Joint User Association and Energy Offloading in Downlink Heterogeneous Cellular Networks

As a key technology in Long-Term Evolution-Advanced (LTE-A) mobile communication systems, heterogeneous cellular networks (HCNs) add low-power nodes to offload the traffic from macro cell and therefore improve system throughput performance. In this paper, we investigate a joint user association and resource allocation scheme for orthogonal frequency division multiple access(OFDMA-) based downlink HCNs for maximizing the energy efficiency and optimizing the system resource. )e algorithm is formulated as a nonconvex optimization, with dynamic circuit consumption, limited transmit power, and quality-ofservice (QoS) constraints. As a nonlinear fractional problem, an iteration-based algorithm is proposed to decompose the problem into two subproblems, that is, user association and power allocation. For each iteration, we alternatively solve the two subproblems and obtain the optimal user association and power allocation strategies. Numerical results illustrate that the proposed iterationbased algorithm outperforms existing algorithms.


Introduction
Shortage of power resource and scarcity of spectrum resource are two major factors in restricting communication development, and thus, green-oriented communication system design has gradually attracted attention of academics particularly in wireless communication filed.Energy consumption in information and communication technology (ICT) industry accounts for about 2%-6% of global total consumption, 60% of which are consumed on base stations (BSs).In recent years, innovations in this area facilitate the unprecedented growth of traffic data which accelerates the problem more seriously [1][2][3][4].In order to improve resource efficiency, energy harvesting can be used [5], but more effectively wireless systems are prone to miniaturization and heterogeneity, which may be composed of various types of networks to support growth of traffic demand.For instance, coordinating with macro cell, for example, pico BSs and femto BSs are used to offload the traffic and energy consumption from the large-scaled BSs. e layout of heterogeneous cellular networks (HCNs) is more reasonable and economical than that of macro-only networks.However, extreme densification of BSs would bring a new challenge: cochannel interference is introduced by spectrum sharing in a local-area, which has significantly negative impact on system capacity [6].Considering its high spectrum efficiency and flexibility in allocating radio resource, orthogonal frequency division multiple access-(OFDMA-) based HCNs system is a good candidate to achieve better performance wireless communications [7].
Resource allocation for HCNs is investigated from different perspectives in one/multi-cell scenarios.In previous researches, studying of user association is more attractive in HCNs [8][9][10][11], as user allocation have an impact on the interference as well as capacity.Power consumption is also a factor that affects the communication performance especially for intra-and intercell interference suppression in networks [12][13][14][15].However, capacity and coverage enhancement are not always achieved by increasing transmit power.Increased transmit power may generate more interference to neighboring cells which has became a challenging issue.As a result, energy-efficient designs have recently attracted a lot of interest to exploit the potential performance gains toward green wireless communication systems [16][17][18].Energy efficiency is defined as the ratio of system throughput to total energy consumption.In [19], the authors proposed a utility-based energy-efficient (UEE) resource allocation algorithm with mixed traffic in downlink HCNs which only achieves a suboptimal solution.Zhou et al. [20] proposed a fractional programming framework, by solving the weighted energy efficiency problem iteratively consisting of channel allocation and power allocation.A non-cooperative resource competition game was introduced in [21] for energy efficiency optimization in dense networks under traffic-related minimum rate requirement.Cheng et al., Zhou et al., and Wang et al. [19][20][21] focused on jointly channel allocation and power control where the set of users associated with the BS were predetermined in the optimal process.In most of the previous works, they only consider either user association or subchannel allocation but not both of them.However, the system performance is affected by both of them.Additionally, for the above works, system power consumption only involves the transmit power and static circuit power.For energy efficient resource allocation, circuit power is also accounted in addition to the transmitted power with the increasing demand for highcapacity networks, which is more practical and general [22,23].
e novelty of this work is to consider both user association and subchannel allocation in the optimization of energy efficiency with circuit power.ese practical conditions have not been studied together in the literature.
In this paper, we formulate an energy efficiency maximization problem via jointly optimizing user association, subchannel association, and power control for OFDMAbased downlink HCNs in terms of QoS requirement and available power constraints.In particular, the circuit power consumption is modeled as a function of system rate, not just as a constant.We address the nonconvex mixed integer optimization problems by applying proposed iterationbased algorithm.By utilizing the Dinkelbach method, it transforms the primary problem to a subtractive form problem.
e EE maximization problem is decomposed equivalently into two subproblems which can then be solved by using the iterative method alternatively.Compared with the previous algorithms, simulation results demonstrate that the proposed scheduling strategy gains a tradeoff between system capacity and overall consumption and then obtains an optimal resource allocation.
e remainder of the paper is formulated as follows: Section 2 briefly introduces the system model and formulates the energy efficiency maximization problem.Based on this model, an iteration-based algorithm is proposed to solve the three-layer problems alternatively; then the algorithm complexity is also analyzed in Section 3.
e numerical results are discussed in Section 4. Finally, the conclusion is drawn in Section 5.

System Model
A range of area may be randomly deployed with numerous small hotspots, providing flexibility and quick access, along with a larger base station (BS) located at the center of cellular covering the entire macro cell space, as shown in Figure 1.In this section, we design a two-layer OFDMA-based downlink HCNs system, which consists of macro base stations (MBSs) and pico base stations (PBSs), as alternative wireless access points for user equipments.In a time slot, channel resources are allocated to users for information interaction according to the user association rule.We assume that each subchannel only can be allocated to a single user at the same time; thus, no interchannel interference exists among user groups.In the following, the set of N � N m ∪ N p � 1, 2, 3, . . ., N { } and K � 1, 2, 3, . . ., K { } represent the index of BSs and users in the considered scenario, respectively.Based on the OFDMA model, we equally divide the bandwidth into S orthogonal spectrum bands and denote S � 1, 2, 3, . . ., S { } as the subchannel index set.In this paper, the received signal to interference and noise ratio (SINR) of terminate k ∈ K from BS n ∈ N on subchannel s ∈ S can be expressed as where P n,s and g s n,k represent the transmit power and channel gain from BS n on subchannel s to user k, respectively.σ 2 k,s is the additive white Gaussian noise (AWGN) power received at the terminal k of the link from subchannel s.When transmitting to BS n on subchannel s, user k is interfered by other cochannel signals from the neighboring cellular.us, we can denote the received data rate when user k is associated with BS n on channel s as where Γ is the SINR gap to capacity involving in the bit error ratio (BER) expectation, coding gain, and noise margin [12].Hence, the total amount of bits delivered by the users and BSs is given by where A n,k,s ∈ 0, 1 { } is the resource allocation indicator.A n,k,s � 1 indicates that the subchannel s of BS n is assigned to user k and A n,k,s � 0 indicates that, the subchannel s of BS n is not assigned to the user k in this time slot.In this case, the subchannel s of BS n is either assigned to another user or not assigned to any user.Considering the energy efficient resource allocation design, we model the energy consumption as where ρ n is the amplifier factor of BS transmit power.P c is the total circuit consumed power.Considering the approach presented in [24], it is reasonable to relate the circuit power consumption to the sum-data rate which can be defined as where P s is the static circuit consumed power, and the dynamic circuit consumed power is proportional to the unit data rate where c is an constant of proportionality.

Mobile Information Systems
e overall energy e ciency (Bits-Hz-Joule) is de ned as the ratio of system throughout and total energy consumption.As a result, the maximum energy e ciency optimization problem can be obtained by where r k, min in (6a) is the minimum received data rate that the user k required.P max in (6b) is the maximum transmit power allowance for each BS used to control the cochannel interference.(6c) and (6d) are imposed to guarantee that each user exclusively associates to one BS to avoid the cross-user interference and one subchannel can serve at most one UE.

Solution to the Problem
e objective function ( 6) is a nonlinear one, coupled with discrete and continuous variables which add the level of computationally complexity.In the following, an iteration-based algorithm is proposed to decouple it into two subproblems, including user-BS association and subchannel power control, which can be solved alternatively.
Since the combinatorial problem is di cult to solve directly, the rst step is to simplify the fractional optimization to a linear objective function using Dinkelbach approach [25,26].us, it can be proved that the maximum EE can be obtained only if where η * is the optimal energy e ciency and A * , P * is the optimal resource allocation scheme.erefore, the original problem is transformed into an objective function in subtractive form and has a unique solution [27].e Dinkelbach method is widely used to solve (7) with the character of super-linear convergence speed [28].e proposed algorithm is summarized in Table 1, and the proof of convergence is illustrated in Appendix.In each iteration in main loop, we solve the inner problem: user association and subchannel power allocation alternatively for a speci c η and then update the value of η each iteration and repeat the process until convergence.

User Association with a Given Subchannel Power
Allocation.For a given η, we focus on the solution for inner problem in the rest of section.e above problem involves user association and subchannel power allocation; therefore, it can be resolved by alternative iteration method.For a given power control, the optimization problem is generalized for maximizing system capacity under considered constraints, which is given by max Since link capacity is limited by interference especially from the cochannels of di erent BSs, an heuristic user allocation scheme is applied to the cellular system, shown in Table 2. Initially, we assume that each subchannel of BSs is allocated with equal transmit power and modeled as identically Rayleigh distributed channel.Each user is assigned to the BSs with the highest SINR.e subchannel allocation follows the cognitive rules that users are associated with good channel conditions and su ering small interference.S 0 is a set of available subchannel which is not occupied.It Mobile Information Systems will be updated after each iteration according to the decisions, which can guarantee the subchannel cannot be reused by other users.

Subchannel Power Resource Allocation with Given User Association.
is subsection details the power allocation procedure.For the case with fixed user allocation set, the optimization problem can be reformulated into Notably, constraint (9a) is nonconvex to P because of the presence of cochannel interference, which makes the objective function rather difficult [29].Specifically, we first set a concave lower bound to relax r by referring the following inequality [30]: e equality is true only when z � z * .With this relaxation, r is redefined as where where P 0 is a reference value.Since the transformed problem is still nonconvex with respect to P, we follow the approach in [31] and define q where e q n,s � P n,s for convexification.us, the subchannel power allocation is given by max en, we solve the subchannel power allocation optimization problem using the Lagrangian dual-decomposition approach for a given user association set with the value of η.

Numerical Results
In the following, we consider two-layer heterogeneous networks where the fixed node MBS is located at the center of a radius of 500 meters, and PBSs are randomly scattered in the cellular.K users are uniformly distributed in the range of service area.It is assumed that the system bandwidth is 6 MHz and the number of subchannels is 32.Users are subjected to −128 dBm/Hz AWGE power spectral density, giving the SINR gap Γ � 0 dBm.e maximum transmit power of MBS is 46 dBm.e coefficient of power amplifier of MBS and PBS are 4 and 2, and the constant power consumption values are 10 W and 0.1 W, separately.e path loss model of MBS and PBS is set to l nk � 128.1 + 37.6 log 10(d) and l nk � 140.7 + 37.6 log 10(d), where d (in km) represents the distance between BS n and user k.Besides, the shadowing fading of all links is set to 0 dB.In addition, assumed system parameters can easily be modified to any other values to demonstrate the energy efficiency in different scenarios.

4.1.
Convergence of the Proposed Algorithm.Figure 2 illustrates the convergence properties of the proposed iterationbased algorithm.e maximum transmit power of PBSs is 32 dBm and the sum-rate factor is 0.38.e number of PBS and amount users is set as 10 and 30.It can be observed from Figure 2(a) that the objective as a function of q converges within 15 iterations in considered scenarios.Figure 2(b) shows that the value of η is converging to the optimal EE within 5 times, demonstrating that the convergence rate of proposed algorithm is high.In summary, the validity of the proposed algorithm is confirmed, and it is efficient for multivariable dynamic programming.

Energy Efficiency and Power Consumption.
We compare the performance of proposed iteration-based algorithm for maximizing energy efficiency (MEE) with MTP proposed in [14] for different number of users versus increasing QoS requirement in Figures 3 and 4. For MTP, its objective is to minimize the power consumption for subchannel assignment and power distribution.We assume that the maximum transmit power of PBS is 32 dBm and the sum-rate coefficient is 0.38. Figure 3 shows that MEE is much better than MTP in energy efficiency.For MEE and MTP, as the increasing dense subscribers, the EE increases at first and then remains stable for all schemes. is is because the cochannel interference would have less impact when the user density was low.However, since more subchannels being allocated, performance is restricted by the limited system resources as the number of users in the system increases.We also observe that the EE declines with the growing minimum data rate requirement in MEE and MTP since the BSs require to enhance the transmit power of subchannel to maintain the throughput requirements which impairs the system energy efficiency.
As seen in Figure 4, the corresponding power consumption of MEE versus different number of users is less than that of MTP, due to our proposed power allocation policy strongly control the unassigned subchannel transmit power resulting in lower transmit power levels.As the user density increases, the spectrum is shared by different tiers, and thus, the cochannel interference will become significant.Hence, extra power consumption is required to narrow the gap of QoS requirements.It simultaneously shows that the EE increases with the descending minimum rate targets for MEE and MTP, while the rate of rise declines.is is because when the threshold is high, more users are unable to meet the requirements, which consumes the excessive transmission to improve the performance of the system.For MEE and MTP, it concluded that the performance improvement of our proposed algorithm outperforms previous research.
Figure 5 investigates the impact of circuit power on the energy efficiency versus the number of users.e maximum transmit power of PBSs is set as 36 dBm.For a fixed factor c, when the number of users is smaller and EE increases significantly for both algorithms, but then progressively slows with the user density increases adequately. is is because that the increasing sum-rate will also make the system consume (1) Initialization: Set e q � (1/S)P n, max , i � 0, t � 0, α 0 , β 0 , T 2 , T 3 ; (2) Repeat (3) Repeat (4) Update P according to (18); (5) Update υ and λ according to (19) and (20), respectively; (6) Set t � t + 1; (7) Until ||] t+1 − ] t || ≤ ε or t � T 2 (8) Set P 0 � P; (9) Update α and β according to (12) and (13), respectively; (10) Mobile Information Systems more extra power for circuit power per unit data rate, which restricts the EE growth.It can be seen from Figure 5 that the EE decreases with the increase of c resulting in higher power consumption.In conclusion, the energy e ciency is in uenced by the sum-data rate of the links and decreases with the increase of circuit power consumption.
Figure 6 illustrates the change of EE of the system under the number of small cells in the network, and we consider the number of users in each cell is 4. It can be seen from the gure that the energy e ciency of MEE is higher than that of MTP in considered scene, due to the proposed maximum EE-based power strategy policy.As the number of cell increases, more users are associated to the network to increase system throughout as well as increase the power consumption on dynamic circuit power.

Conclusion
In this paper, we have studied the jointly the user association and subchannel power allocation problem in the downlink OFDMA-based HCNs under minimum QoS requirement and available power constraints.To tradeo between throughout and energy consumption, the conception of maximum energy e ciency is introduced.We solved the fractional programming by transferring it into two subproblems, that is, user association subproblem and power allocation subproblem, and further proposed an iteration-based algorithm to handle the subproblems alternatively.Simulation results demonstrated that a higher

Appendix
Proof of the Rate of Convergence e alternative iteration algorithm super-linearly converges to the optimal energy e ciency.
Firstly, it has been proved that if the number of iterations is large enough, the sequence of η t converges to the optimal η * [24,28].en, the further proof of convergence speed is detailed as follows.
erefore, the updated values rapidly get close to the optimal solution with respect to t.
Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no con icts of interest.Mobile Information Systems

Figure 1 :
Figure 1: Illustration of BS deployment model of HCNs.

Figure 6 :
Figure 6: Energy e ciency versus di erent numbers of small cells in the network.