In heterogeneous networks (HetNets), user association is one of the most ... work has been down on the design of user association scheme, some important ...
USER ASSOCIATION SCHEME IN HETEROGENEOUS NETWORKS CONSIDERING MULTIPLE REAL-WOLRD POLICIES Heli Zhang, Hong Ji, Yongbin Wang Key Laboratory of Universal Wireless Communication, Ministry of Education Beijing University of Posts and Telecommunications, Beijing, P.R. China, 100876 Email: {zhangheli, jihong, wangyongbin}@bupt.edu.cn Keyword: Heterogeneous Network, User Association, RealWorld Policies, Binary Particle Swarm Optimizer.
Abstract In heterogeneous networks (HetNets), user association is one of the most significant tools to deal with the problem of load balancing or interference mitigation. However, though much work has been down on the design of user association scheme, some important real-world policies are largely ignored and fail to be considered simultaneously. In this paper, we investigate the user association scheme in HetNets with the rules such as traffic capacity constraint, power budget, stable connection guarantee and transmission cost-optimal. Firstly we formulate a multi-objective optimization problem with users of different quality of service (QoS) requirements (minimum bit rate requirement (MBR) users and best effort (BE) users). The objectives of the problem are balancing the load distribution of MBR users, maximizing the throughput of BE users and minimizing network transmission cost, respectively. Then we analyze how to optimize the three objectives jointly and employ binary particle swarm optimizer to solve the problem. Extensive simulations are conducted, the results show that our algorithm can lead to significantly better performances than traditional algorithms, i.e., higher balancing index for MBR users, higher throughput for BE users, low transmission cost and more stable link connection.
1
Introduction
With the deployment of low power nodes (pico/femto/ relay base stations (BSs)) in macrocell, heterogeneous network (HetNet) holds significant promise to enhance the large data transmission and indoor coverage [1]. In this network, various user association schemes have been proposed. However, to the best of our knowledge, the policies considered in previous work are not complete. Some important rules related to the real world such as traffic capacity constraint, power budget, stable connection guarantee and transmission cost-optimal are overlooked. In this paper, we investigate the user association problem along with these crucial policies. The technology of user association concerning on HetNet has been studied intensively in recent years. The simplest (and thus widely accepted) rule is to choose the BS that gives the
strongest downlink pilot signal. Papers [2], [3] and [4] present a revised SINR based scheme and introduce a bias to picocells so that macrocell users can be actively encouraged to use the picocells. Some references pay attention to design the association scheme based on the load of the network. The paper in [5] combines power control and user association together, and designs a distributed load-award association algorithm for users to enhance the network capacity. Ref. [6] and [7] present a jointly optimal mobile association and load balancing framework that aims to release the load from macro BSs. Besides, there have been many efforts in the literature toward developing user association rules with interference mitigation. In [8] and [9], the works combine cell association and inter-cell interference coordination techniques in order to mitigate the overall interference and realize the promised capacity and coverage gains. The works of [10] and [11] present interference aware association policy that couples the transmission rates to users at various base stations. Some works such as [12] [13] and [14] consider user association allied with resource allocation. Recently, as the rise of Green communication, researchers study user association from the aspect of optimizing energy efficiency [15]. Clearly, the vast majority of these works usually focus on user association from the view of mitigating overall network interference or balancing traffic load. However, less work takes the conditions of the real world into account. The conditions including traffic capacity, power budget, connection stability and transmission cost play an important role to the network. “Traffic capacity” reveals the maximum traffic one BS can carry, to avoid network congestion, here we constrain the real traffic lower than the maximum value. “Power budget” refers to the maximum power offered by a BS, the budget for picoBS is 2W, and for femtoBS is 100mW. The total power assigned to users within one cell should be lower than this budget. With the rule of “connection stability guarantee”, we intend to ensure a steady link for users at a specified Bit Error Rate (BER). “Transmission cost-optimal” enables us to minimize the communication energy consumed for normal information transmission. When refereeing to MBR users and BE users, we endow them with different load balancing objectives according to their respective characteristics. For MBR users, the objective is to balance their load distribution between cells and allocate resource to them while satisfying their minimum transmission rate requirement. For BE users, they prefer higher throughput and the target of BE users is to maximize their throughput. Based on the foregoing analysis, we construct a user association
scheme. The contributions of this paper are presented in the following: 1)
Formulate a multi-objective optimization problem
considering various real-world policies. Define load balancing goals for users with different QoS requirements. 2)
Analyze how to optimize the multiple objectives and
introduce binary particle swarm optimizer (BPSO) to solve the proposed problem. The rest of this paper is organized as follows: in section II, the heterogeneous network scenario is described and the multi-objective optimization problem is formulated. In III, analyze how to optimize the three objectives and introduce binary particle swarm optimizer (BPSO) to solve the corresponding problem. In IV, various simulation results demonstrate the property of the proposed scheme. Finally, the paper is concluded in V.
Tkn t , which equals to 1 when user i U is served by cell n A at time t and 0 otherwise. All time t mentioned in this paper represents the time for load balancing.
Physical Link Model: we assume that with pilot detection, every user can obtain the instantaneous signal strength on its serving channel from its serving and neighboring cells. And the channel state information is sent back to its serving cell within uplink transmission or by periodical report.
J in,l W
hin,l W pin,l W
g im,l W pim,l W
¦
k z n , k S
g ik,l W pik,l W N o
where hin,l W and pin,l W are the flat channel gain and transmitting power from cell n to user i on channel l , respectively. gim,l W pim,l W denotes the cross-tier interference generated from macrocell m to user i .
¦
k z n , k S
2 System Model In this section, firstly a two-tier heterogeneous network is presented. And then the problem of multi-objective optimization is formulated.
(1)
gik,l W pik,l W
represents the co-tier interference emitted from nearby PBSs. gik,l W pik,l W is the interference between the CLPN k and user i . gik,l W is the channel gain between neighboring PBS and the user i . The channel gains account for the path loss, shadow fading, antenna gain, and equipment losses. pik,l W and pik,l W are the corresponding power. N o is the additive white Gaussian noise power. Assume ekn t [16] be the average spectrum efficiency of user i connected to cell n during time [t 1, t ) , then we have ekn t
Figure 1 Network Architecture
1 L
¦ 1 Ȗ t [bps
k z n , k S
n i ,l
Hz ]
(2)
Where | | represents the cardinal number of a set. The average spectrum efficiency can be calculated by the serving BS.
2.2 Problem Formulation 2.1 System Model We consider the HetNet architecture illustrated in Fig.1 which deploys multiple pico base stations (PBSs) in a macrocell. PBSs can exchange information with macro base station (MBS) through wireless interface. Coexisting with PBSs is a group of users. Users are free to connect to PBSs or MBS. There are two kinds of users, i.e., minium bit rate (MBR) users with rate requirements and best effort (BE) users with no QoS requirements. Assume the whole system is operated in a time-slotted manner, the MBS and PBSs share the whole spectrum band, and moreover, they are assumed to be perfectly synchronized. Assume the set of cells be A including one macrocell m and a set of picocells S , and A {m} S . Let L {1, }, L} represent the channel vector. Define U , C , E be the set of all users, MBR users and BE users, respectively. It is obvious that U C E . We define the user association indicator as
Here we construct a multi-objective optimization problem considering the real-world factors discussed in section I. 1)
Load Balancing Index for MBR Users:
For MBR users, we intend to balance their load among cells while satisfying the users’ minimum transmission rate. We use \ in t to denote the load of user i connected to cell n . Then function of the load can be written as:
\ in t
Rin t ein t
(3)
where Rin t is the rate requirement of the MBR user. \ in t is the quality of the channels allocated to user i by cell n . For cell n , define O n as the load index, then we have
1 ¦¦\ in t | L | nA iC
O n t
(4)
Based on the analysis above, to balance the load distribution of MBR users among all cells, we introduce jain’s index as the load balancing index:
¦ | O t | n
T t
2
n A
§ · | A | ¨ ¦ | O n t |¸ © n A ¹
(5)
2
A larger T t denotes a more balanced load distribution among cells. Then the objective of user association for MBR users can be changed to maximizing the load balancing index at each time t . 2)
Throughput Maximization For BE Users: After
associating MBR users, the next step is to choose cells for BE users with the purpose of maximizing their throughput. Assume the channels occupied by MBR users in cell n construct a vector Lnc , then the remaining available channel
dynamic wireless environments. Llorca et al. defined a Morse potential function [17] that takes the two factors into account: pin,l (t )
| Lni | n ei t En
(6)
For all BE users, the total throughput can be represented as:
Thr (t )
¦¦ T
n A iE
n
i
Thri n t
(7)
The objective of user association for BE users is to maximize Thr (t ) at time t . 3)
Traffic Capacity Constraint and Power Budget
Note that the transmission capacity of PBSs or MBS is limited, we assume the backhaul network is not the bottleneck. To make this more explicit, let : n be the maximum traffic that cell n can carry. For each cell, the inequality function should be satisfied that:
¦ R t ¦ Thr t d : iC
n i
n
iE
i
n
(8)
In HetNet, the total power consumed by one cell should be lower than a threshold Pn that
¦¦ pin,l (t ) d Pn
(9)
iU lL
4)
Stable Connectivity Guarantee and Transmission
Cost-Optimal: One most important concern in HetNet is to assure stable connectivity and low transmission cost in
(10)
where Din,l (t ) is the dissociation energy and S in relates to directivity and other communication parameters of the wireless link (i, n) . X n and X i denote the location of BS n and user i . This function offers the energy per unit time required to send information from user i to BS n at the specified bit error rate. Based on the Morse potential function, the objective of user association is to minimize the network cost while guaranteeing the association stability of all links.
min E (t )
¦¦¦ p
n i ,l
n A iU lL
(11)
With the help of the foregoing analysis, the user association problem can be formulated as a multiple-objective optimization problem with four restrictions. Then we formulate the following objective function:
^
max T t , Thr t , E t `
vector provided by cell n for BE users is Lne L Lnc . Since there is no transmission rate requirement for BE users, we assign the residual channels to BE users averagely. Let Lne and En stand for the quality of remaining channels and the number of BE users of cell n , then the available throughput of BE user i at time t is: Thri n t
Din,l (t ) 1 exp S in X n X i
C.1
¦ R t ¦ Thr t d : iC
C.2
n i
n
i
iE
n
¦¦ p t d P iU lL
n i ,l
n
(12)
C.3 Tkn t d 1 C.4 Tkn t
^0,1`
The constraint C.3 denotes that one user can only access to one cell at time t .
3 BPSO Based Solution 3.1 Analysis of the Multi-Objective Optimization Problem Since multiple objectives exist in the problem, traditional single-objective algorithms cannot be applied directly as the solution. From reference [18] we know two methods can be utilized: 1) 2)
Divide the solution into multi-phase methods. Convert the multiple objectives into a single- objective function. Considering that all the three objectives are determined by the association between cells and users, we use the method of (2) to solve the problem. Firstly we formulate a single Aggregate Objective Function (AoF) with weighted linear sum method. The AOF is written in the following max G t
PT t Thr t ZE t
(13)
Where P and Z are two weight factors. On one hand, the two factors adjust the value of G t , Thr t and E t to the same order of magnitude. On the other hand, they reflect the proportion of the three objectives. Then the multi-objective
optimization problem can be transformed to the following single-objective problem max G t C.1
¦ R t ¦ Thr t d : iC
C.2
PT t Thr t ZE t n i
The role of velocity is to force particle’s position to zero or one. The position force function is defined as below:
n
iE
i
vMAX as the maximum velocity exists to clamp particles’ velocities on each dimension.
n
¦ ¦ pin,l t d Pn
k 1 i,d
(14)
S
iU lL
C.3 Tkn t d 1 C.4 Tkn t
Considering the variable T t in the user association problem is binary, we employ the artificial intelligence algorithm binary particle swarm optimizer (BPSO) [19] to deal with this problem.
3.2 Description of Binary Particle Swarm Optimizer The binary particle swarm optimizer is originated from the particle swarm optimization (PSO). PSO is a population based stochastic optimization technique developed by Kennedy and Eberhart in 1995 [20]. It mimics swarms’ behavior in performing their tasks like bird flocks and fishes to discover an optimal solution based on the objective function. Compared with other artificial intelligence algorithms, PSO has some appealing features including easy implementation, few parameter tuning and a fast convergence rate. However, the traditional PSO is designed in the continuous space. To allow PSO algorithm to operate in discrete binary variables, a binary particle swarm optimization (BPSO) was developed [19]. The BPSO algorithm consists of a group of individuals named “particles”. Each particle is a potential solution to an ndimensional problem. Two parameters are crucial when searching the solution space: position and velocity. The particles change their state by flying around in the ndimensional search space based on the updated velocity until a relatively unchanging state has been encountered, or until computational limitations are exceeded. The velocity of each particle is calculated using the function below: vin k c1a1 pbestin k sin k
c2 a2 gbestin k sin k
(16)
where a 3 is a random number uniformly distributed between 0
^0,1` n k
vin k 1
1, if a 3 t Sik vik,d1 ° ® k k 1 °¯0, if a 3 Si vi , d
(15)
where i denotes the order of the particle in the swarm, n means the dimension of a particle and k is the iteration number of the algorithm. vin k and sin k are the velocity vector and position vector of the particle i at iteration k . pbestin k is the best local position searched by particle i and gbestin k is the best global position found so far at iteration k by the entire swarm. c1 and c2 are constants denoted as acceleration coefficients (usually c1 c2 1.49 ), a1 and a2 are two independent random numbers uniformly distributed in the range [0,1] , they reveals the importance of the local best position and global best position. What’s more,
and 1, and Sik is a sigmoid function for transforming the velocity to the probability constrained to the interval [0,1] , Sik,d1
1 e
vik,d1
(17)
t
3.3 The BPSO based User Association Algorithm On the basis of BPSO, we design the user association algorithm to solve the problem constructed in e.q.(14). One particle is a solution for the problem. Then the first important aspect of this algorithm is the definition of the particle. The position of one particle represents the user association vector for all cells and users. Assume the association vector for user i as Ti ª¬Ti1 ,Ti 2 }, Ti | A| º¼ , and then position of one particle can be encoded be T
ªT1 , }, T|U| º¼ . Ti n is named as the element of ¬
one particle. The second important aspect is the design of evaluation function characterizing the objectives while taking into account the constraints defined by (14) C.1 ~ C.4 . Firstly, we define a comprehensive evaluation function: < t
PT t Thr t ZE t
§
·
U ¨ : n ¦ Rin t ¦ Thri n t ¸
iC iE © § · G ¨ Pn ¦¦ pin,l (t ) ¸ iU lL © ¹
¹
(18)
Where U and G are weight parameters. Note that this function includes the effects of load balancing for users with different QoS requirement, connectivity stability, network transmission cost, traffic capacity and power budget of the system, which drives the user association optimization in a comprehensive manner. With the help of above definition, we develop a BPSO based algorithm for the optimization of user association. The overall optimization procedure is summarized as follows: 1)
Initialization: Set the iteration time k
0 and
maximum iteration time k MAX ; set the initial position of the
particle T 0 while satisfying e.q.(14). C.3 and C.4 . Accordingly, calculate the evaluation function and output the
assessed
value < 0 .
The
velocity
V 0 T 0 ,
pbestin 0 Ti n 0 , gbestin k Ti n 0 . 2)
Set time k m k 1 ; Calculate the velocity vik k
For each element of the particle according to e.q.(15). 3)
number of MBR users varies from 5~30. The results reveal that our algorithm outperforms the other three and the load distribution of MBR users under BPSO can be well balanced. For RSRP, note that cell is selected for users merely according to the received signal strength, the load imbalance problem is serious and as a result, the value of load balancing index is low.
Update the positions of all the elements of the Particle
according to e.q.(16). Calculate the assessed value < k ; if
< k ! < k 1 n i
gbest
n i
pbest 4)
k k
Ti k n
;
,
T k T k 1
otherwise,
Ti k 1 , gbest n
pbestin k Ti n k
update n i
k
, ˈ
Ti k 1 . n
If the maximum number of iterations k MAX is satisfied,
go to Step 6; otherwise, go to Step 2). 5)
Set time k m k 1 , all the elements of the particle
achieve the new positions, and the user association vector is determined by T k .
4 Simulation Results and Analysis In this section, we present the performance results of the proposed user association scheme and compare its performance to other schemes such as reference signal received power (RSRP), cell range extension (CRE) and binary particle swarm optimizer (BPSO) in a HetNet deployment scenario. The simulation scenario we consider in this section is shown in Fig.1. It assumes a HetNet with one macrocell, 3 picocells and 50 users. The radius of picocell is 50m, the proportion between MBR users and BE users differs according to the simulation scenario. 10 channels are available and the whole bandwidth of the channel is 10MHZ. The noise N 0 9dB , and moreover, the total power constraint for each PBS P n 250mW.
Fig.2, Comparison of the Load Balancing Index for MBR users under BPSO-, RSRP-, CRE- and PSO- based UA algorithms. Fig.2 compares the load balancing index of the BPSO based user association (UA) scheme with the existing RSRP-, CRE and PSO- based UA algorithms. In the network scenario, the
Figure 3, Comparison of the Overall Throughput for BE users under BPSO-, RSRP-, CRE- and PSO- based UA algorithms When the Number of BE users Varies. Fig.3 plots the profiles of throughput under BPSO-, RSRP-, CRE- and PSO- based UA algorithms when the number of BE users changes from 2 to 40. The total number of users is 50. It is obvious that with our proposed scheme, BE users can gain higher throughput. The curves firstly increase rapidly until reach an acme, and then they become stable and fluctuate in a small scale. This happens because in our scenario the total number of users is fixed, as the increment of the number of BE users, the number of MBR users gets smaller. This means more resources can be allocated to BE users and larger throughput can be obtained. RSRP-based UA scheme is inferior to other three schemes because the load is unbalanced under this scheme, as a result, network congestion may occur and low throughput can be obtained.
Fig.4, Comparison of the Total Network Cost under BPSO-, RSRP-, CRE and PSO- based UA algorithms When the Number of users Changes from 2 to 42. In Fig.4, the curves show the network cost with BPSO-, RSRP-, CRE- and PSO- based UA algorithms when the total number of users changes from 2 to 40. The proportion of the MBR users and BE users is 1:1. Through comparison we
observe that more network cost is generated by RSRP-based scheme, this is because with RSRP BSs attempt to improve the transmission power to attract users. The cost is lowest with our proposed BPSO based UA algorithm, because we include the the minimization of network cost as one important objective, and for CRE and RSRP, they ignore this element. PSO is inferior to BPSO, this is because PSO usually fall into a local optimum and fails to find.
Fig.5, Comparison of the Connection Stability under BPSO-, RSRP-, CRE and PSO- based UA algorithms. Fig.5 reveals the effects of the four UA schemes consisting of BPSO, RSRP, CRE and PSO on the link connection stability. The stability is evaluated by the ratio of users who disconnect with the servicing cells at time t, we call it disconnection ratio. Assume the number of disconnection users is N d , then the Nd . 42 users randomly are | E||C| distributed in the network, the proportions of MBR users and BE users are 3:1, 2:1, 1:1, 1:2 and 1:3, respectively. From the bars we know that our BPSO algorithm precedes the other three and the link connections between users and cells are more stable.
disconnection ratio is
5 Conclusion In this paper, we investigate the user association scheme in HetNets combining the mentioned factors and optimize them simultaneously. Firstly we formulate a multi-objective optimization problem with users of different quality of service (QoS) requirements (minimum rate requirements users and best effort users). The problem includes objectives which are balancing the load distribution of MBR users, maximizing the throughput of BE users, and meanwhile, minimizing network transmission cost, respectively. Then we transform the three objectives to one weighted objective and employ binary particle swarm optimizer to solve the problem. Various simulations are conducted, results show that our algorithm can lead to significantly better performances than traditional algorithms, i.e., higher balancing index for MBR users, higher throughput for BE users, low transmission cost and more stable link connection.
Acknowledgements
This paper is sponsored by the Specialized Research Fund for the Doctoral Program of Higher Education (20120005120010), the Scientific Research and Innovation Projects of Central Universities for Youth (2013RC0112), the Scientific Research and Innovation Projects of Central Universities for Youth (2012RC0126).
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