**Energy Splitting for SWIPT in QoS-constraint MTC**

**Network: A Non-Cooperative Game Theoretic Approach**

Kang Kang, Zhenni Pan, Jiang Liu, Shigeru Shimamoto

Graduate School of Fundamental Science and Engineering, Waseda University, Japan

**ABSTRACT**

*This paper studies the emerging wireless energy harvesting algorithm dedicated for machine type communication **(MTC) in a typical cellular network where one transmitter (e.g. the base station, a hybrid access point) with constant power supply communicates with a set of users (e.g. wearable devices,sensors). In the downlink direction, the information transmission and power transfer are conducted simultaneously by the base station. Since MTC only transmits several bits control signal in the downlink direction, the received signal power can be split into two parts at the receiver side. One is used for information decoding and the other part is used for energy harvesting. Since we assume that the users are without power supply or battery, the uplink transmission power is totally from the energy harvesting. Then, the users are able to transmit their measured or collected data to the base station in the uplink direction. Game theory is used in this paper to exploit the optimal ratio for energy harvesting of each user since power splitting scheme is adopted. The results show that this proposed algorithm is capable of modifying dynamically to achieve the prescribed target downlink decoding signal-to-noise plus interference ratio (SINR) which ensures the high reliability of MTC while maximizing the uplink throughput.*

**KEYWORDS**

*Energy harvesting, decoding SINR, uplink throughput maximization*

**1. INTRODUCTION**

Recent years, wireless power transfer is emerging as a possible solution to address the power supply issue in wireless communications. Conventionally, terminals in wireless networks are powered by fixed energy supplies, e.g. power lines and batteries. But for most mobile terminals and remote deployed terminals (e.g. temperature sensor and wind speed monitor), they are mainly supplied by batteries, which extremely limits the lifetime [1]. However, sometimes because of the unreachable deployment location, it is impossible or extremely difficult to replace or charge the battery. Thus, wireless energy transfer is considered as an alternative solution to extend the working time of the network by transfer unlimited power via a wireless method.

**1.1. Related Works**

In [2], Wireless power transfer techniques are summarized into three categories: RF energy transfer, resonant inductive coupling and magnetic resonance coupling. Compared with the other two coupling related techniques, RF energy transfer outperforms in terms of effective distance. Note that in this paper,we only focus on this RF energy transfer technique. In [3], an orthogonal frequency division multiple access (OFDMA) system with simultaneous wireless information and power transfer is considered. The tradeoff between energy efficiency, system capacity, and wireless power transfer are achieved by developing suboptimal iterative resource allocation algorithms. In [4], the authors consider both delay and mobility with wireless energy harvesting. Three issues including optimal transmission policy for the mobile node, energy management strategy and deployment of wireless power sources are solved. In [5], a point-to-point wireless link over the narrowband flat-fading channel with time-varying co-channel interference is considered. Time switcher is used at the receiver side to switch between information decoding and energy harvesting based on the instantaneous channel and interference condition. Various

trades-offs between wireless information transfer and energy harvesting are achieved.

Additionally, multiple-input multiple-output (MIMO) is widely used in wireless energy transfer to improve the performance of wireless energy transfer. In [6], an efficient channel acquisition method for a point-to-point MIMO wireless energy transfer system is designed by exploiting the channel reciprocity. The dedicated reverse-link training from the energy receiver is used by the energy transmitter to estimate the CSI. In [7], wireless energy transfer with MIMO is considered and a general design framework for a new type of channel learning method based on the energy receivers energy measurement feedback is proposed. In [8], the frame is divided into downlink for wireless energy transfer and uplink for wireless information transmission and the optimal time allocation for downlink and uplink is obtained.

Game theory has been widely used as an effective approach to solving resource allocation problems. A Multiservice Uplink Power Control game (MSUPC) is formulated in [9] and the cost function of each user is designed to maximize its own utility. Besides, some optimal power allocation schemes using game theory are proposed in [10], [11] and [12] by considering different network scenarios. In addition, game theory is also used to handle joint resource allocation problems. [13] considers both utility-based uplink transmission power and rate allocation in a non-cooperative game model with pricing. [14] proposes a utility function representing its perceived satisfaction with respect to its allocated power and rate.

**1.2. Contributions**

In this paper, game theory is utilized to derive the balancing ratio for energy harvesting out of the total received power for future MTC networks. Most of the existing works discuss optimal time allocation, throughput maximization and various trades-offs between energy efficiency, capacity and wireless power transfer. Different from these existing papers, our main contributions are listed below.

- We first use game theory to address wireless energy transfer problem. Game theory enables us to obtain a balancing solution under various constraints. In this paper, in order to ensure the downlink received decoding SINR and the uplink throughput of each user, a non- cooperative game model is formed to seek a balancing solution between energy for decoding and energy for harvesting
- We first design a wireless energy transfer algorithm dedicated for MTC networks. Different from common mobile communications, the base station broadcasts control signal, which is only severa bits size, to the machines in the downlink direction while in the uplink direction the machines transmit large amount data to the base station periodically. So these require an extremely high decoding SINR level in the downlink direction to ensure the control signal is decoded correctly and a maximum throughput in the uplink direction. Based on these requirements, a target decoding SINR is set, upon which the uplink throughput is maximized

**Figure 1: **System model

Our solution indicates that in order to ensure the high reliability of MTC, a cell edge machine with poor channel condition utilizes the majority of received energy to do harvesting while a cell center machine with good channel condition utilizes majority of received energy to do information decoding. As a result, the uplink throughput of a cell edge machine is lower than that of a cell centre machine since the harvest-then-transmit protocol is used here. Additionally, the value of target decoding SINR affects the performance of this system as well. When the target decoding SINR increases, the uplink throughput decreases so that more received energy can be used for decoding.

The rest of this paper is organized as follows: Section 2 shows the system model of this wireless energy transfer MTC networks. In Section 3, the wireless energy transfer algorithm is derived based on game theory. The simulation results are presented in Section 4. Finally, this paper is concluded in Section 5.

**2. SYSTEM MODEL**

As shown in Fig. 1, this paper considers a wireless cellular network with mixed wireless information transmission and wireless energy transfer in the downlink direction and pure wireless information transmission in the uplink direction. The system consists of one base station and N devices denoted by MTCDi, i = 1, · · · , N. It is assumed that the base station and all devices operate on the same frequency band. Different from those MIMO systems, we assume that one single antenna is equipped at the base station and all devices. We further assume that all devices are without batteries or power supplies. Therefore, the devices have to harvest energy from the received signals transmitted by the base station in the downlink direction, upon which the devices use the harvested energy to transmit data to the base station in the uplink direction. The downlink and uplink channel gains of ith device are denoted as GDLi

**Figure 2:** Energy harvesting frame

**3. GAME PROBLEM FORMULATION**

In this section, we formulate the energy harvesting problem using non-cooperative game model, upon which the energy harvesting ratio iteration function is derived. In addition, we prove the existence o Nash equilibrium of this algorithm as well as the convergence of this iteration function with certain constraints.

**3.1. Utility Function and Nash Equilibrium Derivation**

A game model consists of three essential elements: player, strategy and utility function. In this paper, each device is regarded as a player participating in this game. The energy harvesting ratio θi is assumed

**3.2. Energy Harvesting Algorithm**

Providing that the interference and noise can be measured at the receiver side, we can get

**So far, we have obtained the energy harvesting control iteration function and the convergence is proved in the next subsection.**

**3.3. Convergence**

For an iterative algorithm, it needs to achieve a stable value after some iterations. In [15], the authors show that when convergence is achieved, three properties need to be satisfied. The proof of convergence is showed as follows

**3.4. Existence of Nash Equilibrium**

In this section, the Implicit Function Theorem [14] is used to prove the existence of a unique solution for this iterative function. According to the Implicit Function Theorem, a new function is established by moving the left-hand side term of (8) to the right-hand side and obtain

**Figure 3: **Convergence of energy harvesting ratios

**4. NUMERICAL RESULTS**

**Figure 4:** Downlink decoding SINR gap with different number of devices in terms of different target decoding SINR

**Figure 5:** Achievable stable θ_{i} under different channel gain in terms of target decoding SINR

and energy harvesting but also affects the uplink throughput of each device. Fig. 6 shows the effects that θ_{i} makes on throughput. As it is discussed before, θ_{i} actually represents the amount of energy for harvesting. And all of this harvested energy is used for uplink transmission since there is no battery for energy storage. So it is clear that with the increase ofθ_{i} , the throughput increases as well. It is worth noting thatθ_{i} varies in different regions under different target decoding SINRs. This is because a device experiencing a poor channel with a high target decoding SINR has to utilize more received energy to reach this target decoding SINR compared with a device experiencing a poor channel with a low target decoding SINR. This explains the starting points locations of these five lines. Additionally, for the devices with good channels, regardless of the target decoding SINRs, all these five lines achieve similar throughput. This is because for a device with a good channel, the target decoding SINR can be easily achieved by consuming little-received energy. As a result, most of the received energy is used for uplink transmission. Therefore, they are capable of achieving the same throughput. This explains the endpoints locations of these five lines.

**5. CONCLUSION**

In this paper, an energy harvesting control algorithm is proposed for future wireless powered MTC networks by involving a non-cooperative game model. This algorithm takes both downlink and uplink transmission into consideration. In the downlink direction, the device splits the received energy into two parts: the information decoding part and the energy harvesting part. Because of the harvest-thentransmit protocol, the harvested energy is in turn used for uplink transmission. Since the high reliability of MTC has to be satisfied with the highest priority, we firstly ensure the downlink decoding SINR achieve the prescribed target decoding SINR, and then we improve the uplink throughput as much as

**Figure 6:** Individual throughput under stable θ_{i} in terms of different target decoding SINR

possible. The simulation and numerical results show that the decoding SINR of each individual device is slightly greater than the target decoding SINR. By varying the target decoding SINR, we evaluate the algorithm performance with different channel gain in terms of stable θ which represents the amount of received energy for harvesting. And also this algorithm reveals the potential relation between the stable θ and throughput with different target decoding SINR. For wireless powered MTC networks, this algorithm is capable of providing a solution which satisfies the reliability of MTC and maximizes the throughput of each device.

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