QoS Aware Energy Allocation Policy for Renewable Energy Powered Cellular Networks

Abstract

The explosive wireless data service requirement accompanied with carbon dioxide emission and consumption of traditional energy has put pressure on both industria and academia. Wireless networks powered with the uneven and intermittent generated renewable energy have been widely researched and lead to a new research paradigm called green communication. In this paper, we comprehensively consider the total generated renewable energy, QoS requirement and channel quality, then propose a utility based renewable energy allocation policy. The utility here means the satisfaction degree of users with a certain amount allocated renewable energy. The energy allocation problem is formulated as a constraint optimization problem and a heuristic algorithm with low complexity is derived to solve the raised problem. Numerical results show that the renewable energy allocation policy is applicable not only to soft QoS, but also to hard QoS and best effort QoS. When the renewable energy is very scarce, only users with good channel quality can achieve allocated energy.

1. Introduction

The continuously growing demand for ubiquitous wireless network access and high data rate lead to the rapid development of wireless cellular networks. The energy consumed to power the bigger and more complex networks, on one hand brings network operator the rapidly rising energy price, on the other hand, generates a large amount of carbon dioxide which results in climate change [1]. Green radio becomes an inevitable trend [2], and is implemented from two different perspectives. The first is to study novel techniques to improve the energy efficiency of wireless networks which can be measured by bits-per-Joule metric [3]-[4]. However for a fixed network size, this kind of energy efficiency design from the physical layer to the MAC layer has already approached the theory limits [5]. The second is to substitute renewable energy such as solar and wind power for traditional energy. The emerging trend of renewable energy powered wireless networks equipped with energy harvesting devices [6] has been widely studied recently. Wireless energy harvesting has been considered as a potential technology for future 5G networks and has been intensively researched [7]. However, the uneven and intermittent intrinsic characteristics of the renewable energy make it a finite resource in renewable energy powered wireless network. Hence, how to efficiently use the renewable energy distributed in energy harvesting wireless network has always been an open issue and many valuable research results have been achieved up to now.

In [8], taking into account channel conditions and energy sources that are time varying, so as to maximize the throughput, an optimal energy allocation with energy harvesting constraints is proposed in several time slots and solved via the use of dynamic programming and convex optimization techniques. In [9]-[10], and the references therein, multi-terminal models, and energy harvesting transmitters and receivers are subsequently studied. Green energy optimization problem in cellular networks powered by hybrid energy which include green energy and traditional energy is studied in [11]-[12] to reduce the power consumption of traditional energy. The study of energy cooperation between base stations (BSs) has been widely researched owing to the recent advancement in smart grid [13] and wireless power transfer [14] technologies. Through a two-way energy transmission between BSs, the throughput-maximization oriented energy cooperation strategies are studied in [15]-[16]. To the best of our knowledge, all the previous work for renewable energy utilization does not consider the various type of quality of service (QoS) of diverse traffic type in the wireless network powered by renewable energy.

In this paper, comprehensively considering the QoS, channel quality and the total available renewable energy, we propose the utility based energy allocation algorithm in the renewable energy powered orthogonal frequency division multiple access (OFDMA) cellular network. The utility here refers to a function which describes the degree of user satisfaction with a certain amount of allocated energy. In every time slot, each transmitter is constrained to use at most the amount of stored energy currently available, although more energy may become available in the future slots. Considering the traffic type with the soft QoS which means the traffic requires a certain preferred resource but will still tolerate resource below this preferred value, the channel quality of each user and the total amount of renewable energy at a BS, we allocate the renewable energy available at each BS to its users in each time slot at the method through which maximize the total utility of all users at the BS. The utility based renewable energy allocation method can balance the fairness and efficiency at various conditions of the reserved renewable energy at each current timeslot, the channel qualities and the traffic type with specific QoS requirement. The contributions of this paper are as follows:

The remainder of the paper is organized as follows. In Section II, we describe the system model. The renewable energy powered BS with OFDMA system is considered in this section. Section III formulates the problem. Considering the utility function of soft QoS traffic type then we formulate the renewable energy allocation problem as the total utility maximization problem. In Section IV, we deduce the solution for the problem posed in Section III. Numerical results and discussions are stated in detail in Section V. We conclude this paper in Section VI and simultaneously present our future work.

 

2. System Model

In this section we first describe the system model and then analyze the energy demand of various type of traffic.

2.1 System Scenario

Consider a single cell downlink OFDMA network with renewable energy powered base station and N active users as shown in Fig. 1. The renewable energy sources can be solar and wind power. The total bandwidth, Wtotal is divided into N subchannels, each subchannel with a bandwidth of Wsub = Wtotal / N for each user. We assume that subcarriers are allocated centrally and each subchannel cannot be assigned to more than one user to avoid interference among different users. At each transmission period, the transmit power is denoted as pk . Assuming perfect channel state information in both transmitter and receiver, the maximum achievable data rate of the kth user, denoted as dk, is

Fig. 1.System Scenario

where N0 is the single-sided noise spectral density, and the channel frequency response of the kth user whose data is transmitted on the kth subchannel is denoted as hk . Consequently, at each transmission period the transmit power for the kth user is as follows.

The total energy consumption of the BS during time slot [ t , t + τ ] is

For each user at each subchannel, there is an exponentially increasing relationship between the consumed energy Ek and data rate dk. The total energy consumed for all N users at N subchannels is

2.2 Energy Demand and Renewable Energy Supply

The equipment parameters of an outdoor 4G BS (which is generally called eNode B and widely deployed throughout the world) produced by FUJITSU [17] are shown in Table 1. The maximum transmit power of eNodeB is 60 W and the transmit power will fluctuate with the traffic load, channel quality and QoS requirement of users.

Table 1.eNode B equipment specifications

We consider solar panels as the green energy generators. Solar panels generate electrical power by converting solar radiation into direct current electricity using semiconductors that exhibit the photo-voltaic effect, more information about the green energy generation and rate can be found in [18] and its reference therein [19]-[20]. We conduct an experiment that measures the power of the solar panel with the model SYK20-18P ( size: 540*350*25mm ) made by Guangzhou SUMYOK. We observed that the maximum power is 20W and solar energy generation depends on various factors, such as the temperature, the solar intensity, and the geolocation of the solar panels. Taking into account of the deployment cost of solar panel (or, windmill generator) and green energy storage devices and the time varying green energy generator rate, the renewable energy generating devices at each BS cannot do infinitely great and the renewable energy currently generated at each BS does not always exceed the transmit power of BS. These factors make renewable energy at each BS a finite resource.

Hence, we consider allocate the finite renewable energy based on the demand of diverse traffic type from various application. Assume that the bandwidth allocated to each subchannel is constant, and from Formula (1) the data rate of each user is mainly determined by the allocated transmit power from BS and the channel quality. Set the data rate as the main QoS metric, and a certain traffic type in the wireless network needs a specific QoS. Generally, under the current network structure, there are three kinds of QoS implementation models. The best effort QoS makes best effort to transfer data packet, but provides no guarantees and no priorization for users. Original internet service such as e-mail, file transfer and remote login belong to this type. The hard QoS has an explicit reservation of network resources for traffic flows before communication starts with strict resource requirement and poor scalability. Applications such as video conference, audio/video phone and tele-medicine need a hard QoS guarantee. As an intermediate step between hard QoS constraints and a pure best effort approach, soft QoS has a flexibility in network resource supply. The soft QoS traffic usually has intrinsic resource requirements, i.e., they have their own preferable resource values, but can still tolerate with a less amount of resource than the preferred amount. Soft QoS traffic also known as elastic traffic, can gracefully adjust their transmission rates to adapt to various network conditions. Interactive multimedia services, video on demand and most applications in current wireless networks are typical examples of soft QoS which has a high adaptability to network conditions and resources.

 

3. Problem Formulation

In this section we first define the utility function then formulate our renewable energy allocation problem. How to model application adaptation for utility function, and what type of overall system utility maximisation can be employed, are stated orderly in detail.

3.1 Utility Function

Preference and Utility: Preference relations are a handy way of talking about how people rank bundles of goods. We mainly use three binary relations to talk about preferences: ≻ (strictly preferred to), ~ (indifferent between), and ⪰ (weakly preferred to). Utility function is used to easily describe preferences. A utility function assigns numerical values to all bundles so that if x ⪰ y , we have u( x ) ≥ u( y ) . As shown in Formula (1), set bandwidth Wsub and the parameters N0 and hk which represent the channel quality as constant, and assume the data rate as the main utility performance metric. Then the utility value is determined by the transmit power pk . If there are two values p1 , p2 of pk and p1 ≥ p2 , i.e., p1 ⪰ p2 , then u(p1 ) ≥ u( p2 ) .

Utility Application: Utility function have been applied in wireline and wireless network resource allocation for many years. The utility function based resource allocation was first proposed in [21]-[23] and recently continued to be researched in [24]-[27] etc. mainly conclude the utility of time, spectrum, and wireless radio resources. The existing works have augmented the utility function model by identifying and classifying the way allocations affect the utility of different application classes. Generally, the utility based resource allocation problems usually have an optimal object which subjects to some network constraint.

Utility Function: In this paper, we studied the utility of energy, since the renewable energy generated at each BS is a finite and dynamic resource. As analyzed above, there is an exponential increasing relationship between utility and the renewable energy. A precise presentation of the utility function of renewable energy should comprehensively take into account of the total available energy, the channel quality and the traffic type. Consider that most applications in current networks are resource-adaptive and the network can allocate energy to users at a flexible way, so that we give attention to the utility function for the soft QoS traffic type. Mathematically, the following function can be used to model the utility function of soft QoS traffic type [28]-[29],

where r is the renewable energy allocated by the BS through a centralized mode, i.e., from the BS to users with diverse traffic flow at different subchannels, q ( 0 ≤ q ≤ 1 ) denotes the channel quality of the user, p determines the slope of the utility function, and rmid denotes the preferable amount of resource for the soft QoS traffic. The marginal utility function is defined by the following equation, which is the first derivative of the utility function U(r) with respect to the given resource r. As shown in Fig. 2, when the allocated renewable energy r equals rmid, the marginal utility function achieve its maximum value.

Fig. 2.Utility function and marginal utility function

Suppose that all traffic flows in a BS system have the same traffic type with the same QoS requirement. According to the utility function stated above, the amount of renewable energy allocated to each specific user at a BS determined by the channel quality q and traffic type of the user to guarantee the level of satisfaction. From the perspective of the whole BS system with finite renewable energy resource we should consider the amount of available renewable energy stored in the last inventory process step and channel conditions of all users to maximize the total utility.

3.2 Problem Formulation

Assume there are N users at our BS system. The total amount of available renewable energy at current energy allocation period is rtot, and the energy allocated to the kth user is denoted as rk. The traffic type and channel quality of each user may not be identical, so that the utility function and levels of satisfaction with the same amount of renewable energy of each user are different. Considering an amount of renewable energy allocated to the kth user with the channel quality qk, due to the path loss, the renewable energy actually available to the kth user is given by Ek = qk · rk . The utility function of the kth user can be expressed as Uk( rk ) = U( rk · qk ) . Considering the channel condition of each traffic flow from corresponding user may not be identical, we denote the preferable amount of resource for the kth traffic flow by rmidk. For the kth traffic flow, k ∈ { 1, 2, ⋯ , N } , Thus the preferable amount of resource for the kth traffic flow

In this paper, we aim at maximize the total utility of all users at a BS system with a limited amount of renewable energy generated in the current energy allocation period. The problem is formulated as,

where rtot is the total amount of renewable energy that can be allocated in this current energy allocation period. The renewable energy allocation R* = { r1, r2, ⋯ , rN } for N users is referred as an optimal allocation if R* can make Formula (6) established, i.e., for all feasible allocation where and The optimal allocation R* may not be unique here.

 

4. Solution

To efficiently solve the constrained maximization problem, we appropriately relax the constraint conditions then deduce a heuristic algorithm.

To keep allocation optimal in the wireless environment changing both in the traffic and energy domain, we need to periodically (re)allocate resources. The available finite energy stored at a BS in this current time period will be allocated to N users at this BS by an optimal allocation algorithm through which makes the total utility value maximum. Due to that an optimal solution to this problem presented in Formula (6) is very hard to find and is dependent on the channel qualities and utility functions of traffic flows, we first relax the constraint conditions then adopt a heuristic renewable energy allocation algorithm for soft QoS traffic flow. According to the number of users being allocated energy, all energy allocation (EA) method can be classified into EA1, EA2, ⋯ EAN . Assume that traffic flows from different users at respective subchannels have the identical traffic type and different channel quality.

Property 1: In an optimal renewable energy allocation method, each allocated user i, i.e., ri > 0 , must have an identical marginal utility value ui(ri ).

Proof: Assume there exists an optimal allocation R in which there are users i and j , ( i ≠ j ) , whose allocated resources ri and rj satisfy ui( ri ) ≠ uj( rj ) and ui( ri ) > uj( rj ) > 0 . There must exist a finite small value Δr , and another allocation R’ with ri' = ri + Δr and rj' = rj - Δr , ( ri' + rj' = ri + rj ).

Put Formula (5) into above equation, and we get,

The derivation declares that allocation R is not optimal which violates the assumption at the beginning.

Property 2: At most one user, say i, with ui'( ri ) > 0 can be allocated energy in an optimal renewable energy allocation.

Proof: Assume there exists an optimal renewable energy allocation R which have more than one allocated user I with ui'( ri ) > 0 denoted as ui'( ri ) > 0 and uj'( rj ) > 0 . There must exist another allocation R’ which allocates users i and j respectively with ri' and rj' , where ri' = ri + Δr and rj' = rj - Δr , i.e., ri' + rj' = ri + rj .

The derivation declares that U( R' ) > U( R ), which vilate the assumption that R is an optimal renewable energy allocation.

According to the above two properties, to reduce the computational complexity and guarantee that the allocation performance is still tightly bounded to the optimal solution, we assume that each user i which has been allocated energy has ui'( ri ) ≤ 0 , i.e., the amount of allocated energy ri must exceed its preferable amount rmidi. We conclude that an optimal renewable energy allocation must satisfy the following three conditions:

1) All renewable energy reserved in last inventory process must be allocated.

2) All allocated users must have an identical marginal utility.

3) All allocated users have ui'( ri ) ≤ 0 .

Set r, rmid, and p in utility function as constant and the value of the utility function is monotone increasing along with q. That is to say, with a same amount of renewable energy, the better the channel quality is, the larger is the utility value. Renewable energy allocation RK = {r1, r2, ⋯, rK }, which allocates renewable energy to the first K users sorted by their channel qualities is the one with the highest utility among EAK. We can find RK through 4 steps.

Table 2.Algorithm programme

 

5. Numerical results and discussions

First, we change the slop of utility function through changing the value of p which is set 0.1, 0.8, 3.2, 14 respectively, and observe how the parameter p impacts the utility function. As shown in Fig. 3, when the value of p changes from 0.1 to 14, the utility function changed from a very flat curve to a steep one. Then we set 20 traffic flows at 20 independent subchannels at a BS, and the channel quality of each subchannel q is randomly selected in the range [0, 1], from 0 to 1. The larger value of q means the better channel quality and q = 1 represents the best channel quality. We set the preferable amount of renewable energy rmid for the best channel quality q = 1 as 10, and set rtot i.e., the total available renewable energy at each current period to be allocated, as 100, 400, and 1200, respectively representing a scarce, moderate, and sufficient amount of renewable energy generated at the current allocation period.

Fig. 3.Utility function with different slope p.

Set the slope of utility function as 0.1. As shown in Fig. 3, the utility function is very flat. Set the amount of renewable energy avaliable at the current allocation period as 400, that is the BS has a moderate amount of renewable energy. As shown in Fig. 4, the better channel quality a user has, i.e., with a larger value of q, the more energy is actually available to the user. This illustrates the system allocates renewable energy to users in a way through which a maximum system throughput is achieved. In this case the energy allocation of the system acts in a best effort QoS method.

Fig. 4.Allocated energy and the energy actually available to users: p=0.1, rtot=400.

Set the slope of utility function as 14. As shown in Fig. 3, the utility function is very steep. Set the amount of renewable energy avaliable at the current allocation period as a moderate level, i.e., rtot=400. Fig. 6 shows that the system allocates more renewable energy to users with poorer channel quality, i.e., a smaller value of q, and the amount of energy actually available at each user in the system is the same. That is to say the system allocates energy in a fair way, i.e., no matter what channel quality the users have, the energy actually available to each user is the same. In this case the energy allocation of the system acts as a hard QoS method.

Fig. 5.Allocated energy and the energy actually available to users: p=0.8, rtot=400.

Fig. 6.Allocated energy and the energy actually available to users: p=14, rtot=400.

Set the total renewable energy generated at the current allocation period at a sufficient level, rtot=1200. As shown in Fig. 7, no matter the slope of the utility function is flat or steep, i.e. p=0.1, 0.8, or 14, all users will be allocated a certain amount of renewable energy. The worse channel quality a user has, the more renewable energy will be allocated to the user. Set the total renewable energy generated at the current allocation period at a scarce level, rtot=100. As shown in Fig. 8, no matter what kind of utility function is adopted, only users with good channel quality will be allocated renewable. It suggests that to achieve the goal of total utility maximization, the optimal renewable energy allocation is determined not only by the traffic type and channel quality, but also by the total amount of the available energy generated at the current allocation period.

Fig. 7.A sufficient amount of renewable energy, rtot=1200.

Fig. 8.A scarce amount of renewable energy, rtot=100.

Set the total renewable energy generated at the current allocation period at a sufficient level, rtot=1200. As shown in Fig. 7, no matter the slope of the utility function is flat or steep, i.e. p=0.1, 0.8, or 14, all users will be allocated a certain amount of renewable energy. The worse channel quality a user has, the more renewable energy will be allocated to the user. Set the total renewable energy generated at the current allocation period at a scarce level, rtot=100. As shown in Fig. 8, no matter what kind of utility function is adopted, only users with good channel quality will be allocated renewable. It suggests that to achieve the goal of total utility maximization, the optimal renewable energy allocation is determined not only by the traffic type and channel quality, but also by the total amount of the available energy generated at the current allocation period.

 

6. Conclusion and future works

In this paper, we studied the renewable energy allocation policy which maximizes the total utility of all users at a BS with a finite amount of renewable energy. In our analysis, we comprehensively considered the traffic type, channel quality and total available renewable energy generated at each current allocation period. We took into account the soft QoS traffic type which most applications in the current wireless networks belongs to. Numerical results showed that when the total amount of renewable energy is moderate and the utility function is very steep, users at independent subchannels with various channel quality achieved the same amount of energy actually available to them. That is to say, when the utility function is pretty steep, the system provides a hard QoS and gives a fairness-oriented renewable energy allocation. When the total amount of renewable energy is moderate and the utility function is very flat, users only with a good channel quality can be allocated renewable energy. That is to say, when the utility function is pretty steep, the system provides a best effort QoS. While the total amount of renewable energy is scarce, no matter what kind of utility function we choose, the renewable energy will only be allocated to the users with good channel quality. However, in the renewable energy powered wireless networks there exists other important scarce resource, i.e., spectrum. In order to provide the users with a high quality of experience (QoE) we will jointly optimize the utilization of the finite renewable energy and spectrum in our future work.