Abstract
We study the relay station (RS) sleep control mechanism in green relay-assisted cellular networks where the base station (BS) is powered by grid power and the RSs are powered by renewable energy. Our motivation is to reduce the grid power consumption of the BS and improve users' quality of service (QoS) at the same time by adopting green RSs. However, due to the uncertainty and stochastic characteristics of the renewable energy, power supply for RSs is not always sufficient. Thus the harvested energy needs to be scheduled appropriately to cater to the dynamic traffic so as to maximize the energy saving in the long term. An optimization problem is formulated to find the optimal sleep ratio of RSs to match the time variation of energy harvesting and traffic arrival. To make full use of the renewable energy, green-RS-first principle is adopted in the user association process. The optimal RS sleeping policy is obtained through dynamic programming (DP) approach, which divides the original optimization problem into per-stage subproblems. A reduced DP algorithm and a greedy algorithm are further proposed to greatly reduce the computation complexity. By simulations, the reduced DP algorithm outperforms the greedy algorithm in achieving satisfactory energy saving and QoS performance.
Abstract
978-1-5090-0243-6/15/$31.00 ©2015 IEEE
I. INTRODUCTION
With the rapid growth of energy demand for information and communication technology (ICT), energy-saving approaches for mitigating energy consumption are urgently required. In recent years, green communications have been proposed to improve the energy efficiency [1] . By exploiting renewable energy, e.g., solar energy, wind energy and so on, traditional energy consumption will be significantly reduced. The energy harvesting technology is proved to be practical. From the measurement results of renewable energy sources, energy harvesting level can sustain the operation of a base station, especially for small cells [2] . Therefore, we introduce renewable energy to power the relay stations (RSs) to reduce traditional energy consumption. In case of the shortage of RSs' renewable energy, the users attached to original RSs will associate the grid-powered BS to maintain QoS.
I. INTRODUCTION
However, there are two key challenges need to be addressed for the utilization of renewable energy in cellular networks: firstly, renewable energy harvesting is highly dynamic and uncertain, which influences the transmission directly; secondly, the traffic load shares the characteristic of dynamic variation in both time and space domain. Thus there exists a mismatch between the traffic variation and energy dynamics. On the other hand, since the energy consumption of a station mainly comes from baseband signal processor, controller, air-conditioner and etc., rather than transmit power [3] , turning stations into sleep mode when the traffic load is low, is considered as an effective way to save the energy consumption. Then, for green RSs equipped with batteries, the saved energy in sleep mode will be stored for future use when the traffic load is high so as to save more energy in the long term.
I. INTRODUCTION
Compared with the BS that is supplied by grid power, RSs cover a much smaller area, require lower transmit power and have no wired backhaul connection [4] . Moreover, users served by RSs mostly experience much higher average signalto-interference-plus-noise-radios (SINRs) [5] . All these good features of RS make it a good option to save energy consumption in cellular networks while improving users' QoS, especially for cell-edge users.
I. INTRODUCTION
Regarding the related work, the issue of green RSs has been discussed in different aspects. In [6] the green RS selection was introduced in cooperative communication networks. A single source-destination non-cooperative link with an green source was considered in [7] . A deterministic energy harvesting model for the Gaussian RS channel was considered in [8] , [9] where delay and no-delay constrained traffic were studied. In [10] , cooperative communication with energy harvesting nodes using an energy sharing strategy was studied. In [11] explicit throughput-optimal and delayoptimal policies were developed for a energy harvesting communication system. The concepts of energy transfer and power allocation in green RS systems were considered in [12] . And several higher layer issues such as transmission time minimization and transmission packet scheduling in energy harvesting systems were investigated in [13] . But the sleep control for green RSs aiming at both energy saving and QoS improvement has not been much studied yet.
I. INTRODUCTION
In this paper, we consider a network scenario to reduce the grid power consumption of cellular networks and improve users' QoS at the same time. By introducing renewable energy powered RSs, the grid power consumption of the BS Fig. 1 . system model is greatly reduced. And by deploying RSs at the edge of the BS's coverage where the channel conditions between users and the BS are usually poor, users' QoS can be significantly improved with the assistance of the RSs. The main contributions of this paper can be summarized as follows.
I. INTRODUCTION
• We give the analytical model of user blocking probability due to the shortage of wireless resource. Then a finite optimization problem is formulated to tradeoff the BS on-grid power consumption and system blocking probability minimization. • A dynamic RS sleep control mechanism based on DP approach is proposed, and a reduced DP algorithm as well as a greedy algorithm is further provided to greatly reduce the computation complexity. The remainder of this paper is organized as follows. In Section II, the system model is described. In section III, we formulate the optimization problem. Section IV presents a DP-based algorithm, and a reduced DP algorithm as well as a greedy algorithm. The simulation results are given in Section V and the conclusion is drawn in Section VI.
II. SYSTEM MODEL
We consider a downlink wireless system, which consists of a BS powered by grid power, and green RSs powered by renewable energy, mainly focusing on the QoS improvement of cell-edge users, whose channel conditions to the BS are usually poor. Therefore, RSs are deployed at the edge of the BS's coverage areas and assumed to be uniformly distributed as depicted in Fig.1 . The distances between RSs and the BS are assumed to be the same, denoted by ( − 2 ), where and denote the coverage radius of the BS and RS respectively. Let = {1, ⋅ ⋅ ⋅ , } denote the set of RSs, and ℳ = {1, ⋅ ⋅ ⋅ , } denote the set of users. The coverage area of the BS and the -th RS are denoted as 0 and respectively, and the area with no RS covering in 0 as˜0. Users in˜0 can only be served by the BS while users in can be served by either the -th RS or the BS. Each RS has two state modes (active or sleep), and a RS in active mode can turn to opportunistic sleep mode. The operational time line (e.g., a period of 24 hours) is divided into time slots (each with index and the length ( ) ).
A. Traffic and Channel Model
In each region, users are considered uniformly distributed and arrive randomly according to a Poisson distribution with a certain arrival rate. The arrival rate in area˜0 and at time are denoted as 0 ( ) and ( ) respectively. Each user has a minimum rate requirement 0 , and the transmission duration of each user follows exponential distribution with mean 1/ . Thus the arriving traffic load in˜0 and are calculated as 0 / and / . All users are assumed to remain stationary until the transmission is completed.
A. Traffic and Channel Model
For the BS, it serves a user through the link between the BS and the user, which is termed as the direct link (DL). For the RSs, each RS accesses the BS through a wireless backhaul link (BL) and forwards data to a user through a wireless access link (AL). The spectrum efficiency (transmission rate per unit bandwidth) for user on DL is expressed as
A. Traffic and Channel Model
where 0 is the transmit power of the BS; 1 and 1 are the path-loss constant and path-loss exponent on DL respectively; 0 is the distance between user and the BS; 2 is the noise power; and 0 is the interference power. We assume that the interference is well taken care of by certain interference management tool and is randomized as noise.
A. Traffic and Channel Model
Similarly, the spectrum efficiency on AL and BL are
A. Traffic and Channel Model
As the long time-scale performance is considered here, we ignore the fast fading effects and assume that the spectrum efficiency is constant during the transmission [14] . Moreover, the transmit power is considered to be fixed. Based on the above assumptions, the spectrum efficiency ( 0 , , 0 ) only depends on the link distance, which is independent of the time period.
A. Traffic and Channel Model
Considering the minimal data rate requirement of each user, the corresponding bandwidth demands imposed on different access links are calculated as
A. Traffic and Channel Model
We assume that the BS and each RS have limited radio resource, denoted as ℎ 0 and ℎ respectively. If the total bandwidth demand of the station exceeds its resource limit, the newly arrived users in its range will be blocked.
B. User Association and RS State Model
To fully utilize RSs' renewable energy and save the BS's grid power, RS-first principle is adopted in the user association process, that is, all users within the coverage of a RS associate the RS first, and only when the RS is in sleep mode do they switch to the BS.
B. User Association and RS State Model
For the green RSs, since the energy harvesting and the traffic arrival are both dynamic, there may exist a mismatch between them. Thus, RSs can turn to sleep mode with a sleep probability denoted as ( ) in the -th time slot, and it can be implemented in time domain. That is, if the traffic load is low and the renewable energy is insufficient, an active RS will turn to sleep mode for a fraction of time ( ) in the time slot to save energy, and the saved energy can be stored in the battery for future use. The capacities of batteries equipped with RSs are considered to be the same and denoted by . Thus, the energy sources of a RS are the battery and the energy harvesting at that time slot.
B. User Association and RS State Model
When a RS turns to sleep mode, users within its range will be served by the BS. The overview of the system operation is as follows: The BS is active all the time, while a RS turns to sleep mode in time slot with the probability ( ) . Moreover, according to the RSs' state mode, user association is performed as: users arrive in˜0 during the time slot will associate with the BS directly and those in associate with the corresponding RS unless it is in sleep mode.
C. Energy Consumption Model
We adopt the model in EARTH project [15] , where the power consumption model of a station consists of two categories: the constant part and the dynamic part relevant to the traffic load. Thus, the energy consumptions of the BS and the -th RS are respectively expressed as
C. Energy Consumption Model
where 0, , , are the fixed part when the station is in active mode; △ 0, , △ , are the variable part related to traffic load; and △ , △ are the variable energy consumption slope, which is referred to inverse of power amplifier efficiency factor. The typical values of △ and △ are different. Considering fixed transmission power of both BS and RS, the dynamic power consumption 
C. Energy Consumption Model
where ( ) 0 , ( ) are the resource utilization;
C. Energy Consumption Model
are the resource limitation (i.e., the resource allocated to the station). As the total bandwidth is shared by the BS and RSs, resource allocated to each station is proportional to its arriving traffic load, i.e.,
C. Energy Consumption Model
).
C. Energy Consumption Model
The power consumption of a RS in sleep mode is assumed to be constant, denoted as , which is far smaller than 0,
C. Energy Consumption Model
. Then the total energy consumption of the BS and the -th RS in time slot are expressed as
C. Energy Consumption Model
where the expressions of ( ) 0 , ( ) can be found in [19] .
D. Blocking Probability Analysis
The blocking probability is defined as the probability that a newly arrived user is blocked, i.e., none of the active stations (BS and RSs) can provide service to the user. For simplicity, we ignore the time index in this section.
D. Blocking Probability Analysis
In area˜0, with the proposed user association scheme, a newly arrived user will be blocked if the required bandwidth exceeds the bandwidth limit of the BS. Therefore, the blocking probability of users in area˜0 in time slot is 0,
D. Blocking Probability Analysis
where 0 ′ is the bandwidth demand of a new user ′ and 0 is the binary association variable which equals 1 if user is associated to the BS and 0 otherwise. The expression of 0, is derived as below
D. Blocking Probability Analysis
where ′ 0 is the traffic of the BS including the traffic moving from RSs; 0 is the average resource utilization of the BS for serving per user. Their expressions can be found in [19] .
D. Blocking Probability Analysis
For renewable energy powered RSs, a blocking event can be caused by either resource limitation or energy depletion. The blocking probability of an active RS caused by resource limitationˆ, can be calculated similarly to 0, , which is expressed asˆ,
D. Blocking Probability Analysis
where the definitions of , are similar to Eq.(12) and detailed derivation can be found in [19] .
D. Blocking Probability Analysis
If the harvested and stored energy is not sufficient, the RS will turn to sleep mode with the probability . Denoting the energy harvesting rate and the energy consumed from the battery as and respectively, the available energy of a RS is + which is used to power the RS, i.e., + = (1 − ) + [16] . Thus, the sleep ratio can be expressed as
D. Blocking Probability Analysis
Hence, the blocking probability for a green RS is
D. Blocking Probability Analysis
As the network is divided into multiple areas and the users are uniformly distributed, the system blocking probability can be calculated as = 0,
D. Blocking Probability Analysis
where ( ′ ∈˜0) and ( ′ ∈ ) are the probability that a newly arrived user ′ belongs to area˜0 and respectively. As the users are assumed uniformly distributed and arrive according to a Poisson distribution, the probability can be expressed as
D. Blocking Probability Analysis
,
D. Blocking Probability Analysis
).
III. PROBLEM FORMULATION
Our objective is to minimize the grid power consumption and system blocking probability with the resource constraints of stations (BS and RSs) and renewable energy constrains of RSs. Then, the optimization problem can be considered as follows: Given the traffic profile
III. PROBLEM FORMULATION
and the renewable energy harvesting profile
III. PROBLEM FORMULATION
=1,⋅⋅⋅ , , we aim to minimize the total grid power consumption (i.e. the power consumption of the BS) and users' blocking probability, through deciding the RSs' sleep ratio = { ( ) } =1,⋅⋅⋅ , =1,⋅⋅⋅ , . Therefore, the optimization problem is formulated as
III. PROBLEM FORMULATION
where is the weighting parameter balancing the two objectives; and ( ) is the weighting factor reflecting the system sensitivity to blocking probability in each time slot, which satisfies ∑ =1 ( ) = 1. By adjusting , the relative importance of the blocking probability minimization is balanced with the grid power reduction. And by considering weighted blocking probability, the QoS can be adjusted more flexibly which can satisfy different QoS requirements at different time periods.
IV. RS SLEEP ALGORITHM
The problem is to optimize the total energy consumption and blocking probability in a long term by deciding the blocking probability of each time slot, which is complicated to slove. As dynamic programming (DP) approach has advantages in dividing the whole problem into simple per-stage sub-problems [17] , we propose the sleep algorithm based on the DP approach to find the optimal policy of the problem.
A. Dynamic Programming Algorithm
The DP algorithm contains three key components: state, action and cost function. In our problem, the state is the battery state (energy level), denoted as . The action is the adjustment of sleep ratio . The per-stage cost is the weighted combination of grid power consumption and system blocking probability, which is expressed as
A. Dynamic Programming Algorithm
As we described above, the DP algorithm breaks the original problem down into sub-problems with respect to the stage (i.e., time slot in our problem). Then we perform a backward induction of the cost-to-go functions from time slot to 1, where the objective of each time slot is to minimize the cost of the current time slot and that of the following slots. Thus the cost-to-go function is defined recursively as
A. Dynamic Programming Algorithm
where ( ) ( ( ) ) denotes the minimal cost for the subproblem with ( ) as its initial state. Considering RS's battery capacity , the saved energy in sleep mode can be stored in the battery for future use. Thus, the current stage's state is a function of the last stage's state and action, expressed as
A. Dynamic Programming Algorithm
Then, by conducting backward induction of Eq.(19) from time slot to 1, we can obtain the minimum cost equal to (1) ( (1) ), which is the optimal solution of the original optimization problem.
A. Dynamic Programming Algorithm
Due to the difficulty of solving this non-convex problem, the optimal sleep ratio is hard to obtain. As the sleep ratio can be calculated by Eq. (14) , we discretize the energy consumed from the battery and denote the energy consumption unit as 0 . The range of is from −( − ) which means the harvested energy is all stored in the battery and the sleep ratio equals to 1, to min{ , − } where is the maximal demanding energy when the sleep ratio equals to 0. Therefore, the number of candidate actions of RS in certain slot is = {min{ , − } + ( − )}/ 0 . Thus, the action and state space of the DP algorithm in certain stage are both ∏ =1 ( ) . The computational requirement is still overwhelming especially when the number of RSs is large. Thus it is difficult to implement the standard DP algorithm to obtain the optimal solution. Then, in the following section we introduce the reduced DP algorithm to simplify the decision process.
B. Reduced DP Algorithms
As the users will be switched only to the BS when a RS turns to sleep mode, the sleep of a RS has no influence on other RSs. Therefore, we develop the reduced DP algorithm which decides the per-RS sleep ratio iteratively. The per-RS cost function in time slot is as follows
B. Reduced DP Algorithms
where˜0 ,˜, is corresponding to only one RS and the expression is omitted here which can be obtained through replacing the summation of all RSs in Eq.(9) and Eq.(16) by one RS. The per-RS's cost-to-go function is
B. Reduced DP Algorithms
The cost-to-go function in Eq. (19) is approximated as the summation of per-RS's cost-to-to function, i.e.,
B. Reduced DP Algorithms
The basic idea of the reduced DP algorithm is to find the optimal local action of each RS iteratively. The detailed description of the algorithm is summarized in Algorithm 1. It reduces the action space of slot from ∏ Store the states and the corresponding cost-to-go function value.
11:
end for 12: Update states and go to next stage. 13: end for By performing Algorithm 1, the sleep ratio of each time slot is decided. Thus, when the RS sleep mechanism is executed from slot 1 to , the corresponding sleep ratio of each RS, which is decided by Algorithm 1, is selected at the beginning of each time slot.
C. Greedy Algorithms
The execution of the greedy algorithm performs from time slot 1 to that in each time slot it selects a action which minimizes the cost of the current stage without considering As the action decision only considers the current stage, the performance might be unsatisfactory. But it is easy to perform and is worth considering if the requirement of algorithm accuracy is not too strict.
V. SIMULATION RESULTS
We consider a cellular network depicted as Fig.1 where = 800 and = 100 . The power consumption model is adopted from the EARTH project [15] and the channel model from LTE standard [18] . For the BS, we set 0, = 750 , Fig.2 with different proportions. For simplicity, the proportion of all RSs are considered the same. The total bandwidth shared by the BS and RSs is 30MHz. And the resource allocation is performed at the beginning of each time slot.
V. SIMULATION RESULTS
To study the performance of the reduced DP algorithm and the greedy algorithm, the average grid power consumption and blocking probability are obtained with different traffic arrival rate which is depicted in Fig.3 . It demonstrates that the average grid power consumption and the blocking probability both increase with the traffic arrival. Comparing the two algorithms, the reduced DP algorithm obviously achieves better performance with lower grid power consumption and blocking probability in various traffic arrival conditions. And the average grid power consumption gap between these two algorithms is not obvious in different traffic conditions while the average blocking probability gap decreases with the increase of the traffic arrival.
V. SIMULATION RESULTS
As the optimization problem weights the power consumption and blocking probability, we obtain the tradeoff results as shown in Fig.4 ( ( ) = 1/ ). The results show that the more strict the blocking probability requirement is, the more grid power consumes. The reason is that when the blocking probability is loose, the system will sacrifice some QoS to minimize the grid power consumption. Comparing the two algorithms, the reduced DP algorithm outperforms the greedy algorithm which achieves both less grid power consumption and lower blocking probability in the same condition (i.e., the same weighting parameter). With the increase of the weighting parameter , the blocking probability decreases while the grid power consumption increases.
VI. CONCLUSION
We consider the dynamic RS sleep control mechanism aiming at reducing the grid power consumption while minimizing system blocking probability for a long term. The RSs' sleep ratio is appropriately scheduled via DP algorithm to cater to the energy harvesting and traffic arrival dynamic. A reduced DP algorithm as well as a greedy algorithm is further proposed to reduce the complexity. The reduced DP algorithm is shown to achieve better performance than the greedy algorithm. To further improve the performance of the reduced DP algorithm, joint optimization of all RSs' sleep control in the per-stage subproblems should be considered in the future. On the other hand. online dynamic RS sleep control without the statistical information of the energy harvesting and traffic arrival is included in the future work.

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