A Cluster-Based Energy-Efficient Resource Management Scheme With QoS Requirement for Ultra-Dense Networks

Ultra-dense networks (UDN) have been considered as one of the best ways to improve the network throughput and energy efficiency (EE). However, massive and unplanned deployment of small cells will cause severe intra-tier interference among small cells and then deteriorate the network EE. For this, a Cluster-based Energy-Efficient Resource Management (CEERM) scheme is proposed to mitigate the interference while guaranteeing the quality of service (QoS) of user equipments (UEs) in this paper. Firstly, we propose a cell clustering algorithm to divide small cells into disjoint cell clusters according to the neighboring relationship. Then, the UEs in each cell cluster are further grouped into UE groups with the target of minimizing intra-cluster interference. Finally, a two-step subchannel allocation and non-cooperative game based power allocation scheme is proposed to maximize the network EE. The simulation results show that the proposed scheme CEERM can effectively boost the network EE with low computation complexity.


I. INTRODUCTION
Together with the rapid increase of mobile internet devices and applications, wireless traffic has encountered another explosive growth in the past few years, which motivates enhanced mobile broadband (eMBB) scenario in the fifth generation (5G) wireless networks. To meet the challenging design target for the eMBB scenario, spatial densification, including the centralized massive multiple input multiple output (M-MIMO) systems [1] and the distributed ultra dense networks (UDN) [2], [3] have been proposed in recent years. Although M-MIMO systems provide considerable benefits in terms of spectral efficiency (SE) and energy efficiency (EE), the associated deployment costs are usually high. UDN, by integrating a large number of low-power and low-cost small base stations (SBSs) in hot spots or coverage holes, is currently recognized as a promising technique to meet the The associate editor coordinating the review of this manuscript and approving it for publication was Wei Wang . eMBB throughput requirement and overcome the deployment drawbacks [1]- [3].
In general, with the coexistence of a large number of heterogeneous SBSs, the inter-cell interference is difficult to deal with due to the dynamic interference environment, which may severely degrade the network EE performance [4], [5]. In the latest research, the problem of mitigating interference is investigated to strike a balance between computational complexity and performance improvement [6]- [15]. For example, [6]- [10] focus on the centralized resource allocation to achieve the maximum energy efficiency gain, with the aid of convex optimization-based [6]- [8], graph-based [9], or even game-based [10] approaches. In order to extend the above energy-efficient approaches to UDN scenarios, one of the most challenging tasks is to perform the corresponding algorithms with a sustainable computational load. A straightforward approach often applied to UDN scenarios is grouping geographically-close SBSs into local clusters [11]- [15]. By this way, the resource allocation problems can be re-constructed hierarchically, i.e. the centralized scheduler allocates resources to SBS clusters and then each SBS cluster coordinates resources usage within its cluster. To be more specific, [11] propose a heuristic semi-dynamic clustering method with low complexity, and for a given cluster, the cluster head manages subchannels and power within the cluster. A distance-based small cell clustering algorithm is investigated in [12], where the two small cells are classified into a cell cluster when the distance between them is smaller than or equals to the threshold. In [13], an affinity propagation power control (APPC) mechanism based clustering is employed to reduce the interference among the cells in the cluster by controlling the transmission power of the cluster center. In [14], the user clustering problem is expressed as correlation clustering and settled by using semidefinite programming method, in which the boolean variable is relaxed. Literature [15] applies a graph coloring algorithm to small cells clustering and resource allocation in UDN. To further improve the network SE, the clustering idea is also extended to the user equipment (UE) side to facilitate the frequency reuse. In [16], a joint user-centric overlapped clustering algorithm is proposed to minimize the total interference within each cluster. To support a more complicated network, particularly dense small-cell network scenarios, a joint UE and SBS clustering method is developed in [17]. In [18], a two-step resource blocks assignment algorithm based on the UE clustering and a power allocation algorithm based on the non-cooperative game are discussed to improve the system EE. [19] proposes a locally distributed scheme suitable for ultra-dense small cellular networks, and divided the initial optimization problem into four steps with reasonable computational complexity, including distributed clustering, subchannel allocation within a cluster, interference resolution between clusters, and power adjustment. However, the above literature does not consider the fairness or the minimum data rate requirements (i.e., QoS requirements) of UEs. To guarantee the user experience, [20]- [30] further take the QoS requirement of UEs into account. Although QoS-aware algorithms based on convex-optimization are investigated to realize different targets, such as system capacity maximization [20], [21], EE maximization [22], the sum of transmits power for all BSs minimization [23], [24], and SE maximization [25], most of these algorithms are unsuitable for large scale UDN due to the high computational complexity. To better apply to UDN, [26] proposes an interference-separation clustering-based scheme to divide the massive small cells into smaller groups with different priorities, which reduces the network scale. A graphbased QoS-aware resource allocation(RA) scheme [27], [28] and a similarity UE clustering-based interference alignment scheme [29] are proposed to maximize the number of UEs while guaranteeing the QoS requirement of UEs. Moreover, the authors in [30] propose a non-cooperative game based joint base station (BS) association and power allocation (PA) scheme to optimize system throughput with satisfying the signal-to-interference-plus-noise ratio (SINR) requirements of all UEs. In summary, most of the existing work either researches the EE optimization problem without constraining the QoS requirements of users [6]- [10], [18], [19], or tries to meet user's QoS requirements with optimizing network performance rather than EE [20]- [30]. The following issues inevitably limit the extended application of the above research in complicated UDN scenarios. Firstly, the user fairness and transmission rate are rarely guaranteed during a scheduling period in the EE optimization problem. Secondly, how to achieve an effective balance between improving user quality of experience (QoE) and reducing energy consumption. Finally, the clustering algorithms generally suffer from the implementation complexity, either in terms of network scale or in terms of convergence rate.
To solve the above problems, our main contributions mainly include the following two aspects: 1) We propose a Cluster-based Energy-Efficient Resource Management (CEERM) scheme for Ultra-Dense Networks to maximize the network EE while guaranteeing the QoS requirement of UEs, where all SBSs are clustered into multiple small cell clusters according to the distance among SBSs and UEs are further divided in each small cell cluster into UE clusters with minimal intra-cluster interference to reduce the computational complexity of channel allocation and power allocation.
2) We propose a distributed power allocation algorithm based on the non-cooperative game, which maximizes the energy efficiency of the whole network under the premise of guaranteeing the QoS requirement of all UEs.
The rest of the paper is organized as follows. In Section II, we first introduce the system model and then formulate the cluster-based EE optimization problem. Section III presents the Cluster-based Energy-Efficient Resource Management scheme. Simulation experiments are provided to verify the effectiveness of our proposed scheme in Section IV. Conclude remarks are given in Section V.

II. SYSTEM MODEL AND PROBLEM FORMULATION
As shown in Fig. 1, we consider a two-tier downlink heterogeneous UDN, where the macro cell base station (MBS) located at the center of the network is responsible for the basic VOLUME 8, 2020 coverage while dense small base stations (SBSs) are deployed in the hotspots under the coverage of macro cell to enhance network capacity and user experience.
In this paper, we consider the scenario of orthogonal deployments, where there is no inter-tier interference. For clarity, we utilize subscripts m and s to distinguish the parameters associated with macro cell and small cells respectively. In this scenario, all available subchannels are divided into two independent fragments: N m subchannels set where p u i s ,n s is the allocated power for u i s on subchannel n s by the ith SBS, h i u i s ,n s is the channel gain between the ith SBS and SUE u i s on subchannel n s . Accordingly, the rate of MUE u m on subchannel n m and the rate of SUE u i s on subchannel n s can be written respectively as where B denotes the bandwidth of one subchannel. Hence, the throughput of macro cell and ith small cell can be expressed as R m = u m ∈U m n m ∈N m x u m ,n m R u m ,n m and R i s = u i s ∈U i s n s ∈N s x u i s ,n s R u i s ,n s , respectively. The binary indicator variable x u i s ,n s indicates whether subchannel n s is assigned to SUE u i s by the ith SBS. Generally, the power consumption of BSs includes basic power consumption and transmit power consumption [10]. Thus, the total energy consumption of macro cell and small cell can be given by where ξ m ≥ 1 and ξ s ≥ 1 denote the reciprocal of drain efficiency of the power amplifier of MBS and SBS, respectively. p b m and p b s represent the basic power consumption of MBS and the ith SBS. In orthogonal deployments, we can treat the macro cell and small cells independently since they do not share spectrum resources. To further mitigate the intra-tier inference, we focus on the RA scheme for small cells while MBS can also utilize the same scheme to realize RA. For small cells, the EE optimization problem for joint subchannel assignment and power allocation can be formulated as follows: arg max where R th denotes the minimum rate requirement of each SUE. Constraints C1 and C2 represent that each subchannel can only be assigned to one SUE in each SBS. C3 and C4 are the linear constrains for power allocation. Constraint C5 guarantees the QoS requirements of users.

III. THE CLUSTER-BASED ENERGY-EFFICIENT RESOURCE MANAGEMENT SCHEME
The optimization problem (7) is a mixed-integer nonlinear fractional program (MINLFP) problem, which is NP-hard. Convex-optimization based centralized schemes [7], [8] are too complex to solve problem (7) effectively in a real-time scenario. For this, we propose a Cluster-based Energy-Efficient Resource Management (CEERM) scheme and then transform the original optimization problem into a new clustering-based optimization problem as problem (8).
where C is defined as the set of generated cell clusters and |C| is the number of cell clusters. ∀k ∈ {1, 2, · · · , |C|} denotes the index of cell cluster. Constraint C6 and C7 indicate that the union set of all cell clusters C form the set of small cells I and the set of any two cell clusters are disjoint.
Problem (8) decomposes the original problem into two subproblems: the clustering sub-problem and RA sub-problem. Firstly, the small cells and SUEs are divided into disjoint clusters one after another to reduce the complexity of RA. Thereafter, the RA sub-problem in each cell cluster is divided into smaller sub-problems like subchannel allocation and power allocation. In this section, we concretely describe the implementation process of cell clustering, UE clustering, subchannel assignment and power allocation in our proposed scheme.
arg max

A. CELL CLUSTERING AND UE CLUSTERING
For the reason that small cells are deployed densely in UDN, the intra-tier interference and energy consumption problem are intractable to tackled by centralized mode. An intuitive way is to group SBSs into local clusters by such as conflict-graph [12], k-means [18] algorithms. The previous clustering researches are most dependent on a self-defined interference threshold and a preset number of clusters while not considering the interference topology of the network.
Assuming that all the cell clusters are sufficiently far away from each other, we can ignore inter-cluster interference.
To reduce intra-cluster interference and maintain better SE, UEs in each cell cluster are further divided into UE clusters.

1) MAX-DEGREE BASED CELL CLUSTERING
To better reflect the proximity relationship between BSs, we propose a max-degree based cell clustering algorithm, which is flexible to group SBSs based on network topology without a predetermined number of clusters. We first determine whether there are neighboring relationships D(i, j) between SBS i and SBS j in UDN according to the distance d ij between them, which is given as where d th represents the threshold of interference distance. D(i, j)=1 denotes that there is an interference relationship between SBS i and SBS j, otherwise, the interference relationship does not exist. A matrix D with an element D(i, j) describes the neighboring relationships of small cells waiting Considering that the closer the small cells are, the higher the interference will be. The purpose of the cell clustering algorithm is to cluster the SBSs close to each other into the same cell cluster as much as possible.
The main idea is to firstly select SBS i * with the largest degree as a cluster center and then take turns choosing SBSs which are closest to SBS i * in D i * as the members of this cluster. Then, cell clusters composed of only one SBS are further merged into the existing cell cluster nearest to them. Finally, we further merge all generated candidate cell clusters according to the neighboring relationship of corresponding cluster centers to avoid strong interference between cell clusters.
The algorithm of cell clustering is summarized in Algorithm 1. S represents the set of SBSs waiting for clustering. S s is the set of SBSs whose cell cluster has only one small cell. ζ denotes the current candidate cell cluster. C c is the set of cluster centers. Fig. 2 shows the cell clustering results with different d th .

2) MAX-CUT BASED UE CLUSTERING
In each cell cluster, we develop a UE clustering algorithm to further mitigate the intra-cluster interference. Because the process of UE clustering in each cell cluster is similar, we take UE clustering in the kth cell cluster as an example. At first, we set up an interference graph G(V, E) in the kth cell cluster, where the vertex set V cinsists of all UEs and the edge set E consists of edges between vertexes. The element E(u i s , u j s ) is the weight of the edge between UE u i s and UE u j s in the kth cell cluster, i.e. ∀i, j ∈ C k .It is defined as where e u i s ,u indicates the path loss between SUE u i s and ith SBS, and E th is the upper bound of the weight, which limits the number of UE in one UE cluster and is set large enough to effectively reuse spectrum resources. From the formula (10), we can see that VOLUME 8, 2020 Select SBS i * = arg max i∈S |D i | as cluster center. If there are more than one maximum, select the SBS with the smallest average distance from the adjacent SBSs.

9:
Remove the SBSs j * from D i * as D i * = D i * \{j * }.
10: end while 11: Remove all SBSs in ζ from S as S = S\ζ , and extract SBSs of ζ as a new cell cluster and save it in C.

12:
Reset ζ =∅. 13: end while 14: for all i ∈ S s do 15: if D i is not empty then 16: Select the cell cluster C k * having SBS j * = arg min j∈D i d ij . 17: UEs in the same small cell cannot be assigned to the same UE cluster. In addition, we give a metric to represent the priority of UE u i s in the kth cell cluster [17], which is given as We develop a UE clustering algorithm to group vertices of the graph into UE clusters with minimum intra-cluster interference. The objective of the UE clustering scheme is to minimize the sum weights of all UE clusters. Therefore, if we assign the same subchannels to UEs in the same UE cluster, the total interference is expected to be mitigated. We select a vertex with maximum priority as the starting point in G(V, E). Iteratively, we traverse G(V, E) to add vertexes that minimize the weight of the current UE cluster. Once the sum weight of all edges in the current UE cluster reaches the upper bound E th , the UE cluster is extracted and a new UE cluster starts to generate from the remaining vertexes. Fig. 3 shows the UE clustering results with different number of UEs per cell, where UE vertices with the same color belong to the same UE cluster, and UE1 represents a user that forms a user cluster Select the vertex v * = arg max v∈V ρ v as the start point and let ς = {v * }.

5:
while the sum weight of ς is less than E th do 6: Select Add the selected vertex v into ς as ς = ς ∪ {v }. Remove the last vertex v as v = v\{v }.

10:
Remove all the UEs of ς from set V as V = V\ς, extract the UEs of ς as a new UE cluster and save it in UC.

11:
Reset ς=∅. 12: end while together with other users, while UE2 represents a user that forms a user cluster alone.
The details of UE clustering algorithm in the kth cell cluster are described in Algorithm 2. ζ is the current candidate UE cluster. v is the set of candidate vertexes to expand the current UE cluster. UC denotes the set of generated UE clusters in the kth cell cluster and each element of UC indicates a UE cluster in the kth cell cluster.

B. SUBCHANNEL ALLOCATION AND POWER ALLOCATION
Since the EE problem is a MINLFP problem, the joint subchannel and power allocation of each cell cluster is computationally intractable. Hence, we solve the problem by subchannel allocation and power allocation iteratively. This scheme has been proved to be effective to achieve good performance with much lower complexity [7].

1) TWO-STEP SUBCHANNEL ALLOCATION
For given PA, we propose a two-step subchannel allocation algorithm for each cell cluster. In the first step, we iteratively assign subchannels to UE clusters with the largest rate requirement according to channel gains. In the second step, the remaining subchannels of each SBS are firstly allocated to SUEs without meeting the rate requirement, and then to SUEs Algorithm 3 Two-Step Subchannel Allocation 1: Initialization: R u = 0, ∀u ∈ ∪ i∈C k U i s . 2: while N s is not empty do 3: if R u ≥ R th , ∀u ∈ ∪ i∈C k U i s then 4: Update R u , ∀u ∈ UC i * and the situation of subchannel allocation ψ.

10:
Remove n * from N s as N s = N s \{n * }. 11: end while 12: for all i ∈ C k do 13: while N i s is not empty do 14: if U i s is not empty then 15: Select the UE u * = arg min u∈ U i s R u . 16 Update R u * and the situation of subchannel allocation ψ.

22:
if U i s is not empty and R u * ≥ R th then 23: U i s = U i s \{u * }.

24:
end if 25: end while 26: end for which have the best channel gains. Similarly, Algorithm 3 is summarized by taking the kth cell cluster as an example. N i s represents the set of remaining subchannels of the ith SBS after the first step in SA. The outcome of SA is denoted by the set ψ with dimension I × N s . The element in ψ records the index of the UE assigned to the subchannel by the corresponding SBS. U i s represents the set of UEs without meeting rate requirement in the ith SBS. R u denotes the acquired rate of UE u.

2) NON-COOPERATIVE GAME BASED POWER ALLOCATION
Due to the huge number of SBS, it is impractical to solve the PA problem with the channel state information of all SBSs.Here, we adopt a distributed PA method based on non-cooperative games, in which each SBS selfishly completes the PA process as a player to maximize its own EE while ensuring QoS requirements. Based on [18], we further satisfy the QoS requirements of UEs. According to the known SA results, we get the number of subchannels assigned to each UE and the UE index allocated on each subchannel for Algorithm 4 Non-Cooperative Game Based Power Allocation 1: Initialization: t = 0 and η C k ,EE (t) = 0. 2: p i,n s = P s /N s , ∀i ∈ C k , ∀n s ∈ N s and λ i = 4: t = t + 1.

5:
Update power strategies of each SBS in kth cluster based on (12), (13) and (14). 6: Calculate λ i (t), ∀i ∈ C k and η C k ,E E (t). 7: end while each SBS. According to the QoS constraints, the lower bound of the transmit power of SBS i on subchannel n s is where N u i s is the number of remaining subchannels of UE u i s .
In each iteration, if p R i ≥ 0 is the remaining power of SBS i in the process of PA, then the upper bound of transmits power for SBS i can be updated as If p min i,n s > p max i,n s , then p min i,n s = p max i,n s . Hence, the optimal transmit power of SBS i on subchannel n s can be obtained as p i,n s (t + 1) = Bp i,n s (t)g i,n s (t) λ s i ξ ln 2(1 + p i,n s (t)g i,ns (t)) p max i,ns p min i,ns (14) where g i,n s = h i,n s (I i,n s + σ 2 ) The algorithm 4 describes the non-cooperative game based PA algorithm. The matrix P C k denotes the PA result in the kth cell cluster. λ i (t) is the EE of SBS i(i ∈ C k )in tth iteration, which can be obtained by R i P C k (t) /P total i P C k (t) ·η C k ,EE (t). ηC k . EE(t) denotes the EE of kth cell cluster in tth iteration, which can be obtained by i∈C k R i P C k (t) / i∈C k P total i P C k (t) . t is the iteration index. T and represent the maximum number of iteration and the maximum tolerance value, respectively.

C. COMPUTATIONAL COMPLEXITY
In this part, we analyze the complexity of CEERM scheme by four processes. The complexity of cell clustering process can be calculated as ((I − 1) + (I − 2) + (I − 3) + . . . + 1), which is O(I 2 ). We define the average number of SBSs and UEs in each cluster asĪ c andŪ c , respectively. U s represents the average number of UEs associated to each small cell. Then, the complexity of UE clustering process is O |C| Ī c − 1 Ū s + Ū s − 1 + . . . + 1 , which can be rewritten as O I 2 U 2 s in the worst case. The complexity of SA process and PA process is Ī c . Although cell clustering algorithm and UE clustering algorithm increase the operational complexity, they are still effective to mitigate the intra-cluster interference in SA process and reduce the computational complexity in PA process.

IV. SIMULATION RESULTS
In this section, simulation results are provided to demonstrate the effectiveness of our proposed CEERM scheme. We consider a two-tier UDN, where massive small cells are randomly deployed in the coverage of macro cell. The values of simulation parameters are chosen following the guidelines of 3GPP [31], and the primary system parameters are summarized in Table 1. We use Rayleigh fading to model the channel between BS and UE. We take average results from 100 times Monte Carlo simulations trials. In each trial, we generate the locations of SBS and UE randomly.
First, the convergence of the CEERM scheme in terms of network EE versus the iteration times is analyzed in Fig. 4. It can be seen from Fig. 4(a) that the curves of network EE in different cell clusters can converge in less than 15 iterations. In other words, the Nash equilibrium is obtained within 15 iterations through the PA algorithm based on  non-cooperative games.Moreover, since the size and topological structure of each cell cluster are different, the final convergence EE of different cell clusters is also different. Fig. 4(b) shows the relationship between average EE of all cell clusters and iteration times. The average EE of all cell clusters can converge in about 12 iterations. Hence, simulation results illustrate the convergence of CEERM scheme.
Here, we examine the network performance under different d th for the proposed CEERM scheme. We set it in the range of 40m-120m, with 20m as the step length. Fig. 5 describes the cumulative distribution function (CDF) of network throughput under different d th . The figure shows that the network throughput increases as d th increases. This is because higher d th can introduce more cooperation among SBSs, so that the proposed CEERM approach can better coordinate interference. At the same time, the computational complexity of the proposed scheme will increase. Thus, we can make a trade-off between performance and complexity by tuning d th .
Next, we compare the network performance under different N m , where N m ∈ {16; 24; 32; 40; 48}. The CDFs of  network EE for these scenarios are presented in Fig. 6. The results show that a higher N m has a lower network EE. Since the central MBS uses more spectrum resources to serve a small number of MUEs instead of a large number of SUEs, the SBS consumes more energy to ensure the QoS of the SUEs, leading to the deterioration of EE Moreover, we analyze the network performance of the proposed CEERM scheme by changing R th . Fig. 7 illustrates that the network EE decreases when R th increases. Since the transmit power of SBSs are increased to satisfy the higher R th , more energy consumption and interference will deteriorate the network EE.
Finally, we compare the proposed CEERM approach with the round robin approach, the existing approach [18], and the distributed without interference coordination (DWIC) approach. For the sake of effective comparison, we adopt the same PA method for different schemes. In the round robin approach, subchannels are allocated to UE clusters by round robin. In the DWIC approach, each cell as a cell cluster adopts the proposed CEERM method. In the existing approach [18], a cell clustering algorithm based  on improved K-means algorithm and a UE grouping algorithm with minimal intra-cluster interference are proposed. However, compared with CRREM, [18] does not guarantee the QoS requirement of UEs. The relationship between the network throughput and the number of SBSs with different schemes is described in Fig. 8. We find that for all solutions, the growth rate of network throughput decreases as the number of SBS increases. This is because more SBSs incur more serious intra-tier interference, thereby effectively improving network performance. This also indicates that the proposed CEERM approach can mitigate interference more effectively than the DWIC approach which does not consider inter-tier interference and intra-tier interference. Fig. 9 plots the relationship curves of network EE and the number of SBS for the four schemes. It can be seen that the network EE first increases at the initial stage, and then declines as the number of small cells increases. Because when the number of small cell reaches a certain level, the increase in energy consumption is faster than the increase in network throughput, which ultimately deteriorates the network EE. In addition, the network EE of the proposed CEERM approach is superior to other schemes.

V. CONCLUSION
In this paper, we design a CEERM scheme consisting of a clustering phase and a RA phase to maximize network EE while ensuring QoS of UEs. In the clustering stage, the small cells are divided into disjoint clusters by the algorithm based on max-degree, and then SUEs in each cell cluster are further grouped into UE clusters by the algorithm based on maxcut, so as to minimize the interference within the cluster. The clustering process not only mitigates the intra-interference, but also reduces the computational complexity of subsequent RA. For the RA stage, each cell cluster executes the two-step SA algorithm and PA algorithm based on non-cooperative game in sequence. The simulation results show that compared with the DWIC approach without interference coordination, the CEERM scheme can significantly enhance network throughput and EE, and as the number of SBSs in UDN increases, its superiority become more and more obvious. In this work, we meet the communication requirements of users by satisfying the user rate requirement. However, with the diversified development of wireless communication services, the service requirements of different users in future network will also vary greatly. We will further consider classifying users according to variety user QoS requirements, and study energy-efficient resource allocation schemes based on user types. and co-directed the research programs for this new institute after he joined Intel Labs in 2013, where he is currently the Director of ICRI-MNC. He has published over 80 peer-reviewed research papers in top international conferences and journals. One of his most referenced articles has over 1200 Google Scholar citations, in which the findings were among the major triggers for the research and standardization of the IEEE 802.11S. He has over 20 U.S. patents granted. Some of these technologies have been adopted in international standards, including the IEEE 802.11, 3GPP LTE, and DLNA. His recent research interests include mobile networking and computing, next generation wireless communication platform, network intelligence, and SDN/NFV.