Abstract: In this paper, we propose an energy efficient user association scheme for uplink heterogeneous networks with machine-to-machine. (M2M) and ...
Radio Resource Management
Energy-Efficient User Association in Heterogeneous Networks with M2M/H2H Coexistence under QoS Guarantees Tian Hui1, Xu Youyun1, Xu Kui1, Jing Jun2, Wu Kun1 Institute of Communication Engineering, PLA University of Science and Technology, Nanjin, Jiangsu, China
1
Postdoctoral Scientific Research Station, PLA Unit No. 66393, Baoding, Hebei, China
2
Abstract: In this paper, we propose an energy efficient user association scheme for uplink heterogeneous networks with machine-to-machine (M2M) and human-to-human (H2H) coexistence. A group based random access protocol is designed for massive number of machine-typecommunications (MTC) user equipments’ (UEs) transmissions. A user association problem for UEs’ energy efficiency maximization is formulated considering the HTC UEs’ quality of service (QoS) guarantees and load balance among multiple BSs, simultaneously. A distributed iterative algorithm is developed to solve the optimization problem. In addition, the convergence of the proposed algorithm is proved. Simulation results show that our proposed scheme outperforms other schemes in terms of energy efficiency and QoS guarantees. Keywords: energy efficiency; QoS; user association; M2M communication; heterogeneous networks
I. INTRODUCTION R e c e n t l y, m a c h i n e - t o - m a c h i n e ( M 2 M ) applications are playing a more and more important role in our daily life, such as, smart grid, vehicular telematics, healthcare, public safety and so on [1]. The characteristics of M2M communications can be summarized
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as massive number of devices, extremely low power consumption, small burst transmission, group control, one-way data traffic (uplink), etc. [1]. Although there are many differences between M2M communications and human-tohuman (H2H) communications, it is impossible to construct a dedicated and separated network for M2M communications. Consequently, the interaction between H2H and M2M will constrain the large-scale application of M2M communications in the future networks. In H2H and M2M coexistence scenarios, quality of service (QoS) of human-type-communications (HTC) user equipments’ (UEs) cannot be jeopardized by machine-type-communications (MTC) UEs [2]-[4]. Heterogeneous networks (HetNets) integrating multiple wireless access technologies can provide a promising architecture for supporting mixed H2H and M2M communications. In a heterogeneous cell, the problem of user association, i.e., the problem of determining which base station (BS) serves a particular user by certain rules, is one of major challenges. In addition, energy efficiency optimization has become an important research area in both M2M communications and user association. Therefore, this paper investigates optimization problem of user association aiming at maximizing the network energy efficiency in a wireless China Communications • Supplement No.1 2015
uplink heterogeneous network, in which the characteristics of both the M2M and H2H communications are considered.
1.1 Related work In the literature, the user association problem has been explored extensively [5]-[13]. In [5], a user association scheme for load balancing was proposed in HetNets. A distributed pricingbased user association scheme was developed for load balancing in downlink heterogeneous cellular networks [6]. In [7], a unified framework was designed for QoS-driven user association. An opportunistic user association scheme was investigated in [8]. An uplink user association scheme based on college admissions game was proposed in [9]. [11] proposed a user association scheme aiming at maximizing BSs’ energy efficiency. In [12], authors developed a joint BS operation and user association algorithm in HetNets. However, the schemes proposed in [5]-[13] are not suitable for massive number of MTC UEs’ transmissions due to allocating fixed resources to each UE. Accordingly, the above mentioned schemes [5]-[13] can not be applied to the user association in H2H/M2M coexistence scenarios directly. Specifically, many studies are devoted to designing energy-efficient schemes for user association at BSs [10]-[12]. However, the energy-efficient optimization in M2M communications usually pays more attention to minimize the energy consumptions at MTC UEs side. Consequently, prior works [10]-[12] cannot be used directly to solve the energy efficient user association problem in the H2H/M2M coexistence scenarios. In addition, the problem of user association in the uplink can be regarded as access control problem. In M2M communications, the massive access control and resources allocation in the uplink have been considered broadly [4], [14][16], [21]. A grouping based algorithm for adaptive massive access management with QoS guarantees was proposed in [14]. A joint access control and resource allocation scheme was developed in [15]. In [16], a distributed group China Communications • Supplement No.1 2015
formulation scheme was designed for massive access management with HTC and MTC UEs coexistences. However, the mentioned studies [4], [14]-[16], [21] do not consider both the MTC UEs’ load balance among multiple access points and HTC UEs’ QoS guarantees simultaneously.
1.2 Contributions and organization In this paper, we propose an energy efficient user association scheme for uplink HetNets, which results in the following main contributions. ● A group based random access protocol is designed for massive number of MTC UEs’ transmissions. ● A user association problem for UEs’ energy efficiency maximization is formulated while considering the HTC UEs’ QoS guarantees and load balance among multiple BSs, simultaneously. ● A distributed algorithm based on dual theory is developed to solve the proposed problem. In addition, the convergence of the proposed algorithm is also proved. ● Finally, simulation results show that our proposed algorithm can achieve the same performance as the exhaustive search algorithm when the number of UEs is small. Regardless of the number of UEs, the proposed scheme outperforms the existing schemes in terms of energy efficiency, load balance and HTC UEs’ QoS guarantees. The rest of this paper is organized as follows. In section II, the network model and massive access control protocol are described. The energy efficiency optimization problem is formulated in section III. A distributed iterative algorithm is developed in section IV. In section V, simulation results are presented. Finally, the conclusions are drawn in section VI.
II. SYSTEM MODEL 2.1 Network model Consider an uplink HetNet consisting of N BSs and M UEs, as shown in Fig. 1, where there are two types of UEs, i.e., HTC and MTC UE,
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Femto BS Femto BS
Pico BS
Macro BS
Pico BS MTCD
Femto BS
UE
Fig. 1 Illustration of a three-tier heterogeneous cellular network
and multiple tiers of BSs, such as macro, pico and femto. The set of all BSs is denoted by
{� 1, 2,..., N} , the set of all UEs is denoted by {� 1, 2,..., M} , and the set of UEs associated with BS j is j . The K conventional HTC UEs are indexed by the set � {1, 2,..., K}, and the D
MTC UEs are indexed by the set � {1, 2,..., D}. In the HetNet, the smallest wireless resources structure is denoted by a resource block (RB), which contains both time and frequency domains resources. The number of available RBs at a given BS is related to scheduling interval duration and system bandwidth. We assume that the total number of available RBs at BS j 1, 2,..., L j }. ( j ∈ ) is indexed by the set j {� The restrictions on power and RB allocation are as follows: 1) a single RB can be allocated to almost one UE; 2) the transmitted power on the allocated RBs to a given UE must be equal. The channel model between UEs and BSs is assumed to be flat-fading and slow-fading. The coherence time and bandwidth of channel are larger than the time and frequency domains interval of an RB, respectively. In this paper, we suppose that a certain interference cancellation technique is adopted by all BSs, such as uplink coordinated scheduling with MU-MIMO [17], the interference caused by UEs belonged to adjacent cells can be ignored. Consequently, the received Signal-to-Noise Ratio (SNR) from UE i ( i ∈ ) to BS j can be expressed as g ij =PiGij|hij|2/N0, where Pi denotes the transmitted power of UE i, hij is the Rayleigh channel fading
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coefficient between UE i and BS j, Gij denotes the effect of large scale fading factor, such as path loss, log normal shadowing and antenna gains, and N 0 denotes the power of Additive White Gaussian Noise. hij is modeled as zeromean, independent and circularly-symmetric complex Gaussian random variables with variance σij2.
2.2 Access control protocol In H2H and M2M coexistence scenarios, we should guarantee the QoS of conventional H2H communications without being affected by M2M communications. Therefore, assuming that the HTC UEs have high priority to obtain wireless resources to satisfy their QoS requirements. In M2M communications, massive MTC UEs’ transmissions are one of key M2M features. An extremely large number of MTC UEs simultaneously or nearly simultaneously attempt to access BS in many application scenarios, such as public safety, healthcare, metering, etc. Accordingly, considering the characteristics of both H2H and M2M communications, for a BS, the access control protocol is designed as follow: for HTC UEs, a fixed number of RBs is allocated to each HTC UE by the BS according to its QoS requirements; then for MTC UEs, due to the constrained resources, it is impossible for the BS to allocate fixed wireless resources to every MTC UE. Consequently, a random access (RA) mechanism [15], [18]-[22], in which each MTC UE competes for the left RBs at the BS, is adopted to solve the problem of massive access requests and obtain load balancing among all MTC UEs. In this paper, we only consider the H2H UEs’ requirements on transmission rate. Since the BSs’ received instantaneous rate varies with fluctuations in wireless channels, it is difficult to adjust the resources allocation scheme timely to satisfy the HTC UEs’ instantaneous rate. Therefore, we focus on guaranteeing the statistical average rate of each HTC UE above its requested rate threshold, which is easier to implement in practice. Taking BS j as an example, firstly, the statistical average received China Communications • Supplement No.1 2015
SNR measured by BS j from HTC UE k (k ∈ = γ kj E= [γ kj ] Pk Gkjσ kj2 N 0 ) can be expressed by , where E[x] denotes the expected value of variable x. Then, given that nij RBs are allocated to HTC UE k by BS j, the statistical average rate at BS j from HTC UE k, denoted rkj , and can be written as rkj = nij ∆f log 2 (1 + γ kj ) , where Δf is the bandwidth of each RB, and nij denotes the number of RBs allocated to UE i by BS j. In order to satisfy HTC UEs’ rate constraint, the statistical average rate should be larger than R the minimum required rate rkR , i.e., rkj ≥ rk . Therefore, to guarantee rate requirements, the R minimum number of required RBs nkj for HTC
rkR ∆f log 2 (1 + γ kj ) , where ⋅ UE k is nkjR = represents the ceiling function. With the number of MTC UEs increasing, the network will be congested and overloaded due to competition among MTC UEs despite the small burst size of M2M traffic data. Therefore, a group based RA mechanism is designed to improve the performance of RA protocol and avoid all available RBs used by one MTC UEs at a BS. Let L j denote the number of remaining RBs at BS j after allocating RBs to all HTC UEs. The number of MTC UEs associated by BS j is Bj. Let βj denote the maximum ratio of available RBs which are allocated to MTC UE
d ( d ∈ j) for contending at BS j. We divide the all available RBs into 1/βj group. The MTC UEs competing for the same RBs form a group. Given L j available RBs at BS j, the probability
a retransmission with the uniform backoff algorithm. Therefore, the interference caused by multiple MTC UEs during the data transmission phase will not considered in this paper.
III. PROBLEM FORMULATION First, we define the energy efficiency of a UE as the number of transmitted bits per unit joule, i.e., bits-per-joule. The energy efficiency of MTC UE d is the ratio of the expected value of MTC UE d’s maximum rate and MTC UE d’s transmitted power, and can be computed by L EedjM = Edjj Pd = β j L j pdjS ∆f log 2 (1 + γ dj ) Pd
(1)
L j dj
where E is the expected value of the MTC UE d’s maximum rate. The energy efficiency of HTC UE k (k ∈ ) is the ratio of the received instantaneous rate at BS j from HTC UE k and HTC UE k’s transmitted power, and can be expressed as EekjH = rkjs Pk = nkjR ∆f log 2 (1 + γ kj ) Pk (2) where rkjs denotes the received instantaneous rate at BS j from HTC UE k. Then, we define a indicator matrix Z [zij] M×N, i ∈ and j ∈ , where each entry z ij is a binary variable, zij {0,1}. When the UEs i is associated with BS , zij = 1; otherwise, zij = 0. In practice, not every UE can access any BSs
due to the limitation of BSs’ coverage. Let i denote the set of available accessing BSs for UE i (i ∈ ). Then, the overall energy efficiency is expressed as K D d of the MTC UE d successfully capturing a RB is = Eeoverall ∑ x EedjM ∑ l k1 ykl EeklH + ∑ β j B j −1 = k 1= = d 1∑ =j 1 dj S = pdj L j pdj 1 − pdj , where pdj denotes the (3) probability of the MTC UE d selecting a certain where |A| denotes the cardinality of set A. ykl RB in its group at BS j. We assume that the ( k ∈ ) is the entry of the HTC UEs’ indicator probability of each MTC UE selecting a certain matrix Y H, i.e., [y kl] K×N. x dj ( d ∈ ) denotes RB at the same group is equal, i.e., psj =pdj =1/( the entry of the MTC UEs’ indicator matrix XD, βj L j), ∀s, d ∈ j , s ≠ d , ∀j ∈ . For simplicity, i.e., X D [xdj]D×N. Consequently, the problem let pj describe the probability of a certain RB of user association for energy efficient is how to ≠ dj,, ∀j ∈ , i.e., pj=1/ selected by a MTC UE at, sBS determine the indicator matrix Z (Z=[(YH)T (XD) T (βj L j). ]) for maximizing the overall energy efficiency. The contention-based RA mechanisms in LTE Then, we divide our proposed problem of user is used for applying for transmission resources association for maximizing energy efficiency and re-establishing a connection upon failure. in (3) into two sub-problems: a HTC UEs’ BS will allocate a RB to a MTC UE if the association sub-problem with rate guarantees MTC UE competes successfully during access and a dynamical MTC UEs’ association substage. If a collision occurs, the UE performs
(
)
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problem. In the first sub-problem, on the one hand, the number of HTC UEs is relatively small compared to MTC UEs. On the other hand, HTC UEs have high priority of using radio resources. Accordingly, we design a distance-based scheme for HTC UEs. Based on the results of the first sub-problem, in the second sub-problem, due to the massive number of MTC UEs, a collision aware dynamical MTC UEs association scheme is designed for energy efficiency maximization and load balance. In the first sub-problem, to maximize the HTC UEs’ energy efficiency and satisfy their QoS requirements simultaneously, it is efficient for them to apply to their closest BS. The HTC UEs association problem is that of determining ykl (ykl ∈ YH) at each BS according to the distances between HTC UEs and BSs. In the second sub-problem, on the basis of HTC UEs’ assignment results, user association scheme for MTC UEs is designed for maximizing the overall MTC UEs’ energy efficiency and balancing load among all BSs. Note that, although using linear utility function can achieve an energy-efficient optimal solution, we adopt logarithmic utility function because it can achieve load balancing and some level of fairness among all MTC UEs, which can also reduce the collision probability at BSs. Then, similar to the first sub-problem, the MTC UEs association problem is also to determine a binary indicator matrix X D to maximize the sum of MTC UEs’ utility of energy efficiency, which can be written as
log ( Ee ∑ ∑ ∑ xx log ( Ee ((xx )))) ∑ subject to to ((aa)) ∑ xx == 1, 1, ∀ ∀dd ∈ ∈ subject ∑ B ,, ∀ = ∀jj ∈ ∈ ∑ = xx B ((bb)) ∑ ∑ BB == DD ((cc)) ∑
max imize imize max XDD X
D D dd dj d 1 =j 1 dj = d 1 =j 1 = dd j =1 dj j =1 dj D D j d =1 ddjj j d =1 N N j =1 j j =1 j
M M dj dj
dj dj
{0,1}, ∀ ∈{0,1}, ∀((dd ,, jj)) ∈ ∈D ××B D B × (4) ((dd )) xxdjdj ∈ where constraint (4a) ensures that each MTC UE can only associate with one BS, and constraint (4c) reflects that the all MTC UEs are served. Note that the combination optimization problem in (4) is NP-hard. To overcome this, similar to [5]-[7], the constraint xdj ∈ {0,1} is relaxed to continuous values with 0 ≤ xdj ≤ 1, i.e.,
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the MTC UEs can be associated with more than one BSs. After relaxation of parameter xdj, the optimization (4) can be rewrite as
log (( Ee Ee (( xx )) )) ∑ ∑ ∑ xx log ∑ subject to to ((aa)) ∑ xx == 1, 1, ∀ ∀dd ∈ ∈ subject ∑ B ,, ∀ = ∀jj ∈ ∈ ∑ = ((bb)) ∑ xx B ∑ BB == DD ((cc)) ∑
max imize imize max XDD X
D dd D d 1 =j 1 dj = d 1 =j 1 dj = dd j =1 j =1 D D d =1 d =1 N N j =1 j =1
M M dj dj
dj dj
dj dj
dj dj
j j
j j
1, ∀ D× B (5) ≤ xxdj ≤ ≤ 1, ∀((dd ,, jj)) ∈ ∈ × ((dd )) 00 ≤ D B dj Since the optimization of (5) is no longer combinatorial problem, the complexity can be relatively reduced compared to the optimization (4). However, in practice, it is more difficult to perform resources scheduling among multiple BSs while considering the multiple-BS association. In the following section, to solve the optimization (3), we propose a distributed algorithm that also takes into account the singleBS association constraint.
IV ALGORITHM In this section, we design a distributed algorithm, having two main phases, to obtain the solutions of the two sub-problems. In the first sub-problem, since each HTC UE selects the nearest BS, ykl is determined by 1 if Dkl = min ( Dkl ′ ) l ′∈l ′ ykl = (6) 0 else where Dkl ( k ∈ , l ∈ k ) denotes the distance between HTC UE k and BS l. It can be seen that the HTC UEs’ association scheme is very efficient for both HTC UEs and BSs. For HTC UEs, they can select the BS that is most likely to guarantee their rate requirements. While for BSs, less number of RBs will be need to satisfy HTC UEs’ rate requirements, and more RBs can be remained for the MTC UEs. In the second sub-problem, we will use a dual decomposition method to solve the dynamical MTC UEs’ association problem (4). Similar to the methods in [5] and [6], we take the parameter B j as an optimization variable in following analysis. Then, we define the Lagrangian function associated with the problem (5) as
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L ( X D , B, µ ,υ ) =
D
d
∑∑ x ( a
d 1 =j 1 =
dj
N
dj
− µ j ) + ∑ B j ( B j − 1) log (1 − p j ) =j 1
N N + ∑ µ j Bj −υ ∑ Bj − D =j 1 = j1
(7)
where adj = β j L j ndj ∆f log 2 (1 + γ dj ) / Pd ,
N
B = ( B1 ,..., BN ) , X = ( x1 ,..., x d ,..., x D ) , thereinto, xd denotes the MTC UE d’s association results. µμ = ( µ1 ,..., µ N ) ( µ j ≥ 0, ∀j ∈ ) denotes the Lagrange multipliers associated with the constraints in (5b), similarly υ(υ≥0) represents Lagrange multiplier associated with the constraint in (5c). We define the Lagrange dual function as the maximum value of the Lagrangian function over XD and B: D
(8) Considering the single-BS association constraint, the solution of optimization in (5) with respect to XD is 1 j arg max adj ′ − µ j ′ = j′ * xdj = adj ′ − µ j ′ 0 j ≠ arg max j′ (9) Note that if there are multiple maximizers in (9), MTC UE can choose any one of them.
( (
) )
Then, taking derivative to respect to Bj, we have
= B*j
υ − µj
2 log (1 − p j )
+
with
1 2
[18]. The Lagrange multipliers μ and υ are updated iteratively in the opposite direction to the gradient. First, it can be seen from (11) that dual function is a differentiable function of υ, by setting its gradient to be 0, the optimal υ can be computed by
(10)
µ j (t )
1
∑ 2 log (1 − p ) − 2 N + D υ (t + 1) = j =1
j
N
1
∑ 2 log (1 − p ) j =1
(13)
j
where t denotes the iteration time. However, since that dual function is not a differentiable function of μ j , by subgradient method, the Lagrange multiplier μj is updated by µ j (t + 1) +
υ (t ) − µ j (t ) 1 D = µ j (t ) − α (t ) + − ∑ xij (t ) 2 log (1 − p j ) 2 d =1 (14) where α(t) represents the step size, [x]+ denotes the maximum of the argument of x and 0, and xij(t) can be obtained according to μj(t). In summary, the distributed iterative algorithm can be briefly described as: in the phase I, each HTC UEs selects BSs based on (6). In the phase II, based on the association results of HTC UEs, i.e., YH, each BS broadcasts its price μj. MTC UEs make decision to associate which BS according to μ j . Then, BSs update their prices μ and υ based on MTC UEs’ decisions.
Substituting (9) and (10) into (8), the Lagrange dual function can be rewritten as
= g ( µ ,υ )
D
∑ max {log ( a ) − µ } d =1
+
j∈d
ij
j
1 N υ − µ j + log (1 − p j ) ∑ log 1 − p 4 j =1 ( j)
(11) 1 × µ j − υ − log (1 − p j ) + υ D 2 The Lagrangian dual problem of (5) is to minimize g(●) over the dual function over μ and υ, (12) The dual optimization problem (12) can be solved by the subgradient projection method China Communications • Supplement No.1 2015
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This procedure repeats and converges to a final solution, i.e., an indicator matrix for MTC UEs X D i f g ( µ (t ),υ (t ) ) − g ( µ (t − 1),υ (t − 1) ) < ε , where ε is an arbitrary number. The detail of the algorithm is summarized as the Algorithm 1. According to the results of operations that preserve convexity in [17], it is easy to obtain that the objective function in (5) is a concave function. By using Slater’s theorem [17], for the optimization problem (5), the optimal duality gap is zero. Moreover, since the single-BS constraint is also considered in the Phase II of Algorithm 1, we can obtain that the optimal solution of the optimization problem (4) can be obtain by the Phase II of Algorithm 1. Proposition 1: The proposed Algorithm 1 can converge to a final indicator matrix Zfinal. Proof: First, for the Phase I of Algorithm 1, it is easy to find that all HTC UEs can be assigned to BSs if adequate resources are available at BSs. Then, by introducing the proposition 6.3.4 in [18], if step size α(t) satisfies following two conditions:
lim α (t ) = 0 and ∑ t = 0 α (t ) = ∞ , starting from t →∞ any initial YH, the Phase II of Algorithm 1 can converge to the optimal solution of the problem (4). Therefore, one can get the result in Proposition 1. ∞
V. SIMULATION RESULTS AND DISCUSSION In this section, numerical simulations are presented to confirm our analysis developed
x 10
9
5.5
4 3.5
D=50 D=100 D=300 D=500 D=800 D=1000
3 2.5 2 1.5 1 0.5 0
0
50
100
150
Iteration
200
250
300
Fig.2 The convergence speed of Algorithm 1 under different numbers of MTC UEs
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with σ ij2 = 1, and large scale path loss and lognormal shadowing are considered for the channel model. We use path loss 128.1+37.6 log 10(r), 140.7+ 36 log10(r), and 127+30 log10(r) for macro BS, pico BSs and femto BSs, respectively. Power spectral density of noise is -174dBm/Hz. System bandwidth is 10 MHz. Bandwidth of a RB is 180 KHz. The minimum required rate of each HTC UE is 2Mbps. Meanings of the terms used in Figs. 2-7 are as follows. UAEE scheme refers to our proposed user association schemes for energy-efficient. UALB scheme refers to the user association scheme for load balancing in [5]. CAG scheme refers to the college admissions game based uplink user association in [10]. Max SNR scheme means that each MTC UEs will be assigned to the BS with largest received SNR [26]. ES stands for exhaustive search algorithm. RA denotes random selection scheme that means that the MTC UEs associate with a BS randomly. AAL represents average allocation scheme, in
The average overall energy efficiency (bits/joule)
The average overall energy-efficiency (bits/joule)
4.5
in the previous sections. A three-tier HetNet is considered in the simulations. The transmitted powers of HTC UE and MTC UE are set to 23 dBm and 18 dBm, respectively. All BSs and UEs are located within a square area with dimensions of 1000m×1000m. One macro BS is fixed at the center of the square area, the rest of BSs and all UEs are randomly located in this area. Note that Nmacro, Npico, and Nfemto denote the numbers of macro BSs, pico BSs and femto BSs, respectively. Small scale Rayleigh fading
x 10
9
UAEE ES CAG UALB Max SNR ALL RA
5 4.5 4 3.5 3
β =1 j βj = 0.7
2.5
βj = 0.5
2
β = 0.3 j
1.5
β = 0.1 j
1 0.5 0 20
30
40
50 60 70 The number of RBs
80
90
100
Fig.3 The average overall energy efficiency against the number of RBs RBnum for different schemes China Communications • Supplement No.1 2015
x 10
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UAEE CAG UALB Max SNR RA ALL
8
The average rate of HTC UEs (bps)
The average sum of MTC UEs' energy efficiency (bits/joule)
9
7 6 5
The minmum required rate of HTC UEs
4 3 2 1 0 100
200
300
400 500 600 700 The number of MTC UEs
800
900
1000
Fig.4 The average rate of HTC UEs versus the number of MTC UEs for different schemes
which MTC UEs are assigned to BSs such that the number of MTC UEs associated with each BS is the same. Note that, due to the lager number of UEs, the RA protocol is adopted for the UALB, CAG, Max SNR, RA, and ALL scheme. Fig. 2 shows the convergence of our designed algorithm under different numbers of MTC UEs, where K=20, βj=0.7, Npico=2, Nfemto=7, the numbers of RBs at macro, pico and femto BSs are RB macro=150, RB pico=100, and RB femto=50, respectively. It can be seen from Fig. 2 that the convergence speed drops with the number of MTC UEs D increasing. Even so, after less than 150 iterations, our algorithm converges to final solution when D=1000, which demonstrates that the proposed iterative algorithm is suitable for the scenarios where there is lager number of MTC UEs. Note that the step size α(t) is set to 0.5/t and ε=0.0012 in this and following simulations. Fig.3 shows the impact of the number of RBs on the average overall energy efficiency for different schemes, where K=2, D=10, and Npico=Nfemto=1. Our UAEE scheme can achieve the same performance as the ES algorithm and outperform the other schemes, which means that the Algorithm 1 can obtain near optimal solution. In addition, we also investigate the effect of group control on the average overall energy efficiency. It can be observed from Fig. 3 that the average overall energy efficiency increases China Communications • Supplement No.1 2015
4
x 10
11
3.5 3 UALB Max SNR UAEE ALL CAG RA
2.5 2 1.5 1 0.5 0 10
20
30
40 50 60 70 The number of HTC UEs
80
90
100
Fig.5 The average sum of MTC UEs’ energy efficiency versus the number of HTC UEs for different schemes
with βj raising due to the increase of available contending RBs for each MTC UE. Fig. 4 shows the effect of the number of MTC UEs on the average rate of HTC UEs for different schemes, where RB macro =150, RBpico=100, RBfemto=50, K=10, βj=0.7, Npico=3 and Nfemto=10. From Fig. 4, the minimum required rate of each HTC UE can be guaranteed in our scheme (the average rate is nearly close to 3 Mbps). Moreover, the average rate of HTC UEs is not affected by the number of MTC UEs due to allocating fixed RBs to each HTC UE according to its rate requirements. While for the other schemes, i.e., UABL, Max SNR, RA and ALL, since the resources is shared among HTC UEs and MTC UEs, the achievable rate of HTC UEs is affected by the number of UEs. In Fig. 5, we demonstrate the impact of the sum of MTC UEs’ energy efficiency on the number of HTC UEs for different schemes, where RBmacro=150, RBpico=100, RBfemto=50, βj = 0.7, Nfemto=3, and Nfemto =15. Since the resources of each BS is relative enough for low load, it can be obtained from Fig. 5 that the variation of the number of HTC UEs has less effect on the energy performance of MTC UEs. The performance of our scheme is better than that of the rest of schemes. However, due to scarifying the performance of MTC UEs to guarantee the HTC UEs’ rate requirements, the gap between the UAEE and the other schemes decreases with the number of HTC UEs.
100
The average number of UEs at each BS
BS1 (Macrocell) BS2 (Picocell) BS3 (Picocell) BS4 (Femtocell) BS5 (Femtocell)
450 400 350 300 250 200 150 100 50 0
RA
Max SNR
UALB
UAEE
CAG
Fig.6 The average sum of MTC UEs’ energy efficiency versus the number of HTC UEs for different schemes
Fig. 6 compares the number of MTC UEs at each BS among different schemes, where K=20, D=1000, βj=0.7, RBmacro=150, RBpico=100, and RB femto=50. The Max SNR scheme results in very unbalance loads: femto BSs are overloaded because of the better channel quality between UEs and femto BSs, while macro BS that possesses the largest number of BSs serves few UEs. Since the user association results of the UALB scheme are more related to the channel condition between UE and BS, there is still slight overload at the femto BSs because of their limited radio resources. While for the UAEE and CAG schemes, two schemes can adaptively adjust the user association results according to the number of both UEs and available RBs at BSs. Fig. 7 shows the effect of each UE’ access restriction on the average overall energy efficiency, where RB macro =150, RB pico =100, RBfemto=50, K=10, βj=0.5, Nfemto=2, and Nfemto=7. Three scenarios are considered, i.e., scenario 1: HTC and MTC UEs can access all BSs; scenario 2: HTC UEs access all BSs, MTC UEs only access femto BSs; scenario 3: HTC UEs access macro and pico BSs, and MTC UEs access femto BSs. For the four schemes, increasing the number of MTC UEs has positive effect on the average overall energy efficiency when the number of MTC UEs is small. When the number of MTC UEs reaches saturation point of the network capacity, more MTC UEs will degrade the energy efficiency performance of the whole
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The average overall energy efficiency (bits/joule)
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Fig.7 The average overall energy efficiency against the number of MTC UEs among different schemes
network. It also can be observed from Fig.7 that our scheme outperforms the other schemes for three scenarios.
VI. CONCLUSIONS In this paper, we propose a user association scheme for energy efficiency maximization in the uplink HetNet with HTC and MTC UEs coexistence. A group based random access protocol is designed for massive number of MTC UEs. The user association problem is formulated as a maximization of the overall UEs’ energy efficiency while considering the HTC UEs’ QoS guarantees and load balance among multiple BSs, simultaneously. Then, a distributed iterative algorithm based on the dual decomposition method is designed for obtaining the user association results. The convergence of the proposed algorithm is also proved. Numerical results show that our proposed scheme not only guarantees the HTC UEs’ rate requirements but also outperforms the existing methods in terms of the load balance and the average overall energy efficiency. Furthermore, it can be observed from the Fig3-Fig7 that the group control is validated for the case of massive number of MTC UEs’ transmissions.
ACKNOWLEDGEMENT This work is supported by Major Research Plan of National Natural Science Foundation of China Communications • Supplement No.1 2015
China (No. 91438115), National Natural Science Foundation of China (No. 61371123, No. 61301165), Jiangsu Province Natural Science Foundation (BK2012055), China Postdoctoral Science Foundation (2014M552612) and Jiangsu Postdoctoral Science Foundation (No.1401178C).
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Biographies Tian Hui* the corresponding author, email: jay t i a n h u i @ 1 6 3 . c o m . H e re c e i v e d B . E . d e g re e i n communication engineering from Tianjin University (TJU) in 2009, and M.S. degree in communication and information system from PLA University of Science and Technology (PLAUST), in 2012., and now is a PhD candidate in Nanjing Institute of Communication Engineering, PLAUST, Nanjing China. His research interests are focus on wireless communication, cognitive radio networks, heterogeneous network etc.
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Xu Youyun received the Ph.D. degree in information and communication engineering in 1999 from Shanghai Jiao Tong University (SJTU), China. He is currently a professor with Nanjing Institute of Communication Engineering, PLA University of Science and Technology, China. His research interests are focus on new generation wireless mobile communication system (LTE, IMT-Advanced, and Related), advanced channel coding and modulation techniques, multiuser information theory and radio resource management, and cognitive radio networks. Xu Kui received the B.S. degree in wireless communications from the PLA University of Science and Technology, Nanjing, China in 2004, and the Ph.D. degree in software defined radio from the PLA University of Science and Technology, Nanjing, China, in 2009. He is currently a lecturer in the College of Communications Engineering, PL A University of Science and Technology. His research interests include broadband wireless communications, signal processing for communications, network coding, wireless communication networks. Jun Jing received the B.S. degree, MS degree, and PH.D degree from the PLA University of Science and Technology, Nanjing, China in 2003, 2007, and 2011, respectively. His research interests include signal processing for communications, wireless communication networks. Wu Kun received BS degree from Nanjing University of Science and Technology in 2009, and M.S. degree in communication and information system from PLA University of Science and Technology (PLAUST), in 2012. Now He is a PhD candidate in Nanjing Institute of Communication Engineering, PLAUST, Nanjing China. His research interests are focus on cooperative communication, network selection channel coding, compressive sensing etc.
China Communications • Supplement No.1 2015
