Green Resource Allocation and Energy Management in Heterogeneous Small Cell Networks Powered by Hybrid Energy

Previous researches have provided an overview on resource allocation and interference management in a two-tier HetNet in recent years. Palanisamy and Nirmala [11] have presented a comprehensive survey on downlink interference management strategies in HetNets. Zhang et al. [12] studied resource optimization for the interference management and self-organization schemes in a hybrid self-organized small cell network. In [13], the authors considered the sum-rate optimization problem with power control for uplink transmission in a HetNet, then a new practical near-optimal distributed algorithm that eliminates these network overheads was proposed. Lang et al. [14] adopted the heterogeneous genetic algorithm to solve the resource allocation problem for cognitive decode-and-forward relay network. A game-theoretical scheme using energy-efficient resource allocation and interference pricing was proposed in [15] for an interference-limited environment without complete channel state information.

Apart from designing efficient resource allocation policies, there are some energy-saving studies for HetNet. The deployment of renewable energy has been considered in [16, 17, 18, 19]. Gong et al. [16] considered energy-efficient wireless resource management in cellular networks powered by renewable energy. The goal is to minimize the average grid power consumption while satisfying the users’ QoS (blocking probability) requirements. It uses statistical information for traffic intensity and renewable energy to adaptively switch BSs’ on-off state and adjust the allocated resource blocks. Zhang et al. [17] considered coordinated multi-point (CoMP) communication systems and integrated renewable energy sources (RES) into smart grid. A convex optimization problem is formulated to minimize the worst-case energy transaction cost while guaranteeing the QoS of users. Yang et al. [18] jointly considered the resource allocation and energy management of HetNet powered by hybrid energy with the consideration of spatio-temporal diversity of traffic and renewable energy. Qin et al. [19] investigated the resource allocation for orthogonal frequency-division multiple access (OFDMA) wireless networks powered by renewable energy and traditional grid. There is a trade-off between network throughput and grid energy consumption. The proposed main solution is similar to [18].

Due to the finite spectrum resources, several spectrum sharing algorithms have been proposed in literature such as [20, 21, 22, 23, 24, 25]. Specifically, spectrum sharing in the same operator is considered in [20, 21, 22]. Zhang et al. [20] proposed a distributed resource management scheme in a HetNet, which divides the problem into two sub-problems: BS cluster and subchannel allocation. Note that only the BSs in the same cluster are allowed to share the spectrum band. Lee et al. [21] utilized the cognitive radio (CR) technique to improve the performance of wireless powered communication network. Two coexisting models for spectrum sharing were proposed and the authors considered the interference between two models to protect the primary user transmission. The coexisting network including device-to-device links and cellular links was adopted and a new game model called Bayesian overlapping coalition formation game was proposed in [22]. Moreover, multi-MNO coordinate their spectrum resources sharing in [23, 24, 25]. A common spectrum pool to share spectrum was investigated in [23]. It formulates the sharing between the MNOs as a repeated game and determines rules to decide whether to participate in the game at each stage game. An underlay/overlay (hybrid) transmission mode to share the spectrum of licensed users was introduced in [24]. The objective is to maximize network throughput and eliminate interference. Zhang et al. [25] considered the spectrum sharing among multi-MNO in the unlicensed spectrum. A hierarchical game including Kalai-Smorodinsky bargaining game and Stackelberg game is proposed to reduce the interference.

Motivated by the above works, we can use renewable energy to reduce energy consumption and share spectrum to improve spectrum utilization. There are some existing works in this field. But most proposed solutions ignore the fairness between BSs and time-varying of network states. Although some studies, e.g. [26] consider a fair resource allocation, they focused mainly on the network throughput without sharing costs. However, selfish BSs emphasize on improving their own utility without considering other BSs of different MNOs. Thus, we need to design incentive mechanism to promote the BSs to share idle spectrum resource.

In this paper, we consider joint subchannel allocation and power control under cross-tier interference, fairness between SBSs and renewable energy constraints. The main contributions of this paper are as follows:

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  First, we jointly consider subchannel allocation and power control strategy for spectrum sharing in a HetNet, while considering the cross-tier interference constraint.

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  Second, a multi-person bargaining problem is modelled to measure the fairness among SBSs. An online dynamic resource allocation scheme consisting of spectrum pricing, admission flow control and resource allocation is developed by solving a stochastic optimization problem.

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  Third, simulation results are presented to show the effectiveness of the proposed approach. Our approach can substantially achieve the trade-off between transmission profits and network throughput.

The rest of this paper is organized as follows. In Section II, we illustrate the system model and constraint conditions. Section III formulates a stochastic optimization problem based on the Nash bargaining. We present an online dynamic resource allocation and energy management scheme in section IV. Numerical results are given in Section V with discussions. Conclusion and future work are presented in Section VI.

We consider a downlink OFDMA two-tier HetNet. As shown in Fig.1, SBSs belonging to different MNOs are overlaid in the coverage of a MBS. There are two types of mobile user equipments (UEs): macro-cell UE (MUE) and small cell UE (SUE) corresponding to the service BSs. All SBSs are assumed to be close access mode that allows only the authorized SUEs to access the corresponding SBS. We assume that the SBSs occupy different spectrum bands. Thus, the co-tier interference between SBSs can be considered to be negligible.

Accordingly, let $\mathcal{N}_{0}=\left\{0,1,2,...,N\right\}$ denote the BS set, where $n=0$ represents MBS and $\mathcal{N}=\left\{1,2,...,N\right\}$ denotes SBSs. As a consequence, the set of MUEs served by MBS is $\mathcal{U}_{0}$ and the set of SUEs associated with SBS $n$ is $\mathcal{U}_{n}=\left\{1,2,3,...,U_{n}\right\}$. The OFDMA system has a bandwidth $F$ divided into $M$ subchannels, i.e., $\mathcal{M}=\left\{1,2,...,M\right\}$ and the bandwidth of subchannel $m$ is $\varpi_{m}$, while the spectrum band occupied by SBS $n$ is denoted by $\mathcal{M}_{n}\in\mathcal{M}$, and $\cup_{n\in\mathcal{N}}\mathcal{M}_{n}=\mathcal{M},\mathcal{M}_{i}\cap\mathcal{M}_{j}=\varnothing,\forall i\neq j$. Moreover, since MBS has the priority to choose subchannels, it is assumed that each subchannel is always occupied by one MUE at a given time, and to guarantee the QoS of MUEs, the SBSs adjust their power to reduce the cross-tier interference.

As the subchannel conditions and energy harvesting process change dynamically, we consider the HetNet operates in a time-slotted manner where the subchannel and energy harvesting conditions keep stable in a time slot. We use $\mathcal{T}=\left\{0,1,2,...,t,...,T\right\}$ to denote the time-slot set and the length of each time slot defaults to 1.

At the beginning of time slot $t$, each SBS observes the channel state information (CSI) and current queue state information (QSI). We use $p_{mk}^{M}(t)$ to denote the power allocated to MUE $k$ served by MBS on subchannel $m\in\mathcal{M}_{n}$ and $h_{nmu}^{M}(t)$ to denote the interference subchannel gain from MBS to SUE $u$ in SBS $n$ on subchannel $m\in\mathcal{M}_{n}$. The received signal-to-interference-plus-noise ratio (SINR) of the $u$th SUE from SBS $n$ on subchannel $m\in\mathcal{M}_{n}$ at the $t$-th time slot is given by:

where $p_{nmu}(t)$ represents the transmission power of SBS $n$ to SUE $u$ on subchannel $m\in\mathcal{M}_{n}$. $h_{nmu}(t)$ is the channel gain between the SUE $u$ and SBS $n$ on subchannel $m\in\mathcal{M}_{n}$ including pathloss, shadowing and other factors. $\sigma^{2}$ denotes the noise power level. Compared with the cross-tier interference, the co-tier interference can be considered to be de minimis. Therefore, the SBSs are primarily interfered by the MBS.

The transmission rate of SBS $n$ to SUE $u$ on subchannel $m\in\mathcal{M}_{n}$ in the non-cooperative case is

Then, the total throughput of SUE $u$ serviced by SBS $n$ can be computed by:

We define a binary variable $x_{nmu}(t)$ as subchannel allocation index. $x_{nmu}(t)=1$ indicates the subchannel $m\in\mathcal{M}_{n}$ is allocated to SUE $u$ of SBS $n$ and otherwise, $x_{nmu}(t)=0$. In this transmission model, each subchannel can be occupied by at most one SUE at the given time. Limited by the transmission characteristics, we have the following limitations:

Subchannel allocation constraint: Each subchannel can be allocated to at most one SUE in each SBS at time slot $t$ to avoid intra-cell interference. Each SBS uses different subchannels to avoid inter-tier interference. Thus, we have

SBS power constraint: Each SBS has a peak transmission power $p_{n}^{max}$ to avoid the overload. Each SBS’s transmission power is limited by

Cross-tier interference constraint: The interference from a SBS to a MUE occurs when the SBS transmits in the same subchannel occupied by the MUE. To protect the QoS of MUEs, we denote $I_{m}^{S}(t)$ as the maximum tolerable cross-tier interference temperature in subchannel $m$ for the assigned MUE $b$ at time slot $t$. Thus, we have

where $h_{nmb}(t)$ is the interference channel gain on subchannel $m$ from SBS $n$ to MUE $b$ served by the MBS at time slot $t$. The interference constraint means that SBSs are allowed to transmit signals on the same subchannel with the MBS only if the total interference is kept under a tolerable level.

In this paper, we focus on the joint power control and subchannel allocation problem to improve network performance.

We assume there is a data buffer for each SUE to store the arriving packets. Let the stochastic process $A_{nu}(t)\in\left[0,A^{max}\right]$ denote the arrival traffic amount for SUE $u$ of SBS $n$ in time slot $t$. $A_{nu}(t)$ is independent and identically distributed (i.i.d) over different time slots with the average arrival rate $\lambda_{nu}$, i.e., $\mathbb{E}[A_{nu}(t)]=\lambda_{nu}$, where $\mathbb{E}[\cdot]$ represents the expectation. To achieve the normal transmission, the admitted traffic amount $D_{nu}(t)$ has the following constraint:

Thus, the finite data queue backlog $Q_{nu}(t)$ of SUE $u$ in small cell $n$ is formulated as

where $R_{nu}(t)$ and $D_{nu}(t)$ are the output and input rate of data queue $Q_{nu}$ respectively and $\left[x\right]^{+}=max\left\{x,0\right\}$. At the beginning, we assume $Q_{nu}(0)=0$. Due to the time-varying subchannels and packet arrival process, the arrival and departure processes are both stochastic. Thus, the $Q_{nu}$ is varying over time slot. Let $R(t)$ and $D(t)$ be the output rate and input rate at time slot t for queue $Q(t)$, respectively. For discrete time process $Q(t)$ evolves as following,

we need to guarantee the queue stability. According to [27], a queue is defined as strongly stable if

A network is called strongly stable if all the individual queues are strongly stable. Therefore, it is a crucial prerequisite for the network to guarantee the stability of all queues.

According to the EARTH project,we adopt a linear approximation power consumption as[28]:

where $P_{n}^{c}$ is the static power consumption including the cooling system, baseband processor and so on. $\Delta_{n}$ is the slope of the transmission power dependent power consumptions. According to the maximum power constraint (6), the power consumption satisfies the following constraint:

To avoid the transmission interruption, the MBS uses a conventional grid source and the SBSs are powered by not only renewable energy generation but also the power grid. Each SBS harvests energy from ambient energy sources such as solar and stores the energy in its battery. If the storage energy is not enough for transmission, the SBS will be supplied by the grid. We model the energy harvest process as a random process. Let $E_{n}(t)$ denote the harvested energy in time slot $t$ in small cell $n$. $E_{n}(t)$ is assumed to be i.i.d. with the maximum value $E_{n}^{max}$. Notice that SBS may have no a priori knowledge of energy harvest process, which is appropriate for the situation.

At time slot $t$, the battery level $S_{n}(t)$ is determined by previous battery level, harvested energy and SBS power consumption as follows:

where $F_{n}(t)$ and $J_{n}(t)$ are the discharge energy and charge energy of the battery device in SBS $n$ at time slot $t$ respectively. The storage energy cannot exceed the capacity of the battery, i.e., $S_{n}(t)\leq S_{n}^{max}$.

The power consumption of SBS $n$ consists of two parts: discharge energy from battery devices $F_{n}(t)$ and power grid $G_{n}(t)$. Then, we have

The discharge energy should be less than the battery energy level and the charge energy should consider the battery capacity. Thus, the discharge energy and charge energy should satisfy the following constraints:

Let $\overline{F}_{n}=\underset{T\rightarrow\infty}{\lim}\frac{1}{T}\sum_{t=0}^{T-1}\mathbb{E}\left\{F_{n}(t)\right\}$ and $\overline{J}_{n}=\underset{T\rightarrow\infty}{\lim}\frac{1}{T}\sum_{t=0}^{T-1}\mathbb{E}\left\{J_{n}(t)\right\}$ denote the time-average discharge energy and the time-average charge energy respectively. The stability of energy queue $S_{n}(t)$ should be guaranteed.

At each time slot, the common spectrum pool formed by MNOs from reusing the spectrum of MBS is partitioned between the SBSs. The total spectrum band allocated to SBS $n$ at time slot $t$ is $B_{n}(t)=\sum\limits_{u\in\mathcal{U}_{n}}\sum\limits_{m\in\mathcal{M}_{n}}\varpi_{m}x_{nmu}(t)$. We assume that each SBS uses the same amount of subchannels without any payment in the initial state. However, the SBS pays for an extra payment if it uses more subchannels than it has put in the common pool. Similarly, a SBS can rent its free spectrum resource to other SBSs for benefits.

We define a utility of SUE $u$ of SBS $n$ in terms of admitted data rate to represent the satisfaction that SBS $n$ sends data to SUE $u$, then the time-average expected profit of SBS $n$ is given as

where

$\phi$ is a constant to balance gains from spectrum capacity and power consumption, which is a constant. $B_{n}^{0}$ denotes the initial spectrum band of SBS $n$. $\alpha_{n}(t)$ is the per-unit price of spectrum transferred from SBS $n$ to other SBSs and $\beta_{n}(t)$ is the per-unit price of extra spectrum rented from other SBSs. The spectrum prices all have the maximum $q_{n}^{max}$. Notice that during any time slot, the SBS $n$ can only choose one spectrum sharing scheme: lease or rent spectrum band.

According to the queues, $\mathbf{Q}=\left\{Q_{nu}(t)\right\}$, $\mathbf{S}=\left\{S_{n}(t)\right\}$, $\mathbf{Y}=\left\{Y_{n}(t)\right\}$, $\mathbf{Z}=\left\{Z_{n}(t)\right\}$, and $\Theta(t)=[\mathbf{Q},\mathbf{S},\mathbf{Y},\mathbf{Z}]$. We define the Lyapunov function as

where $\rho_{n}$ is a perturbation factor, which ensures there is enough energy in the energy queue. Without loss of generality, we assume that all queues are empty when $t=0$ such that $L(\Theta(t))=0$.

The Lyapunov function $L(\Theta(t))$ is a scalar measure of network congestion. Intuitively, if $L(\Theta(t))$ is small then all queues are small; and if $L(\Theta(t))$ is large then at least one queue is large. Thus, by minimizing the drift in the Lyapunov function (i.e., by minimizing a difference in the Lyapunov function from one time slot to the next), queues $Q_{nu}(t)$, $S_{n}(t)$, $Y_{n}(t)$, $Z_{n}(t)$ can be stabilized. By using expression (31), the drift in the Lyapunov function (i.e., the expected change in the Lyapunov function from one time slot to the next) can be written as

We now use the drift-plus-penalty minimization method to solve optimization problem OP₂. In this method, a control policy that solves OP₂ is obtained by minimizing the upper bound on the following drift-plus-penalty expression. We can obtain the following drift-plus-penalty term:

where $V$ is a non-negative tunable parameter which balances the maximization of network utility and the minimization of queue length to a state level. According to [30], when $V$ is sufficiently large, the optimization algorithm approaches the optimal capacity.

Lemma 1. The drift-plus-penalty term is upper bounded as

where $W_{n}(t)=Y_{n}(t)+Z_{n}(t)$ denotes the value of virtual queues. $H$ is a positive constant that satisfies the following inequality constraint for all time slots:

proof: See Appendix A.

By Lemma 1, we have transformed the optimization problem OP₂ into minimizing the right-side term of (73) at each time slot $t$. According to [26], the control policy should be adjusted to minimize the upper bound. Thus, we will decompose the optimization problem and present an online dynamic control algorithm for the green resource allocation and energy management.

By observing the second and third terms on the right-hand side of (73), we can get the rate control problem regardless of the other variables:

We can observe the monotonicity (36) and then the solution of the above problem can be solved easily,

Each SBS decides the auxiliary variable $\mu_{n}(t)$ by

$\log(x)$ is the non-decreasing concave utility function, and then we get the optimal solution. $\mu_{n}^{max}$ is the maximal profit by sharing spectrum resources.

where $\mu_{n}^{*}$ should satisfy $V\log^{\prime}(\mu_{n}^{*})=Y_{n}(t)$.

We can formulate the pricing problem as

We can find that the subchannel price $\alpha_{n}(t)$ and $\beta_{n}(t)$ are related to the state of virtual queue $W_{n}(t)$. The longer the queue length of $W_{n}$, the more utility gain the SBS $n$ will obtain by renting its free spectrum resources and vice versa. Moreover, it is easily seen that the pricing problem is tightly coupled with the power and subchannel allocation problem. In the following, to facilitate problem solving, we firstly analyze the resource allocation in two-SBS case, and then extend the results to the multi-SBS case.

1) Two-SBS case ($N=2$): According to the spectrum pricing problem, the SBS with the longer queue length of $W_{n}$, which is supposed the SBS 1, will rent spectrum resources to another one (SBS 2). The price is chosen as

By observing the remaining term on the right-hand side of (73), we can formulate the resource allocation problem with the given spectrum sharing scheme as follows:

We relax the binary variable $x_{nmu}(t)$ to a continuous variable $\hat{x}_{nmu}(t)\in\left[0,1\right]$. For notational brevity, denote the power allocated to SUE $u$ on subchannel $m$ as $s_{nmu}=\hat{x}_{nmu}p_{nmu}$. The optimization problem can be rewritten as:

where $\theta_{nm}(t)$ is related to $\alpha_{n}(t)$, $\beta_{n}(t)$, $\varpi_{m}$ and $W_{n}(t)$, ${\theta_{nm}}\left(t\right)=-q_{n}^{\max}{\varpi_{m}}{W_{n}}\left(t\right)$ and $\eta_{n}(t)=S_{n}(t)-\rho_{n}-\phi W_{n}(t)$. $I_{0mu}=p_{mk}^{M}(t)h_{nmu}^{M}(t)$. The subchannel and power allocation strategy in (43) can be solved by using the Lagrangian dual decomposition method. By ignoring the time variables, the partial Lagrangian function is given by