Energy-efficient Resource Allocation with QoS Support in Wireless Body Area Networks Zhiqiang Liu , Bin Liu , Chang Chen and Chang Wen Chen‡

Key Laboratory of Electromagnetic Space Information, Chinese Academy of Sciences, P. R. China University of Science and Technology of China, School of Information Science and Technology Email: [email protected], [email protected], [email protected] ‡ University at Buffalo, State University of New York, Dept. of Computer Science & Engineering, USA Email: [email protected]

Abstract—Wireless Body Area Network (WBAN) has become a promising type of networks to provide applications such as real-time health monitoring and ubiquitous e-Health services. One challenge in the design of WBAN is that energy efficiency needs to be ensured to increase the network lifetime in such a resourceconstrained network. Another critical challenge for WBAN is that quality of service (QoS) requirements, including packet loss rate (PLR), throughput and delay, should be guaranteed even under the highly dynamic environment due to changing of body postures. In this paper, we design a unified framework of energyefficient resource allocation scheme for WBAN, in which both constraints of QoS metrics and the characteristics of dynamic links are considered. A transmission rate allocation policy (TRAP) is proposed to carefully adjust the transmission rate at each sensor such that more strict PLR requirement could be achieved even when the link quality is very poor. A QoS optimization problem is then formulated to optimize the transmission power and allocated time slots for each sensor, which minimizes energy consumption subject to the QoS constraints. Numerical results demonstrate the effectiveness of the proposed transmission rate allocation policy and the resource allocation scheme.

Keywords: Wireless body area network (WBAN), quality of service (QoS), energy efficiency, transmission rate allocation policy, resource allocation I. I NTRODUCTION With the rapid increase of the aging population, the healthcare cost for the elderly becomes more and more expensive and wireless body area network (WBAN) [1] has emerged as a key technology to provide applications with high healthcare efficiency. The publishing of IEEE 802.15.6 standards for WBAN [2] tremendously facilitates the development of WBAN. However, there are still several research issues that need to be overcome in the context of WBAN. Firstly, WBAN system is a heterogeneous system which contains one resource-rich hub and several resource-constrained wireless body sensor nodes. Considering the requirement of lightweight and non-instrusive, the size of body sensors is limited, and the resources such as processing, storage and battery energy supply are extremely constrained comparing with ordinary wireless sensors. While the hub is a PDA or smartphone which has rich resources. Secondly, channel fading seen by links of on-body sensors is subject to the distance between the transmitter and receiver and a number of factors such as clothing, obstructions and so on [3]. When the posture changes, some factors of the link will inevitably change. Therefore, on-body sensor networks have to deal with such link dynamism caused by the changing of the posture. The last but not the least, resource-constrainted body sensors acquire

the vital data streams and transmit them to the hub through the dynamic links in a WBAN. A loss or an excessive delay of the vital data streams acquired by body sensors may cause a fatal accident [4]. Therefore, guaranteeing the quality of service (QoS) of WBAN becomes an important issue [5]. To combat the aforementioned issues to improve WBAN performance, many strategies have been provided in the literature. Transmission power control as a classic approach of reducing communication cost has been studied to improve energy efficiency of wireless network in [3], [6]–[8]. A power control scheme [8] was proposed to adjust transmit power based on feedback from the receiver and the parameters of the scheme can be tuned to achieve different trade-offs between energy savings and reliability. In [6], the authors presented a novel channel prediction scheme utilizing the partial-periodicity of measured BAN channels. However, complex and rapid changes of the body postures seriously affect the accuracy of the channel prediction. In [3], the dynamic nature of on-body links with varying body postures was characterized, then a dynamic postural position inference (DPPI) mechanism was proposed to assign the best possible power level to a link, which was based on the linear relationship between transmission power (TP) and received signal strength indicator (RSSI) [9]. However, the linear relationship was studied about the wireless sensors in a fixed position. Thus it was inappropriate to directly adopt it in WBAN case. Recently, many resource allocation methods have been designed for WBAN to improve the performance of WBAN [4], [10]–[12]. Compared with TPC, more parameters, such as transmission rate, allocated slots and so on, can be adjusted for better performance in these methods. The authors in [4] optimized transmission power and source rate to provide a high-quality service in health monitoring systems. However, the data streams with QoS support are delivered from the hubs to the base station rather than from the nodes to the hub. The author in [11] jointly studied the data routing and relay positioning problem, and formulated a mixed integer linear programing model which optimized the number and location of relays and the data routing to minimize both installation cost and energy consumed by wireless sensors. However, additional relays placed on body sometimes were not acceptable for patients. Particularly, when the number of the bio-sensors was already large, the additional relays would seriously influence the experience of wearing. The transmission power control methods and the resource allocation methods mentioned above only consider part of re-

978-1-4799-5952-5/15/$31.00 ©2015 IEEE

Ă

Beacon

ĂĂ

Inactive Slots

Slot

Ă

Scheduled forothers

Slot

Scheduled forNodeB

Slot

Ă

Slot

Slot

Beacon

Ă

Scheduled forNodeA

Ă

Superframe(beaconperiod)

Fig. 2 Scheduled access mechanism in beacon mode with superframe boundaries

Fig. 1

A typical structure of WBAN

quirements in WBAN whereas failing to consider other specific features. And none of the above works has introduced an unified framework for dealing with these issues such as energy efficiency, dynamic link and QoS metrics. Different from the aforementioned works, we investigate all these issues and design a unified framework to minimize energy consumption, in which we consider both the characteristics of dynamic links with different postures and constraints of QoS metrics. The key contributions of this paper are two-fold: First, we introduce a transmission rate allocation policy (TRAP) into the framework to achieve more strict P LR constraint by adjusting transmission rate. When link quality is very poor, adopting fixed transmission rate cannot guarantee stricter P LR constraint, even if transmission power is set to the maximum. However, with the same signal-to-noise ratio (SNR), reducing transmission rate can gain lower P LR. Therefore, we develop the TRAP that dynamically adjusts transmission rate based on link quality and P LR requirement. TRAP is easy to implement, and can be tuned for desired trade-off between energy consumption and attainable P LR with stricter P LR constraint. Secondly, we propose an optimization problem to minimize energy consumption, subject to constraints of QoS metrics, such as P LR, delay and throughput. The original nonlinear and non-convex optimization problem is successfully transformed to the form of Generalized Geometric Programming (GGP) which can be solved efficiently. We also take the characteristics of dynamic links with different postures into consideration and reallocate resources for each sensor by resolving the optimization problem when the posture changes. The remainder of this paper is organized as follows: The detail of system model is presented in Section II. In Section III, we describe the QoS constraints of on-body sensors. The optimization problem is described and solved in Section IV. The simulation results are provided in Section V, and the conclusion is drawn in Section VI. II. S YSTEM MODEL A. Network Setting We consider a typical WBAN model as shown in Fig. 1, which contains one hub and N sensor nodes deployed on the different positions of human body. As recommended by IEEE 802.15.6 standards [2], one hop star topology is adopted in this paper. At the data-link layer, scheduled access mechanism

in beacon mode with superframe boundaries is adopted. As presented in Fig. 2, the hub broadcasts beacons to define the superframe boundaries and reallocate resource to all the sensors, and each sensor node turns active in its dedicated slots to transmit data. At the physical layer, the Industrial, Scientific, and Medical (ISM) band is adopted, and Differential Phase Shift Keying (DPSK) modulation is used [2]. Four level information data rates are optional through configuring the parameters related to the Bose-Chaudhuri-Hocquenghem (BCH) code rate and modulation order. B. Energy Model In WBANs, transmission energy consumption at an energyconstraint sensor is the most part of total energy consumption while energy consumption of processing and listening can be negligible [8], [13]. The total transceiver energy consumption Econ mainly consists of two parts: circuitry energy consumption Eelec and transmit amplifier energy consumption Etx [14]. We assume that total transceiver energy consumption Econ is proportional to transmit amplifier energy consumption Etx [15]. In addition, total transceiver energy consumption at the transmitter is unchanged with the transmission rate in the case of the IEEE 802.15.6 compliant transmitter with DBPSK modulation [7]. Therefore, the formula of the energy model is shown as follows, Econ = Eelec + Etx = (α + 1) Etx

(1)

where α is the factor of proportionality, and Etx = Ptx t, t is the time of receiving a data packet. C. Channel Model In this paper, we focus on the on-body propagation model [16], [17]. By including shadowing, total path loss in dB between the transmitting and the receiving transceivers can be modeled as follows, P L (d) = P LF r (d) + Xσ = P0,dB + 10nlog10

d d0

+ Xσ

(2)

where P0,dB is the path loss at a reference distance d0 , and n is the path-loss exponent, and the shadowing Xσ in dB follows a normal distribution N 0, σ 2 . The standard deviation of the shadowing varies correspondingly with the posture of human body, such as still, walk and run [18]. D. Queuing Model The WBAN traffic can be classified into normal and emergency traffic [19]. Each sensor can classify the arriving packets into two classes: normal packets and emergency packets, which are put into the corresponding queue in sensor‘s memory. For normal traffic, we assume the periodic arrivals of the normal S T during packets Ai,n at node i are a constant λi,n = Li,n i,n a superframe. Here Si,n is the average source rate of normal

traffic at node i, T is the length of the superframe in seconds, and Li,n is the length of the normal packet in bits at node i. The normal packet transmission process can then be modeled as a D/G/1 queuing model, and the service rate μ follows a Binomial Distribution due to the packet loss. The upper boundary of average queue delay Wq can be expressed as follows [20], 2 λσB T (3) Wq ≤ 2 (1 − ρ) LR)Rt 2 where ρ = μλ , μ = (1−P LLR)Rt , and σB = P LR(1−P .R L is the transmission rate. t is the length of scheduled time, and P LR is the packet loss rate. For emergency traffic, we assume the arrivals of the emergency packets Ai,m at node i follow a Poisson process with S T an average rate λi,m = i,m,ave . Thus we can model the Li,m emergency packet transmission process as a M/G/1 queuing model. Here Si,m,ave is the average source rate of the emergency traffic, and Li,m is the length of the emergency packet. The average queuing delay of the emergency packet is given by [20], 2 ρ2 λ + λσB T (4) Wq = 2(1 − ρ)

where μ =

(1−P LR)Rt , L

2 σB =

P LR(1−P LR)Rt , L

ρ=

λ μ.

A. Packet Loss Rate Constraint In the ISM band, the vital data firstly need to be coded using BCH codes, then the coded data go through the Differential Phase Shift Keying (DPSK) modulator to be further transmitted to the hub [2]. The bit Signal to Noise Ratio (bit SNR) of sensor i can be expressed as, Pi,tx,dB −P L(di )−PN 10

B Ri

(5)

where Pi,tx,dB indicates the transmission power in dB at sensor i, PN is the power of noise in dB, B is the system bandwidth. The bit error rate (BER) performance using the DPSK modulation and BCH code can be expressed as [21], Pb,B (γi ) ≈ Pb,D (γi ) − Pb,D (γi )(1 − Pb,D (γi ))n−1

(6)

where Pb,D (γi ) = 12 exp (−γi ) is the bit error rate only using DPSK modulation at sensor i, n is the length of the BCH code. We assume the bit errors occur independently in a packet. Therefore, P LR of sensor i can be given by, P LR(γi ) = 1 − (1 − Pb,B (γi ))

and we finally have, Pi,tx Ri−1 ≥ B −1 10

µi,th +P LF r (di )+PN 10

= θi,th

(10)

B. Throughput Constraint For both normal and emergency traffic, the queuing system needs to satisfy the throughput condition ( μ ≥ λ ) to be stable [20]. For normal traffic, the throughput constraint μi,n ≥ λi,n at sensor i can be expressed as, (1 − P LRi,n,th ) Ri,n ti,n Si,n T ≥ Li,n Li,n

(11)

For emergency traffic,

III. Q O S C ONSTRAINTS

γi = 10

distribution as shadowing in mW . μγdB denotes the average of γdB . σγdB is the standard deviation of γdB , which changes with the postures [18]. Since the average P LR is a monotonically decreasing function of μγdB , the average packet loss rate constraint (8) can be transformed into the μγdB constraint expressed as, B μγdB = E 10log10 + Pi,tx,dB − P L (di ) − PN Ri B (9) = 10log10 Pi,tx − P LF r (di ) − PN Ri ≥ μi,th

L

(7)

Due to the time-varying channel, the path loss in the current superframe cannot be known in advance. Especially, when body postures change, the path loss cannot even be estimated appropriately based on the history of the link. Therefore, we calculate average P LR of sensor i for different postures as follows, +∞ P LRi = P LR(γi )P (γi |μγdB , σγdB )dγi ≤ P LRi,th (8) 0

where P LRi,th is the upper boundary of the average packet loss rate for sensor i, P (γi |μγdB , σγdB ) indicates the probability density function of bit SNR, and follows a Log-normal

(1 − P LRi,m,th ) Ri,m ti,m Si,m,ave T ≥ Li,m Li,m

(12)

C. Delay Constraint The total delay that a packet suffers contains three parts: access delay Wa , propagation delay Wp and queuing delay Wq [22], (13) W = W a + W q + Wp where the average access delay is half of the superframe time T 2 when we assume the packets arrive uniformly. Propagation delay is related to the service rate in the queuing system. For normal packets, the delay constraint can be expressed as, Wi,n ≤

2 λi,n σi,n,B ti,n T + T+ ≤ Di,n,th 2 2 (1 − ρi,n ) μi,n

(14)

For emergency packets, 2 ρ2i,m λi,m + λi,m σi,m,B ti,m T Wi,m = + T+ ≤ Di,m,th 2 2 (1 − ρi,m ) μi,m (15) where Di,n,th , Di,m,th are the thresholds of the delay for normal packets and emergency packets at sensor i respectively. IV. DYNAMIC RESOURCE ALLOCATION A. Transmission Rate Allocation Policy As recommended by IEEE 802.15.6 standards [2], the optional transmission rates Rate = {Rate1 , · · · , Rateh } in the narrowband physical layer are discrete. The discrete nature of transmission rates makes the following optimization problem difficult to be solved when the transmission rates are involved. Thus hub allocates the transmission rates based on P LR requirement and link quality first before solving the optimization problem.

When P LR requirement is relaxed and can be satisfied through adjusting the transmission power, the maximum transmission rate is preferred. However, when P LR requirement becomes stricter and cannot be met just through adjusting transmission power, the transmission rate allocation policy (TRAP) is proposed to obtain lower P LR through adjusting the transmission rate. According to the P LR requirement and Algorithm 1 Transmission Rate Allocation Policy (TRAP) Initialization: 1: Calculate θi,n,th , θi,m,th at sensor i. µth +P LF r (d)+PN 10 θth = B −1 10 2: Calculate Ri,th which satisfies θi,th with Ptx,max . P Rth = tx,max θth , μth = 10log10 (θth B) − P LF r (d) − PN 3: Obtain initial Ri,n,cur , Ri,m,cur at sensor i. ⎧ ⎪ Ratej ≤ Rth < Ratej+1 ,1 ≤ j < h Rate j ⎨ Rcur = Rateh Rateh ≤ Rth ⎪ ⎩ Rate1 Rth < Rate1 4: Calculate sumSlot with Ri,n,cur , Ri,m,cur . Itertion: 5: while sumSlot > β · totalSlot do 6: Update R i,n,new , Ri,m,new at sensor i. Rcur = Rateh Rcur Rnew = Ratej+1 Ratej ≤ Rcur < Ratej+1 7: Recalculate P LR cost ωi,n , ωi,m at sensor i. |μth −μRnew | Rcur < Rateh μth ω= inf Rcur = Rateh P

8: 9: 10: 11: 12: 13: 14: 15: 16:

where μRnew = 10log10 Rtx,max B − P LF r (d) − PN new if ω of each sensor is equal to inf then break; end if Choose the node by ind = arg (min (ωi,n , ωi,m )). Rind,cur = Rind,new , μind,Rcur = μind,Rnew . Recalculate sumSlot. end while Return: Obtain Ri and recalculate θi,th of the P LR constraint for the following optimization problem. Ri = Ri,cur , θi,th = B −1 10

µi,R +P LF r (di )+PN cur 10

link quality, the hub can get the transmission rate threshold Ri,th for sensor i, which just satisfies the P LR constraint (10) with the maximum transmission power Pi,tx,max . Ri,th = θi,th = B −1 10

Pi,tx,max θi,th µi,th +P LF r (di )+PN 10

(16)

Which nodes should be chosen to raise the transmission rates Rcur to satisfy the slot number limitation is the key issue in TRAP. Once nodes are chosen to raise transmission rates Rcur , it means that their P LR constraints cannot be guaranteed. So we need to try our best to reduce the cost due to the raise of the transmission rate. For better choosing nodes, we evaluate the cost of each nodes using the following P LR cost function. μi,th − μi,Rnew (18) ωi = μi,th where Ri,new indicates the candidate of the transmission rate at node i in the current loop. μi,Rnew is the average of bit SNR in dB when node i adopts Ri,new and the maximum transmission power Pi,tx,max . Here, the difference between μi,Rnew and μi,th is used to estimate the difference between P LRi,Rnew and P LRi,th due to the fact that the average P LR is a monotone decreasing function of the argument μ. In TRAP, the parameter β is designed to tune the desired trade-off between energy consumption and attainable P LR. The smaller β is, the stricter the slot number limitation is. Thus more nodes need to be set to the larger grade, correspondingly stricter P LR cannot be attained, but less energy is consumed, and vice versa. The details of the proposed TRAP are described in Algorithm 1. B. QoS Optimization Problem The QoS optimization problem can be stated as the minimization of sum energy consumption, subject to constraints of QoS metrics, such as P LR, throughput and delay. The P LR constraint is given in (10). And (11) (12) show the details of throughput constraints. For the delay constraint, (14) (15) are for normal packets and emergency packets respectively. Mathematically, the problem is formulated as follows, min

N

(Econ,i,n + Econ,i,m )

i=1

s.t

P LRi,n ≤ P LRi,n,th , P LRi,m ≤ P LRi,m,th , μi,n ≥ λi,n , μi,m ≥ λi,m , Wi,n ≤ Di,n,th , Wi,m ≤ Di,m,th , ti,n , ti,m ≥ 0, N

(ti,n + ti,m ) ≤ T,

i=1

(17)

where Ri,cur is chosen from the optional transmission rates, which is just smaller than Ri,th for satisfying the constraint (10). However, reducing the transmission rate means increasing the number of allocated slots in the superframe to satisfy the throughput constraint. Therefore, we need to limit the total number of allocated slots sumSlot in a superframe to a pre-defined number β · totalSlot and raise some nodes’ transmission rate to satisfy the slot number limitation. Here, totalSlot is available number of slots in a superframe, and the parameter β is within [0,1].

Pi,min,dBm ≤ Pi,dBm ≤ Pi,max,dBm , where ti,n , ti,m are the allocated time for normal packets and emergency packets at sensor i in a superframe respectively. Pi,min,dBm , Pi,max,dBm are the minimum and maximum transmission power in dBm respectively. Since the above optimization problem is a nonlinear and non-convex problem, it is difficult to be solved. Referring to [23], the QoS optimization problem satisfies the GGP conditions except the delay constraints (14) (15). Fortunately, they can be successfully transformed into the form of generalized posynomial inequalities based on advanced techniques in [23].

Then the GGP problem can be solved reliably and efficiently [24]. By solving this QoS optimization problem, we can obtain the optimal transmission power and the time slots for each sensor.

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A. Simulation Setting

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Fig. 4 Relationship between total energy consumption and average delay of normal packets and emergency packets. Optimal Transmission Rates for Normal Packets

Optimal Transmission Rates for Emergency Packets

Node1 971.4 Node2 Node3 Node4 Node5

971.4

Optimal value of Transmission Rates(Kbps)

We compare results averaged on 10000 superframes among four schemes: 1) UPA with maximum transmission rates, 2) TPC with maximum transmission rates, 3) the scheme with Optimized Resource Allocation and without Transmission Rate Allocation Policy (ORA without TRAP) and in which the transmission rates at each sensors are set to the maximum, 4) the scheme with Optimized Resource Allocation and Transmission Rate Allocation Policy (ORA with TRAP), in which transmission rates at each sensors are set based on TRAP. In Fig.3, we illustrate the relationship between the total energy consumption and average P LR of all sensors, for the normal packets and the emergency packets, respectively. As seen in Fig.3, the proposed ORA-based schemes outperform both TPC scheme and UPA scheme in energy efficiency. Since the proposed optimization problem is carefully designed to minimize the energy consumption under the QoS constraints. The same trend can alse be seen in Fig.4, which illustrate the relationship between the total energy and the average delay. We can also see from Fig.3 that the P LRs of UPA, TPC and ORA without TRAP schemes only achieve the value 2.5% rather than the minimum value 0.5%. This is because at same bad link scenarios, even if the transmission powers are set to the maximum,

6

3

Optimal value of Transmission Rates(Kbps)

B. Simulation Results

TPC:Normal Packet TPC:Emergency Packet UPA:Normal Packet UPA:Emergency Packet ORA without TRAP:Normal Packet ORA without TRAP:Emergency Packet ORA with TRAP:Normal Packet ORA with TRAP:Emergency Packet

9

V. S IMULATIONS Five sensors and a hub are included in a WBAN and placed on the body in accordance with Fig. 1 operating at 2.4GHz with 1KHz bandwidth. The detailed information of sensors and the channel coefficients changing with postures are set based on the measurement results in [17], [18]. Here we only consider three types of body postures, i.e., still, walk and run, and their steady-state probabilities are set to 0.5, 0.3 and 0.2 respectively. The extension to the case with more body postures is straightforward. We assume that the path loss for each sensor remains unchanged during a superframe period. The detail of these standard deviations for different postures can be found in [18]. The length of the superframe is set to 100ms while the length of one slot is set to 0.5ms. And the transceiver has four optional transmission rates, 121.4Kbps, 242.9Kbps, 485.7Kbps, 971.4Kbps. Additionally the range of the transmission power is from -30dBm to 0dBm. The parameter α in the energy mode is set to 2.4 [25]. In order to evaluate the performance, we compare our approach with two other approaches. One is the uniform power allocation (UPA) approach, and the other is the transmission power control (TPC) approach [8]. In UPA, each sensor has the same transmission power. In TPC, we set the time slots of TPC to satisfy the throughput constraint with the maximum transmission rate. We study the performance comparison of three approaches with the P LR threshold in the range from 0.5% to 30% under different scenarios. The thresholds of the delay for normal and emergency packets are set to 200ms and 150ms. The simulation runs on the Matlab platform.

PLR VS Energy Consumption

x 10

485.7

242.9

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Node1 Node2 Node3 Node4 Node5

485.7

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(a) Normal Packets

Still

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(b) Emergency Packets

Fig. 5 Comparison of allocated transmission rates of five nodes in different postures using TRAP with P LR threshold of 1% :(a) for normal packets. (b) for emergency packets. the P LR threshold cannot attain the minimum 0.5%. Thus all of three schemes cannot satisfy some strict P LR constraints in some scenarios which may be vital in health monitoring applications. However, the ORA with TRAP scheme can satisfy the strict P LR constraint, i.e., reaching the minimum threshold 0.5% of P LR, by using the proposed TRAP, as shown in Fig.3. Furthermore, the transmission rate has to be adjusted in the ORA with TRAP scheme to satisfy the P LR constraint, which

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(b) energy consumption vs β

Fig. 6 Attainable average P LR with expectations of 0.5% and Total energy consumption versus the value of β using Transmission Rate Allocation Policy(TRAP). results in more time slots requirement and thus more energy consumption, the performance of the ORA with TRAP scheme is still similar to that of the ORA without TRAP scheme. This is because the proposed transmission rate adjusting strategy in TRAP is designed to minimize the penalty introduced by adjusting transmission rate. Additionally, the effect of different postures to the transmission rate allocation is shown in Fig.5, where we can easily see that with different postures, the results from TRAP are different to fit different channel states. As seen in Fig.3, the lower attainable P LR threshold is at the cost of more energy consumption. Here, we examine the effect of parameter β in TRAP, which is designed to be tuned for desired trade-off between energy consumption and attainable P LR. As shown in Fig.6, when the value of β is raised, the lower P LR can be attained, while the energy consumption is much larger. VI. C ONCLUSION In the paper, we design an optimization framework to maximize the energy efficiency while fully consider both the characteristics of the dynamic links and the QoS constraints, such as the delay constraint, the throughput constraint and the packet loss rate constraint, in WBANs. A Transmission Rate Allocation Policy is proposed to allocate the transmission rates of each node to guarantee more strict P LR constraints. A QoS optimization problem is then formulated and solved, in which we jointly optimize the transmission power and the scheduled slots at each node to ensure QoS performance. The simulation results demonstrate that the Transmission Rate Allocation Policy can guarantee more strict P LR constraint, and the resource allocations improve the system energy efficiency while satisfying QoS constraints. ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Grant No. 61202406) and the USTC Grand Master Professor Funds (ZC9850290097). R EFERENCES [1] E. Jovanov, A. Milenkovic, C. Otto, P. De Groen, B. Johnson, S. Warren, and G. Taibi, “A wban system for ambulatory monitoring of physical activity and health status: applications and challenges,” in Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the. IEEE, 2006, pp. 3810–3813.

[2] A. Astrin et al., “Ieee standard for local and metropolitan area networks part 15.6: Wireless body area networks: Ieee std 802.15.6-2012,” The document is available at IEEE Xplore, 2012. [3] M. Quwaider, J. Rao, and S. Biswas, “Body-posture-based dynamic link power control in wearable sensor networks,” Communications Magazine, IEEE, vol. 48, no. 7, pp. 134–142, 2010. [4] Y. He, W. Zhu, and L. Guan, “Optimal resource allocation for pervasive health monitoring systems with body sensor networks,” Mobile Computing, IEEE Transactions on, vol. 10, no. 11, pp. 1558–1575, 2011. [5] M. Ameen, A. Nessa, and K. S. Kwak, “Qos issues with focus on wireless body area networks,” in Convergence and Hybrid Information Technology, 2008. ICCIT’08. Third International Conference on, vol. 1. IEEE, 2008, pp. 801–807. [6] D. B. Smith, L. W. Hanlen, and D. Miniutti, “Transmit power control for wireless body area networks using novel channel prediction,” in Wireless Communications and Networking Conference (WCNC), 2012 IEEE. IEEE, 2012, pp. 684–688. [7] Q. Zhang, “Energy saving efficiency comparison of transmit power control and link adaptation in bans,” in Communications (ICC), 2013 IEEE International Conference on. IEEE, 2013, pp. 1672–1677. [8] S. Xiao, A. Dhamdhere, V. Sivaraman, and A. Burdett, “Transmission power control in body area sensor networks for healthcare monitoring,” Selected Areas in Communications, IEEE Journal on, vol. 27, no. 1, pp. 37–48, 2009. [9] S. Lin, J. Zhang, G. Zhou, L. Gu, J. A. Stankovic, and T. He, “Atpc: adaptive transmission power control for wireless sensor networks,” in Proceedings of the 4th international conference on Embedded networked sensor systems. ACM, 2006, pp. 223–236. [10] S. Nabar, J. Walling, and R. Poovendran, “Minimizing energy consumption in body sensor networks via convex optimization,” in Body Sensor Networks (BSN), 2010 International Conference on. IEEE, 2010, pp. 62–67. [11] J. Elias, “Optimal design of energy-efficient and cost-effective wireless body area networks,” Ad Hoc Networks, vol. 13, pp. 560–574, 2014. [12] K. Deepak and A. Babu, “Optimal packet size for energy efficient wban under m-periodic scheduled access mode,” in Communications (NCC), 2014 Twentieth National Conference on. IEEE, 2014, pp. 1–6. [13] B. Gyselinckx, R. J. Vullers, C. Van Hoof, J. Ryckaert, R. F. Yazicioglu, P. Fiorini, and V. Leonov, “Human++: Emerging technology for body area networks.” in VLSI-SoC, 2006, pp. 175–180. [14] W. R. Heinzelman, A. Chandrakasan, and H. Balakrishnan, “Energyefficient communication protocol for wireless microsensor networks,” in System Sciences, 2000. Proceedings of the 33rd Annual Hawaii International Conference on. IEEE, 2000, pp. 10–pp. [15] A. Y. Wang and C. G. Sodini, “On the energy efficiency of wireless transceivers,” in Communications, 2006. ICC’06. IEEE International Conference on, vol. 8. IEEE, 2006, pp. 3783–3788. [16] K. Y. Yazdandoost, K. Sayrafian-Pour et al., “Channel model for body area network (ban),” IEEE P802, vol. 15, 2009. [17] E. Reusens, W. Joseph, B. Latr´e, B. Braem, G. Vermeeren, E. Tanghe, L. Martens, I. Moerman, and C. Blondia, “Characterization of on-body communication channel and energy efficient topology design for wireless body area networks,” Information Technology in Biomedicine, IEEE Transactions on, vol. 13, no. 6, pp. 933–945, 2009. [18] R. DErrico and L. Ouvry, “A statistical model for on-body dynamic channels,” International journal of wireless information networks, vol. 17, no. 3-4, pp. 92–104, 2010. [19] S. Ullah and K. S. Kwak, “An ultra low-power and traffic-adaptive medium access control protocol for wireless body area network,” Journal of medical systems, vol. 36, no. 3, pp. 1021–1030, 2012. [20] D. Gross, J. F. Shortle, J. M. Thompson, and C. M. Harris, Fundamentals of queueing theory. John Wiley & Sons, 2013. [21] A. Goldsmith, Wireless communications. Cambridge university press, 2005. [22] K. Khan and H. Peyravi, “Delay and queue size analysis of tdma with general traffic,” in Modeling, Analysis and Simulation of Computer and Telecommunication Systems, 1998. Proceedings. Sixth International Symposium on. IEEE, 1998, pp. 217–225. [23] S. Boyd, S.-J. Kim, L. Vandenberghe, and A. Hassibi, “A tutorial on geometric programming,” Optimization and engineering, vol. 8, no. 1, pp. 67–127, 2007. [24] J. Lofberg, “Yalmip: A toolbox for modeling and optimization in matlab,” in Computer Aided Control Systems Design, 2004 IEEE International Symposium on. IEEE, 2004, pp. 284–289. [25] A. C. W. Wong, M. Dawkins, G. Devita, N. Kasparidis, A. Katsiamis, O. King, F. Lauria, J. Schiff, and A. J. Burdett, “A 1 v 5 ma multimode ieee 802.15. 6/bluetooth low-energy wban transceiver for biotelemetry applications,” Solid-State Circuits, IEEE Journal of, vol. 48, no. 1, pp. 186–198, 2013.

Key Laboratory of Electromagnetic Space Information, Chinese Academy of Sciences, P. R. China University of Science and Technology of China, School of Information Science and Technology Email: [email protected], [email protected], [email protected] ‡ University at Buffalo, State University of New York, Dept. of Computer Science & Engineering, USA Email: [email protected]

Abstract—Wireless Body Area Network (WBAN) has become a promising type of networks to provide applications such as real-time health monitoring and ubiquitous e-Health services. One challenge in the design of WBAN is that energy efficiency needs to be ensured to increase the network lifetime in such a resourceconstrained network. Another critical challenge for WBAN is that quality of service (QoS) requirements, including packet loss rate (PLR), throughput and delay, should be guaranteed even under the highly dynamic environment due to changing of body postures. In this paper, we design a unified framework of energyefficient resource allocation scheme for WBAN, in which both constraints of QoS metrics and the characteristics of dynamic links are considered. A transmission rate allocation policy (TRAP) is proposed to carefully adjust the transmission rate at each sensor such that more strict PLR requirement could be achieved even when the link quality is very poor. A QoS optimization problem is then formulated to optimize the transmission power and allocated time slots for each sensor, which minimizes energy consumption subject to the QoS constraints. Numerical results demonstrate the effectiveness of the proposed transmission rate allocation policy and the resource allocation scheme.

Keywords: Wireless body area network (WBAN), quality of service (QoS), energy efficiency, transmission rate allocation policy, resource allocation I. I NTRODUCTION With the rapid increase of the aging population, the healthcare cost for the elderly becomes more and more expensive and wireless body area network (WBAN) [1] has emerged as a key technology to provide applications with high healthcare efficiency. The publishing of IEEE 802.15.6 standards for WBAN [2] tremendously facilitates the development of WBAN. However, there are still several research issues that need to be overcome in the context of WBAN. Firstly, WBAN system is a heterogeneous system which contains one resource-rich hub and several resource-constrained wireless body sensor nodes. Considering the requirement of lightweight and non-instrusive, the size of body sensors is limited, and the resources such as processing, storage and battery energy supply are extremely constrained comparing with ordinary wireless sensors. While the hub is a PDA or smartphone which has rich resources. Secondly, channel fading seen by links of on-body sensors is subject to the distance between the transmitter and receiver and a number of factors such as clothing, obstructions and so on [3]. When the posture changes, some factors of the link will inevitably change. Therefore, on-body sensor networks have to deal with such link dynamism caused by the changing of the posture. The last but not the least, resource-constrainted body sensors acquire

the vital data streams and transmit them to the hub through the dynamic links in a WBAN. A loss or an excessive delay of the vital data streams acquired by body sensors may cause a fatal accident [4]. Therefore, guaranteeing the quality of service (QoS) of WBAN becomes an important issue [5]. To combat the aforementioned issues to improve WBAN performance, many strategies have been provided in the literature. Transmission power control as a classic approach of reducing communication cost has been studied to improve energy efficiency of wireless network in [3], [6]–[8]. A power control scheme [8] was proposed to adjust transmit power based on feedback from the receiver and the parameters of the scheme can be tuned to achieve different trade-offs between energy savings and reliability. In [6], the authors presented a novel channel prediction scheme utilizing the partial-periodicity of measured BAN channels. However, complex and rapid changes of the body postures seriously affect the accuracy of the channel prediction. In [3], the dynamic nature of on-body links with varying body postures was characterized, then a dynamic postural position inference (DPPI) mechanism was proposed to assign the best possible power level to a link, which was based on the linear relationship between transmission power (TP) and received signal strength indicator (RSSI) [9]. However, the linear relationship was studied about the wireless sensors in a fixed position. Thus it was inappropriate to directly adopt it in WBAN case. Recently, many resource allocation methods have been designed for WBAN to improve the performance of WBAN [4], [10]–[12]. Compared with TPC, more parameters, such as transmission rate, allocated slots and so on, can be adjusted for better performance in these methods. The authors in [4] optimized transmission power and source rate to provide a high-quality service in health monitoring systems. However, the data streams with QoS support are delivered from the hubs to the base station rather than from the nodes to the hub. The author in [11] jointly studied the data routing and relay positioning problem, and formulated a mixed integer linear programing model which optimized the number and location of relays and the data routing to minimize both installation cost and energy consumed by wireless sensors. However, additional relays placed on body sometimes were not acceptable for patients. Particularly, when the number of the bio-sensors was already large, the additional relays would seriously influence the experience of wearing. The transmission power control methods and the resource allocation methods mentioned above only consider part of re-

978-1-4799-5952-5/15/$31.00 ©2015 IEEE

Ă

Beacon

ĂĂ

Inactive Slots

Slot

Ă

Scheduled forothers

Slot

Scheduled forNodeB

Slot

Ă

Slot

Slot

Beacon

Ă

Scheduled forNodeA

Ă

Superframe(beaconperiod)

Fig. 2 Scheduled access mechanism in beacon mode with superframe boundaries

Fig. 1

A typical structure of WBAN

quirements in WBAN whereas failing to consider other specific features. And none of the above works has introduced an unified framework for dealing with these issues such as energy efficiency, dynamic link and QoS metrics. Different from the aforementioned works, we investigate all these issues and design a unified framework to minimize energy consumption, in which we consider both the characteristics of dynamic links with different postures and constraints of QoS metrics. The key contributions of this paper are two-fold: First, we introduce a transmission rate allocation policy (TRAP) into the framework to achieve more strict P LR constraint by adjusting transmission rate. When link quality is very poor, adopting fixed transmission rate cannot guarantee stricter P LR constraint, even if transmission power is set to the maximum. However, with the same signal-to-noise ratio (SNR), reducing transmission rate can gain lower P LR. Therefore, we develop the TRAP that dynamically adjusts transmission rate based on link quality and P LR requirement. TRAP is easy to implement, and can be tuned for desired trade-off between energy consumption and attainable P LR with stricter P LR constraint. Secondly, we propose an optimization problem to minimize energy consumption, subject to constraints of QoS metrics, such as P LR, delay and throughput. The original nonlinear and non-convex optimization problem is successfully transformed to the form of Generalized Geometric Programming (GGP) which can be solved efficiently. We also take the characteristics of dynamic links with different postures into consideration and reallocate resources for each sensor by resolving the optimization problem when the posture changes. The remainder of this paper is organized as follows: The detail of system model is presented in Section II. In Section III, we describe the QoS constraints of on-body sensors. The optimization problem is described and solved in Section IV. The simulation results are provided in Section V, and the conclusion is drawn in Section VI. II. S YSTEM MODEL A. Network Setting We consider a typical WBAN model as shown in Fig. 1, which contains one hub and N sensor nodes deployed on the different positions of human body. As recommended by IEEE 802.15.6 standards [2], one hop star topology is adopted in this paper. At the data-link layer, scheduled access mechanism

in beacon mode with superframe boundaries is adopted. As presented in Fig. 2, the hub broadcasts beacons to define the superframe boundaries and reallocate resource to all the sensors, and each sensor node turns active in its dedicated slots to transmit data. At the physical layer, the Industrial, Scientific, and Medical (ISM) band is adopted, and Differential Phase Shift Keying (DPSK) modulation is used [2]. Four level information data rates are optional through configuring the parameters related to the Bose-Chaudhuri-Hocquenghem (BCH) code rate and modulation order. B. Energy Model In WBANs, transmission energy consumption at an energyconstraint sensor is the most part of total energy consumption while energy consumption of processing and listening can be negligible [8], [13]. The total transceiver energy consumption Econ mainly consists of two parts: circuitry energy consumption Eelec and transmit amplifier energy consumption Etx [14]. We assume that total transceiver energy consumption Econ is proportional to transmit amplifier energy consumption Etx [15]. In addition, total transceiver energy consumption at the transmitter is unchanged with the transmission rate in the case of the IEEE 802.15.6 compliant transmitter with DBPSK modulation [7]. Therefore, the formula of the energy model is shown as follows, Econ = Eelec + Etx = (α + 1) Etx

(1)

where α is the factor of proportionality, and Etx = Ptx t, t is the time of receiving a data packet. C. Channel Model In this paper, we focus on the on-body propagation model [16], [17]. By including shadowing, total path loss in dB between the transmitting and the receiving transceivers can be modeled as follows, P L (d) = P LF r (d) + Xσ = P0,dB + 10nlog10

d d0

+ Xσ

(2)

where P0,dB is the path loss at a reference distance d0 , and n is the path-loss exponent, and the shadowing Xσ in dB follows a normal distribution N 0, σ 2 . The standard deviation of the shadowing varies correspondingly with the posture of human body, such as still, walk and run [18]. D. Queuing Model The WBAN traffic can be classified into normal and emergency traffic [19]. Each sensor can classify the arriving packets into two classes: normal packets and emergency packets, which are put into the corresponding queue in sensor‘s memory. For normal traffic, we assume the periodic arrivals of the normal S T during packets Ai,n at node i are a constant λi,n = Li,n i,n a superframe. Here Si,n is the average source rate of normal

traffic at node i, T is the length of the superframe in seconds, and Li,n is the length of the normal packet in bits at node i. The normal packet transmission process can then be modeled as a D/G/1 queuing model, and the service rate μ follows a Binomial Distribution due to the packet loss. The upper boundary of average queue delay Wq can be expressed as follows [20], 2 λσB T (3) Wq ≤ 2 (1 − ρ) LR)Rt 2 where ρ = μλ , μ = (1−P LLR)Rt , and σB = P LR(1−P .R L is the transmission rate. t is the length of scheduled time, and P LR is the packet loss rate. For emergency traffic, we assume the arrivals of the emergency packets Ai,m at node i follow a Poisson process with S T an average rate λi,m = i,m,ave . Thus we can model the Li,m emergency packet transmission process as a M/G/1 queuing model. Here Si,m,ave is the average source rate of the emergency traffic, and Li,m is the length of the emergency packet. The average queuing delay of the emergency packet is given by [20], 2 ρ2 λ + λσB T (4) Wq = 2(1 − ρ)

where μ =

(1−P LR)Rt , L

2 σB =

P LR(1−P LR)Rt , L

ρ=

λ μ.

A. Packet Loss Rate Constraint In the ISM band, the vital data firstly need to be coded using BCH codes, then the coded data go through the Differential Phase Shift Keying (DPSK) modulator to be further transmitted to the hub [2]. The bit Signal to Noise Ratio (bit SNR) of sensor i can be expressed as, Pi,tx,dB −P L(di )−PN 10

B Ri

(5)

where Pi,tx,dB indicates the transmission power in dB at sensor i, PN is the power of noise in dB, B is the system bandwidth. The bit error rate (BER) performance using the DPSK modulation and BCH code can be expressed as [21], Pb,B (γi ) ≈ Pb,D (γi ) − Pb,D (γi )(1 − Pb,D (γi ))n−1

(6)

where Pb,D (γi ) = 12 exp (−γi ) is the bit error rate only using DPSK modulation at sensor i, n is the length of the BCH code. We assume the bit errors occur independently in a packet. Therefore, P LR of sensor i can be given by, P LR(γi ) = 1 − (1 − Pb,B (γi ))

and we finally have, Pi,tx Ri−1 ≥ B −1 10

µi,th +P LF r (di )+PN 10

= θi,th

(10)

B. Throughput Constraint For both normal and emergency traffic, the queuing system needs to satisfy the throughput condition ( μ ≥ λ ) to be stable [20]. For normal traffic, the throughput constraint μi,n ≥ λi,n at sensor i can be expressed as, (1 − P LRi,n,th ) Ri,n ti,n Si,n T ≥ Li,n Li,n

(11)

For emergency traffic,

III. Q O S C ONSTRAINTS

γi = 10

distribution as shadowing in mW . μγdB denotes the average of γdB . σγdB is the standard deviation of γdB , which changes with the postures [18]. Since the average P LR is a monotonically decreasing function of μγdB , the average packet loss rate constraint (8) can be transformed into the μγdB constraint expressed as, B μγdB = E 10log10 + Pi,tx,dB − P L (di ) − PN Ri B (9) = 10log10 Pi,tx − P LF r (di ) − PN Ri ≥ μi,th

L

(7)

Due to the time-varying channel, the path loss in the current superframe cannot be known in advance. Especially, when body postures change, the path loss cannot even be estimated appropriately based on the history of the link. Therefore, we calculate average P LR of sensor i for different postures as follows, +∞ P LRi = P LR(γi )P (γi |μγdB , σγdB )dγi ≤ P LRi,th (8) 0

where P LRi,th is the upper boundary of the average packet loss rate for sensor i, P (γi |μγdB , σγdB ) indicates the probability density function of bit SNR, and follows a Log-normal

(1 − P LRi,m,th ) Ri,m ti,m Si,m,ave T ≥ Li,m Li,m

(12)

C. Delay Constraint The total delay that a packet suffers contains three parts: access delay Wa , propagation delay Wp and queuing delay Wq [22], (13) W = W a + W q + Wp where the average access delay is half of the superframe time T 2 when we assume the packets arrive uniformly. Propagation delay is related to the service rate in the queuing system. For normal packets, the delay constraint can be expressed as, Wi,n ≤

2 λi,n σi,n,B ti,n T + T+ ≤ Di,n,th 2 2 (1 − ρi,n ) μi,n

(14)

For emergency packets, 2 ρ2i,m λi,m + λi,m σi,m,B ti,m T Wi,m = + T+ ≤ Di,m,th 2 2 (1 − ρi,m ) μi,m (15) where Di,n,th , Di,m,th are the thresholds of the delay for normal packets and emergency packets at sensor i respectively. IV. DYNAMIC RESOURCE ALLOCATION A. Transmission Rate Allocation Policy As recommended by IEEE 802.15.6 standards [2], the optional transmission rates Rate = {Rate1 , · · · , Rateh } in the narrowband physical layer are discrete. The discrete nature of transmission rates makes the following optimization problem difficult to be solved when the transmission rates are involved. Thus hub allocates the transmission rates based on P LR requirement and link quality first before solving the optimization problem.

When P LR requirement is relaxed and can be satisfied through adjusting the transmission power, the maximum transmission rate is preferred. However, when P LR requirement becomes stricter and cannot be met just through adjusting transmission power, the transmission rate allocation policy (TRAP) is proposed to obtain lower P LR through adjusting the transmission rate. According to the P LR requirement and Algorithm 1 Transmission Rate Allocation Policy (TRAP) Initialization: 1: Calculate θi,n,th , θi,m,th at sensor i. µth +P LF r (d)+PN 10 θth = B −1 10 2: Calculate Ri,th which satisfies θi,th with Ptx,max . P Rth = tx,max θth , μth = 10log10 (θth B) − P LF r (d) − PN 3: Obtain initial Ri,n,cur , Ri,m,cur at sensor i. ⎧ ⎪ Ratej ≤ Rth < Ratej+1 ,1 ≤ j < h Rate j ⎨ Rcur = Rateh Rateh ≤ Rth ⎪ ⎩ Rate1 Rth < Rate1 4: Calculate sumSlot with Ri,n,cur , Ri,m,cur . Itertion: 5: while sumSlot > β · totalSlot do 6: Update R i,n,new , Ri,m,new at sensor i. Rcur = Rateh Rcur Rnew = Ratej+1 Ratej ≤ Rcur < Ratej+1 7: Recalculate P LR cost ωi,n , ωi,m at sensor i. |μth −μRnew | Rcur < Rateh μth ω= inf Rcur = Rateh P

8: 9: 10: 11: 12: 13: 14: 15: 16:

where μRnew = 10log10 Rtx,max B − P LF r (d) − PN new if ω of each sensor is equal to inf then break; end if Choose the node by ind = arg (min (ωi,n , ωi,m )). Rind,cur = Rind,new , μind,Rcur = μind,Rnew . Recalculate sumSlot. end while Return: Obtain Ri and recalculate θi,th of the P LR constraint for the following optimization problem. Ri = Ri,cur , θi,th = B −1 10

µi,R +P LF r (di )+PN cur 10

link quality, the hub can get the transmission rate threshold Ri,th for sensor i, which just satisfies the P LR constraint (10) with the maximum transmission power Pi,tx,max . Ri,th = θi,th = B −1 10

Pi,tx,max θi,th µi,th +P LF r (di )+PN 10

(16)

Which nodes should be chosen to raise the transmission rates Rcur to satisfy the slot number limitation is the key issue in TRAP. Once nodes are chosen to raise transmission rates Rcur , it means that their P LR constraints cannot be guaranteed. So we need to try our best to reduce the cost due to the raise of the transmission rate. For better choosing nodes, we evaluate the cost of each nodes using the following P LR cost function. μi,th − μi,Rnew (18) ωi = μi,th where Ri,new indicates the candidate of the transmission rate at node i in the current loop. μi,Rnew is the average of bit SNR in dB when node i adopts Ri,new and the maximum transmission power Pi,tx,max . Here, the difference between μi,Rnew and μi,th is used to estimate the difference between P LRi,Rnew and P LRi,th due to the fact that the average P LR is a monotone decreasing function of the argument μ. In TRAP, the parameter β is designed to tune the desired trade-off between energy consumption and attainable P LR. The smaller β is, the stricter the slot number limitation is. Thus more nodes need to be set to the larger grade, correspondingly stricter P LR cannot be attained, but less energy is consumed, and vice versa. The details of the proposed TRAP are described in Algorithm 1. B. QoS Optimization Problem The QoS optimization problem can be stated as the minimization of sum energy consumption, subject to constraints of QoS metrics, such as P LR, throughput and delay. The P LR constraint is given in (10). And (11) (12) show the details of throughput constraints. For the delay constraint, (14) (15) are for normal packets and emergency packets respectively. Mathematically, the problem is formulated as follows, min

N

(Econ,i,n + Econ,i,m )

i=1

s.t

P LRi,n ≤ P LRi,n,th , P LRi,m ≤ P LRi,m,th , μi,n ≥ λi,n , μi,m ≥ λi,m , Wi,n ≤ Di,n,th , Wi,m ≤ Di,m,th , ti,n , ti,m ≥ 0, N

(ti,n + ti,m ) ≤ T,

i=1

(17)

where Ri,cur is chosen from the optional transmission rates, which is just smaller than Ri,th for satisfying the constraint (10). However, reducing the transmission rate means increasing the number of allocated slots in the superframe to satisfy the throughput constraint. Therefore, we need to limit the total number of allocated slots sumSlot in a superframe to a pre-defined number β · totalSlot and raise some nodes’ transmission rate to satisfy the slot number limitation. Here, totalSlot is available number of slots in a superframe, and the parameter β is within [0,1].

Pi,min,dBm ≤ Pi,dBm ≤ Pi,max,dBm , where ti,n , ti,m are the allocated time for normal packets and emergency packets at sensor i in a superframe respectively. Pi,min,dBm , Pi,max,dBm are the minimum and maximum transmission power in dBm respectively. Since the above optimization problem is a nonlinear and non-convex problem, it is difficult to be solved. Referring to [23], the QoS optimization problem satisfies the GGP conditions except the delay constraints (14) (15). Fortunately, they can be successfully transformed into the form of generalized posynomial inequalities based on advanced techniques in [23].

Then the GGP problem can be solved reliably and efficiently [24]. By solving this QoS optimization problem, we can obtain the optimal transmission power and the time slots for each sensor.

5

10

8 7 Energy Consumption (uJ)

A. Simulation Setting

5 4

2 1 0

0

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Fig. 3 Relationship between total energy consumption and average P LR of normal packets and emergency packets. 5

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Delay VS Energy Consumption

x 10

TPC:Normal Packet TPC:Emergency Packet UPA:Normal Packet UPA:Emergency Packet ORA without TRAP:Normal Packet ORA without TRAP:Emergency Packet ORA with TRAP:Normal Packet ORA with TRAP:Emergency Packet

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7 6 5 4 3 2 1 0 50

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Fig. 4 Relationship between total energy consumption and average delay of normal packets and emergency packets. Optimal Transmission Rates for Normal Packets

Optimal Transmission Rates for Emergency Packets

Node1 971.4 Node2 Node3 Node4 Node5

971.4

Optimal value of Transmission Rates(Kbps)

We compare results averaged on 10000 superframes among four schemes: 1) UPA with maximum transmission rates, 2) TPC with maximum transmission rates, 3) the scheme with Optimized Resource Allocation and without Transmission Rate Allocation Policy (ORA without TRAP) and in which the transmission rates at each sensors are set to the maximum, 4) the scheme with Optimized Resource Allocation and Transmission Rate Allocation Policy (ORA with TRAP), in which transmission rates at each sensors are set based on TRAP. In Fig.3, we illustrate the relationship between the total energy consumption and average P LR of all sensors, for the normal packets and the emergency packets, respectively. As seen in Fig.3, the proposed ORA-based schemes outperform both TPC scheme and UPA scheme in energy efficiency. Since the proposed optimization problem is carefully designed to minimize the energy consumption under the QoS constraints. The same trend can alse be seen in Fig.4, which illustrate the relationship between the total energy and the average delay. We can also see from Fig.3 that the P LRs of UPA, TPC and ORA without TRAP schemes only achieve the value 2.5% rather than the minimum value 0.5%. This is because at same bad link scenarios, even if the transmission powers are set to the maximum,

6

3

Optimal value of Transmission Rates(Kbps)

B. Simulation Results

TPC:Normal Packet TPC:Emergency Packet UPA:Normal Packet UPA:Emergency Packet ORA without TRAP:Normal Packet ORA without TRAP:Emergency Packet ORA with TRAP:Normal Packet ORA with TRAP:Emergency Packet

9

V. S IMULATIONS Five sensors and a hub are included in a WBAN and placed on the body in accordance with Fig. 1 operating at 2.4GHz with 1KHz bandwidth. The detailed information of sensors and the channel coefficients changing with postures are set based on the measurement results in [17], [18]. Here we only consider three types of body postures, i.e., still, walk and run, and their steady-state probabilities are set to 0.5, 0.3 and 0.2 respectively. The extension to the case with more body postures is straightforward. We assume that the path loss for each sensor remains unchanged during a superframe period. The detail of these standard deviations for different postures can be found in [18]. The length of the superframe is set to 100ms while the length of one slot is set to 0.5ms. And the transceiver has four optional transmission rates, 121.4Kbps, 242.9Kbps, 485.7Kbps, 971.4Kbps. Additionally the range of the transmission power is from -30dBm to 0dBm. The parameter α in the energy mode is set to 2.4 [25]. In order to evaluate the performance, we compare our approach with two other approaches. One is the uniform power allocation (UPA) approach, and the other is the transmission power control (TPC) approach [8]. In UPA, each sensor has the same transmission power. In TPC, we set the time slots of TPC to satisfy the throughput constraint with the maximum transmission rate. We study the performance comparison of three approaches with the P LR threshold in the range from 0.5% to 30% under different scenarios. The thresholds of the delay for normal and emergency packets are set to 200ms and 150ms. The simulation runs on the Matlab platform.

PLR VS Energy Consumption

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Fig. 5 Comparison of allocated transmission rates of five nodes in different postures using TRAP with P LR threshold of 1% :(a) for normal packets. (b) for emergency packets. the P LR threshold cannot attain the minimum 0.5%. Thus all of three schemes cannot satisfy some strict P LR constraints in some scenarios which may be vital in health monitoring applications. However, the ORA with TRAP scheme can satisfy the strict P LR constraint, i.e., reaching the minimum threshold 0.5% of P LR, by using the proposed TRAP, as shown in Fig.3. Furthermore, the transmission rate has to be adjusted in the ORA with TRAP scheme to satisfy the P LR constraint, which

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Fig. 6 Attainable average P LR with expectations of 0.5% and Total energy consumption versus the value of β using Transmission Rate Allocation Policy(TRAP). results in more time slots requirement and thus more energy consumption, the performance of the ORA with TRAP scheme is still similar to that of the ORA without TRAP scheme. This is because the proposed transmission rate adjusting strategy in TRAP is designed to minimize the penalty introduced by adjusting transmission rate. Additionally, the effect of different postures to the transmission rate allocation is shown in Fig.5, where we can easily see that with different postures, the results from TRAP are different to fit different channel states. As seen in Fig.3, the lower attainable P LR threshold is at the cost of more energy consumption. Here, we examine the effect of parameter β in TRAP, which is designed to be tuned for desired trade-off between energy consumption and attainable P LR. As shown in Fig.6, when the value of β is raised, the lower P LR can be attained, while the energy consumption is much larger. VI. C ONCLUSION In the paper, we design an optimization framework to maximize the energy efficiency while fully consider both the characteristics of the dynamic links and the QoS constraints, such as the delay constraint, the throughput constraint and the packet loss rate constraint, in WBANs. A Transmission Rate Allocation Policy is proposed to allocate the transmission rates of each node to guarantee more strict P LR constraints. A QoS optimization problem is then formulated and solved, in which we jointly optimize the transmission power and the scheduled slots at each node to ensure QoS performance. The simulation results demonstrate that the Transmission Rate Allocation Policy can guarantee more strict P LR constraint, and the resource allocations improve the system energy efficiency while satisfying QoS constraints. ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Grant No. 61202406) and the USTC Grand Master Professor Funds (ZC9850290097). R EFERENCES [1] E. Jovanov, A. Milenkovic, C. Otto, P. De Groen, B. Johnson, S. Warren, and G. Taibi, “A wban system for ambulatory monitoring of physical activity and health status: applications and challenges,” in Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the. IEEE, 2006, pp. 3810–3813.

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