a unified algorithm for mobility load balancing in 3gpp lte multi-cell networks

7/29/2019 A Unified Algorithm for Mobility Load Balancing in 3GPP LTE Multi-cell Networks

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. RESEARCH PAPER .Special Issue

SCIENCE CHINA

Information SciencesFebruary 2013, Vol. 56 022311:1022311:11

doi: 10.1007/s11432-012-4769-2

c Science China Pres s and Springer- Verlag B erlin H eidelberg 2013 info. scichina.com w ww. springerlink.com

A unified algorithm for mobility load balancingin 3GPP LTE multi-cell networks

WANG Hao1,2, LIU Nan1, LI ZhiHang1, WU Ping2, PAN ZhiWen1 & YOU XiaoHu1

1National Mobile Communications Research Laboratory, School of Information Science and Engineering,

Southeast University, Nanjing 210096, China;2Department of Engineering Sciences, Uppsala University, Uppsala 75121, Sweden

Received September 20, 2012; accepted October 19, 2012

Abstract 3GPP long term evolution (LTE) is a promising candidate for the next-generation wireless network,

which is expected to achieve high spectrum efficiency by using advanced physical layer techniques and flat

network structures. However, the LTE network still faces the problem of load imbalance as in GSM/WCDMA

networks, and this may cause significant deterioration of system performance. To deal with this problem, mobility

load balancing (MLB) has been proposed as an important use case in 3GPP self-organizing network (SON), in

which the serving cell of a user can be selected to achieve load balancing rather than act as the cell with the

maximum received power. Furthermore, the LTE network aims to serve users with different quality-of-service

(QoS) requirements, and the network-wide objective function for load balancing is distinct for different kinds of

users. Thus, in this paper, a unified algorithm is proposed for MLB in the LTE network. The load balancing

problem is first formulated as an optimization problem with the optimizing variables being cell-user connections.

Then the complexity and overhead of the optimal solution is analyzed and a practical and distributed algorithm

is given. After that, the proposed algorithm is evaluated for users with different kinds of QoS requirements, i.e.,

guaranteed bit rate (GBR) users with the objective function of load balance index and non-GBR (nGBR) users

with the objective function of total utility, respectively. Simulation results show that the proposed algorithm

leads to significantly balanced load distribution for GBR users to decrease the new call blocking rate, and for

nGBR users to improve the cell-edge throughput at the cost of only slight deterioration of total throughput.

Keywords self-organizing network (SON), mobility load balancing (MLB), quality-of-service (QoS), load

balance index, total utility

Citation Wang H, Liu N, Li Z H, et al. A unified algorithm for mobility load balancing in 3GPP LTE multi-cell

networks. Sci China Inf Sci, 2013, 56: 022311(11), doi: 10.1007/s11432-012-4769-2

1 Introduction

3GPP long term evolution (LTE) network can achieve high spectrum efficiency due to the usage of flat

network structures and advanced physical layer techniques, i.e., orthogonal frequency division multiple

access technology and multi-input and multi-output antennas [13]. However, as in GSM/WCDMA net-works, the system performance is still influenced by unbalanced load distribution among nearby cells [46].

To deal with this problem, real-time inter-cell optimization is needed. Previous inter-cell optimizations in

Corresponding author (email: hao [email protected])


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Wang H, et al. Sci China Inf Sci February 2013 Vol. 56 022311:2

GSM/WCDMA networks are usually performed at the network planning stage, and often done manually;

thus it cannot remain optimal when the environments change. Hence, it is necessary for the network

to conduct inter-cell optimization dynamically and adaptively according to its environments, especially

when the loads of cells are not uniformly distributed, namely not balanced, and vary with time. This

issue has received much attention in 3GPP LTE self-organizing network (SON) [7], in which mobility

load balancing (MLB) is an important use case.

There have been lots of methods considering load balancing problem in wireless cellular networks,

among which cell breathing is a universal one applicable to arbitrary networks, e.g., WCDMA, WLAN

and LTE. Using cell breathing, the coverage of congested (or idle) cells is contracted (or expanded)

either by reducing (or raising) the pilot power [8,9] or by increasing (or reducing) the threshold of

handover [1012], thus making the load more balanced among cells. However, the granularity of cell

breathing is too large since lots of cell-edge users may be switched out to nearby cells indiscriminately

when only considering power factor, in which the discrepancy among users are ignored. Therefore, cell

breathing can hardly achieve the global optimum of the network-wide load balancing objective function

for all users. In circuit-switched networks (e.g., GSM), each active user is allocated a dedicated chan-

nel, and load balancing can be achieved through channel borrowing or dynamic channel allocation.

Please refer to [13] and the reference therein. However, neither of the two methods can be applied to

packet-switched networks (e.g., LTE and WCDMA), in which to support more users, a cell would use an

effective scheduling algorithm to allocate its time-frequency resources and therefore dedicated channels

no longer exist. Hence, the corresponding load balancing in packet-switched networks is often modeled

as an optimization problem on matching between users and cells according to different metrics [1417].

However, most previous researches on load balancing in packet-switched networks only consider users

without any quality-of-service (QoS) requirements, and therefore may be incomplete in the LTE networkwhich aims to serve users with different QoS requirements.

In this paper, we propose a unified algorithm to achieve MLB for users with different QoS require-

ments in the LTE network. In the proposed algorithm, a unified load balancing objective function for

homogeneous users with the same kind of QoS requirement is constructed with the variables being cell-

user connections. Then the complexity of the optimal solution is analyzed, which is proved to be an

NP-hard problem, and a practical and distributed algorithm is given. Then the proposed algorithm is

applied to two main QoS requirements in the LTE network [18], i.e., guaranteed bit rate (GBR) users

and non-GBR (nGBR) users, respectively. For GBR users, the load balancing objective is formulated as

the load balance index while that for nGBR users is formulated as the total utility. The effectiveness of

the proposed algorithm is verified by exhaustive simulations. Simulation results show that the proposed

algorithm performs very well for both GBR and nGBR users, thus lead to significantly balanced load

distribution for GBR users to decrease the new call blocking rate and for nGBR users to improve the

cell-edge throughput with only slight deterioration of total throughput. Finally, we consider the case

where both GBR and nGBR users exist in the network.

The rest of this paper is organized as follows. In Section 2, we give the system model. In Section 3,

the unified optimization problem is formulated and the complexity/overhead of the optimal solution is

analyzed, and then a practical and distributed algorithm is proposed. After that, both the problem

formulation and the proposed algorithm are applied to GBR and nGBR users respectively in Section 4.

Simulation results are given in Section 5. Coexistence of both GBR and nGBR users in the LTE network

is considered in Section 6 and the whole paper is concluded in Section 7.

2 System model

2.1 Network model

The unified problem formulation and algorithm proposed in this paper can be applied to LTE network

with any topology. For easy of presentation, a hexagonal network is considered here. As shown in Figure 1,

there are seven cells numbered with 1, . . . , 7, respectively, and each cell is controlled by a central eNodeB.


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3

1

24

5

6

7

Current link Possible link

b

eNodeB User

c

a

Figure 1 Network model.

Cell 1 is assumed to be an over-loaded one with more users than other cells. Its cell-edge users a, b

and c can also be served by cells 3 and 4, 5, 2 and 7, respectively. If cell 1 wants to handover some

users for load balancing, which users and which target cells should be chosen? In the following, we deal

with this problem by taking into consideration a unified load balancing objective function for all users

in the network. Throughout this paper, cell and eNodeB are used interchangeably, and the following

assumptions are made:

1) Each user knows the instantaneous signal strength from its serving cell and all the neighboring cells

through pilot measurements. All users send them back to their respective serving eNodeBs periodically.

2) Each eNodeB allocates power equally to all the PRBs being used.

3) Neighboring eNodeBs can exchange their load status information periodically through the X2 in-

terface [19].

4) Twelve adjacent subcarriers are grouped into a physical resource block (PRB), which is the smallest

unit that can be allocated to each user in a subframe (1 ms) [1].

5) All time t mentioned in this paper represents the time point to conduct load balancing handover,

and the span between any t and t + 1 is a load balancing cycle, which is much larger than a subframe.

C, K and Ki are used to denote the sets of cells, users and users served by cell i, respectively. A

cell-user connection variable Ii,k(t) is defined, which equals 1 when user k K is served by cell i C at

time t, and 0 otherwise.

2.2 Link model

The instantaneous signal to interference plus noise ratio (SINR) for user k K received on PRB l from

cell i C at a subframe is

SINRi,l,k() =gi,l,k() pt

N0 +

jC,j=i gj,l,k() pt, (1)

where

1) gi,l,k() represents the instantaneous channel gain between eNodeB i and user k on PRB l at

subframe . The channel gain takes into account the path loss, log-normal shadowing and fast fading.

2) pt represents the equal transmit power on each PRB. And gi,l,k() pt is the instantaneously received

signal strength of user k from cell i on PRB l at subframe .

3) N0 is the additive white Gaussian noise (AWGN) on a PRB. Without loss of generality, we assume

the noise level is the same for all PRBs.

(1) is justified for the case where all of the system resources are exhausted. Even for the case where

there are residual system resources, (1) is still meaningful and can be seen as a conservative low-bound of


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the practical received SINR. Given SINRi,l,k(), the instantaneous bandwidth efficiency ei,l,k() of user

k in cell i on PRB l at subframe is

ei,l,k() = log2[1 + SINRi,l,k()] (bps/Hz). (2)

Since load balancing is periodically conducted on a larger time scale rather than a subframe, we use

ei,k(t) to denote the expectation of the instantaneous bandwidth efficiency in (2) among all available

PRBs and subframes between time [t 1, t). Then the load occupied by user k in cell i at time t is

defined as

i,k(t) = f1(ei,k(t)), (3)

where f1() represents the mapping relation between the occupied load and the bandwidth efficiency of

user k in cell i, and it will be defined later in Section 4. Then the total load of cell i at time t is

i(t) =

kKi

i,k(t). (4)

2.3 A unified network-wide load balancing objective function

In this subsection, a unified network-wide load balancing objective function is defined as

Obj(t) = f(1(t), 2(t), 3(t), . . .), (5)

where f() denotes the mapping relation between the network-wide load balancing objective function and

the load of each cell in the network, which will be defined in Section 4 for both GBR and nGBR users.

3 Problem formulation, complexity/overhead analysis, and practical algo-rithm

3.1 Problem formulation and complexity/overhead analysis

A unified load balancing optimization problem is formulated with the optimization variables being cell-

user connections. Our objective is to make use of enforced handover to perform load balancing for

all users in the network, such that the maximum (or minimum) of the network-wide load balancing

objective function with the optimal cell-user connections can be achieved. This is equivalent to the

following constrained optimization problem:

P1: max Obj(t) (6)

s.t.iC

Ii,k(t) = 1, k K, (7)

iC

Ii,k(t)ei,k(t) , k K. (8)

Constraints in (7) imply that one user can only be served by one cell at a certain time t. Constraints

in (8) explain that the minimum bandwidth efficiency of any user k has to be satisfied strictly in its

serving cell, which is reasonable because a cell-center users often may not be served by nearby cells. It

is well-known that all minimization problems can be transformed into maximization problems with the

negative objective function. The optimization problem is formulated as a maximization problem in (6)for simplicity.

The above P1 is an integer optimization problem with the variable as cell-user connection Ii,k(t), which

is similar to the optimization problem in [17] and has been proved to be an NP-hard problem even if

the mapping relation f() is simple enough to be a linear combination of each cells load. To the best

of our knowledge, there are no effective methods, except brute-force search (BFS), to find the optimum.

However, the computational complexity of BFS is too tremendous. For example, if there exist p cells


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and q users in the network, the computational complexity of BFS increases with O(pq). Apart from the

computational complexity, BFS also has implementation difficulties. Firstly, a central unit to run BFS

is indispensable. Secondly, bandwidth efficiency information feedback from all users to the central unit

as well as the distribution of central unit s decision definitely brings a huge overhead to the network.

3.2 Practical and distributed algorithm

In this subsection, a practical and distributed algorithm is proposed for the above optimization problem

P1. Since the objective function is optimized at each time t, we omit the symbol t in the following for

convenience.

In cell i, if a user k is switched to a neighboring cell j for load balancing, the gain of the handover for

load balancing is defined as i,j,k = Obj(j, k) Obj(i, k), (9)

where Obj(j, k) and Obj (i, k) stand for the network-wide load balancing objective function in (5) after

and before the handover, respectively. It is obvious that i,j,k should be large than 0, otherwise the

handover is harmful, thus affecting the objective function.

In each cell i, there may be lots of users with a positive load balancing gain at the same time. To

avoid ping-pong effect, in each load balancing cycle, cell i only chooses the user and its corresponding

target cell with the largest load balancing gain defined in (9), and meanwhile the constraints in (7) and

(8) should be satisfied. That is, for all users in cell i, the user k and its target cell j are chosen as

k(j) = arg maxkKi, jCk

i,j,k, (10)

where Ck is the set of neighboring cells that user k can be served, as is decided by the constraints in (8).

4 Algorithm application for both GBR and nGBR users

In this section, the unified problem formulation and algorithm proposed in Section 3 are applied to GBR

and nGBR users, respectively.

4.1 Application for GBR users

In this subsection, we first apply the unified problem formulation and algorithm to GBR users. For GBR

user k in cell i, a minimal number of PRBs are allocated to guarantee its GBR requirement

wGBRi,k =

kei,k

, (11)

where k is the GBR requirement of user k, and ei,k is the bandwidth efficiency of user k in cell i. x

refers to the minimum integer larger than or equal to x. Then the load of GBR user k in cell i is

GBRi,k =wGBRi,k

si, (12)

where si means the total resources in cell i. Since all cells often have equal resources, we use s instead of

si in the following analysis for simplicity. And GBRi,k is used to denote the load occupied by GBR user k in

cell i, which comes from the definition in (3). Obviously, mapping function f1() in (3) equals k/ei,k/s

here for any GBR user k in cell i. And the load of cell i is decided by (4) with all GBRi,k (k Ki).

For GBR users, Jains fairness index [20] is used as the network-wide load balancing objective function

OGBRbj =(1 + 2 + 3 + )

2

|C|(12 + 22 + 32 + ), (13)

where |C| is the number of cells in the network, and OGBRbj denotes the network-wide load balancing

objective function for GBR users, referred to as the load balance index. The load balance index takes


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value in the interval [1/|C|, 1]. A larger OGBRbj means a more balanced load distribution among cells.

The objective of load balancing for GBR users is to maximize OGBRbj . Then the unified load balancing

problem P1 in (6)(8) is transformed for GBR users as

P2: max OGBRbj (14)

s.t. (7), (8);iC

Ii,kwGBRi,k ei,k k, k K. (15)

The newly added constraints for GBR users in (15) insures that the GBR requirement k of any user k

has to be satisfied strictly in its serving cell.

For GBR user k in cell i, switching it to cell j should increase the load balance index OGBRbj . LetOGBRbj (i, k) and O

GBRbj (j, k) be the load balance index before and after the switch (handover). Then

user k should only be switched from cell i to j if OGBRbj (i, k) < OGBRbj (j, k). Assume the numerator of

OGBRbj (i, k) and OGBRbj (j, k) are the same, which is reasonable because it is preferable to choose boundary

users for load balancing handover that consume almost equal resources in the original and the target cell.

Then OGBRbj (i, k) < OGBRbj (j, k) together with (12) and (13) yields

2i + 2j > (i w

GBRi,k /s)

2 + (j + wGBRj,k /s)

2 wGBRi,k (2s w

GBRi,k )

wGBRj,k (2s + wGBRj,k )

> 1. (16)

Then GBRi,j,k = wGBRi,k (2s w

GBRi,k )/(w

GBRj,k (2s + w

GBRj,k )) is defined as the GBR user load balancing gain

for switching user k from cell i to j. In each load balancing cycle, each cell i only chooses the user k

and its target cell j which satisfies constraints in (8) and (15), and meanwhile achieves the largest gain

k(j) = arg maxkKi, jCk

GBRi,j,k . (17)

A newly arriving GBR user m will be admitted to cell i if and only if there are enough time-frequency

resources satisfying its GBR requirement, that is,

s

kKi

wGBRi,k wGBRi,m . (18)

4.2 Application for nGBR users

In this subsection, we apply the unified problem formulation and algorithm to nGBR users, which is quitedifferent from that applied for GBR users in the above subsection.

Since all nGBR users are without any rate requirements and with the same priority, cell i allocates

resources to all its serving users equally. Then, for nGBR user k in cell i, the quantity of PRBs allocated

to it is

wnGBRi,k =s

|Ki|, (19)

where |Ki| is the number of all nGBR users in cell i. Then the load of nGBR user k in cell i is

nGBRi,k = loga(wi,kei,k), (20)

where wi,kei,k is the achievable throughput of nGBR user k in cell i, and loga() (a > 1) is the commonly

used utility function [21] for nGBR users. Similar to GBR users, the load of nGBR users in cell i isdecided by (4) with all nGBRi,k (k Ki).

For nGBR users, total utility, denoted by OnGBRbj , is used as the network-wide load balancing objective

function

OnGBRbj =iC

i =iC

kKi

nGBRi,k =iC

kKi

loga(wi,kei,k). (21)


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The unified load balancing problem P1 in (6)(8) is transformed for nGBR users as

P3: max OnGBRbj s.t. (7), (8). (22)

For nGBR user k in cell i, switching it to cell j should increase the total utility OnGBRbj . Let OnGBRbj (i, k)

and OnGBRbj (j, k) be the total utility before and after the switch (handover), together with (19)(21), then

we have

OnGBRbj (i, k) = loga

mKi

ei,m wnGBRi

nKj

ej,n wnGBRj

+

lC,l=i,l=j

l, (23)

OnGBRbj (j, k) = loga

mKi,m=k

ei,m wnGBR

i

nKj

ej,n wnGBR

j

ej,k w

nGBR

j

+

lC

,l=i,l=j

l, (24)

where m and n represent nGBR user in cell i and cell j, respectively. Since resource is equally allocated

in each cell, let wnGBRi and wnGBRj denote the resource allocated to each user in cell i and cell j before

the handover, while let wnGBR

i and wnGBR

j denote the resource allocated to each user in cell i and cell

j after the handover, respectively. Together with the resource allocation criterion in (19), OnGBRbj (i, k)

a unified algorithm for mobility load balancing in 3gpp lte multi-cell networks

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