Xiaolan Liu, Fengye Hu,＊, Meiqi Shao, Dan Sui, Gengxin He

1 College of Communication Engineering, Jilin University, Changchun, China

2 The North West China Research Institute of Electronic Equipment, Xian, Shanxi, 710065, China

* The corresponding author, email: hufy@jlu.edu.cn

I. INTRODUCTION

Wireless Body Area Networks (WBANs) consist of a large number of sensors located on or in the human body to monitor physiological parameters which are collected by an Access Point (AP), then the AP communicates with the medical center. These sensors are used to monitor crucial biological parameters continuously in many biomedical and clinical applications [1]. The propagation environment around the human body is complex because the person has different postures, so a human body posture recognition algorithm based on BP neural network for WBAN is proposed in [2]. In order to achieve energy efficient WBAN, a sparse sensor array synthesis algorithm for WBAN with minimized side lobe via convex optimization is proposed in [3].And reference [4] proposes an energy-efficient medium access approach for WBAN based on body posture. In addition, reducing the risk of infection and operating early diagnosis for health risk are necessary, which needs reliable communication link. In this paper, the outage probability is used to measure the reliability of WBAN. In WBAN, the communication link suffers from complex dynamic propagation environment, which implies that detection information should be transmitted to the AP with high transmit power [5]. Since the energy harvesting technology provides a new way for supplying energy to sensors, we optimize the outage probability to perform power allocation with the harvested energy as constraints. Generally, it is recommended to keep the sensor as the maximum transmit power below a required level for ensuring the Quality of Service (QoS)of communication link [6].

In this paper, the authors optimize the outage probability with the harvested energy as constraints.

Outage probability is typically used to measure the performance of communications in wireless networks, and also used in WBAN operating over the fading channels [7]. The complex propagation mechanisms of radio frequency signals on the surface and inside the human body cause a high outage probability[8]. Due to the interference existing in WBAN,the interference mitigation approach which is effective to reduce the outage probability is proposed in [9] [10]. Based on these References, we find that the outage probability can be reduced by increasing the transmit power of the sensor. However, the transmit power can not increase infinitely because of the limited battery capacity. The energy harvesting technology is introduced to solve this problem in this paper.

Energy harvesting is a promising technology to supply energy for sensors continuously,which prolongs networks lifetime and reduces maintenance cost in communications [11].With energy harvesting, sensors do not have to consider saving energy at work. Therefore,optimal power allocation of sensor nodes with energy harvesting has become a popular research issue. Researches on resource allocation methods also can benefit this problem.Reference [12] proposes Game-Theoretic resource allocation methods for device-to-device communication, it demonstrates that the game theoretic models are useful for designing radio resource allocation algorithms. In [13],a cognitive radio enabled TD-LET test-bed to realize the dynamic spectrum management over TV white space (TVWS) is proposed.Following the Markov decision process, an optimal transmission power policy based on 1-bit channel feedback information for energy harvesting over the Rayleigh fading channels is proposed in [14]. In case of QoS provisioning, optimal offline and online resource allocation schemes in energy harvesting systems are developed in [15]. The work in [16] analyzes the influence of energy arrival process on the optimal power allocation policy based on the discretized energy arrival model. In [17], it optimizes the time and the transmit power allocation to provide sustainable and high quality service in WBAN. WBAN is a high efficient network, which needs continuous energy supply. It is necessary to perform power allocation at the transceiver by introducing the energy harvesting. Additionally, there are few references referred to the reliability under energy harvesting in WBAN, only a few related references focus on the protocols.

WBAN is powered by energy-limited battery, and its network performance, such as lifetime and reliability can not be improved without continuous energy supply. In order to solve this problem, energy harvesting technology is introduced into power allocation in WBAN. There are several potential energy harvesting technologies, such as thermal energy harvesting used to sensors attached on the skin, chemical energy harvesting used to sensors implanted in the body, vibration energy harvesting used to sensors worn on the wrist and so on [18]. Additionally, Radio Frequency(RF) energy harvesting has been considered in[19] [20], a chip circuit is designed to transfer the harvested energy for available power efficiently. In addition, energy harvesting on Media Access Control (MAC) protocol is an effective method to improve the performance of network, e.g, throughput, average delay and energy efficiency in WBAN, like the Cooperative Energy Harvesting MAC (CEH-MAC)[21] and the Human Energy Harvesting MAC(HEH-BMAC) [22]. The power allocation has been a popular and challenging research problem in WBAN. As mentioned above,there are few references to perform research on the power allocation under energy harvesting in WBAN. When the sensor uses energy harvesting technology, power allocation will become a new research problem in WBAN.It is meaningful to perform research on this new problem, since energy harvesting is an effective technology to solve the problem of energy-limited battery in WBAN.

In this paper, we study the power allocation problem to minimize the outage probability under energy harvesting in WBAN. To obtain the specific closed-form expression of outage probability, we first assume that one of the on-body to on-body communication channel over the Rayleigh fading is considered. Next,an optimization problem is formed with the outage probability as the objective function,and the constraints are related to the harvested energy. It is difficult to solve this problem because the problem is non-convex with the transmit power. Finally, we convert the non-convex optimization problem into convex by Taylor series expansion, then which can be solved by the Lagrange multiplier method.Simulations show that the proposed algorithm can effectively reduce the outage probability under energy harvesting, which can provide the protection for communications in WBAN.And we demonstrate that the average outage probability is decreasing with the increasing of the harvested energy.

The rest of this paper is organized as follows. Section II presents the system model. In Section III, we derive the specific closed-form of outage probability, and an optimal problem is formulated by minimizing the outage probability under energy harvesting constraints.In Section IV, simulation results are detailed.Section V draws the conclusion.

II. SYSTEM MODEL

In this paper, one of the on-body to on-body communciation channel is considered. As shown in Fig. 1, the communication link between the sensor (W) worn on the wrist and the AP (O) attached on the waist is analyzed. The communication channel model and the data transmission time slots model under energy harvesting are shown in Fig. 2 and Fig. 3, respectively. We assume that the sensor can harvest energy through vibration energy harvesting technology. For simplicity, an offline scheme is considered where the channel state information(CSI) and the harvested energy are known.

For instance, the communication link between the AP and the sensor is analyzed to propose an optimal algorithm for minimizing the average outage probability. In Fig. 2,Pout_1denotes the outage probability of communciation process from the AP to the sensor, andPout_2denotes the outage probability of the contrary communciation process. The data transmission time slots model between the AP and the sensor is presented in Fig. 3. Assuming that there are K time slots from the AP to the sensor and from the sensor to the AP also has K time slots. We assume that both communication processes suffer from the same fading channels. So the outage probability is defined as that the communication outage happens when the AP and the sensor perform information interaction.

III. MINIMIZATION OUTAGE PROBABILITY

3.1 Outage probability

Based on the average error rate, outage probability is another standard performance criterion of communication systems operating over the fading channels [23]. In addition, the outage probability is defined as that the instantaneous combined Signal-to-Noise Ratio (SNR)γfalls below a certain thresholdγth

Fig. 1 The body channel model

Fig. 2 The communication channel model

Fig. 3 The data transmission time slots model

In this paper, taking the communication channel between the AP and the sensor into consideration, we assume that both communication processes are independently and suffer from the same Rayleigh fading channel.Therefore, the outage probability is defined as equation (2), which implies that the communication outage happens when the AP and the sensor perform information interaction in one slot.

When the channel suffers from Rayleigh fading, we can derive its PDF

Then the outage probability in thetime slot can be derived.

We assume the sensor can harvest energy from the vibration of the wrist, andis a constant. However, the outage probabilityis a non-convex function of the transmit power. Since the sensor can harvest continuous energy, the value of transmit poweris unrestricted. In this paper, we optimize the minimum transmit power that is. The Tylor series expansion is introduced to convert the non-convex function into convex [24]. The expression (5) becomes as follows, which is proved in appendix A.

3.2 Optimization problem

In this paper, in order to obtain the lower bound result of the actual scenario, we develop an offline scheme which assuming complete CSI and the harvested energy is available. Therefore, the optimization problem is formed with the objective is the average outage probability, and the constraints are related to the harvested energy.We formulate the optimization problem through the goal programming as:

whereC1shows that the transmit powerof the sensor should be less than the maximum power since the RF emissions is harmful to the human body.C2is the non-negative constraints onshows the energy arrival causality[25][26] which means the energy consumption should be less than the sum of the harvested energy and the initial energy of the battery.C4presents that the residual energy can not exceed the capacity of the battery to avoid the situation of energy overflow.

The period of each time slot isand the amount of the harvested energy at the sensorWin thetime slot is denoted asSo the consumption energy and the harvested energy can be calculated, the formulation (7) is changed as:

As mentioned above, the constraints2,C3andC4are linear inequalities overThe objective function is a convex overTherefore, the optimization problem can be solved by convex optimization techniques and tools. The Lagrange function is obtained as(9) shown in the bottom at this page, whereare the Lagrange multiplier vectors associated withC1,C2,C3andC4.is the vector of allThe Lagrangian function in thetime slot can be presented as:

The outage probability is a monotonic function with the transmit powerwhich is proved in appendix B. The dual problem is given by

The optimization problem (OP3) can be solved through the dual decomposition method. In addition, the iterative method is achieved, where in each of iteration some subproblems and a master problem are solved. We give the Lagrangian multiplier initial values,then through iteration the primal variables are found using Karush-Kuhn-Tucker (KKT)conditions for the given multipliers. So the sub-gradient method is used to update the multiplier in the master problem. The first order necessary condition is

In order to obtain the minimum outage probability, we plugin the equation (5).

After solving the subproblem, we obtain the optimal values of primal variables for the given multipliersTo solve the master problem, sub-gradient method is used to update the Lagrange multipliers.

Fig. 4 The convergence curve of transmit power

Fig. 5 The convergence curve of outage probability

Table I The simulation parameters of WBAN

IV. SIMULATION RESULTS

In this section, firstly, the convergence curves of the transmit power and the outage probability are obtained, which implies that the optimization problem is solvable. Then, we optimize the outage probability by performing power allocation at the sensor. Simulations show that the characteristic of the average outage probability is decreasing with the increasing of the harvested energy.

4.1 The convergence curve

The outage probability is a monotonic function with the transmit powerFor minimizingthe optimization problem (OP3) is solved with maximizing thethrough the Lagrange multiplier method. At first, considering in thetime slot, after 500 iterations, the characteristic curves ofandconverge to the stable points in Fig. 4 and Fig. 5, respectively.The simulation parameters over the Rayleigh fading channel in WBAN is given in Table I.

As shown in Fig. 4, the transmit powerconverges to 1.04 mW, which is less than the maximum level shown in Table I. Plunginginto the outage probability expression (5), and through solving the master problem, we can obtain the outage probabilityconverges to a constant valueThe value is fitted to the results in [5]. From Fig. 4 and Fig.5, we can see that the transmit power converges to the maximum value, correspondingly the outage probability converges to the minimum value.

4.2 The analysis of outage probability under energy harvesting

Through solving the optimization problem under energy harvesting, we obtain the maximumPwand the minimum outage probabilityPout.The optimization problem is demonstrated to be solvable. Then, we discuss the influence of the harvested energy on the outage probability.We find that both the energy harvesting rate and the number of time slots are influence factors of the amount of the harvested energy[15].

Fig. 6 and Fig. 7 illustrate characteristic ofandversus the number of time slots with different energy harvesting rates (He). We observe thatincreases with the increasing number of time slots, correspondinglyis

In Fig. 8 and Fig. 9, the characteristic curves ofandare given versusHein different time slots. Another influence factor which decide the amount of the harvested energy is presented in this part. As expected,by increasing energy harvesting rateHe, the available energy at the sensorWincreases,which in turn increases the transmit powerPw,and correspondingly decreases the average outage probabilityAs mentioned above,the transmit power of the sensor can increase decreased. This is because that the harvested energy is increasing with the increasing number of time slots. However, the large transmit power will be harmful to the human health and the hardware circuit is difficult to achieve recently. Additionally, the capacity of the sensor battery is finite in the actual scenario.So the transmit power can’t increase infinitely. In this section, we find that the transmit power become infinitely when the harvested energy exceed the battery capacity. Therefore,the amount of the harvested energy should be controlled. As shown in Fig. 6, at a same time slot, the larger the energy harvesting rateHe, the larger the transmit power, even large enough to exceed the maximum power. When the number of time slots is 47, the value ofHeshould be less than 2. Hence, an appropriateHeis necessary in actual WBAN. In this part,50(K) time slots are considered to discuss the influence ofHeon the probability of link outage, the other factor is presented in the following.infinitely with the increasing of the harvested energy, which is shown in Fig. 8. When the energy harvesting rate is fixed, the transmit power increases with the increasing number of time slots, even large enough to exceed the maximum transmit power. Similarly, Fig.8 demonstrates that the number of time slots cannot exceed 47 whenHeis 2. Hence, choosing an appropriate number of time slots in one transmission block should to be considered in practice. As shown in Fig. 9, the outage probability is decreasing with the increasing ofand time slotsK. And the value of the outage probability is fitted to the value in [5].

Fig. 6 The Pw in the lth time slots versus the number of time slots(K)

Fig. 7 The average Pout in K time slots versus the number of time slots(K)

Fig. 8 The Pw in K time slots versus the energy harvesting rate

Fig. 9 The average Pout in K time slots versus the energy harvesting rate

V. CONCLUSION

In this paper, the power allocation under energy harvesting in WBAN is studied, which is achieved by optimize the outage probability. Firstly, the closed-form expression of the outage probability is derived. Secondly, the optimization problem is formed to minimize the outage probability, where the constraints are related to the harvested energy. In order to solve the optimization problem, we convert the non-convex objective function into convex by Taylor series expansion. In thetime slot,the Lagrange multiplier method is introduced.Finally, simulations show that, the optimization problem is solvable, and the minimum convergence outage probability is obtained.We also demonstrate that the outage probability is decreasing with the increasing of time slots and the energy harvesting rate. Therefore,choosing appropriate number of time slots in one transmission block and energy harvesting rateshould be considered in practice.

ACKNOWLEDGMENT

This work was supported by the National Natural Science Foundation of China(No.61671219 and 61273064), Jilin Provincial Science and Technology Department Key Scientific and Technological Project(No.20140204034GX) and Jilin Province Development and Reform Commission Project(No.2015Y043).

APPENDIX A Proof for the outage probability of equation (6)

The Taylor series expansion is defined as: supposed that the functionin a neighborhood ofhaving up toderivative, so in this neighborhood, then-order Taylor formula ofis

and the exponent function Taylor expansion can be defined as:

Let us consider (5), which is written as:

The outage probability is a non-convex function over the transmit powerit is difficult to solve it. Conventionally, we keep the low transmit powerto save energy.When the energy harvesting technology is introduced, the value ofis unrestricted.In this paper, we optimize the minimum transmit power that isThen we take a Taylor series expansion of the exponent in the RHS of the equation, that is

with this result, (5) can be written as equation(6)

Therefore, we convert the non-convex problem into convex optimization problem to minimize the outage probability.

APPENDIX B Proof for decremental monotonicity of the outage probability

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