Multi-Objective Energy Efficient Resource Allocation in Massive Multiple Input Multiple Output-Aided Heterogeneous Cloud Radio Access Networks

In this work, a novel energy efficient multi-objective resource allocation algorithm for heterogeneous cloud radio access networks (H-CRANs) is proposed where the trade-off between increasing throughput and decreasing operation cost is considered. H-CRANs serve groups of users through femto-cell access points (FAPs) and remote radio heads (RRHs) equipped with massive multiple input multiple output (MIMO) connected to the base-band unit (BBU) pool via front-haul links with limited capacity. We formulate an energy-efficient multi-objective optimization (MOO) problem with a novel utility function. Our proposed utility function simultaneously improves two conflicting goals as total system throughput and operation cost. With this MOO, we jointly assign the sub-carrier, transmit power, access point (AP)(RRH/FAP), RRH, front-haul link, and BBU. To address the conflicting objectives, we convert the MOO problem into a single-object optimization problem using an elastic-constraint scalarization method. With this approach, we flexibly adjust trade-off parameters to choose between two objective functions. To propose an efficient algorithm, we deploy successive convex approximation (SCA) and complementary geometric programming (CGP) approaches. Finally, via simulation results we discuss how to select the values of trade-off parameters, and we study their effects on conflicting objective functions (i.e., throughput and operation cost in MOO problem). Simulation results also show that our proposed approach can offload traffic from C-RANs to FAPs with low transmit power and thereby reduce operation costs by switching off the under-utilized RRHs and BBUs. It can be observed from the simulation results that the proposed approach outperforms the traditional approach in which each user is associated to the AP (RRHs/FAPs) with the largest average value of signal strength. The proposed approach reduces operation costs by 30 % and increases throughput index by 25 % which in turn leads to greater energy efficiency (EE).


I. INTRODUCTION A. MOTIVATIONS
To meet the demand of expanding services in fifth-generation (5G) wireless networks (e.g., services from vertical industries, enterprises, and Internet companies), networks with high data rates and enhanced quality-of-service (QOS) are The associate editor coordinating the review of this manuscript and approving it for publication was Mehdi Sookhak . increasingly expected. Indeed, with the proliferation of massive number of online heterogeneous devices, such as tablets, sensors for home security, and wearable health monitors, the energy consumption of future networks could result in serious restrictions, which must be considered [1]. This tremendous increase in mobile data traffic with high data rates raises new challenges in terms of increasing energy efficiency (EE) and providing high-quality services for various traffic types in 5G networks [1], [2], [3]. Cloud radio access networks (C-RANs), massive multiple input multiple output (MIMO) and heterogeneous networks (HetNets) are three key technologies suggested for 5G that can significantly enhance EE [1], [2], [3].
Massive MIMO systems provide opportunities for increasing spectral efficiency (SE) and simultaneously improving EE [4], [5], [6]. In addition, the deployment of small-cell variations, such as low-power femto access points (FAPs), in HetNets is a promising approach for handling massive heterogeneous traffic. FAPs also enhance SE and EE in 5G. By applying traffic offloading, FAPs can provide data distribution to release the pressure of macro access points and improve the QoS of users, particularly for cell-edge users, which may lead to switching off of under-utilized high-power macro access points [7], [8].
Moreover, C-RANs are a promising architecture for significantly enhancing EE in 5G. enhance EE [9], [10], [11]. In C-RANs, by separating the remote radio head (RRH) from the baseband units (BBUs), all baseband processing functions are carried out through a centralized cloud called a BBU pool. BBUs are connected to the RRHs by limited capacity front-haul links. With their fully centralized processing and management design, C-RANs are able to achieve cooperative gains, such as interference management and load balancing. Thus by switching off RRHs and BBUs, EE can be improved [11], [12].
To leverage these three technologies, heterogeneous cloud radio access networks (H-CRANs) have been introduced, which include a large number of RRHs equipped with massive MIMO in order to enhance EE [13]. Combining them offers a large set of parameters and flexibility in system design, but at the expense of highly complex multi-objective resource allocation (MORA) problems [14], [15]. In high density H-CRANs, handling all users by high throughput and low energy consumption cost is important. By deploying a large number of RRHs in a cell, SE and the throughput of the whole network will be improved, which may lead to under-utilized RRHs and BBUs, and consequently increased energy consumption costs and decreased EE [16]. Therefore, to reduce energy consumption costs, simultaneously maximizing the throughput and minimizing the number of active RRHs and BBUs are considered two conflicting objective functions for improving EE [17]. Hence, 5G should follow other frameworks, such as a MORA, where conflict objectives can be integrated in a multi-objective optimization (MOO) problem [14], [18].
To address these challenges, the main contributions of this paper are summarized as follows: 1) We formulate a centralized EE MORA optimization problem in MIMO-aided H-CRAN. In so doing, we propose a novel utility function and a new set of constraints that aim to maximize the total system throughput while minimizing operation costs in order to jointly assign cloud assignment parameters (CAPs), including sub-carrier, access points (APs)(RRH/FAP) assignment, RRH and front-haul link to active BBUs, and transmit power allocation to each user. Our proposed resource allocation problem in this paper highlights the new aspects of H-CRAN with a combination of three technologies (e.g., C-RANs, MIMO and Het-Nets), a new utility function, and a novel set of assigned resource parameters. 2) We discuss how to select the values of trade-off parameters, and we study their effects on conflicting objective functions (i.e., throughput and operation cost in MOO problem). The simulation results show that by adjusting the value of trade-off parameters and by considering energy consumption cost of RRHs, BBUs and total transmit power of all users as operation costs in utility function, the traffic of users associated with underutilized RRHs can be offloaded to neighboring FAPs with low transmit power. Consequently, under-utilized RRHs and BBUs and their corresponding front-haul links can be switched off for greater EE. Simultaneous reduction of these three costs is the novelty of the MORA algorithm in this work.
3) The conflicting objectives and highly complex relation between various optimization variables and their effects on each other make the formulated MOO problem much more difficult to solve. To tackle this issue, we apply an elastic-constraint scalarization method [18], [19] to convert the MOO problem into a single-objective optimization (SOO) problem with low computational complexity, which allows for trade-off parameters and a flexible choice between increasing throughput and decreasing operation cost functions for different preferences. 4) Due to interference among users from different APs and the existence of binary variables, the proposed optimization problem is inherently non-convex, NPhard, and suffers from high computational complexity. By applying successive convex approximation (SCA) and complementary geometric programming (CGP) techniques to various transformations and convexification approaches [20], [21], [22], such as arithmetic-geometric mean approximation (AGMA), we convert the SOO problem into a convex problem, which can be solved with available software (e.g., CVX) [23]. 5) The simulation results showed that our proposed approach can offload traffic from C-RANs to FAPs with low transmit power, and reduce operation costs by switching off under-utilized RRHs and BBUs. Also, the simulation results illustrate that Pareto optimal solutions are different under diverse sets of system parameters.

B. RELATED WORKS
Many systems or applications have been developed for distributed environments with the goal of attaining multiple objectives in the face of environmental challenges such as VOLUME 11, 2023  high dynamics/hostility, or severe resource constraints (e.g., energy or communications bandwidth). Often the multiple objectives are conflicting with each other, requiring optimal tradeoff analyses between the objectives [18]. In this context, MOO problems are considered when balancing the trade-off among two or more objectives [24], [25]. There are common solution approaches for MOO problems, such as weighting method, goal programming, and elastic-constraint scalarization method [19]. This work focuses on the intersection of two main areas in H-CRAN resource allocation problems: EE and MOO. In the area of EE, there has been a surge of research (e.g., in [4], [8], [13], [16], [26], [27], and [28]). In these works, the EE MOO problem is not considered. For example, in order to maximize EE in HetNets, the authors in [8] and [28] formulated a joint power and sub-carrier assignment as a noncooperative game. Reference [13] used a Lagrange dual decomposition method to minimize the power consumption of users while allocating access points (APs) and power to each user in a H-CRAN.
Reference [15] formulated the MOO resource allocation problem for maximizing the achievable rate/SE and minimizing the total power consumption by using the sum weighted method. The authors applied the generalized framework of the resource allocation for the EE-SE trade-off to optimally allocate the subcarriers' power for OFDMA with imperfect channel estimation. Reference [19] studied two contradictory objectives, namely, total flowtime and total energy consumption (TEC) in a green permutation flowshop environment. To address the conflicting objectives of minimizing TEC and total flowtime, the augmented epsilon-constraint approach was employed to obtain Paretooptimal solutions. In [29] and [30], the authors formulated a joint dynamic radio resource allocation MOO problem for massive MIMO-enabled HetNets with the aim of maximizing EE and SE simultaneously. The studies in [29] and [30] employed the weighted sum method and weighted Tchebycheff method, respectively, to transform the MOO problem into an SOO problem. In [31], the researchers formulated a joint design for RRH selection, RRH user association, and transmit beamforming, where a branch-and-reduce-andbound algorithm was applied to simultaneously optimize the achievable sum rate and total power consumption using the MOO concept in C-RANs. The authors in [17] formulated an EE MOO problem for uplink multi-cell networks using a joint design for sub-channel assignment, power control, and antenna selection, where the weighted Tchebycheff method was deployed. Reference [32] formulated a joint SE-EE based design as a MOO problem to achieve a good trade-off between SE and EE. This work exploited a priori articulation scheme combined with the weighted sum approach to transform the original MOO problem as a conventional SOO problem and used SCA technique to solve the non-convex SOO problem. In [33] the EE-SE tradeoff problem modeled as a MOO through jointly optimizing power allocation, active precoding at the BS, and passive precoding at the in intelligent reflecting surface (IRS) millimeter wave (mmWave) non-orthogonal multiple access (NOMA) systems. Then, the authors used the weighted-sum method to transform the MOO problem into a SOO problem. The above mentioned works are summarized in Table 1. However, to the best of our knowledge, no other works have considered the EE MORA problem in H-CRANs. Moreover, none of the aforementioned works has considered user association jointly with dynamic radio resource allocation and C-RAN limitations (e.g., maximum BBU capacity and front-haul capacity) with a view to reducing RRHs and BBUs energy consumption costs, particularly by switching off under-utilized RRHs and BBUs in MIMO-aided H-CRAN. This work aims to fill this gap.
In what follows, Section II describes the system model and formulation of the MORA problem. Section III introduces the proposed two-step iterative MORA algorithm, followed by an analysis of its computational complexity. Section IV presents the simulation results. Section V concludes this paper.

II. SYSTEM MODEL AND PROBLEM FORMULATION
We consider a down-link transmission in a two-tier orthog-  Table 2, M = R F denote the set of all APs in this region. Each RRH r ∈ R is equipped with J r ≫ 1 antennas (i.e., massive MIMO) and is connected to the BBU pool by a limited capacity front-haul link. FAPs are connected to the core network through back-haul links. A BBU pool consists of a set of B = {1, . . . , B} BBUs to process the received baseband signals from all RRHs. The total bandwidth W is divided into a set of sub-carriers S = Let p s m,n and h s m,n represent the transmit power and channel gain of user n ∈ N to AP m ∈ M on sub-carrier s ∈ S, respectively. We consider the number of simultaneously served users by a RRH r, be smaller than the number of transmit antennas as J r ≫ N r . The achievable throughput of user n ∈ N over sub-carrier s ∈ S VOLUME 11, 2023 33483 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.
in AP m ∈ M is as [30], [ where I s m,n = ∀m ′ ∈M,m ′ ̸ =m ∀n ′ ̸ =n p s m ′ ,n ′ h s m,n ′ is the interference to user n ∈ N in AP m ∈ M and sub-carrier s ∈ S, and σ 2 is the noise power. Moreover, P, α, and β are matrices of all p s m,n , α s m,n and β m,n , respectively, for all n ∈ N , ∀m ∈ M and s ∈ S. Due to the dense deployment of RRHs and the capability of turning them on or off, we consider a vector of all RRHs as τ = [τ r ] 1×R , where τ r denotes the on and off states of RRH r ∈ R as The RRHs and BBUs are connected by a limited capacity front-haul link. Therefore, the binary variable z r,b is introduced to assign RRH r to BBU b, and stipulates front-haul link between them as Hence, Z = [z r,b ] R×B is defined as a matrix of associated RRHs to BBUs. The binary variable matrix X = [x b ] 1×B is introduced to describe the on and off states of BBU b ∈ B as We consider ℑ = {α, β, P, τ , Z, X}, and with the aim of decreasing network operation cost, we define a novel network utility function as which is the total throughput (U 4 (α, β, P)) minus the total operation cost function. We define operation cost function as the sum of the energy consumption cost of active RRHs, active BBUs, and total transmit power of all users, which are denoted by U 1 (τ ), U 2 (X) and U 3 (α, β, P), respectively. Simultaneous reduction of these three costs is the novelty of the MORA algorithm in this work. In (2), we consider the energy consumption cost of RRHs; in other words, U 1 (X) is proportional to the total rate transmitted rate by the number of allocated antennas to active RRHs. Hence, µ a is defined as the energy consumption cost of each antenna, which is static and proportional to the maximum transmission rate of each antenna, and its unit is bps/Hz. Furthermore, µ b is defined as the energy consumption cost of each BBU b ∈ B, which is static and proportional to its maximum load capacity [35]. Hence, the unit of U 2 (X) will be bps/Hz. In (2), due to the fact that different objective functions have different units (e.g. bps/Hz for throughput and Watt for transmit power), and the values of objective functions are not in the same range [8], µ p is considered to be a dimension regulation factor and a cost of the total transmit power of all users, and accordingly its unit is bps/Hz/Watt. This means that the unit of utility function (2) is bps/Hz, and, based on (2), the MORA problem to maximize EE can be written as ∀r ∈ R, C8 : r∈R n∈N s∈S z r,b α s r,n β r,n R s r,n (P, β) In (3), C1 denotes the transmit power of each AP m ∈ M limited by p max m . The required minimum reserved rate (i.e., R rsv n ) of each user can be indicated by C2. Due to OFDMA constraints, C3 and C4 stipulate that each user n ∈ N can only be served by at most one AP, and each sub-carrier must be associated to at most one user within each AP, respectively. C5 stipulates that AP m can allocate sub-carrier s to user n when Ap m is assigned to user n. C6 stipulates that each RRH r ∈ R can be assigned to at most one BBU. Based on C7 and C8, the total allocated load to the front-haul link z r,b and the BBU b is bounded by F max r,b and T max b , respectively. A fronthaul link can be activated between RRH r ∈ R and BBU b ∈ B when BBU b is switched on. Consequently, RRH r ∈ R can be activated when at least one corresponding front-haul link is switched on (i.e., the variable τ r should be equal to one). To mathematically represent these two practical considerations, we have C9 and C10. Finally, C11 stipulates that each user n can be associated to RRH r when RRH r is active and ϱ ≫ 1 is a constant value.
(3) represents a MOO problem because it consists of conflicting objectives U 1 , U 2 , U 3 , and U 4 . For example, with increasing P, U 3 , U 4 will increase while U 3 decreases (3). Hence, there is a trade-off between the increasing total throughput and the decreasing total operation cost. Therefore, finding optimal solutions for (3) is an over-constrained problem [18]. To tackle this computational complexity, we apply the elastic-constraints method [18] ( See Appendix I), which allows us to generate a single objective function by selecting one of the multiple objective functions (i.e., U 4 ) as the primary objective function and to consider the remaining objective functions as constraints. To apply the elastic-constraints method, we rewrite (3) as Then, based on the elastic-constraints method, we consider the total throughput as the primary objective function (i.e., U 4 ) and objectives U 1 , U 2 and U 3 as new constraints. Therefore, (4) can be reformulated as an SOO problem accordingly; In (5), slack variables L i and surplus variables s ′ i are utilized to convert the upper bound ε i on the objective value U i into an equality constraint, and π i is the penalty coefficient for a given objective U i . We consider ε 1 , ε 2 , and ε 3 as the upper bounds of the energy consumption costs of RRHs, BBUs, and the total transmit power of all users, respectively. In this context, by changing the values of ε i for a given objective U i , a set of Pareto optimal solutions is derived [36]. Then, according to network conditions, one of the Pareto optimal solutions can be selected. In Section IV, we will investigate the effect of the variation value of ε i s as trade-off parameters on the network performance through simulation results. Now, we first focus on solving (5), which is a non-convex and NP-hard resource allocation problem with high computational complexity [37].

III. TWO-STEP ITERATIVE ALGORITHM FOR DYNAMIC RESOURCE ALLOCATION
To solve (3), we propose an efficient two-step iterative algorithm as summarized in Table 3. Each step is also iterative. At each iteration t, Step 1 with a given (fixed) power allocation vector computes the Pareto optimal solution for the CAPs, i.e., α, β, τ , Z, X. Then, in Step 2, the transmit power is allocated among users based on a given fixed set of CAP parameters derived in Step 1. The whole process can be explained as where t ≥ 0 is the iteration index in each step. Also, α * (t), β * (t),τ * (t), Z * (t), X * (t), and P * (t) are optimal values obtained at iteration t. The iterative procedure stops when the VOLUME 11, 2023 convergence criteria are met. That is, when However, the optimization problems of Steps 1 and 2 are still non-convex and encounter high computational complexity. To solve them, by using CGP [22] along with various transformations and convexification approaches, we convert non-convex problems into the equivalent lower-bound GP problems. See Section III-A in [37] for more information about the preliminaries of CGP.

A. STEP 1: CAP ALLOCATION ALGORITHM
Assuming a fixed value of P(t) in a high signal-tointerference-plus-noise ratio (SINR) scenario, we have where γ s m, is the SINR of user n ∈ N at AP m ∈ M on sub-carrier s ∈ S and it has a fixed value for this step. Therefore, at iteration t 1 , (5) is converted to In (7) the optimization variables are ℑ, L i , and s ′ i , and (7) has less computational complexity than (5). However, due to the binary variables and the non-linear function of the throughput, (7) is still a non-convex optimization problem. To overcome these issues, we aim to convert (7) into the standard form of GP. Since, in (7), N m is a function of β m,n . Therefore, converting (7) into the standard form of GP suffers from high computational complexity. Hence, we first relax the binary variables as α s Then, by applying various transformations and DC approximation, we try to develop the analytical framework to transform the non-convex optimization problems into the equivalent lower-bound standard form of GP. Hence, at iteration t 1 , (7) is converted into (see   1) . Now, based on (8), AGMA, and Proposition 1, we derive the GP approximation of (7) for each iteration. We assume t 1 as the index of iterations in Step 1.

B. STEP 2: POWER ALLOCATION ALGORITHM
From the values obtained of α * (t), β * (t), τ * (t), Z * (t), and X * (t) obtained from Step 1, the optimization problem for power allocation in Step 2 is where t 2 is the index of iterations in Step 2. Note that in (35), the only optimization variable is P. Therefore, (35) has less computational complexity than (3). Since, τ and X have fixed values, the objectives U 1 and U 2 are constant and do not affect the problem solution of this step. Hence, similar to (5), by considering the total throughput (i.e., U 4 ) as the primary objective function and the total transmit power of all users (i.e., U 3 ) as constraint C0, we can transform (35) into a single objective optimization problem as follows: where the slack and surplus variables L 4 (t 2 ) and s ′ 4 (t 2 ) are associated with the bound ε 3 on objective U 3 . Also, π 4 is the penalty coefficient. Since R s m,n (P(t 2 )) is a non-linear function, (36) is a non-convex optimization problem. To tackle this computational complexity, we first apply DC approximation of R k,s,n (P) at iteration t 2 , and then by using AGMA, we will convert (36) into a GP approximation as shown in Proposition 2.

C. CONVERGENCE AND COMPUTATIONAL COMPLEXITY
Based on [40], our proposed resource allocation algorithm belongs to block SCA algorithm. It was shown in [41] that with AGMA approximation, the SCA method converges to a locally optimal solution that satisfies the Karush-Kuhn-Tucker (KKT) conditions. Thus, by applying AGMA approximation, the convergence of (9) and (37) to a local optimal solution are guaranteed.
CVX uses interior point method for solving GP sub-problems in Steps 1 and 2. According to [42], using this method, the required number of iterations to solve this is log(c/(νt 0 )) log ζ , where c, ν, and t 0 are the total number of constraints, the stopping criterion, and the initial point to approximate the accuracy, respectively. Also, ζ is used for updating the accuracy of the method. The numbers of constraints in (9) and (37)  Step 2. Furthermore, for each iteration in Steps 1 and 2, i 1 = 2FNS + 3RNS + MNS + 2RB + 6 and i 2 = 2NSRB + 3FNS + 3RNS + 2 are the number of calculations required to transform the non-convex problems using AGMA into the GP approximations, respectively. Consequently, the total number of calculations for Steps 1 and 2 of our proposed algorithm is i 1 × log(c 1 /(ν 1 t 1 0 )) log ζ 1 and i 2 × log(c 2 /(ν 2 t 2 0 )) log ζ 2 , respectively. According to this analysis, the computational complexity of Step 1 and 2 become logarithm functions O((NS(R + F + M ) + RB) log(MNS + RB)) and O(NS(F + RB) log(N + M + RB)), respectively, with polynomial complexity and not exponential complexity (as summarized in Table 5). The computational complexity of Steps 1 and 2 are sensitive to the number of users (i.e., N). Fig. 2 illustrates that with increasing N, the number of iterations required for convergence of both Step 1 and 2 will be increased.

IV. SIMULATION RESULTS
To evaluate the performance of our approach, we consider N ∈ [20, 300] users uniformly distributed inside a region served by three RRHs (R = 3), two BBUs (B = 2), and nine FAPs (F = 9). The channel gain between user n ∈ N and AP m ∈ R and m ∈ F are modeled as h s m,n = 1 1+(d m,n ) 4 and h s m,n = ℘ m,s,n d −ι m,n , respectively, where d m,n > 0 is the distance of user n ∈ N to AP m ∈ M, ι = 3 is the path loss exponent, and ℘ m,s,n ∼ Exp(1) [43]. We set µ P = 1 and κ 1 = κ 2 = κ 3 = κ 4 = 10 −3 for all of the simulations. Furthermore, we assume the ratio for the VOLUME 11, 2023    maximum transmit power of RRHs to FAPs to be equal to 0.5. The values of the maximum BBU load, front-haul link capacity, energy consumption cost of active BBUs and each antenna, and the number of antennas mounted on the RRH r ∈ R are randomly chosen, as shown in Table 4.
In the following, we investigate the effects of different trade-off parameters (e.g., ε 1 , ε 2 , and ε 3 ) on the Pareto optimal sets derived by the proposed MORA algorithm. Based on C0 and C1 in (36), the total transmit power of all users and the transmit power of each AP are bounded to ε 3 and p max m , respectively. Therefore, C1 significantly affects and limits C0, while choosing different values of ε 3 does not affect the Pareto optimal sets derived by the proposed MORA algorithm. But simulation results reveal that ε 1 and ε 2 significantly impact the Pareto optimal sets. Since ε 1 and ε 2 are randomly chosen from a predetermined rang, the appropriate selection of these parameters can significantly enhance network performance in terms of H-CRAN operation cost, outage probability, total throughput, and EE. Therefore, we evaluate their effects on two major conflicting objective functions, namely throughput and operation cost. Also, to study the performance of the proposed algorithm in terms of coverage, we evaluate traffic offloading and outage probability for different values of ε 1 . In Fig. 3, the effect of ε 1 on the network operational cost is demonstrated. As we can see, the operation cost increases in function of ε 1 . This is because, based on C12 in (5), total energy consumption cost of RRHs is bounded to ε 1 . This constraint affects the feasibility region of (5). Therefore, by increasing ε 1 , the upper bound allowable energy consumption cost of RRHs will increase, which leads to more active RRHs. For instance, in Fig. 3 when ε 1 = 60, only one RRH is in state on (e.g., τ 1 = 1, τ 2 = τ 3 = 0) and total operation cost is 142.5 bps/Hz, which is lower than 180.3 bps/Hz when ε 1 = 120 and two RRHs are in state on (e.g., τ 1 = τ 2 = 1, τ 3 = 0). Similarly, in Fig. 4, with increasing ε 2 , more BBUs become active, which leads to a higher energy consumption cost of BBUs.
Besides, by decreasing ε 1 , some under-utilized RRHs will be switched off; therefore, the chance to choose sub-carriers and APs, and assign transmit power to each user will be reduced. To tackle this issue, in the proposed approach, joint radio resource assignment (e.g., sub-carrier, transmit power and AP allocation to each user) manages the inter-tier interference between different APs. Thus, the traffic of users associated to the under-utilized RRHs can be offloaded to neighboring low-power FAPs. Consequently, under-utilized  RRHs and BBUs can be switched off, which leads to greater EE. We define the ratio of network traffic offloading (η) as η = Total number of users moved from RRHs to FAPs Total number of users . Fig. 5 shows that η increases with decreasing ε 1 and increasing the number of users to satisfy the minimum guaranteed rate of each user. Vs with increasing ε 1 , the more RRHs will be switched on, which leads to improved coverage for users. Therefore, users who are located near RRHs can obtain a higher SINR with less transmit power and interference, which leads to a decrease of η. For instance, in Fig. 5, when ε 1 = 60, only one RRH is switched on and traffic offloading is more than that of when ε 1 = 130 and two RRHs are switched on. Additionally, Fig. 5 indicates that for ε 1 = 60 and ε 1 = 80, the results are close to each other. This because in both cases, due to the minimal difference in ε 1 values, only one RRH will be switched on, leading to a similar feasibility region of resource allocation and traffic offloading. Consequently, by adjusting the value of ε 1 , traffic can be effectively offloaded from the C-RAN to low-power < R rsv n }. Fig. 6 shows the outage probability relative to the total number of users. As we can see, the outage probability increases as the number of users increases. We can also see that increasing ε 1 in (5) from ε 1 = 80 to ε 1 = 130 leads to more RRHs being switched on; therefore, the feasibility region of resource allocation will improve to meet the minimum guaranteed rate of each user. Consequently, it can provide better coverage and a more achievable rate of all users, which leads to a decrease in the outage probability and infeasibility of (5). However, the operation cost will increase as more RRHs are switched on.
In Fig. 7, the effect of minimum required rate of each user, e.g., R rsv n , on the operation cost is illustrated. As we can see, as there in an increase in R rsv n to meet C2, the operation cost increases, which leads to an increase in ε 1 and the number of active RRHs and energy consumption cost of RRHs. This figure also shows that immediately after R rsv n = 0.2 bps/Hz, τ 1 = τ 2 = 1, e.g., RRH 1 and RRH 2 are switched on. Therefore, the operation cost linearly increases as R rsv n increases. For R rsv n ∈ [0.1, 0.2], this operation cost with increasing R rsv n does not have a significant increment. This is because RRH 2 and RRH 3 are switched off, while only RRH 1 is switched on.
For different values of ε 1 , namely ε 1 = 80 and ε 1 = 130, the performance of our approach with a traditional wireless network scenario in terms of the total throughput.  In the traditional approach, each user is associated to the AP (RRHs/FAPs) based on the largest value of received SINR [44]. In Fig. 8, due to multi-user diversity gain [37], the total throughput increases as the number of users increases. In both scenarios, Fig. 8 shows that when ε 1 = 80, the total throughput is less than that of ε 1 = 130. This is mainly because in the case of ε 1 = 130, there are more RRHs switched on. Therefore, users are assigned to the RRHs with the higher channel gain, which is due to the close distance. Hence, with less transmit power, users can obtain high data rate which leads to an improvement in the total throughput.
Moreover, as we can see in Fig. 8, the proposed approach outperforms the traditional algorithm in both cases (i.e., ε 1 = 80 and ε 1 = 130). For instance, Fig. 8 shows that when N = 300 and ε 1 = 130 in the proposed approach, the total throughput achieved is more than 25% higher than the traditional algorithm. This is because in the proposed approach effective control of inter-tier interference between APs, traffic offloading from the C-RAN to FAPs, and spectrum reuse by FAPs increase the throughput. Compared to the traditional algorithm, the AP assignment is predetermined and there is no traffic offloading. Users are assigned to RRHs, regardless of the maximum load capacity of the front-haul links, BBUs, and the upper bound limitations of allowable energy consumption cost of RRHs and BBUs. Therefore, some of users may not be connected to the network.
The Pareto optimal sets achieved by the two scenarios are compared in Fig. 9. In both scenarios, as the curve moves from left to right, the value of ε 1 increases at each step. In both scenarios, as ε 1 increases, the priority of the operation cost objective decreases; therefore, more RRHs becomes active, which leads to higher operation costs. By contrast, at the same time as ε 1 increases, the priority of the throughput objective increases, which leads to higher data rates. For instance, when data traffic is low (e.g., N = 60), Fig. 9 shows that by setting ε 1 = 80 bps/Hz, the minimum required rate of users can be satisfied with only one active RRH (τ 1 = 1). Yet by increasing the data traffic (e.g., N = 300), the priority of the throughput objective increases compared to the operation cost objective. Hence, the value of ε 1 should increase. Therefore, by setting ε 1 = 190 bps/Hz, all three RRHs are activated to satisfy the minimum required rate of all users since their energy consumption cost is not important.
To compare the two scenarios in terms of the total throughput and the total operation cost, Fig. 9 shows that when the achieved total throughput is equal to 50 bps/Hz, the proposed approach has a lower total operation cost of 185.8 bps/Hz, compared to 268.3 bps/Hz with the traditional algorithm which is 30% less than it. In this case, with our proposed approach, τ 1 , τ 2 and x 1 are equal to one. This means that RRH 1, RRH 2, and only one BBU with the lowest operation cost (µ b ) are switched on. By contrast, in the traditional algorithm, all three RRHs and two BBUs are switched on. This is because our proposed approach can offload traffic from the C-RAN to FAPs with low transmit power. Therefore, under-utilized RRHs and high cost BBUs can be switched off. Consequently, the total throughput and operation cost in the proposed approach will be enhanced compared to that of the traditional approach, which leads to improved EE.
All simulation results are based on randomly chosen ε 1 and ε 2 from a predetermined rang. An appropriate selection of these parameters can considerably improve network performance in terms of EE, total throughput, operation cost of H-CRANs, and outage probability. For instance, in high data traffic, when it more critical to provide higher throughput than it is to decrease energy consumption costs, we can choose higher values of ε 1 . Conversely, in low data traffic, where energy consumption costs are more important than the throughput, ε 1 can be decreased. On the other hand, ε 1 is a trade-off parameter that adjusts the priority of each utility function according to the application type, QoS requirements, and traffic variations. For this reason, one of the Pareto optimal solutions can be selected by adjusting the value of trade-off parameters (e.g., ε 1 and ε 2 ) in the elastic-constraints method. Consequently, choosing ε 1 and ε 2 can be considered a planning design factor in resource allocation problems. Investigating the optimal value of these parameters relative to network conditions is a topic we will examine in future research.

V. CONCLUSION
In this paper, we proposed an EE MORA framework for H-CRANs to reduce operation costs, which involved introducing a novel utility function to minimize the energy consumption costs of RRHs, BBUs, and total transmit power of users. We formulated the problem as a joint AP, sub-carrier, RRH-BBU, and front-haul link assignment and power allocation optimization problem in MIMO-aided H-CRANs while ensuring that the minimum rate of each user was met. In high density H-CRANs, throughput and operation cost are considered to be two conflicting objective functions. To tackle this issue, we converted the MOO problem into an SOO problem using an elastic-constraint scalarization method, which allows for trade-off parameters and a flexible choice between increasing throughput and decreasing operation cost functions for different preferences. choosing trade-off parameters can be considered a planning design factor in resource allocation problems. Investigating the optimal value of these parameters relative to network conditions is a topic we will examine in future research. The simulation results showed that our proposed approach can offload traffic from C-RANs to FAPs with low transmit power, and reduce operation costs by switching off under-utilized RRHs and BBUs. Also, the simulation results illustrate that Pareto optimal solutions are different under diverse sets of system parameters.
where L, O, and Y represent the number of objective functions, inequality constraints, and equality constraints, respectively. The elastic-constraints method is a class of scalarization techniques, which is a generalization of both the weighted sum method and the ε-constraint method which generates all Pareto optimal solutions for MOO problems [11], [18]. Via this method, the objective functions are combined form a single objective optimization problem; therefore, (47) is formulated as where f e (x) and f k (x), k ̸ = e are objective functions in the primary MOO problem (47). By applying the elastic-constraints method, f e (x) and f k (x) are considered to be the objective function and new equality constraint, respectively. ε k is an upper bound on violated objective value, which is used to penalize the constraint violation, and t k is the penalty coefficient for a given objective k [45], [46]. The elastic-constraints method uses two sets of variables, including slack variables, L k , and surplus variables, s k , in order to transform the upper bounds on objective values into equality constraints for any x ∈ A (i.e., a set of feasible solutions) based on an appropriate selection of s k and L k . In the other words, the values of ε k specify the priority of objective functions relative to each other, and the Pareto optimal solutions can be derived by considering different ε k for the objective functions.
Step 1: For this step we have two cases: • When m ∈ F, we can rewrite C2 as m∈F s∈S α s m,n (t 1 )β m,n (t 1 ) R s m,n (P(t), β) ≥ R rsv n , By applying AGMA, we come to C2.1 in (9).
• Based on (6), when m ∈ R, C2 is not in a GP standard form because throughput is a non-linear function. Therefore, we apply DC approximation and by substituting (50) into C2, we have Now, by applying AGMA, we come to C2.2 in (9).
(52) can be rewritten as U i +L i q i (t 1 ) ≤ 1 and q i (t 1 ) s ′ i +ε i ≤ 1. Since the above constraints do not satisfy the properties of posynomial functions, we approximate them to posynomial functions by using AGMA for i = [1], [2], [3] as follows: where e i (t 1 ) and d i (t 1 ) are introduced in (33) and (34), respectively.