Optimal joint transmission and harvested energy scheduling for renewable energy harvesting enabled cellular network under coordinated multi-point transmission
- Zejue Wang^{1},
- Hongjia Li^{1}Email author,
- Dan Hu^{2} and
- Song Ci^{3}
https://doi.org/10.1186/s13638-015-0313-6
© Wang et al.; licensee Springer. 2015
Received: 20 September 2014
Accepted: 2 March 2015
Published: 1 April 2015
Abstract
On-grid energy consumption of base stations (BSs) contributes up a significant fraction of the total carbon dioxide (CO_{2}) emissions of cellular networks, among which remote radio units (RRUs) absorb most of the energy consumption. To eliminate the on-grid energy consumption and the corresponding CO_{2} emission, we propose a new transmission framework, in which all RRUs and associated power amplifiers (PAs) are powered by hybrid energy sources including on-grid energy source and off-grid renewable energy source. Based on the framework, we pursue a systematic study on the joint transmission and harvested energy scheduling algorithm for the hybrid energy powered cellular transmission system under coordinated multi-point (CoMP) transmission. Firstly, we formulate an optimal offline transmission scheduling problem with a priori knowledge about channel state information (CSI), under constraint of available amount of harvested energy and stored energy at each transmission time interval. Considering a practical constraint of limited pre-knowledge about CSI, we further transform the offline problem into an energy-aware energy efficient transmission problem. To solve the proposed problems, we undertake a convex optimization method to the optimal offline transmission scheduling problem and design corresponding optimal offline joint transmission and energy scheduling algorithm, which provides the upper bound on actual system performance. Then, we extend the non-linear fractional programming to the transmission scheduling problem with limited pre-knowledge about CSI and design corresponding joint transmission and energy scheduling algorithm, named as online algorithm. Numerical results show that the performance of the proposed online algorithm is close to that of the obtained upper bound and outperforms the existing algorithm. We also find that at each transmission time interval during the finite transmission period, the transmit power of each RRU is proportional to the weighted channel-gain-to-noise ratio (CNR) of each sub-channel.
Keywords
1 Introduction
The need for network operators to reduce their on-grid energy consumptions as well as carbon dioxide (CO_{2}) emissions is currently steering research in communications toward more efficient and environmentally friendly networks. According to [1], cellular network worldwide consumes approximately 60 billion kWh per year, among which the energy consumption of base stations (BSs) accounts for 80%. Fortunately, natural resources, such as wind and solar, are envisaged to be green energy resources, due to their pollution-free and renewable natures [2]. According to statistics, powering one BS which has an average power consumption of 1,400 Watts with renewable energy can reduce coal consumption of 2.5 tons with a carbon footprint of 11 tons per year [3]. Therefore, powering cellular network by renewable energy, named as renewable energy harvesting (REH) enabled cellular network in this paper, has been widely accepted as a promising avenue to reduce CO_{2} emission and on-grid power consumption, e.g., the technique report [4] and the technique specification [5] of 3rd Generation Partnership Project (3GPP) clearly indicate that the use of renewable energy resources is explicitly encouraged in mobile network, and researching on it is suggested to have high priority.
On the other hand, coordinated multi-point (CoMP) transmission, which enables cooperation among multiple nodes or remote radio units (RRUs) to transmit data to the same served users with the identical time-frequency resources by the multi-antenna techniques, is regarded as a key enabling technology for elevating system performance and quality of service (QoS) [6]. Due to the promising advantage in terms of the higher spectral efficiency of its air-interface, the CoMP transmission has been accepted in the long term evolution-advanced (LTE-A) specification [7].
We focus on joint transmission and harvested energy scheduling for optimizing the utility efficiency of harvested energy in hybrid energy (including on-grid energy and off-grid renewable energy) powered cellular transmission system where the off-grid REH system, mainly consisting of the energy harvester, the battery module, and the controller, is embedded into BSs.
Energy efficiency improvement is a hot topic in the research area of green wireless communication. For example, [8-10] study the energy efficient link transmission and resource allocation schemes in the orthogonal frequency division multiplexing (OFDM) system. [11] studies the energy efficient cooperative relay transmission exploiting the fractional programming approach. As for energy efficient transmission in CoMP system, [12] proposes an energy efficient power allocation algorithm for the downlink transmission, and [13] studies energy-efficient precoding for CoMP transmission in heterogeneous network.
Since the energy harvesting characteristics, i.e., the energy arrival and the amount of energy being harvested, is determined by the changing surrounding environment, e.g., the energy harvested through wind turbines varies with wind force and direction, and the energy harvested through photovoltaic panels varies with solar radiation and ambient temperature, the opportunistic energy harvesting results in a highly random energy availability. Additionally, the battery module, which can be seen as the energy buffer, provides the basis of harvested energy scheduling in the dimension of time for further improving the utilization efficiency of harvested energy. Therefore, the basic optimization problem and the optimization variables for energy efficient transmission in REH enabled cellular network are different from that in on-grid energy powered cellular network, cf., Sections 3, 4, and 5.
Flashing back to the literature, the study of REH enabled network stems from wireless sensor network (WSN), since sensor node is often deployed under a complicated and adverse condition where a reliable on-grid power connection is not available. The short-term throughput, i.e., the amount of data transmitted during a finite time period, maximization problem is formulated in [14,15]. The optimal packet scheduling problem in additional white Gaussian noise (AWGN) broadcast channel is investigated in [16,17]. However, cellular network is more complex than WSN in terms of techniques in physical, media access control, and network layers. Besides, the energy consumption and the QoS requirement of the BS in cellular network are much higher than those of the sensor node. Therefore, it is hard to directly port the research results of REH enabled WSN to REH enabled cellular network.
As for prior studies on REH enabled cellular network, there are first some prior arts focusing on single BS transmission without considering the transmission cooperation among multiple BSs which is regarded as a promising technique for 4G and beyond cellular networks. In [18], an effective algorithm is proposed to maximize the utilization of green energy in such network. To maximize the utilization of green energy, an energy packet scheduler is proposed in [19] to optimize the packet scheduling. The resource allocation problem of a single cell powered by hybrid energy sources is studied in [20]. The authors analyze the relationship between energy input and transmission outage probability which is defined as the probability that the users’ throughput is less than a given threshold. An energy efficient resource allocation algorithm in an OFDM access downlink network is proposed in [21].
More recently, researchers begin to draw attentions on the study of REH enabled cooperation transmission. In [22], the throughput maximization problem is investigated for only renewable energy powered relay nodes, and yet the time-varying characteristics of wireless channel are not considered. In [23], an optimal transmission scheme for a two-hop relay network is proposed under the assumption that the energy storage capacity of the battery module in REH system is infinite. In [24], a weighted sum-rate maximization problem is formulated for CoMP system powered by hybrid energy sources. Because it is assumed that there is no battery module in the energy harvesting system, the harvested energy cannot be scheduled in the dimension of time to further improve the energy efficiency of CoMP transmission and the utilization efficiency of the harvested energy. Therefore, there should be the finite energy storage module especially for the off-grid REH system.
Driven by the above considerations, the joint transmission and harvested energy scheduling problem is studied for a hybrid energy powered cellular network equipped with finite energy storages. Due to the random characteristic of harvested energy arrival, in such network, renewable energy is viewed as a supplement to the total amount of energy required for transmission. It is desirable to know how to sufficiently utilize renewable energy to reduce the on-grid energy consumption and the corresponding CO_{2} emission. Therefore, in this paper, we focus on optimizing the utilization of harvested energy, jointly considering the practical constraint of the energy harvesting system, and a priori knowledge and limited pre-knowledge about channel state information (CSI), which result in the following main contributions.
1) Considering space and cost limitations of a BS, we propose in this paper a new REH enabled transmission framework, in which all RRUs and associated power amplifiers (PAs) are powered by hybrid energy including on-grid energy and off-grid renewable energy, to realize a green and reliable transmission.
2) Based on the framework, we pursue a systematic study on the joint transmission and harvested energy scheduling algorithms for REH enabled transmission under CoMP transmission. Firstly, we formulate an optimal offline transmission scheduling problem with a priori knowledge about CSI, under constraint of available amount of harvested energy and stored energy at each transmission time interval. Then, considering practical constraint of limited pre-knowledge about CSI, we transform the optimal offline transmission scheduling problem into an energy-aware energy-efficient transmission problem.
3) We undertake a convex optimization method to the proposed optimal offline transmission scheduling problem and design corresponding optimal offline joint transmission and energy scheduling algorithm, which provide the upper bound on actual system performance. Then, we extend the non-linear fractional programming to the transmission scheduling problem with limited pre-knowledge about CSI and design corresponding joint transmission and energy scheduling algorithm, which named as online algorithm, considering temporal variabilities of channel and harvested energy. Numerical results show that the performance of the proposed online algorithm is close to that of the obtained upper bound. We also find that at each transmission time interval during the finite transmission time period, the transmit power of each RRU is proportional to the weighted channel-gain-to-noise ratio (CNR) of each sub-channel.
The rest of the paper is organized as follows. The system model is described in Section 2. The transmission scheduling problems are formulated in Section 3. The offline solution and the proposed offline transmission scheduling algorithm are described in detail in Section 4. Section 5 provides the online solution and the proposed online transmission scheduling algorithm. Section 6 presents the numerical results and analyses. Finally, Section 7 draws up the conclusion.
2 System model
where i∈{1,2,…,M}. \({E_{i}^{l}}\) denotes the arrived energy of RRU l at time instant t _{ i } and can be predicted by using renewable power prediction model, e.g., Takagi-Sugeno-Kang (TSK) model [26] and fuzzy inference method [27].
3 Formulation of transmission scheduling problems
In this section, we formulate the transmission scheduling problems for REH enabled network under CoMP transmission. We first formulate an offline transmission scheduling problem with the assumption that prior knowledge about CSI is available. With consideration of practical constraint of limited pre-knowledge about CSI, we further formulate an online transmission scheduling problem by making an extension of the offline transmission scheduling problem.
3.1 Formulation of offline transmission scheduling problem
In (2), \(\gamma _{n,l,i}^{2} = G_{n,l,i} |h_{n,l,i}|^{2} /\sigma ^{2}\) denotes the CNR of RRU l on sub-channel n at the ith time interval. G _{ n,l,i } is the large-scale path-loss from RRU l on sub-channel n at the ith time interval and defined by \(G_{n,l,i} \propto \left (d_{n,l,i}^{} / d_{\textit {REF}} \right)^{- \alpha }\) where d _{ n,l,i } and d _{ REF } are the distances between the UE allocated to sub-channel n and the RRU l at the ith time interval and the reference distance, respectively. α is the path-loss exponent valued between 2 and 6. |h _{ n,l,i }| stands for the gain of the Rayleigh fading channel at the ith time interval, modeled by i.i.d. complex Gaussian with unit variance, i.e., \(h_{n,l,i} \sim \mathcal {N}_{C} (0,1)\). σ ^{2} is the power of AWGN. Without loss of generality, it is assumed that the noise power is the same for all the sub-channels. p _{ n,l,i } is the transmit power of RRU l on sub-channel n at the ith time interval.
where m∈{1,2,…,M},m ^{′}∈{1,2,…,M+1} and l∈{1,2,…,L}. \(E_{l,i}^{con} = \left (\xi \sum \limits _{n = 1}^{N} {p_{n,l,i}} + P_{C}\right)s_{i}\) denotes the energy consumption of RRU l at the ith time interval. ξ is defined as ξ=ε/η, where ε denotes the peak-to-average power ratio (PAPR) and η denotes the PA efficiency. P _{ C } stands for the power consumption of other facilities in the RRU. (·)^{+} is defined as (·)^{+}= max{0, ·}. Non-overflow constraint C1 states that in order to prevent energy overflow in the battery of RRU l, ∀l∈{1,2,…,L}, at least \(\left ({\sum \limits _{i = 0}^{m} {E_{l,i}} - E_{C}} \right)^ +\) amount of energy must be consumed by the time the mth energy arrives. In other words, the total amount of energy stored in the battery of each RRU never exceeds the battery capacity E _{ C }. Causality constraint C2 implies that during every transmission period [0,t _{ m }), ∀m∈{1,2,…,M+1}, the energy that can be drawn from the battery of RRU l to cover the energy requirement at the PA is constrained to consume at most the amount of available energy currently stored in the battery [21]. Which means that even more energy will be harvested in future time but can not be used to meet the energy requirement currently.
3.2 Formulation of online transmission scheduling problem
So far in our formulation, we have considered the offline problem with the assumption that a priori knowledge about CSI during the whole transmission period [0,T) is available. However, in practice, it is difficult to obtain the prior knowledge about CSI during the whole transmission period [0,T) [28]. Fortunately, with channel prediction technology which has been extensively investigated in the literature [29,30], it is possible to obtain the predicted CSI for a finite time period. Specifically, we further formulate the transmission scheduling problem in an online manner by assuming the knowledge about the predicted CSI for each two consecutive time intervals.
The online problem is formulated in two steps, and details are given as follows.
where \(\overline {U}_{\textit {EE}} \) denotes average energy efficiency, measured in bit/Joule. Hence, with the prior knowledge about CSI during the whole transmission period [0,T), to maximize the total number of transmitted bits is to maximize the average energy efficiency of the system.
In (5), n∈{1,2,…,N}, l∈{1,2,…,L} and u∈{k,k+1}. \(B_{n,i}^{'}\) is the bits transmitted on sub-channel n at the ith time interval and given by \(B_{n,i}^{'}= \log _{2} \left ({1 + \left ({\sum \limits _{l = 1}^{L} {\gamma _{n,l,i} \sqrt {\widehat {p}_{n,l,i}} }} \right)^{2}} \right)s_{i}\), where \(\widehat {p}_{n,l,i}\) is the transmit power of RRU l on sub-channel n at the ith time interval. \(E_{l,i}^{'} = \left (\xi \sum \limits _{n = 1}^{N} {\widehat {p}_{n,l,i}} + P_{C} \right)s_{i}\) denotes the energy consumed by RRU l at the ith time interval. \(\left \{ B_{n,i}^{'} \right \}\) and \(\left \{ E_{l,i}^{'}\right \}\) are constant sequences which have been determined by resolving the above optimization problem during the transmission period [0, t _{ i+1}), ∀i∈{1,2,…,k−1}. Note that in (5), \(\sum \limits _{i = 1}^{k - 1} {B_{n,i}^{'} }\) and \(\sum \limits _{i = 1}^{k - 1} {E_{l,i}^{'} }\) are equal to zero when k=1 for ∀n.
4 Offline solution and joint transmission and energy scheduling algorithm
The offline optimization problem (3) can be proved to be concave with the composition rules of concavity and the first order condition [31], with details as follows.
Proof 1.
Since D({p _{ n,l,i }}) is a linear combination of D _{ n,i }, D({p _{ n,l,i }}) is concave if D _{ n,i } is concave.
where n∈{1,2,…,N} and i∈{1,2,…,M+1}, respectively.
Since log_{2}(·)is concave and non-decreasing, and f _{ n,i } is linear, D _{ n,i } is concave if g _{ n,i } is concave according to the composition rules of convexity [31]. The concavity of g _{ n,i } is verified with the first order condition [31].
i.e. g _{ n,i }(x _{ 1 })−g _{ n,i }(x _{ 2 })≤∇g _{ n,i }(x _{ 2 })^{ T }(x _{ 1 } − x _{ 2 }).
Hence, g _{ n,i } is concave and consequently, D({p _{ n,l,i }}) is concave.
where {ς _{ l,m }} and \(\{ \mu _{l,m^{\prime }} \}\) denote the Lagrange multiplier matrices associated with constraints C1 and C2, respectively.
where \(\mathcal {K}_{l_{1},i} \cdot \gamma _{n,l_{\vartheta },i}\) can be viewed as the weighted CNR of RRU l _{ 𝜗 }.
According to (16), the optimal \(\varphi _{n,i}^{\ast }\) need to be selected, which may need to search over 2^{ L } cases for each time interval. However, we will prove in following that there are only two possible cases for \(\varphi _{n,i}^{\ast }\). To describe our theory, two lemmas are first given as follows.
Lemma 1.
The solution satisfying (16) with all \(p_{n,l,i}^{\ast } > 0\), i.e., \(\varphi _{n,i}^{\ast } = \{ 1,2,\ldots,L\}\), is an extreme point solution. Moreover, it is also the optimal solution of (3), if exists, due to the concavity of the objective function in (3).
Lemma 2.
The solutions satisfying (16) with at least one \(p_{n,l,i}^{\ast } = 0\), i.e., \(\varphi _{n,i}^{\ast } \subset \{ 1,2,\ldots,L\}\), are boundary point solutions. When the extreme point is not feasible, the optimal solution must be one of these solutions.
To solve the optimization problem (3), it is natural that to first check whether the extreme point is feasible. If not, then check each boundary point solution.
With the above two lemmas, the following theorem is provided.
Theorem 1.
If the extreme point solution does not exist, then the feasible solution of (3) must be the solution with all \(p_{n,l,i}^{\ast } = 0\), i.e., \(\varphi _{n,i}^{\ast } = \emptyset \).
Proof 2.
where \(\varphi _{n,i}^{\ast } = \{ 1,2,\ldots,L\}\).
i.e., the solution \(\left \{ p_{n,l,i}^{\prime } \right \}\) is not feasible. Hence, except the solution with \(p_{n,l,i}^{\ast } = 0\) and \(\varphi _{n,i}^{\ast } = \emptyset \), none of the boundary point solutions is feasible.
where ∀n∈{1,2,…,N}, ∀l∈{1,2,…,L} and ∀i∈{1,2,…,M+1}.
where l∈{1,2,…,L}; m∈{1,2,…,M}; m ^{′}∈{1,2,…,M+1}; υ is the iteration number; \(\kappa _{1}^{\upsilon }\) and \(\kappa _{2}^{\upsilon }\) are the sequences of scalar step size.
5 Online solution and joint transmission and energy scheduling algorithm
In (23), q∈R is referred as a parameter which determines the relative weight of the total energy consumption of system and can be intuitively interpreted as the overhead caused by energy consumption [32].
and the corresponding q denotes the optimal average energy efficiency in (5).
where {ρ _{ l }} and {ψ _{ l,u }} denote the Lagrange multiplier vector and matrix associated with constraint C3 and constraint C4, respectively.
Thus, the power allocated at the kth time interval for signal transmission of RRU l on sub-channel n is determined by \(\widehat {p}_{n,l,k}^{\ast } = \left \{ \widehat {p}_{n,l,i}^{\ast } |n \in \{ 1,2,\ldots,N\},l \in \{ 1,2,\ldots,L\}\right. \), \(\left.\vphantom {\widehat {p}_{n,l,i}^{\ast }}i = k\right \}\).
where l∈{1,2,…,L}; u∈{k,k+1}; υ is the iteration number; \(\kappa _{3}^{\upsilon }\) and \(\kappa _{4}^{\upsilon }\) are the sequences of scalar step size.
The proposed offline and online transmission scheduling algorithms are summarized in Algorithm 1 and Algorithm 2, respectively. The proofs of convergence of proposed offline and online algorithms are similar to Appendix B in [34].
6 Performance evaluation and analysis
Simulation parameters
Simulation parameter | Value |
---|---|
Number of RRUs L | 2 |
Number of sub-channels N | 12 |
Number of time intervals M+1 | 10 |
Length of each time interval s _{ i } (s) | 1 |
Battery capacity E _{ C } (J) | 300 |
Static circuit power consumption P _{ C } (dBm) | 40 |
Power amplifier efficiency η | 0.3 |
Peak-to-average power ratio ε (dB) | 12 |
Path-loss exponent α | 4 |
Noise power σ ^{2} (dBm) | −128 |
Reference distance d _{ REF } (m) | 35 |
Comparisons of average energy efficiency, average data rate, and reduced CO _{ 2 } emissions of different algorithms
I1 ^{ a } | I2 ^{ b } | I3 ^{ c } | |
---|---|---|---|
Offline under CoMP | 0.71 | 109.06 | 3.36 |
Online under CoMP | 0.62 | 102.25 | 3.14 |
SRT with a priori knowledge about CSI | 0.29 | 73.17 | 1.17 |
SRT with limited pre-knowledge about CSI | 0.22 | 61.95 | – |
7 Conclusions
In this paper, we propose a new REH enabled transmission framework powered by hybrid energy sources including on-grid energy source and off-grid renewable energy. Based on the framework, the joint transmission and harvested energy scheduling algorithms are investigated for the hybrid energy powered cellular transmission system under CoMP transmission. Firstly, we formulate an optimal offline transmission scheduling problem with a priori knowledge about CSI. Considering practical constraint of limited pre-knowledge about CSI, we further transform the offline problem into an energy-aware energy-efficient transmission problem. By extending convex optimization method and non-linear fractional programming to the offline problem and the online problem, respectively, we design two joint transmission and energy scheduling algorithms. Moreover, we prove that at each transmission time interval during the finite transmission period, the transmit power of each RRU is proportional to the weighted CNR of each sub-channel. Numerical results show that the performance of the proposed online algorithm is close to that of the proposed offline algorithm and outperforms the MDP-based algorithm. Besides, the proposed REH enabled transmission framework not only reduces the CO_{2} emissions but also improves the energy utilization efficiency of renewable energy.
So far, the transmission scheduling problems have been considered with the assumption that all data packets have arrived at RRUs before transmissions begin. Interesting topics for future work include investigating joint transmission and harvested energy scheduling algorithm for random data packets arrival scenario where data packets arrive at arbitrary time instants during the course of transmission and each packet contains an individual transmission constraint. As RRU cannot transmit the data that has not arrived yet, the transmission algorithm is not only subject to individual transmission delay constraint but also to transmission causality constraint. The design of the transmission scheduling algorithm becomes even more challenging when taking into account the random characteristics of data packet arrival time and transmission delay requirement.
Declarations
Acknowledgements
This work was supported by the National Nature Science Foundation of China (No. 61302108), US National Science Foundation (1145596, 0830493) and National Key Technology R&D Program (2012BAH06B02).
Authors’ Affiliations
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