Revisiting Transmission Scheduling in RF Energy Harvesting Wireless Communications Yu Luo, Lina Pu, Yanxiao Zhao
Wei Wang
South Dakota School of Mines and Technology {yu.luo,lina.pu,yanxiao.zhao}@sdsmt.edu
San Diego State University
[email protected]
Qing Yang
Zheng Peng
University of North Texas
[email protected]
The City College of New York
[email protected]
ABSTRACT The transmission scheduling is a critical problem in radio frequency (RF) energy harvesting communications. Existing transmission strategies are mainly designed based on a classic model, in which the harvested energy is assumed pre-determined and considered as prior knowledge in offline approaches. In this extended abstract, we challenge this assumption showing that the harvested energy is affected by the transmission scheduling and becomes unknown and not pre-determined. In the new model, we add a feedback line from the data transmission to the harvested energy. It properly indicates the interplay between the energy harvest and the data transmission but challenges the transmission scheduling in the meantime. We formulated the optimal transmission scheduling based on the new model and advocate a recursive solution.
CCS CONCEPTS • Computing methodologies → Modeling and simulation;
KEYWORDS
affected by the transmission scheduling on EHD. However, in a real RF energy harvesting system, the arrived energy and the harvested energy are two distinct concepts. The former is the efficient energy that reaches an EHD after considering the propagation loss and the power conversion efficiency, while the latter is the energy captured and conserved into the EHD’s battery. Due to the nonlinear charge characteristic of batteries, the harvested energy is not only determined by the arrived energy but also affected by the residual energy in the battery [2]. Although the nonlinear charge is a well-known characteristic of batteries, it is not taken into account in the commonly-used energy harvesting model. As illustrated in Fig. 1 (a), the impact of residual energy on the energy harvest process is not considered in the classic model. As a result, it is widely assumed that EHDs performing different transmission scheduling strategy can harvest an equivalent amount of energy as long as the arrived energy is the same. Accordingly, most of offline transmission scheduling methods seek a curve within a predetermined feasible energy tunnel to optimize the communication performance [3].
RF energy harvesting, transmission scheduling, nonlinear charge. ACM Reference Format: Yu Luo, Lina Pu, Yanxiao Zhao, Wei Wang, Qing Yang, and Zheng Peng. 2018. Revisiting Transmission Scheduling in RF Energy Harvesting Wireless Communications. In Proceedings of MobiHoc’18. ACM, Los Angeles, CA, USA, 2 pages. https://doi.org/10.1145/3209582.3225204
1
Classic energy harvesting model Energy from energy source
Transmission scheduling strategy
Harvested energy
(a) New feedback-based energy harvesting model
INTRODUCTION
Due to the features of self-sustainability and pollution-free, harvesting energy from radio frequency (RF) environment becomes a promising technology to drive low-power devices in future wireless sensor networks. An effective strategy to manage the energy received by an energy harvesting device (EHD) plays a crucial role to achieve the desired network performance in terms of throughput, transmission delay, and communication reliability. Existing transmission scheduling strategies are mainly based on a classic energy harvesting model, where the harvested energy is usually modeled as an independent random process [1], which is determined by the transmission power of energy sources (e.g., a TV tower or a cellular base station) and path loss, but is rarely Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from
[email protected]. MobiHoc’18, June 26-29, 2018, Los Angeles, CA, USA © 2018 Association for Computing Machinery. ACM ISBN ACM ISBN 978-1-4503-5770-8/18/06. . . $15.00 https://doi.org/10.1145/3209582.3225204
Data transmission
Energy from energy source
Arrived energy
Transmission scheduling strategy
Harvested energy
Nonlinear charge
Data transmission
+
+ X
Residual energy
(b)
Figure 1: The classic and new energy harvesting models. Unfortunately, the above assumption may not be true in real energy harvesting systems. This is because the transmission scheduling strategy can affect the energy harvesting process by controlling the remaining energy in the battery. In other words, an EHD cannot estimate what amount of energy it can harvest from an energy packet before scheduling its transmissions, and we call it as the causality of energy harvest. The interplay between the transmission scheduling and harvested energy has been completely neglected in the literature. It calls for a new energy harvesting model and re-examination of challenges identified in the existing research. In this work, we propose a new energy harvesting model integrating the causality of energy harvest, as illustrated in Fig. 1 (b). In the proposed model, a feedback loop (the red line in Fig. 1 (b))
from a data transmission to the harvested energy is established that factors the nonlinear charge characteristics of a battery. What distinguishes the classic energy harvesting model is that the feasible energy tunnel is not fixed: its bounds are affected by transmission strategies. Therefore, the formulation of an optimal transmission strategy based on the new model has to be revised. With the new model, the optimal offline transmission scheduling faces grand challenge introduced by the feedback line: on the one hand, the design of an offline transmission scheduling strategy needs to know the amount of energy an EHD can harvest in the future; on the other hand, the transmission scheduling affects the energy harvesting process through the residual energy in a battery.
2
NEW TRANSMISSION SCHEDULING
In this section, we investigate an offline optimal transmission scheduling to maximize the throughput of RF energy harvesting systems following the new feedback-based energy harvesting model. Compared to solutions from the classic model, a primary innovation and challenge are to establish a correct connection between the harvested energy and the transmission strategy. The problem of optimal transmission scheduling is reformulated with two new constraints and eventually solved with a recursive algorithm. In the energy harvesting wireless communications, the relationship between residual and harvested energy can be expressed as: Z ti i−1 X Eir = E hj − p(t ) dt, i = 1, . . . , N +1, (1) 0
j=0
where E 0h = e 0 is the initial energy in the battery. The two terms in the right-hand side of (1) represent the cumulation of energy harvesting and energy consumption, respectively. Based on the relationship between harvested energy and residual energy in battery charge, Eih can be recursively represented by p(t ), i.e., Eih = Qi ( p(t )) ,
0 ≤ t < ti , i = 1, . . . , N .
(2)
Here, we call Q (·) as the power-harvest function, which reflects the impact of transmission scheduling, p(t ), on harvested energy, Eih . This relationship indicates that an EHD cannot estimate the amount of energy it can harvest from an energy packet before scheduling its data transmissions, and we call it as the causality of energy harvest. The power-harvest function reveals the inherent relationship between p(t ) and Eih , which allows for a more realistic and accurate description of energy harvesting process compared with the classic model. Designing an optimal transmission strategy to maximize the throughput of an EHD in the new model is formulated as follows: Z t N+1 P1 arg max G ( p(t )) dt, p (t )
Z ti i−1 X p(t ) dt − Q j −E 0h ≤ 0, 0
C2 E 0h +
i = 1, . . . , N +1,
(3)
j=1 i X j=1
Eir =
i−1 X
E hj −
j=0
i X
pj lj ,
i = 1, . . . , N +1.
(4)
j=1
Using (4), Qi ( p(t )) in (2) can then be represented as Q˜ i (p1 , . . . , pi ). According to the piecewise linear feature of pi and (4), in an additive white Gaussian noise channel P1 is converted into: N +1 X li P2 arg max log2 (1 + pi ), 2 pi i=1 s.t. i i−1 X X (5) C1 i = 1, . . . , N +1, p j l j − Q˜ j −E h ≤ 0, 0
j=1
C2 E 0h +
j=1 i X
i X
Q˜ j −
j=1
p j l j ≤ em ,
i = 1, . . . , N .
j=1
From (5), it can be observed that P2 is a nonlinear maximization problem with inequality constraints, and the optimal solution can satisfy the Karush-Kuhn-Tucker (KKT) conditions in P2. Although the objective function is concave, it is hard to identify whether the constraints C1 and C2 are convex or not due to the nonlinear and complex Q˜ j function. Therefore, KKT equations are necessary conditions but may not be sufficient and multiple solutions may exist in KKT. Hence, we substitute each solution into P2 and select the one that maximizes the objective function subject to the constraints as the optimal strategy.
3
CONCLUSIONS
A new feedback-based model has been proposed for RF energy harvesting communications. Taking the charge characteristic of an energy harvesting circuit into account, the new model reveals the impact of data transmission on harvested energy, which introduces a new constraint called the causality of energy harvest for the design of energy harvesting strategy. With such a constraint, the feasible energy tunnel is not fixed; its bounds change with different transmission strategies dynamically. The offline optimal transmission strategy design is formulated based on the new model and the solution can be found by utilizing the KKT conditions.
0
s.t. C1
feasible energy tunnel, in which data transmission is scheduled, is not fixed anymore but varies with different transmission strategies. In such a tunnel, the transmission policy and the harvested energy interact with each other, which causes an endless loop problem. Referring to the proof of Lemma 2 in [4], it can be proved that the optimal transmission power, which is denoted by p ∗ (t ), is a piecewise linear function. Let pi be the EHD’s transmission power at epoch i, then the residual energy in (1) can be rewritten as:
Z ti p(t ) dt ≤ em , i = 1, . . . , N . Qj − 0
The new optimization problem P1 differs from the conventional one with two distinct constraints, C1 and C2. In these two constraints, the interplay between the harvested energy (i.e., E h ) and the data transmission policy (i.e., p(t )) is fully incorporated in the powerharvest function, Q (·). In the new energy harvesting model, the
REFERENCES [1] Yu Luo, Lina Pu, Yanxiao Zhao, Guodong Wang, and Min Song. Optimal energy requesting strategy for RF-based energy harvesting wireless communications. In Proceedings of the International Conference on Computer Communications (INFOCOM), pages 1–9. IEEE, 2017. [2] Alessandro Biason and Michele Zorzi. On the effects of battery imperfections in an energy harvesting device. In Proceedings of International Conference on Computing, Networking and Communications (ICNC), pages 1–7. IEEE, 2016. [3] Sennur Ulukus, Aylin Yener, Elza Erkip, Osvaldo Simeone, Michele Zorzi, Pulkit Grover, and Kaibin Huang. Energy harvesting wireless communications: a review of recent advances. IEEE Journal on Selected Areas in Communications, 33(3):360– 381, 2015. [4] Jing Yang and Sennur Ulukus. Optimal packet scheduling in an energy harvesting communication system. IEEE Transactions on Communications, 60(1):220–230, 2012.
