TY - JOUR
AU - Qiao,, Xiaoyu
AB - Abstract Ultra dense networks are a promising technique to achieve increasing 1000 times data rate requirements of the fifth generation (5G) wireless communications. However, due to the ‘tidal effect’ of mobile Internet traffic, the energy efficiency of the 5G communication system decreases dramatically, especially in off-peak hour, such as midnight. The software-defined wireless networks (SDWN) architecture provides a solution to reduce the energy consumption via cells management. To facilitate wide usage of cells management in SDWN, we consider in this paper the problem of joint ultra dense cells management and resource allocation, with the objective to minimize the network power consumption while guaranteeing the quality of service requirements of users and the coverage rate requirement. The problem is formulated as a mixed-integer nonlinear programming problem. To deal with this problem, we utilize the sparse characteristics of the beamforming vector and the method of reweighted l1 norm to approximate l0 norm. Because the coverage rate requirement constraint is still non-convex, we propose an iterative algorithm to derive the lower bound of the problem, and then propose a heuristic iterative algorithm to obtain a practical solution. Simulation results confirm that minimizing the total network power consumption results in sparse network topologies, and some of the small cells are inactivated when possible. The performance of the proposed heuristic algorithm is only increased by 13.09% compared with the lower bound, while the target signal-to-interference-plus-noise ratio grow from 0 to 8 dB. And the proposed heuristic algorithm can achieve good performance compared with the conventional sparsity-based algorithm. 1. INTRODUCTION Since wireless data traffic has been growing enormously in recent years, it is expected that by 2020 there will be more than 50 billion mobile users, and the data rate of users will increase 1000 times [1]. In order to achieve the quality of service (QoS) requirements of the fifth generation (5G) era, ultra dense networks (UDN) is a promising technique to improve the network capacity. However, traffic characteristic leads to unnecessary energy consumption in UDN. As is known to all, one characteristic of the mobile Internet traffic is that users are frequently moving from one place to another from rush hour to non-rush hour. This phenomenon is called ‘tidal effect’, which is much more obvious in UDN. For example, at the working time, a large number of users move from residential areas to central office areas for work; after work, users move back to their homes. Another example is that a large number of users are in the central office areas during the working time, but there are only a few users in the office areas during the lunch break. These small cells are lightly loaded but still consume almost the peak power because of some equipments, such as air conditioners and power amplifiers [2–4]. Therefore, how to efficiently manage these ultra dense cells for saving unnecessary energy consumption is a significant problem in the future 5G wireless communications. Software-defined networks is considered as a future network paradigm for improving the flexibility of networks [5–9]. Since the mobile data traffic increase exponentially, software-defined wireless networks (SDWN) is proposed for vast amount of traffic management. Meanwhile, SDWN can be self-configuration and implement applications through programmability, such as firewall support and distributed denial of service mitigation [10]. In order to improve the energy efficiency of the networks, SDWN provides an effective method to manage the small cells. A heterogeneous UDN is shown in Fig. 1. Figure 1. Open in new tabDownload slide System model. Figure 1. Open in new tabDownload slide System model. In this network, macro base stations (BSs) and small cells play different roles. Macro BSs can provide seamless coverage and low data rate services for the users. Small cells are utilized for high data rate transmission, and their work modes (active or inactive) can be adjusted flexibly by SDWN controller according to the traffic requirement. Although the method increases the transmit power of the neighboring small cells, inactivating small cells saves power much larger than the data transmit power [2–4]. Therefore, in order to save energy, the most effective way is to inactivate the small cells as many as possible. Recently, the small cells management has attracted considerable attention. There are two different ways to study the small cells management. One way is by resource allocation. To get the minimization of the power consumption at the BSs, Liao et al. [11] adapted alternating direction method of multipliers to determine the active set of BSs. To reduce the power consumption, a joint remote radio heads (RRHs) selection and beamforming design method were proposed [12]. Cheng et al. [13] considered the problem of joint downlink beamforming and network optimization, with the objective to minimize the overall BS power consumption while guaranteeing the QoS requirements of the users. To determine the active BSs, a joint downlink and uplink multiuser-access point association and beamforming design method were proposed [14]. Another way is by studying the change of traffic load. Zhang et al. [15] proposed two small cells inactive schemes with the time-varying traffic under the outage probability guarantee. Based on the predicted future traffic load, the small cells can be dynamically activated/inactivated [16]. A small cells inactive algorithm was proposed in [17], where the small cells were inactivated probabilistically according to the change of traffic load. All previous works are assumed that the users can be severed by all BSs. However, in practical engineering, the coverage area of ultra dense cells is limited, which means that not all the users can be severed by all the small cells. Therefore, the coverage area of small cells should be considered in SDWN. The most important feature of SDWN is the separation of control layer and forwarding layer [18]. We consider the energy minimization problem based on the decisions of control layer in this paper. These decisions include cells management and resource allocation. The forwarding layer is only responsible for the implementation of control layer decisions. In this paper, we focus on the energy minimization problem with QoS requirement and coverage rate requirement constraints in SDWN, which is a joint ultra dense cells management and resource allocation problem. Since the problem is a non-convex problem, we utilize the sparse characteristics of the beamforming vector to simplify the problem firstly, and then utilize the reweighted l1 norm to approximate l0 norm. However, because the constraint of coverage rate requirement is still non-convex, we propose an algorithm to get a lower bound of the problem. Then, we propose a heuristic algorithm to obtain a practical solution for the energy minimization problem. Simulation results show that the power consumption of the proposed heuristic algorithm is only increased by 13.09% compared with the lower bound, when the target signal-to-interference-plus-noise ratio (SINR) grow from 0 to 8 dB. And also the proposed heuristic algorithm can achieve good performance compared with the conventional sparsity (SP)-based algorithm. The rest of this paper is organized as follows. In Section 2, we introduce the system model, including network model, channel model, coverage rate requirement and power consumption model. In Section 3, the network consumption minimization problem is formulated and reformulated, followed by some analysis. Section 4 presents the lower bound algorithm. The heuristic algorithm is presented in Section 5. Numerical results and discussions are presented in Section 6. Finally, we conclude the paper in Section 7. 2. SYSTEM MODEL In this section, the system model of software-defined ultra dense wireless networks is described firstly. Since this work focuses on the energy management, the power consumption of the target system is modeled. 2.1. Network model In this paper, we consider a heterogeneous UDN which consists of one macro cell, L small cells equipped with N antennas and K single antenna users. The system model is shown in Fig. 1. In this system, the macro BS is used to deliver the control signals and guarantee the seamless coverage for the users. The macro BS transmits signals with constant power and exclusive frequency resource, thus the resource and power allocation of the macro BS is ignored. The small cells radio coverage is provided by RRHs. Each RRH connects to the SDWN controller through wireless link. RRH is just a signal transmission and reception point for radio frequency (RF) signal processing. The baseband signals of multiple RRHs are jointly processed in the SDWN controller, which can share processing resources, enable mobility management and interference management. Since the baseband signal processing migrated to the SDWN controller, the RRHs can be deployed in a large scale with low cost. Considering the enhanced mobile broadband requirements of IMT2020 and beyond, such as Gigabytes/s per user, the RRHs should be deployed densely [19]. But for the high-density cells deployment, the high energy cost should be concerned. Therefore, it is highly desirable to inactivate more RRHs in idle traffic duration to reduce the energy consumption with the constraints of users’ QoS requirements and the coverage rate requirement. Therefore, the network layer of SDWN controller is responsible for active/inactive management of small cells. 2.2. Channel model Let hlk∈CN×1 denote the frequency-flat quasi-static channel vector between the lth RRH and the kth user, the SDWN controller has knowledge of the instantaneous channel vector hlk. We denote the transmit beamformer from the lth RRH to the kth user as wlk∈CN×1 ⁠. Let L={1,…,L} is the set of RRH indices and K={1,…,K} denotes the set of user indices. The transmission signal between the lth RRH and the kth user can be expressed as xl=∑k=1Kwlksk,∀l∈L, (1) where sk is a complex scalar denoting the data symbol for user k. In general, we assume that E[∣sk∣2]=1 and sk is independent with each other. The received signal can be expressed as yk=∑l∈LhlkHwlkxk+∑j=1,j≠kK∑l∈LhlkHwljxj+zk,∀k∈K, (2) where zk denotes the additive white Gaussian noise at the kth user with mean zero and variance σk2,∀k∈K. The SINR for user k is given by γk=∣∑l∈LhlkHwlk∣2∑j=1,j≠kK∣∑l∈LhlkHwlj∣2+σk2,∀k∈K. (3) 2.3. Coverage rate requirement In this work, the small cells are deployed densely, which may cause a large number of overlapping coverage area. We introduce a binary variable αlk∈{0,1} to indicate that the kth user is within the coverage area of the lth RRH with αlk=1 ⁠, and αlk=0 otherwise. The SDWN controller can get the coverage information of all users. The other binary variable βlk∈{0,1} is introduced to indicate that the kth user is served by the lth RRH with βlk=1 ⁠, and βlk=0 otherwise. If a user is served by a RRH, the user must be in the coverage area of the RRH. However, the users which are in the overlapping coverage area may not be served by all the covered RRHs. We denote alk∈{0,1} to indicate whether the kth user is within the service range of the lth RRH and served by it, which can be expressed as a function of alk=αlkβlk,∀l∈L,∀k∈K. (4) Since the active/inactive mode of RRH can be controlled by the SDWN controller, we adopt the binary indicator bl∈{0,1} to indicate that the lth RRH is in active mode with bl=1 ⁠, and bl=0 otherwise. Coverage rate is an important performance metric in wireless communication system design. In heterogeneous UDN, the macro BS can guarantee the seamless coverage and provide the basic services for all the users. The small cells can provide high data rate services for the users which are in the coverage area of these small cells. In order to save power and resources, considering that the small cells with very few users can be inactivated, we introduce the coverage rate. 2.4. Power consumption model Because the power consumption of macro BS is fixed to guarantee the seamless coverage for the users, we ignore the power consumption of macro BS in this paper. The network power consumption model is essential for investigating the energy efficiency of SDWN, which can be described as follows: (1) RRH power consumption model: According to [20], we utilize the following linear model for the power consumption of a RRH: Plrrh=Pa,lrrh+∑k=1KalkPlkcomp+1ηlPlout,ifPlout>0Ps,lrrh,ifPlout=0, (5) where Pa,lrrh is the active RRH power consumption, which depends on the number of antennas. Ps,lrrh is the inactive RRH power consumption. Plkcomp represents the fixed power consumption for forwarding data and the beamforming weights wlk of the kth user to the lth RRH. Plout is the transmit power. ηl is the drain efficiency of the RF power amplifier. The typical values for RRH are set according to [20], where Pa,lrrh=6.8W ⁠, Ps,lrrh=2W ⁠, Plkcomp=0.2W and ηl=0.25 ⁠. Through this analysis, we can find that it is essential to inactivate more RRHs in order to save energy. (2) SDWN controller power consumption model: Because the complex signal processing and beamforming vector design are finished in SDWN controller, the power is mainly used for computing. According to [21], the SDWN controller power consumption is proportional to the computation capacity. In this paper, we assume that the computation capacity of SDWN controller is fixed. Therefore, the SDWN controller power consumption Pcontrol is fixed. (3) Network power consumption: Based on the above discussion, the network power consumption is given by Psum=Pcontrol+∑l=1LblPa,lrrh+∑k=1KalkPlkcomp+1ηlPlout+∑l=1L(1−bl)Ps,lrrh=∑l=1Lbl(Pa,lrrh−Ps,lrrh)+∑l=1Lbl∑k=1KalkPlkcomp+∑l=1Lbl1ηlPlout+Pcontrol+∑l=1LPs,lrrh, (6) where Plout=∑k=1K∥wlk∥22 ⁠. If the RRH set L in SDWN is given, the terms (⁠ Pa,lrrh−Ps,lrrh ⁠) and (Pcontrol+∑l=1LPs,lrrh) are constant. Based on the binary variables alk and bl, we can find the following facts [13]: if the lth RRH is in inactive mode, the lth RRH cannot serve any users, i.e. alk=0,∀k∈K ⁠. Hence, bl=0 implies {alk=0,wlk=0,∀k∈K} ⁠. The aforementioned properties regarding the binary variables {alk,bl,∀k∈K,∀l∈L} can be presented as follows: wlk=alkwlk,∀l∈L,∀k∈K, (7) bl∑k=1K∥wlk∥22=∑k=1K∥wlk∥22,∀l∈L, (8) bl∑k=1KalkPlcomp=∑k=1KalkPlcomp,∀l∈L. (9) Through (7), (8) and (9), the network power consumption by omitting the constant term (Pcontrol+∑l=1LPs,lrrh) can be expressed as P(alk,bl,wlk)=∑l=1lblPl+∑l=1L∑k=1KalkPlkcomp︸staticpower+∑l=1L∑k=1K1ηl∥wlk∥22︸transmitpower, (10) where Pl=Pa,lrrh−Ps,lrrh ⁠. We called the first part and the latter part of Equation (10) as static power consumption and transmit power consumption, respectively. 3. PROBLEM FORMULATION AND REFORMULATION Based on the power consumption model, we first formulate a problem of joint ultra dense cells management and resource allocation, with the objective to minimize the network power consumption while guaranteeing the QoS requirements of users, and then utilize the sparse characteristics of the beamforming vector to reformulate the problem. 3.1. Power saving methods and problem formulation In this section, we consider the network power minimization problem. The network power includes static power and transmit power. According to (10), the network power consumption can be reduced via two ways: Reduce the transmit power consumption. Inactivate more RRHs and reduce the number of users served by RRHs. However, these two ways are different in reducing the effect of energy consumption. As we know, the transmit power of the RRHs is only a small part of the whole network energy consumption. Of this, 72% of the energy consumption is from small cells equipments, such as air conditioners and other facilitate equipments [1]. With a large proportion of energy spent on cooling, main supply, idle-mode signaling and processing, a BS with little or no traffic load may almost consume more than 90% of its peak energy [22]. Therefore, if we only reduce the transmit power, the whole network energy will not be reduced obviously [2–4]. The most effective way is to inactivate the RRHs as many as possible firstly, and then reduce the transmit power consumption. In this paper, we assume that the SDWN controller can get the perfect channel state information (CSI). The network power consumption minimization problem with target SINRs γth=(γth1,…,γthk) can be formulated as (P1)minalk,bl,wlkP(alk,bl,wlk)=∑l=1lblPl+∑l=1L∑k=1KalkPlkcomp+∑l=1L∑k=1K1ηl∥wlk∥22 (11a) subjecttoγk≥γth,∀k, (11b) ∑k=1K∥wlk∥22≤Plmax,∀l, (11c) K′K≥δ, (11d) alk={0,1},bl={0,1},∀l,k, (11e) where ′ is the number of users served by the RRHs, and δ is the coverage rate requirement of the SDWN. Constraints (11b) mean the SINR requirements for each user. Constraints (11c) denote the sum-power of each RRH constraints. Constraint (11d) is the coverage rate requirement. Problem (P1) is a mixed-integer nonlinear programming problem, which is difficult to solve in general. In the following part, the basic idea to solve the problem is given. 3.2. Basic idea Because each user is expected to be severed by a small number of small cells, the network beamforming vector should be sparse [12]. In this paper, we utilize the sparse characteristics of beamforming vector to present the binary indicators alk, bl and the number of served users K′ ⁠. As we know, the kth user is served by the lth RRH if and only if its beamforming vector wlk is nonzero. Therefore, we utilize the ∥∥wlk∥22∥0 to replace alk. To represent the RRHs in active/inactive mode, we define the network beamforming vector as wl=[wl1T,wl2T,…,wlkT]T∈CNl×1 for each RRH l={1,2,…,L} ⁠, where Nl=N×K ⁠. If the beamforming vector wl is 0, the lth RRH is in inactive mode. Therefore, we utilize the ∥∥wl∥22∥0 to replace bl. For the number of served users K′ ⁠, we denote the network beamforming vector by wk=[w1kT,w2kT,…,wlkT]T∈CNk×1 for each user k={1,2,…,K} ⁠, where Nk=N×L ⁠. If the beamforming vector wk is 0, the kth user is not served by any RRH. Therefore, we utilize the ∑k=1K∥∥wk∥22∥0 to replace K′ ⁠. Based on the above analysis, the problem (P1) can be reformulated as (P2)minwlkP(wlk)=∑l=1l∥∥wl∥22∥0Pl+∑l=1L∑k=1K∥∥wlk∥22∥0Plkcomp+∑l=1L∑k=1K1ηl∥wlk∥22 (12a) subjecttoγk≥γth,∀k, (12b) ∑k=1K∥wlk∥22≤Plmax,∀l, (12c) ∑k=1K∥∥wk∥22∥0K≥δ. (12d) However, the problem (P2) is hard to solve due to the l0 norm involved in the objective function and the constraints. 3.3. Problem reformulation Because the problem (P2) is hard to solve, we discuss the approximation of l0 norm for the objective function and the constraints, and then analyze this problem. The l0 norm minimization problem is NP-hard problem [23]. In this section, we utilize the reweighted l1 norm to approximate l0 norm [24], which is given as ∥x∥0≈∑iλi∣xi∣, (13) where λi is positive weight. The reweighted l1 norm method increases the sparsity level of the solution and it is suitable for our problem due to the beamforming vector. With this method, problem (P2) can be approximated as (P3)minwlkP(wlk)=∑l=1lλl∥wl∥22Pl+∑l=1L∑k=1Kλlk∥wlk∥22Plkcomp+∑l=1L∑k=1K1ηl∥wlk∥22 (14a) subjecttoγk≥γth,∀k, (14b) ∑k=1K∥wlk∥22≤Plmax,∀l, (14c) ∑k=1Kλk∥wk∥22K≥δ, (14d) where λlk is the weight associated with RRH l and user k, λl is the weight of RRH l and λk is the weight of user k, which can be updated iteratively according to λlk=1∥wlk∥22+τ,∀l,k, (15) λl=1∥wl∥22+τ,∀l, (16) λk=1∥wk∥22+τ,∀k, (17) where τ is variable which should be smaller than the ∥wlk∥22 ⁠, ∥wl∥22 and ∥wk∥22 for all l∈L ⁠, k∈K ⁠. Constraints (14b) are equivalent to the following second order cone constraints [25] ∑j∈K∣Hjwj∣2+σ2≤1+1γkR(Hkwk),∀k, (18) where R(·) denotes the real part of a complex variable. Based on the reformulation, we can notice that the objective function (14a) is convex in wlk ⁠. Constraints (14b) and constraints (14c) are all convex constraints. However, constraint (14d) is not a convex constraint. Therefore, problem (P3) cannot be solved by classical convex optimization methods. 4. LOWER BOUND ANALYSIS We utilize the method of reweighted l1 norm to approximate l0 norm, problem (P3) becomes a convex problem except the constraint (14d). In this section, we propose an algorithm to obtain the lower bound of problem (P3). By observing the problem (P3), we find a fact that the problem (P3) is a convex problem in ∥wlk∥22 without considering the constraints (14b). The objective of problem (P3) is to minimize the network power consumption, and the variable of objective function is ∥wlk∥22 ⁠. Therefore, it is enough to obtain the value of ∥wlk∥22 ⁠. If the constraints (14b) can be relaxed as convex constraints in ∥wlk∥22 ⁠, the problem (P3) can be solved. Applying the Cauchy–Schwarz inequality to constraints (14b), we have 1σk2∑l∈L∥hlk∥22∑l∈L∥wlk∥22≥γth,∀k∈K. (19) It becomes a convex constraint in ∥wlk∥22 ⁠. The problem (P3) can be relaxed as (P4)min∥wlk∥22(∥wlk∥22) (20a) subjectto1σk2∑l∈L∥hlk∥22∑l∈L∥wlk∥22≥γth,∀k∈K, (20b) ∑k=1K∥wlk∥22≤Plmax,∀l, (20c) ∑k=1Kλk∥wk∥22K≥δ. (20d) Based on the analysis, the problem (P4) becomes a convex problem in ∥wlk∥22 ⁠, and it can be solved by the standard convex optimization solver such as CVX [26]. In fact, Equation (19) ignores the impact of the interference. If there is no interference effect, more RRHs can be inactivated. Therefore, the solution of problem (P4) is the lower bound of problem (P3). From the above discussion, we present an iterative algorithm to obtain the lower bound of problem (P3). We first give an initial value of ∥wlk∥22 ⁠, λlk ⁠, λl and λk ⁠. And then, we utilize the CVX package to solve problem (P4) and get ∥wlk∥22 ⁠. At last, we update λlk ⁠, λl ⁠, λk through (15), (16), (17) and update the optimal ∥wlk∥22 ⁠. The lower bound analysis algorithm is shown in Algorithm 1. Algorithm 1 Lower bound analysis algorithm. 1: Initialize ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk,∀k∈K,l∈L ⁠; 2: repeat 3:  if problem (P4) is feasible then 4: Find the optimal ∥wlk∥22 by solving the convex problem (P4) under fixed ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk; 5: Update weighted variable λlk ⁠, λl and λk according to (15), (16) and (17). 6: Update ∥w¯lk∥22=∥wlk∥22 7: end if 8: until convergence 1: Initialize ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk,∀k∈K,l∈L ⁠; 2: repeat 3:  if problem (P4) is feasible then 4: Find the optimal ∥wlk∥22 by solving the convex problem (P4) under fixed ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk; 5: Update weighted variable λlk ⁠, λl and λk according to (15), (16) and (17). 6: Update ∥w¯lk∥22=∥wlk∥22 7: end if 8: until convergence 1: Initialize ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk,∀k∈K,l∈L ⁠; 2: repeat 3:  if problem (P4) is feasible then 4: Find the optimal ∥wlk∥22 by solving the convex problem (P4) under fixed ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk; 5: Update weighted variable λlk ⁠, λl and λk according to (15), (16) and (17). 6: Update ∥w¯lk∥22=∥wlk∥22 7: end if 8: until convergence 1: Initialize ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk,∀k∈K,l∈L ⁠; 2: repeat 3:  if problem (P4) is feasible then 4: Find the optimal ∥wlk∥22 by solving the convex problem (P4) under fixed ∥w¯lk∥22 ⁠, λlk ⁠, λl and λk; 5: Update weighted variable λlk ⁠, λl and λk according to (15), (16) and (17). 6: Update ∥w¯lk∥22=∥wlk∥22 7: end if 8: until convergence 5. PROPOSED HEURISTIC ALGORITHM Due to the constraint (14d) is a non-convex constraint, problem (P3) cannot be solved. In this section, we propose a heuristic algorithm to solve the problem (P3). The objective of problem (P3) is to get the minimal power consumption of the network, and constraint (14d) is the coverage rate requirement, which means that the number of users served by all small cells cannot be less than the requirement. Based on the analysis, the solution should satisfy the following two points: (i) inactivate more small cells with the constraints (14b) and (14c); (ii) the number of users severed by small cells should be larger or equal to ⌈δK⌉ ⁠, where ⌈·⌉ denotes the nearest integers greater than or equal to. It means that K−⌈δK⌉ users do not have to be served. Therefore, the problem can be transferred to how to select the users which do not have to be severed. The main idea of the proposed heuristic algorithm is to select the users which only severed by one RRH. It is because that if these users do not have to be severed, the corresponding RRHs can be in inactive mode. The heuristic algorithm is elaborated as follows: Step 1. Determine the number of users which do not have to be served. Because the SDWN controller can get the whole information of the network, we can know the coverage area of each RRH, the position information and the CSI of each user. Step 2. Let Θ denote the set of the number of users only in one RRH coverage area, and sort them in the ascending order: θ1≤...≤θL ⁠, where θl is the order of the lth RRH. Sorting the BS does not affect the generalization. B denotes the number of users only in the chosen RRHs overlapping coverage area. Step 3. Choose the RRHs in the ascending order, and get Θ and B. (1) If θl+B≤K−⌈δK⌉ is feasible, the users in the lth RRHs coverage area will not be severed. And then, choose the next RRH to determine whether θl+B≤K−⌈δK⌉ is feasible. (2) If θl+B≤K−⌈δK⌉ is infeasible, the users whose channel condition are worst will not be severed. (3) If two or more sets are feasible, the set of the users whose channel condition are worst will not be severed. (4) If two or more sets can inactivate the same number of RRHs, the set of the users which can reduce the transmit power consumption of the networks will not be severed. As is shown in Fig. 2, we give an illustration of the heuristic algorithm. There are 20 users in the SDWN and the coverage rate requirement is 85%. Through above analysis, we know that there are three users which do not have to be severed. Because the SDWN controller can get the whole information of the network, the set of the number of users severed by only one RRH from 1 to 6 is 2, 1, 2, 2, 3 and 2. We sort them in the ascending order as RRH2, RRH1, RRH3, RRH4, RRH6 and RRH5. We first choose RRH2, θ1=1 ⁠, B = 0, 1≤3 ⁠, the θ1+B≤K−⌈δK⌉ is feasible. Therefore, the users in RRH2 coverage area do not have to be severed. And then, we choose RRH1, θ2=3 ⁠, B = 1, 4>3 ⁠, the θ2+B≤K−⌈δK⌉ is infeasible. For the same reason, RRH3 (⁠ θ3 ⁠) and RRH4 (⁠ θ4 ⁠) are all infeasible. For RRH6, we find θ5=3 ⁠, B = 0, 3≤3 ⁠, the θ5+B≤K−⌈δK⌉ is feasible. Therefore, the users in RRH2 and RRH6 coverage area do not have to be severed. Figure 2. Open in new tabDownload slide An example of heuristic algorithm. Figure 2. Open in new tabDownload slide An example of heuristic algorithm. Based on the analysis, the users which do not have to be severed are chosen. We denote problem (P3) without constraint (14d) as problem (P3-1), which becomes a convex second-order cone programming (SOCP) problem, and it can be solved by the interior point method and the CVX solver [26]. We can utilize the same method of algorithm 1 to update λlk and λl and obtain the optimal wlk. The heuristic iterative algorithm is shown in Algorithm 2. For Algorithm 2, when we determine which users have to be severed, the main computational complexity comes from solving a SOCP problem at each iteration. In particular, with a large number of RRHs, when we utilize the interior method, the computational complexity of a SOCP problem is approximately O(L3.5) [25]. Algorithm 2 Heuristic iterative algorithm. 1: Determine which users have to be severed by the heuristic algorithm. 2: Initialize w¯lk ⁠, λlk and λl ⁠, ∀k∈K,l∈L; 3: repeat 4:  if problem (P3-1) is feasible then 5:    Find the optimal wlk by solving the convex problem (P3-1) under fixed w¯lk ⁠, λlk and λl; 6:    Update weighted variable λlk and λl according to (15) and (16); 7:    Update w¯lk=wlk ⁠. 8:  end if 9: until convergence 1: Determine which users have to be severed by the heuristic algorithm. 2: Initialize w¯lk ⁠, λlk and λl ⁠, ∀k∈K,l∈L; 3: repeat 4:  if problem (P3-1) is feasible then 5:    Find the optimal wlk by solving the convex problem (P3-1) under fixed w¯lk ⁠, λlk and λl; 6:    Update weighted variable λlk and λl according to (15) and (16); 7:    Update w¯lk=wlk ⁠. 8:  end if 9: until convergence 1: Determine which users have to be severed by the heuristic algorithm. 2: Initialize w¯lk ⁠, λlk and λl ⁠, ∀k∈K,l∈L; 3: repeat 4:  if problem (P3-1) is feasible then 5:    Find the optimal wlk by solving the convex problem (P3-1) under fixed w¯lk ⁠, λlk and λl; 6:    Update weighted variable λlk and λl according to (15) and (16); 7:    Update w¯lk=wlk ⁠. 8:  end if 9: until convergence 1: Determine which users have to be severed by the heuristic algorithm. 2: Initialize w¯lk ⁠, λlk and λl ⁠, ∀k∈K,l∈L; 3: repeat 4:  if problem (P3-1) is feasible then 5:    Find the optimal wlk by solving the convex problem (P3-1) under fixed w¯lk ⁠, λlk and λl; 6:    Update weighted variable λlk and λl according to (15) and (16); 7:    Update w¯lk=wlk ⁠. 8:  end if 9: until convergence 6. RESULTS AND DISCUSSIONS In this section, we provide extensive simulation results to validate the proposed lower bound algorithm and heuristic algorithm. The simulation parameters are shown in Table 1 [12, 13]. Table 1. Parameters in simulation. Parameter description Value Channel bandwith 10 MHz Path loss from RRH to user 138.1+37.6log10(d) Small-scale fading distribution CN(0,I) Noise power −102 dBm RF drain efficiency 25% The number of RRHs 10 Antenna number of each RRH 2 The number of users 20 Coverage rate requirement 95% Maximum transmit power of RRH 1 W Pa,lrrh 6.8 W Pa,lrrh 2 W Plkcomp 0.2 W τ 10−10 Parameter description Value Channel bandwith 10 MHz Path loss from RRH to user 138.1+37.6log10(d) Small-scale fading distribution CN(0,I) Noise power −102 dBm RF drain efficiency 25% The number of RRHs 10 Antenna number of each RRH 2 The number of users 20 Coverage rate requirement 95% Maximum transmit power of RRH 1 W Pa,lrrh 6.8 W Pa,lrrh 2 W Plkcomp 0.2 W τ 10−10 Open in new tab Table 1. Parameters in simulation. Parameter description Value Channel bandwith 10 MHz Path loss from RRH to user 138.1+37.6log10(d) Small-scale fading distribution CN(0,I) Noise power −102 dBm RF drain efficiency 25% The number of RRHs 10 Antenna number of each RRH 2 The number of users 20 Coverage rate requirement 95% Maximum transmit power of RRH 1 W Pa,lrrh 6.8 W Pa,lrrh 2 W Plkcomp 0.2 W τ 10−10 Parameter description Value Channel bandwith 10 MHz Path loss from RRH to user 138.1+37.6log10(d) Small-scale fading distribution CN(0,I) Noise power −102 dBm RF drain efficiency 25% The number of RRHs 10 Antenna number of each RRH 2 The number of users 20 Coverage rate requirement 95% Maximum transmit power of RRH 1 W Pa,lrrh 6.8 W Pa,lrrh 2 W Plkcomp 0.2 W τ 10−10 Open in new tab The proposed two algorithms are compared with the conventional SP-based algorithm [27]. In this algorithm, the RRHs are also given an order, and the algorithm inactivated the RRHs for the ∑k=1K∥wlk∥212 in the ascending order. The overall computational complexity is O(L3.5N6.5+KL1.5N2.5) [27]. For the coverage rate requirement constraint, the users which have the worst channel condition will not be served in the conventional SP-based algorithm. In the following part, we simulate the performance by averaging 50 randomly generated network topologies and comparing the proposed two algorithms with the conventional SP-based algorithm with regard to the network power consumption. Figure 3 illustrates the average network power consumption versus target SINR, which shows that the proposed heuristic algorithm outperforms the conventional SP-based algorithm. It is because that the basic idea of proposed heuristic algorithm is to inactivate the RRHs as many as possible, but the basic idea of the conventional SP-based algorithm is to inactivate the RRHs with minimum transmit power. The proposed heuristic algorithm may inactivate more RRHs than the conventional SP-based algorithm. For example, the number of users is 20 and the coverage rate requirement is 95%, if there is only one user in a RRH coverage area, the proposed heuristic algorithm will inactivate the RRH with the coverage rate requirement constraint. However, this RRH may not be the minimum transmit power, thus it will not be inactivated for the conventional SP-based algorithm. This figure also demonstrates that, when the target SINR increases, the performance gap between the lower bound algorithm and the other algorithms increases. In particular, the lower bound algorithm does not consider the effect of interference. When the target SINR is small, the effect of interference is also small. With the target SINR increasing, the effect of interference becomes serious. Therefore, the gap is small at the beginning, and with the target SINR increasing, the gap becomes large. From the figure, we can see, when the target SINR is 0 dB, the power consumption of lower bound reduces by 8.66% compared with the proposed heuristic algorithm. However, when the target SINR is 8 dB, the power consumption of lower bound reduces by 13.38%. Figure 3. Open in new tabDownload slide Average network power consumption versus target SINR. Figure 3. Open in new tabDownload slide Average network power consumption versus target SINR. Figure 4 illustrates the average network static power consumption versus target SINR. For these three algorithms, the average network static power consumption increases with the target SINR increasing. It is because that a large number of active RRHs are needed to guarantee the QoS of users. However, with the target SINR increasing, the increasing rate of network static power consumption becomes slow. It is because that RRHs are almost active to serve users when the target SINR becomes large. Figure 4. Open in new tabDownload slide Average network static power consumption versus target SINR. Figure 4. Open in new tabDownload slide Average network static power consumption versus target SINR. Figure 5 illustrates the average network transmit power consumption versus target SINR. From this figure, we can see that with the target SINR increasing, a higher beamforming gain is needed. Therefore, the average network transmit power consumption increases. Figure 5. Open in new tabDownload slide Average network transmit power consumption versus target SINR. Figure 5. Open in new tabDownload slide Average network transmit power consumption versus target SINR. Figure 6 illustrates the average network power consumption versus the number of mobile users. The target SINR of users is 2 dB. From this figure, we can see that with the number of mobile users increasing, the average network power consumption also increases. This is because when the number of mobile users increases, a large number of RRHs need to be activated in order to guarantee the QoS of users. Figure 6. Open in new tabDownload slide Average network power consumption versus the number of mobile users. Figure 6. Open in new tabDownload slide Average network power consumption versus the number of mobile users. Figure 7 illustrates the average network power consumption versus the coverage rate requirement. The target SINR of users is 2 dB. From this figure, we can see that with the coverage rate requirement increasing, the average network power consumption also increases. This is because the coverage rate requirement increases, more users have to be severed. Therefore, more RRHs need to be activated. Figure 7. Open in new tabDownload slide Average network power consumption versus the coverage rate. Figure 7. Open in new tabDownload slide Average network power consumption versus the coverage rate. 7. CONCLUSION In this paper, we investigated the ultra dense cells management in SDWN. We formulated a problem of joint ultra dense cells management and resource allocation, with the objective to minimize the network power consumption while guaranteeing the QoS requirements of users and the coverage rate requirement. Because the problem is a non-convex problem, we utilized the sparse characteristics of the beamforming vector and the method of reweighted l1 norm to approximate l0 norm to reformulate this problem. And then we proposed an iterative algorithm to get a lower bound of the problem and proposed a heuristic iterative algorithm to obtain a practical solution. Simulation results have demonstrated that the proposed lower bound algorithm and the heuristic algorithm can achieve good performance. The system architecture provides a new view point to reduce the unnecessary energy consumption of UDN in the 5G wireless communications. The proposed joint cells management and resource allocation scheme can be easily used in the future 5G system energy efficiency optimization. For this paper, there are two aspects which can be extended. (i) The SDWN controller is composed of a large number of virtual machines (VMs) which can be in active/inactive model according to the fluctuating traffic. We will consider the active/inactive model of VMs and focus on joint VMs and RRHs resource allocation to minimize the power consumption. (ii) For the users, the power consumption of users’ equipments needs to be considered. Based on the first work, we will focus on joint VMs, RRHs and users to minimize the total power consumption subject to the users’ QoS requirements. FUNDING National Key Research and Development Program of China (No. 2016YFB1200102); the National Natural Science Foundation of China (Nos. 61501023, 61501024, U1334202 and U1534201); the State Key Laboratory of Rail Traffic Control and Safety (Nos. RCS2015ZT001 and RCS2016ZZ004); the Project of China Railway Corporation under Grant (No. 2016X003-O). REFERENCES 1 Mobile , C. ( 2011 ) C-RAN: The Road Green RAN White Paper V3.0 , China Mobile Research Institute , Beijing, China . Google Preview WorldCat COPAC 2 Imran , M.A. and Katranaras , E. ( 2011 ) Energy Efficiency Analysis of the Reference Systems, Areas of Improvements and Target Breakdown , ICT-EARTH Project, Deliverable D2. 3, EC-IST Office , Brussels, Belgium . Google Preview WorldCat COPAC 3 Guo , X. , Niu , Z. , Zhou , S. and Kumar , P.R. ( 2016 ) Delay-constrained energy-optimal base station sleeping control . IEEE J. Sel. Area. Commun. , 34 , 1073 – 1085 . Google Scholar Crossref Search ADS WorldCat 4 Wu , J. , Bao , Y. , Miao , G. , Zhou , S. and Niu , Z. ( 2016 ) Base-station sleeping control and power matching for energy delay tradeoffs with bursty traffic . IEEE Trans. Veh. Technol. , 65 , 3657 – 3675 . Google Scholar Crossref Search ADS WorldCat 5 Rawat , D.B. and Reddy , S. ( 2016 ) Recent Advances on Software Defined Wireless Networking. 2016 SoutheastCon, Norfolk, VA, 30 March–3 April, pp. 1–8. IEEE, Piscataway. 6 Kong , L. , Lin , S. , Xie , W. , Qiao , X. , Jin , X. , Zeng , P. , Ren , W. and Liu , X.Y. ( 2016 ) Adaptive barrier coverage using software defined sensor networks . IEEE. Sens. J. , 16 , 7364 – 7372 . Google Scholar Crossref Search ADS WorldCat 7 Kong , L. , Liu , X.Y. , Tao , M. , Wu , M.Y. , Gu , Y. , Cheng , L. and Niu , J. ( 2015 ) Resource-efficient data gathering in sensor networks for environment reconstruction . Comput. J. , 58 , 1330 – 1343 . Google Scholar Crossref Search ADS WorldCat 8 Zhou , Q. , Wang , C.X. , McLaughlin , S. and Zhou , X. ( 2015 ) Network virtualization and resource description in software-defined wireless networks . IEEE Commun. Mag. , 53 , 110 – 117 . Google Scholar Crossref Search ADS WorldCat 9 Wang , Y. and Bi , J. ( 2016 ) Software-defined mobility support in IP networks . Comput. J. , 59 , 159 – 177 . Google Scholar Crossref Search ADS WorldCat 10 Reddy , Y. , Krishnaswamy , D. and Manoj , B.S. ( 2015 ) Cross-Layer Switch Handover in Software Defined Wireless Networks. In 2015 IEEE Int. Conf. Adv. Netw. Telecommun. Syst. (ANTS), Kolkata, India, December 15–18, pp. 1–6. IEEE, Piscataway. 11 Liao , W.C. , Hong , M. , Liu , Y.F. and Luo , Z.Q. ( 2014 ) Base station activation and linear transceiver design for optimal resource management in heterogeneous networks . IEEE Trans. Signal Process. , 62 , 3939 – 3952 . Google Scholar Crossref Search ADS WorldCat 12 Shi , Y. , Zhang , J. and Letaief , K.B. ( 2014 ) Group sparse beamforming for green cloud-RAN . IEEE Trans. Wirel. Commun. , 13 , 2809 – 2823 . Google Scholar Crossref Search ADS WorldCat 13 Cheng , Y. , Pesavento , M. and Philipp , A. ( 2013 ) Joint network optimization and downlink beamforming for comp transmissions using mixed integer conic programming . IEEE Trans. Signal Process. , 61 , 3972 – 3987 . Google Scholar Crossref Search ADS WorldCat 14 Luo , S. , Zhang , R. and Lim , T.J. ( 2015 ) Downlink and uplink energy minimization through user association and beamforming in C-RAN . IEEE Trans. Wirel. Commun. , 14 , 494 – 508 . Google Scholar Crossref Search ADS WorldCat 15 Zhang , S. , Gong , J. , Zhou , S. and Niu , Z. ( 2015 ) How many small cells can be turned off via vertical offloading under a separation architecture . IEEE Trans. Wirel. Commun. , 14 , 5440 – 5453 . Google Scholar Crossref Search ADS WorldCat 16 Morosi , S. , Piunti , P. and Re , E.D. ( 2013 ) Sleep mode management in cellular networks: a traffic based technique enabling energy saving . Trans. Emerg. Telecommun. Technol. , 24 , 331 – 341 . Google Scholar Crossref Search ADS WorldCat 17 Zhang , S. , Wu , J. , Gong , J. , Zhou , S. and Niu , Z. ( 2014 ) Energy-Optimal Probabilistic Base Station Sleeping under a Separation Network Architecture. In 2014 IEEE Global Commun. Conf., Austin, TX, December 8–12, pp. 4239–4244. IEEE, Piscataway. 18 Arslan , M.Y. , Sundaresan , K. and Rangarajan , S. ( 2015 ) Software-defined networking in cellular radio access networks: potential and challenges . IEEE Commun. Mag. , 53 , 150 – 156 . Google Scholar Crossref Search ADS WorldCat 19 ITU-R, M ( 2014 ) Framework and Overall Objectives of the Future Development of IMT for 2020 and Beyond , International Telecommunications Union , Geneva, Switzerland . Google Preview WorldCat COPAC 20 Auer , G. et al. . ( 2011 ) How much energy is needed to run a wireless network . IEEE Wirel. Commun. , 18 , 40 – 49 . Google Scholar Crossref Search ADS WorldCat 21 Tang , J. , Tay , W. and Quek , T. ( 2015 ) Cross-layer resource allocation with elastic service scaling in cloud radio access network . IEEE Trans. Wirel. Commun. , 14 , 5068 – 5081 . Google Scholar Crossref Search ADS WorldCat 22 Oh , E. , Krishnamachari , B. , Liu , X. and Niu , Z. ( 2011 ) Toward dynamic energy-efficient operation of cellular network infrastructure . IEEE Commun. Mag. , 49 , 56 – 61 . Google Scholar Crossref Search ADS WorldCat 23 Bonami , P. , Kilin , M. and Linderoth , J. ( 2012 ) Algorithms and software for convex mixed integer nonlinear programs. In Mixed Integer Nonlinear Program. , 1 – 39 . Springer . Google Preview WorldCat COPAC 24 Candes , E.J. , Wakin , M.B. and Boyd , S. ( 2008 ) Enhancing sparsity by reweighted l1 minimization . J. Fourier Anal. Appl. , 14 , 877 – 905 . Google Scholar Crossref Search ADS WorldCat 25 Boyd , S. and Vandenberghe , L. ( 2004 ) Convex Optimization , Cambridge University Press , Cambridge . Google Scholar Crossref Search ADS Google Preview WorldCat COPAC 26 Grant , M. and Boyd , S. ( 2014 ) CVX: matlab software for disciplined convex programming, version 2.1. http://cvxr.com/cvx. 27 Mehanna , O. , Sidiropoulos , N.D. and Giannakis , G.B. ( 2013 ) Joint multicast beamforming and antenna selection . IEEE Trans. Signal Process. , 61 , 2660 – 2674 . Google Scholar Crossref Search ADS WorldCat 28 Rengarajan , B. , Rizzo , G. and Marsan , M.A. ( 2011 ) Bounds on QoS-Constrained Energy Savings in Cellular Access Networks with Sleep Modes. In 2011 23rd Int. Teletraffic Congress (ITC), San Francisco, CA, September 6–9, pp. 47-54. IEEE, Piscataway. Author notes Handling editor: Linghe Kong © The British Computer Society 2017. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
TI - Ultra Dense Cells Management and Resource Allocation in Green Software-Defined Wireless Networks
JF - The Computer Journal
DO - 10.1093/comjnl/bxx028
DA - 2017-10-01
UR - https://www.deepdyve.com/lp/oxford-university-press/ultra-dense-cells-management-and-resource-allocation-in-green-software-VbPyuqMqxE
SP - 1472
VL - 60
IS - 10
DP - DeepDyve
ER -