Surrogate based centralized automated optimizationapplied to LTE mobility load balancing

Yasir Khan, Berna SayracOrange Labs

38, rue du Gnral Leclerc92794, Issy les Moulineaux, France

Email: {yasir.khan,berna.sayrac}@orange.com

Eric MoulinesDpartement Traitement du Signal et des Images,

Tlcom Paris Tech, 46, Rue Barrault75634, Paris Cedex 13, France

Email: moulines@telecom-paristech.fr

AbstractDeployment of Long Term Evolution (LTE) & LTE-Advanced networks will be challenged by cost and complexity.Self Organizing Network (SON) functionalities promise signif-icant improvement of the network in terms of reducing OP-erational EXpenditure (OPEX) and performance improvement.In this paper, we propose a recursive automated optimizationmethod which builds statistical models of the functional re-lationships between noisy Key Performance Indicators (KPIs)and network parameters; and performs stochastic optimizationduring the model building process. The proposed methodologyis applied to a centralized intra-LTE Mobility Load Balancing(MLB) problem and its performance is evaluated through systemlevel simulations. The results show that the proposed modelingand optimization approach is a promising solution for centralizedintra-LTE MLB in terms of optimization performance andconvergence under noisy data.

Index TermsAutomated Optimization; Mobility Load Bal-ancing; Self-optimization; Kriging; Expected Improvement

I. INTRODUCTION

Self Organizing Networks (SON) is a promising conceptwhich improves capacity, quality, reduces operational costsand delays infrastructural investments [1]. Among the self-optimizing use cases defined in [2], intra-LTE Mobility LoadBalancing (MLB) aims at autonomously adapting mobilityparameters to provide a balanced load between the EvolvedNode Bs (abbreviated as eNodeBs or eNBs) thus increasingthe capacity and improving the Quality of Service (QoS) forthe users in the overloaded eNB(s).

A great majority of intra-LTE MLB solutions put forwardso far are distributed solutions where mobility parametersare adjusted by the serving eNB which cooperates with theneighboring eNBs [3], [4], [5]. Alternatively, solutions wherea centralized entity that is typically located at the operatorsmanagement plane have attracted limited attention [6], [7],[8]. Although distributed solutions have the potential to followtraffic variations at a smaller scale and therefore provide afiner load balance, high-performance centralized solutions arenecessary for the operators not only as a benchmark, but alsoas an efficient means to perform and control their own networkoptimization.

The focus of this paper is on centralized intra-LTE MLBwhich has been rarely considered in the literature so far [6],[7], [8]. In [8], the authors have proposed a simple heuristic

algorithm whose solution is found by integer programming. In[6], [7], a statistical learning framework is used to estimate thefunctional relationships between the KPIs and Radio ResourceManagement (RRM) parameters. After a training phase wherean initial model is built from a training dataset, a recursive al-gorithm that simultaneously enhances the model and performsoptimization is proposed. The main challenge of this approachis to construct a reliable model. Several techniques havebeen discussed such as Multiple Linear Regression (MLR)[6] and Logistic Regression (LR) [7]. Although LR modelsthe saturation effects at the extremities better than MLR, theyboth suffer from the same drawbacks such as the necessity ofhaving a large training dataset and the sensitivity of the initialmodel to measurement errors/noise. Besides, they are basedon fixed predefined model shapes (linear, logistic).

This paper follows the line of work [6], [7] and focuses oncentralized automated optimization based on statistical mod-eling. Statistical models rely on observations. In a centralizedoptimization context, these observations are KPIs which areobtained through statistical processing of the measurementmetrics, counters etc. at the management plane. These KPIshave a relatively low temporal granularity (from hours toyears). Considering that the reliability of statistical modelsincreases with increasing number of data points, the re-quired amount of time for a reliable statistical model maybe prohibitively large. Furthermore, learning-based automatedoptimization algorithms may perform parameter changes atthe extremes of the parameter value range, creating a risk ofQoS deterioration for the end user. Therefore, model-buildingand optimization must be done with a minimum number ofparameter changes.

This paper addresses all the above mentioned challenges andproposes a stochastic model-based fast converging optimiza-tion method for centralized intra-LTE MLB. The stochasticmodel acts as a surrogate for the parameter-KPI relationshipsand does not require a large training dataset. The optimizationuses this surrogate model to find the parameter value thatmaximizes the expectation of a stochastic improvement criteria[9], [10], [11], which is linked to the MLB objective function.The surrogate model construction and the optimization ofthe expected improvement criteria follow one another in arecursive fashion until the optimization solutions converge. To

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

Figure 1: A typical MLB scenario

the best of our knowledge, such a problem within the contextof self-optimization has not been studied in the literature sofar, and this forms the main contribution of this paper.

The remainder of the paper is organized as follows. SectionII provides a description of the LTE system and the loadbalancing scenario. Section III details out the surrogate basedautomated optimization technique with description of Krigingused for model development and the constrained expectedimprovement criteria used for recursive optimization. SectionIV provides the simulation descriptions and the results arepresented in Section V. The paper is concluded in Section VI.

II. LTE MOBILITY LOAD BALANCINGLet us assume a cluster of cells in a network as shown in

Figure 1. A typical MLB scenario consists of one or moreneighboring overloaded cells, also known as a hotspot trafficzone as shown. Let G1 denote the group of loaded cells andG2 the group of unloaded cells in the cluster of interest.Let us assume neighboring cell pairs with indexes (s, t). TheHandover Margin (HM) from cell s to cell t is denoted byHMs,t (in dB), where s G1, t G2 Ns and Ns is theneighbor set index of cell s.

Intra-LTE MLB consists of tuning the HM parameter of thehandover procedure defined by the A3 event for LTE [1]. Theaim of MLB is to balance the loads between neighboring eNBsby offloading loaded eNBs towards less loaded eNBs. Duringthe handover procedure, the mobile is handed over from thesource cell s to the target cell t if RSRPt RSRPs+HMs,t,where RSRPx is the Reference Signal Received Power fromcell x in dBm. For better sensitivity of the eNB loads toHM changes, we assume a bi-directional change of HM, i.e.HMt,s = 10dB HMs,t.

For the scenario considered in Figure 1, we assume auniform setting of the HM parameter, i.e. only one HMs,tvalue, s G1, t G2 Ns (shown by red arrows in thefigure). Let us denote this value of HMs,t by x. Then, theobjective function of the MLB can be written as:

x = argmin f (x)x

s.t. BCRt (x) ThBCR, t G2 Ns

DCRt (x) ThDCR, t G2 Ns (1)where f (x) =

sG1,tG2Ns [loads (x) loadt (x)]

2,

loads (x) and loadt (x) are the cell loads, BCRt (x) andDCRt (x) are the Block Call Rate (BCR) and the Drop CallRate (DCR) of cell t respectively, ThBCR and ThDCR arethe upper limit thresholds on the BCR and DCR respectively,s G1, t G2 Ns.

III. STOCHASTIC MODELING AND OPTIMIZATIONWe propose to solve this optimization problem by defining

stochastic models that describe the following relationships:f (x), BCRt (x), DCRt (x), s G1, t G2 Ns. Thisstochastic modeling is carried out through a technique knownas Kriging. Models developed using Kriging are then usedin a stochastic sequential optimization technique based on aninfill criteria called Expected Improvement.A. Kriging model

Let Y denote the variable (KPI and/or a function of theKPIs) that we would like to model, i.e. f (x), BCRt (x),DCRt (x), s G1, t G2 Ns. The aim is to find astochastic model for Y (x). Kriging assumes that Y (x) maybe expressed as follows [9]:

Y (x) = + Z (x) + (x)

where R is the unknown but deterministic constant trend,Z (x) is the underlying stochastic model which is a Gaussianprocess with zero mean and transition-invariant covariancekernel (x, x), x R. (x) is the additive noise term withzero mean and covariance kernel 2 (x, x) , x R, (x, x)is the Kroenecker delta function and 2 is the noise variance. (x) is assumed to be independent from Z(x).

Given the noisy observations of Y (x), Yn = [y1y2...yn]Tat the x values Xn = [x1x2...xn]T, where yi = Y (xi) , i =1...n, Kriging finds the Best Linear Unbiased Prediction(BLUP) Yn (x) at any unobserved point x, (Best being interms of conditional quadratic error criterion), i.e. Krigingminimizes the prediction error variance conditioned on theobservations as [10]:

E[(

Yn (x) Y (x))2

| Yn]

(2)

where E [. | .] denotes conditional expectation.The value of Yn (x) which minimizes (2) is the conditional

mean of Y (x) given by mYn (x) E {Y (x) | Yn}. Itsprediction error variance is s2Yn (x). Solving the minimizationin (2) for a linear predictor yields [9]:

mYn (x) = n + n (x)T1n (Y

n 1n) (3)

s2Yn (x) = 2

[An +

A2n1Tn

1n 1n

](4)

where An = 1 n (x) T1n n (x), n is the n ncorrelation matrix whose (i, j)thentry is equal to:

n (i, j) =

{ (xi, xj) + 2 i = j

(xi, xj) i = jfor i, j = 1..n

n =1Tn

1n Yn

1Tn1n 1n

is the best linear unbiased estimate of ,n (x) = [ (x, x1) (x, x2) ... (x, xn)]

T is the correlationof the unobserved point with the existing (observed) points,1n is the n 1 vector of 1s and 2 is the estimated noisevariance. A Gaussian anisotropic covariance kernel is assumed,given by (x, x) = 2 exp

[ (x x)p] , x, x R. Theestimation of the covariance kernel parameters p, 2 and are based on the Maximum Likelihood Estimation (MLE)which maximizes the likelihood function of Yn conditionedon p, 2and . This is equivalent to minimizing the negativelog-likelihood with respect to p, 2and given by [9]:

log (det [n]) + (Yn 1n)T 1n (Yn 1n) (5)

B. Expected ImprovementSuppose we have built the Kriging models for f (x),

BCRt (x), DCRt (x), t G2 Ns based on the nobservation data points (Xn,Yn):

Fn (x) is the Kriging model for f (x) which is Gaussianwith conditional mean mFn (x) and variance s2Fn (x),

BCRtn (x) is the Kriging model for BCRt (x) which isGaussian with conditional mean mBCRtn (x) and variances2BCRtn

(x), DCRtn (x) is the Kriging model for DCRt (x) which is

Gaussian with conditional mean mDCRtn (x) and variances2DCRtn

(x).

Since the model Fn (x) of the objective function is notdeterministic but random, we proceed as follows for its mini-mization:

We first define the "improvement" achieved by the Krigingprediction Fn(x) over the n observed values: In (x) fminn Fn (x) where fminn = minx{x1,x2,...,xn} F (x) [9], [10], [11].Thus In (x) is also Gaussian with mean fminn mFn (x) andvariance s2Fn (x). The optimum x value, x

, which minimizes

Fn(x) is that value which maximizes our expectation of havingan improvement over all the n observed values. The solutioncan thus be given by:

x = argmaxx

E [In (x)]

whereE [In (x)] = sFn (x)

{u2

[1 + erfc

(u2

)+ 1

2eu

2/2]}

,

u = fminn mFn (x)

sFn (x).and erfc (.) is the complementary error

function [10]. However, it must be noted that x must alsosatisfy the constraints on BCR and DCR of equation (1). Inother words, those values of x which do not satisfy theseconstraints must be discarded. Thus, we restrict the solutionspace to those x values which satisfy the constraint by defininga measure of feasibility:

Fn (x) =

tG2NsPr[

BCRtn (x) ThBCR]

Pr[

DCRtn (x) ThDCR]

Figure 2: Functional block diagram of the proposedautomated optimization

Considering the Kriging model of BCRtn (x) and DCRtn (x)which are Gaussian random variables, it can be shown that[10]:

Fn (x) =

tG2Ns

{1 1

2erfc

[ThBCR mBCRtn (x)

2sBCRtn (x)

]}{1 1

2erfc

[ThDCR mDCRtn (x)

2sDCRtn (x)

]}

This feasibility measure is incorporated into the constrainedoptimization problem as a multiplicative term which rendersthe objective function zero for those x values that do not satisfythe constraints. Thus the optimum x value can be obtained by:

x = argmaxx

{E [In (x)]Fn (x)} (6)

C. Iterative modeling and optimization

The Kriging model and the subsequent stochastic optimiza-tion yield x, i.e. an optimum value for HMs,t. By injectingthis value into the network, we obtain the correspondingKPI/function values of loads(x), loadt(x), f (x), BCRt (x),DCRt (x), s G1, t G2 Ns for x. It means that, foreach KPI/function, we obtain y = Y (x). This value can beappended to the existing dataset [Xn,Yn] as the (n + 1)stobservation point. Hence, the new observation dataset (foreach KPI/function) now has n+ 1 points represented as:

Xn+1 = [x1x2...xnxn+1]T,Yn+1 = [y1y2...ynyn+1]

T

We can update the Kriging model for each KPI/function withthis new observation dataset and then carry out a stochasticoptimization (Expected Improvement) with the refined Krigingmodels, at the end of which, we obtain another optimumHMs,t value. Proceeding this way, we can have an iterativeprocedure where: 1-we start with an initial observation datasetwith n points, 2-at each iteration k, we carry out a Krigingmodeling followed by stochastic optimization and we obtaina new (optimum) observation point, 3-this point is appendedinto the observation set to be used at the next iteration. Theblock diagram of such an iterative procedure is depicted inFigure 2.

Parameters SettingsSystem bandwidth 5 MHz

Cell layout 15 sites, tri-sectorMaximum eNB transmit power 32 dBm

Inter-site distance 1.5 to 2 KmSubcarrier spacing 15 kHz

PRBs per eNB 25Path loss L=128.1+37.6log10(R), R in Km

Thermal noise density -173 dBm/HzShadowing standard deviation 6 dB

Traffic model FTPFile size 8000 Kbits

PRBs assigned per mobile 1 to 4 (First-come, first-served basis)Mobility of mobiles 90%

Mobile speed 30 Km/hCall arrival rate 2.4 users/second (50% in hotspots)HMmax 10dB

Regional traffic distribution 50% (hotspot), 50% (Non hotspot)

Table I: System level simulation parameters

IV. SIMULATOR DESCRIPTIONA typical regular network layout comprising 15 sites with

3 cells (eNBs) per site is used [6], [7]. We consider downlinktransmissions. Table I lists the simulation parameters used. AnLTE simulator developed in MATLAB tool and describedin [3], [7] has been used for simulations. The simulatorperforms correlated snapshots, and at the end of each timestep of 1s, new mobiles enter the system, those that end theircommunications leave and the spatial positions of mobiles incommunication are updated. Each simulation yields a datapoint (xi, yi), i = 1, ..., n, ..., n + k, ..., n + K, for themodel building and lasts for 3000s. This corresponds to thetemporal granularity of the filtering period of KPIs foundtypically in real networks. The KPIs are used by the automatedoptimization method to determine the new parameter settingswhich are then fed to the simulator for the next 3000s ofsimulation.

V. RESULTSIn our simulations, s {1} and t {2, 3, 11, 14, 15, 18}

is the first tier geographical neighbors of s. The network isassumed to be non-optimized, operating at HMs,t = 10 dBs G1, t G2Ns. Two other initial data points at 0 and6 dB are assumed to be known, thus n = 3. Figure 3, Figure4 and Figure 5 show the observed data points and the Krigingcurves for the DCRs, BCRs and f as a function of HMs,t foreNBt, t G2 Ns.

Figure 6 shows the expectation of improvement and theconstrained expectation of improvement curves for the opti-mization steps. At k = 1, the expectation of improvementE [I (HM)], is high in the region close to the minimum off , but the constrained expectation of improvement forces thealgorithm to move in the direction of constraint feasibility,proposing a solution at HMs,t = 8.242 dB. Although at thisiteration, the constraint is satisfied, there is scope for furtherimprovement in the objective minimization, as is indicatedby E [I (HM)]F (HM) curve, resulting in the next proposedsetting HMs,t = 7.5 dB. Convergence of the algorithm is

0 1 2 3 4 5 6 7 8 9 100

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

HM (dB)

Mea

n D

CR

Observed data of eNB11Observed data of eNB14Observed data of eNB15Observed data of eNB2Observed data of eNB18Observed data of eNB3Kriging curve of eNB11Kriging curve of eNB14Kriging curve of eNB15Kriging curve of eNB2Kriging curve of eNB18Kriging curve of eNB3Constraint

Figure 3: DCR observation points and corresponding Krigingcurves as a function of HM (ThBCR = 0.05)

0 1 2 3 4 5 6 7 8 9 100.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

HM (dB)

Mea

n BC

R

Observed data of eNB11Observed data of eNB14Observed data of eNB15 Observed data of eNB2Observed data of eNB18Observed data of eNB3Kriging curve for eNB11Kriging curve for eNB14Kriging curve for eNB15Kriging curve for eNB2Kriging curve for eNB18Kriging curve for eNB3Constraint

Figure 4: BCR observation points and corresponding Krigingcurves as a function of HM (ThBCR = 0.05)

indicated by a very low E [I (HM)]F (HM) at K = 2. Notethat due to constraints, the optimum parameter setting hasmoved towards the right hand side of HMs,t = 4 dB, eventhough the minimum of the objective function exists towardsits left. As can be observed from Figures 7 and 8, the optimizedparameter setting substantially enhances the QoS in s, whilecausing a tolerable QoS degradation in t within the initiallyset constraint limits. The optimization results in a 55.83% and16% reduction in DCR and BCR respectively.

We can clearly see from Figures 7 and 8 that as the BCRconstraint is loosened to 6.5%, more traffic is offloaded toneighboring eNBs thus further improving the user perceivedQoS. It can also be observed that the optimum HM value is acompromise between the guaranteed QoS for the neighboringeNBs and the quantity of traffic to be offloaded from theoverloaded eNB.

VI. CONCLUSIONWe presented in this paper, a novel centralized recursive

automated optimization method for intra-LTE MLB, whichuses a stochastic model as a surrogate for the function to be

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

HM (dB)

f(HM)

Observed dataPredictionTrue function

Figure 5: Objective function points and correspondingKriging curves as a function of HM (ThBCR = 0.05)

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

E[I(H

M)]

k=0

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

Cons

tr. E

[I(HM)

]

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

E[I(H

M)]

k=1

0 1 2 3 4 5 6 7 8 9 100

2

4x 103

Cons

tr. E

[I(HM)

]

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

E[I(H

M)]

HM (dBm)

k=2

0 1 2 3 4 5 6 7 8 9 100

2

4x 10134

Cons

tr. E

[I(HM)

]

HM (dBm)

Figure 6: Updates using maximum E [I (HM)]F (HM)(ThBCR = 0.05)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

eNB1 eNB11 eNB14 eNB15 eNB18 eNB2 eNB3

Mea

n BC

R

Before optimizationAfter optimization 5% BCR constraintAfter optimization 6.5% BCR constraint

Figure 7: Neighboring eNB BCRs with reference andoptimized solutions

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

eNB1 eNB11 eNB14 eNB15 eNB18 eNB2 eNB3

Mea

n D

CR

Before optimizationAfter optimization 5% BCR constraintAfter optimization 6.5% BCR constraint

Figure 8: Neighboring eNB DCRs with reference andoptimized solutions

optimized. The proposed approach has several advantages: thealgorithm converges in extremely small number of iterationsto find the optimal network setting thus making it well suitedfor centralized implementations at the management plane, thealgorithm has been shown to yield promising results with noisynetwork data and can be used to model any smooth functionshape thus making this approach very generic. Besides itnever requires a regularly spaced sampled data. Future workis positioned towards studying the effect of the number ofinitial data points on the Kriging model and to study thesensitivity of the optimization method to system parameters.Multi-parameter optimization which is a common challenge inmanagement of complex networks is also envisaged.

REFERENCES[1] J. Ramiro, K. Hamied, Self-Organizing Networks (SON): Self-

Planning, Self-Optimization and Self-Healing for GSM, UMTS andLTE, Wiley, 2011.

[2] 3GPP, Self-configuring and self-optimizing network use cases andsolutions, TR 36.902, Sophia-Antipolis, France, Tech. Rep., 2009.

[3] R. Nasri, Z. Altman: Handover Adaptation for Dynamic Load Balanc-ing in 3GPP Long Term Evolution Systems, 5th MoMM2007, 3-5December, 2007.

[4] A. Lobinger et al., Load balancing in downlink LTE self-optimizingnetworks, IEEE 71st vehicular technology conference (VTC 2010-Spring), May 1619, 2010.

[5] I. Viering et al., A mathematical perspective of self-optimizing wirelessnetworks, IEEE ICC 2009, May 2009.

[6] M. I. Tiwana et al., Statistical learning for automated RRM: Applicationto eUTRAN mobility IEEE Int. Conf. on Communications, ICC 2009,Aug. 2009.

[7] M. I. Tiwana et al., Statistical learning-based Automated Healing:Application to Mobility in 3G LTE Networks IEEE Int. Symp. onPIMRC, Sept. 2010.

[8] J. Suga et al., Centralized mobility load balancing scheme in LTEsystems, 8th ISWCS 2011, November 6-9, 2011.

[9] V. Picheny et al., "A benchmark of kriging-based infill criteria for noisyoptimization", Structural and Multidisciplinary Optimization, on press,2013, preprint: http://hal.archives-ouvertes.fr/hal-00658212/

[10] A. I. J. Forrester et al., Engineering Design via Surrogate Modelling:A Practical Guide, John Wiley & Sons, Chichester, ISBN 978-0-470-06068-1.

[11] D. Jones, A taxonomy of global optimization methods based onresponse surfaces, Journal of Global Optimization, Vol. 21, pp. 345-383, 2001.

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