) for a fixed bandwidth vector B

and, afterwards, the optimal bandwidth vector is obtained with a directed search algorithm. 1) User Association: In the first step of the alternating optimization, the cell areas Li and the corresponding cell loads η are computed for a fixed bandwidth vector B, i. e., for fixed subband widths. Using (13) we define our loaddependent and throughput-optimal UAR as s(u, η) = argmax tj (u, η) j∈N

(16)

We then define the cell areas as Li = {u ∈ L | i = s(u, η)}

(17)

The cell areas Li in (10) are therefore a function of the load vector η. Nevertheless, Iteration (12) can still be applied and, thus, the user association and the computation of the cell areas Li are inherent in the computation of the cell loads. It is important to note that determining the fixed point in (12) with the cell area definition in (17) exactly gives a solution to (15) for a given bandwidth vector B, compare, [3], [9]. According to (16), users tend to connect to lower loaded BSs in order to experience an increased throughput, which constitutes our method for MLB. Note that the cell areas defined by (17) need be transformed to standard-compliant cell individual offsets (CIOs) or cell range expansion (CRE) offsets for small cells for which a method can be found in [3]. 2) Bandwidth Allocation: In the second step, the bandwidth vector B (i.e., the widths of the subbands) is optimized. Since (15) contains the non-affine equality constraint η = f (η), it is not a convex optimization problem. Furthermore, the calculation of the derivatives — both analytically and by numerical approximation — is very complex due to the implicit definition of the cell load η. Therefore, standard minimization algorithms, which are fast and do guarantee global optimality, are not applicable. Instead, we use a modified version of the Nelder and Mead algorithm (NMA) [10] to optimize B 3 . We use the NMA to solve (15) by optimizing the bandwidth vector B for a fixed partition P. However, the NMA does not guarantee the convergence to the global optimum. Nevertheless, the NMA improves Φ, which is sufficient for network optimization because the global optimum might only be found at a prohibitively large cost. Originally, the NMA is an algorithm for unconstrained problems. However, there are a number of equality and inequality constraints in Problem (15). The constraints on the load vector η are handled by solving System (11) with the help of the fixed point iteration at each point the OF is evaluated at. The upper and lower bound for each element in B are handled by projecting any infeasible points to the boundary of the optimization space. Finally, the equality constraint on B is handled by optimizing only over the first m−1 elements of B. The remaining element is then explicitly given by the equality constraint and can be calculated as bm = 1 − l=m bl . If bm 3 NMA evaluates the objective function Φ at certain points in the optimization space and from this information it makes ’smart’ guesses as to where to search for an improved Φ.

violates the bounds in order to fulfill the equality constraint, a penalty function is added to the OF. The two steps user association and bandwidth allocation are alternated until the OF Φ converges or a defined number of iterations exceeds a maximum.

Macro BS Pico BS Base traffic HS traffic

Algorithm 1 Capacity Management Algorithm

Analysis area

1: repeat 2: 3: 4: 5: 6: 7: 8: 9:

solve system (11) with iteration (12) for fixed B executeNelderMead on B for fixed P until Φ(k) − Φ(k−1)  <  or k > kmax for all (i ∈ N ) do  if l ai,l bl = 0 then turn BS i off end if end for

C. Smart Cell Switching For a low traffic demand, mBS may serve the users well without the support of pBS. We observe that the bandwidth allocation optimization in Section III-B2 tends to allocate zero bandwidth to pBS in low traffic scenarios. A simple ESM procedure to decrease energy consumption is therefore to simply switch off  the BSs which have not been allocated any bandwidth, i. e., l ai,l bl = 0. This last step, which we call smart cell switching, is executed only for pBSs after the alternating optimization as described in the previous section has terminated. An overview of the combination of the three mechanisms can be found in Algorithm 1, with k being an iteration index. IV. N UMERICAL S TUDIES In order to verify our optimization approach, we numerically assessed the algorithm’s performance using a basic test scenario. A. Evaluation Scenario We use an evaluation scenario as depicted in Fig. 1. It consists of a generic hexagonal macro layer on a flat plane with an inter-site distance of 1050 m. In order to avoid boundary effects, we consider an additional outer ring of base stations, located in the simulation area (dashed line borders), and only evaluate the performance in the analysis area (solid line borders). The former and the latter areas have a size of approx. 2.72 km2 and 0.96 km2 , respectively. The analysis area essentially contains one site with three sectors served by mBSs with directional antennas. Users inside the analysis area are never served by the outer mBS, and vice versa. Also, only the BS in the analysis area are optimized and our OF (14) is only evaluated there. In addition to the mBS, seven pBS are located within the analysis area, where groups of two, four, and one pBS are deployed in the serving cell areas of the mBS, respectively. An overview of BS parameters and scenario settings can be found in Table I. We consider a heterogeneous traffic distribution consisting of a homogeneous ’base’ layer and a ’hot spot’ layer with

Simulation area

Fig. 1.

Evaluation scenario layout.

TABLE I BASE STATION AND SCENARIO PARAMETERS .

Scenario Parameter Link budget User association Traffic User mobility Scheduler User rate BS Parameter Carrier frequency Max. bandwidth Noise figure Height over ground Max. transmit power Antenna gain

Description COST-Hata path loss [11], realistic 3D ant. patterns throughput optimal (16) mean arrival intensity, mean file size (2MByte) (3) static Round Robin Shannon capacity (9) mBS

pBS

2.1 GHz 10 MHz 6 dB 30 m 43 dBm 18 dBi

2.1 GHz 10 MHz 6 dB 12 m 30 dBm 11 dBi

rectangular hot spots of 100 m×100 m centered at the pBS sites as can be seen in Fig. 1. We independently configure the traffic densities of the base and hot spots layers with the hot spot density typically being higher. For our purposes, we consider varying the arrival density of the hot spots only, except for the lowest traffic demand, where the traffic intensity of the base layer is also reduced. For the bandwidth allocation optimization, the pBS are grouped according their common location in the macro serving cell areas as described above. Consequently, considering three mBS and three groups of pBS, there exist six different admission vectors Ai and 26 − 1 = 63 subbands bl , which is in the same order of magnitude as the 50 PRBs in a 10 MHz LTE system. B. Simulation Results 1) Effects on the User Throughput: The results in terms of the user throughput (13) are depicted in Fig. 2. It depicts the 5th, 50th, and 95th percentile of the user throughput for different traffic demands, both for the unoptimized FFR case with all BSs being turned on and the optimized case. It can be observed that all percentiles decrease for increasing traffic, which is due to the overall higher load in the BSs. However, we can further observed that there exist two regions,

one for low traffic demand where the decrease is steady in both cases and one for higher demand where the unoptimized throughput drops much steeper. The two regions can be explained when taking smart cell switching into account. throughput percentiles in Mbps

100

10

1

Q5FFR Q5 Q5optopt Q50 11 Q50FFR q50 opt Q50opt q95 11 FFR Q95 q95 opt Q opt " "95

0.1

0.01 0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 total traffic in Mbps

1.2

8 7

1

6 0.8

common bandwidth number of pico BS on

0.6

5 4 3

0.4

2 0.2

1

0

number of pico BS on

normalized common bandwidth

Fig. 2. Percentiles of user throughput before and after bandwidth optimization as a function of the total traffic demand.

0 0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32

total traffic in Mbps

Fig. 3. Size of the common band and number of pBS that are turned on as a function of the total traffic demand.

As can be studied in Fig. 3, for a total traffic demand below 20 Mbps several pBS are turned off. In contrast, all pBS are turned on for demands higher than 20 Mbps. At the same time, the common bandwidth is one for low traffic and only starts to decrease at the point where all pBS are turned on. This means, that for low traffic, pBS can be turned off while the rest of the BSs employ FFR. This yields only small improvement in throughput compared to the FFR case where all BS are turned on, but in addition saves energy. For high traffic demand, all BS are turned on and the bandwidth is split between cells to achieve ICIC. In high traffic scenarios, the range extension effect of the UAR for pBS is considerably large and induces that many users are forced to connect to a cell that offers suboptimal rates and hence suffer from strong interference. Therefore, ICIC has its greatest effect and greatly improves the user throughput. We can conclude that bandwidth allocation only makes sense in high load scenarios. 2) Smart Cell Switching: The smart cell switching is a direct by-product of the bandwidth allocation algorithm. This is a remarkable result as no sophisticated additional algorithm is needed, it is an inherent property of maximizing the OF (14) including the bandwidth optimization. For a low traffic demand, the pBS serve only few users, yet act as interferers for many. Therefore, it is beneficial to assign zero bandwidth to certain pBSs. V. C ONCLUSIONS In this work, we extended a verified framework for cell area optimization to get a joint optimization for MLB, ICIC/eICIC,

and ESM SON use cases. We added a bandwidth allocation as an effective ICIC scheme to the framework by fractioning the available bandwidth and allowing only certain BSs to transmit in each subband. Using this scheme, the bandwidth allocation can continuously be varied between orthogonal frequencies for each BSs and full frequency reuse. We apply the well-known Nelder-Mead algorithm to optimize this bandwidth allocation and combined it iteratively with an existing algorithm for the MLB use case. We evaluated the joint algorithm in a simple heterogeneous test scenario and show that the proposed method can not only greatly increase the throughput in times of high traffic demand, but during hours of low traffic the joint algorithm inherently determines which BSs can be turned off because it assigns zero bandwidth to those BSs. By exploiting this property, an optimization for the ESM use case could also be included into the algorithm. ACKNOWLEDGEMENT The work presented in this paper was partly sponsored by the government of the Free State of Saxony, Germany, and by the European Regional Development Fund (ERDF) within the Cool Silicon Cluster of Excellence under contracts 31529/2794 and 14056/2367. R EFERENCES [1] L. Schmelz, M. Amirijoo, A. Eisenbltter, R. Litjens, M. Neuland, and J. Turk, “A coordination framework for self-organisation in LTE networks,” IFIP/IEEE International Symposium on Integrated Network Management, Dubin, Ireland, May 2011. [2] A. Lobinger, S. Stefanskiy, T. Jansen, and I. Balan, “Coordinating Handover Parameter Optimization and Load Balancing in LTE Self– Optimizing Networks,” in IEEE VTC Spring, Budapest, Hungary, 2011. [3] A. Fehske, H. Klessig, J. Voigt, and G. Fettweis, “Concurrent load-aware adjustment of user association and antenna tilts in self-organizing radio networks,” Vehicular Technology, IEEE Transactions on, vol. PP, no. 99, pp. 1–1, 2013. [4] P. Fotiadis, M. Polignano, D. Laselva, B. Vejlgaard, P. Mogensen, R. Irmer, and N. Scully, “Multi-Layer Mobility Load Balancing in a Heterogeneous LTE Network,” IEEE Vehicular Technology Conference (VTC), Quebec City, Quebec, Canada, September 2012. [5] J. Peng, P. Hong, K. Xue, and H. Tang, “A Dynamic Energy Savings Scheme Based on Enhanced Mobility Load Balancing,” IEEE Vehicular Technology Conference (VTC), Quebec City, Quebec, Canada, September 2012. [6] A. Damnjanovic, J. Montojo, J. Cho, H. Ji, J. Yang, and P. Zong, “UE’s role in LTE advanced heterogeneous networks,” Communications Magazine, IEEE, vol. 50, no. 2, pp. 164–176, 2012. [7] A. J. Fehske and G. P. Fettweis, “Aggregation of Variables in Load Models for Cellular Data Networks,” in Proceedings of the International Conference on Communication, ICC 2012, 2012. [8] S. B. Fred, T. Bonald, A. Proutiere, G. R´egni´e, and J. W. Roberts, “Statistical bandwidth sharing: A study of congestion on flow level,” in Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications - SIGCOMM ’01, vol. 31, no. 4. New York, New York, USA: ACM Press, Aug. 2001, pp. 111–122. [9] H. Kim, G. de Veciana, X. Yang, and M. Venkatachalam, “Distributed α-Optimal User Association and Cell Load Balancing in Wireless Networks,” IEEE ACM Transactions on Networking, vol. 20, no. 1, pp. 177–190, Feb. 2012. [10] J. A. Nelder and R. Mead, “A simplex method for function minimization,” The Computer Journal, vol. 7, no. 4, pp. 308–313, 1965. [11] COST Hata pathloss model, Online: http://www.lx.it.pt/cost231/ final report.htm, 2/26/2012.