Dynamic Power Control and Optimization Scheme for QoS-Constrained Cooperative Wireless Sensor Networks

Transcription

1 IEEE ICC 2016 Ad-hoc and Sensor Networking Symposium ynamic Power Conol and Optimization Scheme for QoS-Consained Cooperative Wireless Sensor Networks Ziqiang Feng, Ian Wassell Computer Laboratory University of Cambridge, UK {zf232, Absact Cooperative ansmission can significantly reduce the power consumption associated with long distance ansmission in wireless sensor networks WSNs. In this paper, we analyze the optimal power consumption of cluster-based multi-hop ansmission for a cooperative WSN. With specific Quality of Service QoS consaints on delay and channel capacity, we show that the power optimization problem of the whole network has no closed-form solution in a slow flat Rayleigh fading environment. Thus we propose a dynamic power conol and optimization PCO scheme that can jointly determine the optimal number of cooperative sensors and their ansmission power. We further propose a channel approximation algorithm that can significantly reduce the computational complexity of the PCO scheme. I. INTROUCTION Energy optimization is an important issue in wireless sensor networks WSNs where the low-power sensors are expected to operate for many years without battery replacement. Furthermore, certain applications may have Quality of Service QoS requirements on delay and channel capacity. For instance, it is important for the sink node to receive data in a timely manner in an indusial conol system [1]. Traditional energy optimization techniques may not always guarantee the QoS requirements in WSNs, especially in fading environments. It has been proved that multi-antenna system use less energy for data ansmission in fading channels compared to singleantenna systems [2]. However, a multi-antenna system requires complex ansceiver circuits that are not practical for low-cost wireless sensors. Cooperative multiple-input-multiple-output MIMO [3] and virtual MIMO techniques [4] are proposed to enable MIMO techniques to be utilized in WSNs. For the single-hop cooperative MIMO systems analyzed in [3], it is shown that for long-distance ansmission, they are more energy efficient compared to a single-antenna system. In [5], multi-hop cooperative MIMO channels are analyzed, where the design target is to minimize the outage probability given an energy consaint and target outage channel capacity. However, the minimum outage probability may not give the maximum average outage channel capacity [6]. Minimizing the outage probability may also lead to full-power operation which significantly decreases the lifetime of the WSN. In this paper, we investigate the energy consumption in a cluster-based multi-hop cooperative WSN with QoS requirements on delay and channel capacity. We mainly focus on the physical layer optimization and we assume that the clustering and routing problems are handled by upper layers. The multi-hop ansmission consists of several single-hop cluster-to-cluster ansmissions. Each single-hop ansmission consists of three phases, namely the Preparation Phase PP, the Broadcast Phase BP and the Cooperation Phase CP. In the PP, the cluster head of the ansmitter cluster calculates the ansmission power to be used in the BP and CP. In the BP, the cluster head broadcasts the data along with the power conol message in the ansmitter cluster. In the CP, all nodes of the ansmitter cluster that received the data successfully in the BP cooperatively ansmit the data to the cluster head of the receiver cluster through a multiple-input-single-output MISO channel. For ina-cluster ansmission in the BP, we assume that all nodes in the cluster have perfect ansmit and receive channel state information CSI. For inter-cluster ansmission in the CP, we assume that nodes in the receiver cluster know the CSI and that nodes in both clusters know the disibution of the CSI. Note that our MISO approach can be extended to a MIMO approach by utilizing selection diversity in the receiver cluster [5]. To minimize the total energy consumption, we propose a dynamic power conol and optimization PCO scheme that can optimize the total energy consumption without violating the QoS requirements. Given the number of cooperative n- odes as an input condition, the scheme first calculates the conditional optimal power consumption using the dynamic power conol PC algorithm. Then it determines the optimal number of cooperative sensors using the results of conditional optimal power consumption. We show that the PC algorithm converges to the optimum in O 1 iterations. We further propose a channel approximation algorithm that can significantly reduce the computational complexity of the PCO scheme. The rest of the paper is organized as follows: Section II describes the system model of the multi-hop cluster-based cooperative WSN and expresses the QoS requirements. The PCO scheme is proposed in Section III. We further propose an approximation algorithm to reduce the computational complexity of the PCO scheme. Section IV shows the simulation results of the proposed scheme. Finally, we conclude the paper in Section V. II. SYSTEM MOEL We consider a multi-hop cluster-based WSN. The ansmission between two adjacent clusters is defined as a single /16/$ IEEE

2 Fig. 1. Multi-hop cluster-based cooperative wireless sensor network hop ansmission. In our model, we assume that the nodes are grouped into N clusters and we have N 1 hops during the ansmission. The routing path is predefined. Before the ansmission, each cluster selects a node as its cluster head. Efficient clustering and routing algorithms such as those in [7], [8] can be used. The cluster head of cluster 1 is assumed to be the source node. The system model of the cooperative WSN is shown in Fig. 1. A. Transmission Scheme The ansmission between adjacent clusters has three phases, namely the preparation phase PP, the broadcast phase BP and the cooperation phase CP. The time duration of the three phases are λ 1 T, λ 2 T and λ 3 T respectively where λ 1 +λ 2 +λ 3 =1and T is the time duration of each single-hop ansmission. We assume that each cluster contains n sensors that are uniformly deployed in the cluster and the cluster head is located near the center of the cluster. 1 Preparation Phase: In the PP, the cluster head in the ansmitter cluster calculates the optimal number of cooperative nodes n, the ansmission power in the BP P bt and CP P ct using the PCO scheme. The value of n, P bt and P ct are carried in the power conol message and sent to other cooperative nodes along with the data in BP. 2 Broadcast Phase: In the BP, the cluster head broadcasts the data along with the power conol message to the cooperative sensors within its cluster with power P bt. The sensors that received the data successfully are selected to ansmit with the cluster head in the CP. Since we assume that the sensors in the cluster are uniformly deployed and the cluster head is located in the center of the cluster, the number of the active sensors is proportional to P bt and the total number of sensors n in each cluster. By selecting an appropriate level of P bt to broadcast the data, we can have n nodes selected as the cooperative nodes including the cluster head itself in the CP. 3 Cooperation Phase: In the CP, the cooperative nodes jointly ansmit the data to the cluster head in the receiver cluster using an orthogonal Space-Time Block Code STBC. We assume that the number of cooperative nodes is n, including the cluster head itself. The total ansmission power P ct is equally divided among the cooperative nodes. The ansmission power used by each sensor is consequently Pct n. B. QoS Requirements We consider a multi-hop cluster-to-cluster communication scheme containing N clusters see Fig. 1. We assume the cluster head is located in the center of each cluster. The distance between the centers of two adjacent clusters is denoted by d. We also assume long-range ansmission between adjacent clusters since cooperative ansmission is more energy efficient in that case [3]. Therefore the distances between the sensors in the adjacent clusters are approximately equal. We modeled the channel in the BP and CP using the additive white Gaussian noise AWGN channel and slow flat Rayleigh fading channel with AWGN respectively, since the inter-cluster distance is much larger than the ina-cluster distance [3]. Without loss of generality, we consider the ansmission between cluster m and cluster m+1. In the CP, the cooperative sensors jointly ansmit the data to the next cluster head using STBC through a MISO channel. The received signal at the cluster head of cluster m +1 is given by: Y m+1 = ΛHX m + N m+1 1 where Λ=βd α is the path loss, β is the path loss constant related to the channel and antennas i.e., the wavelength of the signal and the antenna gain and α is the path loss exponent. The elements of the 1 n channel vector H are independent identical disibution complex Gaussian random variables with zero mean and unit variance. X m is the n l ansmitted signal with ansmission power Pct n, where l is the length of the STBC. N m+1 N 0,σ 2 is the l 1 AWGN at the receiver. The ansmission power of the ansmitted space-time codeword is Pct n per node. Considering the nodes in the ansmitter cluster only know the disibution of the CSI, the outage capacity C out [bps/hz] of the CP is defined as [6]: C out = λ 3 log γ out, 2 where γ out is the minimum signal-to-noise ratio SNR for successful decoding at the receiver side. The outage probability p out is defined as: p out =Prγ<γ out, 3 where γ is the actual SNR at the receiver side. According to our channel model in 1, γ is given by: γ = ΛP ct H 2 F n σ 2, 4 where σ 2 is the noise power and H 2 F is the squared Frobenius norm of the 1 n channel vector H. According to the definition of H, H 2 F χ2 2n is a chi-square variable with 2n degrees of freedom. The average outage capacity is given by: C out =1 p out C out = λ 3 log γ out. 5 1 elay Requirement: We consider the delay of the multihop cluster-to-cluster communication using an automatic repeat request ARQ protocol. We assume that the outage probabilities are equal in each of the N 1 hops. Therefore,

3 for ansmission through N 1 hops, the number of failures k follows the negative binomial disibution: k NBN 1; p out. 6 The probability mass function of the negative binomial disibution is k + N 2 f k; N 1,p out = p k k out N 1. 7 Proposition 1: Given the delay requirement, the average delay of the ansmission through N 1 hops is given by: T = E [k + N 1 T ]= N 1 T. 8 Thus we can have reliable ansmission if p out 1 N 1T for any delay requirement >N 1 T.If N 1 T, it is impossible to have reliable ansmission under the delay requirement. Proof: We first prove that E [k] = N 1pout 1 p out. Since the number of failures k follows the negative binomial disibution, the mean value of k can be calculated as: E [k] = kf k; N 1,p out k=0 k k + N 2! = p k k!n 2! out N 1 k=0 = N 1 p out k + N 2! k 1! N 1! pk 1 out N = N 1 p out = N 1 p out. k=1 f k; N,p out 9 k=0 Note that in 8 N and T are constants. Thus the average delay is given by: T = E [k + N 1 T ]= N 1 T. 10 For any delay requirement > N 1 T, we must have T = N 1T 1 p out and thus p out 1 N 1T to satisfy the reliable ansmission requirement. Note that 0 <p out < 1. If N 1 T, we should have p out 1 N 1T 0 for reliable ansmission, which is impossible to satisfy. 2 Capacity Requirement: We assume that there are a total of L bits for ansmission. In order to have reliable ansmission in the CP, we have L T R ct C out, 11 where R ct [bps/hz] is the ansmission data rate in the CP. In the BP, the ansmission data rate R bt [bps/hz] should be no less than the ansmission data rate in the CP. Thus we have R bt R ct L T. 12 Proposition 2: For any ansmission under the QoS requirement and > N 1 T, there exists p out that can maximize C out, which can be denoted as follows C out =max{λ 3 log γ out } p out s.t. Cout L T, 0 <p 13 out 1 N 1T where γ out = ΛPctF 1 p out 2n n σ and F 1 p v is the inverse chi-square cumulative disibution 2 function CF for a given probability p and v degrees of freedom. Proof: From 2, 3 and 5, we know that F 1 p v is directly proportional to p for any given v. Let ξ = F 1 1 NT 2n ].Forpout 0, 1 N 1T,wehave lim C out =0, p out 0 lim p out 1 NT C out = λ 3 log 2 1+ ΛPctξ n σ 2 14 Since lim C out > 0 and 5 is continuous at p out p out 1 NT ] 0, 1 N 1T, according to the exeme value theorem, ] there exists p out 0, 1 N 1T that can maximize C out. C. Energy Consumption Analysis For the ansmission in each hop, the total power consumption is given by: P t = λ 1 P PCO + λ 2 P bt + λ 3 P ct + n P cir, 15 where P PCO is the power consumption of the PCO scheme in the PP, P cir is the circuit power consumption of the sensor and n is the number of sensors used for ansmission. The total energy consumption for the ansmission through N 1 hops is give by: E t = P t T = N 1 P t T. 16 In the BP, we assume the channel is AWGN with free space path loss i.e., α =2. Thus given the ansmission data rate R bt,wehave P bt = r 2 σ 2 2 R bt λ 2 1, 17 where r is the inacluster ansmission range. We assume that the average cluster range is r c and n sensors are normally deployed in each cluster. Therefore the approximate number of sensors that can successfully decode the broadcast message is given by: 2 r P bt n n = n =. 18 r c rcσ R bt λ 2 1 In the CP, a slow flat Rayleigh fading channel is assumed in the channel model. From 4 and 5, we have γ out n σ 2 P ct = ΛF 1 p out 2n = 2 C out λ 3 1 p out 1 ΛF 1 p out 2n n σ 2. 19

4 From 19, we can see that there is no closed-form solution for cooperative ansmission power. In the next section, we propose a dynamic power conol and optimization PCO scheme to determine the optimal value of n, P bt and P ct for the total energy consumption. We further propose an approximation algorithm for the PCO scheme that can reduce its computational complexity. III. YNAMIC POWER CONTROL AN OPTIMIZATION SCHEME A. Scheme escription For each single-hop ansmission, the PCO scheme is running in the PP. Given any QoS requirement with the delay > N 1 T, we aim to find the optimal value of P ct, P bt, n and p out for each single-hop ansmission and thus minimize the total energy consumption of the multihop ansmission 16. Note that n is directly related to P bt given the value of R bt in 18. Thus n and P bt are jointly optimized. From Proposition 2 and 19, we know that given n, the ansmission power P ct n is directly proportional to the maximum average outage capacity C out. According to the QoS requirement, we have C out L T and p out 1 N 1T. P ct n is optimized when p out n =p out n and C out = L T. Therefore, P ct and p out are also jointly optimized. The optimization problem can now be denoted as: { P ct n,n } = argmin P ct n,n E t Pct n,n. 20 Note that the value of Pct n depends on the choice of n. However in order to determine n, we need to figure out Pct n for every possible n. P ct n and n are interrelated with each other in the optimization process. P ct v In the PCO scheme, we first find the conditional optimal for all possible v, which is given by: Pct v =argmin E t Pct v v, 1 v n P ct v s.t. P ct,min P ct v P ct,max, 21 where P ct,min and P ct,max are the minimum and maximum value of P ct v respectively. Then we can determine the optimal n as n =argmine t v Pct v, 1 v n. 22 v We then have the optimal Pct n, P bt n and thus the optimal Et according to 15 and 16. Since there is no closed-form solution for cooperative ansmission power P ct v, we use a dynamic power conol PC algorithm to find the conditional optimal Pct v. We will show that given any n = v, P ct v converges to its optimum with a sufficient small change δ in O 1 iterations. P ct v In Algorithm 1, we use P ct v,imax as the approximation of Pct v since Pct v,imax Pct v δ where δ is sufficient small. For energy saving purpose, there is no need to cooperatively ansmit the data if the QoS requirement cannot be fulfilled with the maximum ansmission power P ct,max. Algorithm 1 PCO scheme Initialization: n =1, E t,min =, P ct n = P ct,max for each v Ω={1, 2,...,n} do PC algorithm initialization: P ct v,0 = P ct,max, η 0 =1, π 0 = Pct,max Pct,min M, M Z + for 1 i I max do 1 According to 13, calculate C out,i using P ct v,i 1. 2 η i = sgn C out,i L T where sgn is the signum function. } 3 π i =min{ 3+ηi 1η i 4, 1 π i 1. 4 ˆP ct v,i = P ct v,i 1 { { η i π i. } 5 P ct v,i =max min ˆPct v,i,p ct,max,p ct,min }. if P ct v,i =P ct,max then break the current for loop end if end for Calculate E t v using P ct v,imax and v. if P ct,min <P ct v <P ct,max and E t v <E t,min then E t,min = E t v, n = v, P ct n = P ct v end if end for if P ct n = P ct,max then No possible ansmission can fulfill the QoS requirement. end if Proposition 3: Given n = v in the PC algorithm, P ct v converges to Pct v with a sufficient small change δ in O 1 iterations and we can use P ct v,imax as the approximation of P ct vṗroof: If P ct,min <P ct v <P ct,max, Pct v must fall into one of the M equal parts in interval [P ct,min,p ct,max ]. We also notice that π i will not halve its value until η i 1 η i = 1. Thus we have M iterations at most before π i halves its value. After the first time π i is decreased by half, it is easy to see that π i can only stay unchanged for two iterations at most. We define δ as δ = π 0 2 K = P ct,max P ct,min 2 K 23 M where K is a positive integer that makes δ sufficient small compared with π 0. According to the algorithm it is obvious that P ct v,i Pct v π i after π i first halves itself. Thus we have P ct v,i Pct v δ in O M +2K =O 1 iterations. Let I max >M+2K and we can then use P ct v,imax as the approximation of P. ct v We assume that n sensors are normally deployed in each cluster with the cluster range r c. Since the minimum value of R bt is L T,givenn = v, the optimal broadcast ansmission power Pbt v is denoted as vrcσ L λ 2T 1 Pbt v =. 24 n After we have Pct v and P bt v for all possible n = v, we can determine n according to 22 and thus in turn determine Pct n and P bt n.

5 B. Approximation Algorithm To reduce the computational complexity in the PCO scheme, we propose an approximation algorithm. Note that the computational complexity in PCO scheme is mainly inoduced by the PC algorithm. The PC algorithm is used for the optimization problem in 13 and 21 and there is no closed-form expression for F 1 p v. If we can get an approximation of F 1 p v which can be quickly evaluated, the computational complexity will be significantly reduced. Inspired by the work in [9], we estimate the MISO channel in our model using a Gaussian approximation. Since H 2 F in 4 follows a chi-square variable with 2n degrees of freedom, we can calculate the mean value of γ as: μ γ = ΛP ] ct [ H n σ 2 E 2 F = 2ΛP ct σ We also calculate the variance of γ as: 2 σγ 2 ΛPct = n σ 2 var H 2 F = 1 2 2ΛPct n σ If we expand 2 in Taylor series at μ γ we have k λ 3 μγ γ C out γ =λ 3 log μ γ. 27 k ln 2 1+μ γ k=1 According to 27 the second-order approximation for μ C is given by μ C =E [C out ] λ 3 log μ γ λ 2 3 σγ 28 2ln2 1+μ γ where σγ 2 is the variance of γ. Note that the approximation is only valid for γ μ γ < 1. If we expand Cout 2 in a Taylor series, the second-order approximation for σc 2 is given by: σc 2 = E [ Cout] 2 E [Cout ] 2 29 [ ] 2 λ3 σγ 2 ln μ γ 2 σγ μ γ 4. We assume that the approximate channel capacity C out follows a normal disibution with a mean μ C and a standard deviation σ C, which is denoted as C out N μ C,σC 2.We further define the outage probability p out for C out, which is given by: p out =Pr C < C out = Cout 2 erf μ C 30 2σC where erf is the error function. From 30 we have C out = μ C + 2σ C erf 1 2 p out 1 31 where erf 1 is the inverse error function, which can also be defined in terms of the Maclaurin series. π erf 1 z = z + π12 2 z3 + 7π2 480 z The approximate average outage capacity is defined as C out =1 p out C out 33 1 p π μ C σ C p + π12 p3 + 7π2 480 p5 Fig. 2. n Performance of the dynamic power conol algorithm with different where p =2 p out 1. Compared with 13, we can see that 33 is a polynomial function on p that has a saightforward solution for the optimization of C out. If we substitute C out for Cout and p out for p out respectively, the computational complexity in the first step of the PC algorithm can be significantly reduced. IV. SIMULATION AN ANALYSIS In this section, we give the simulation results to show the efficiency of PCO scheme. We also show that the approximation algorithm provides accurate channel estimations. The parameters in the simulation are given in TABLE I. TABLE I. PARAMETERS FOR SIMULATION Symbol escription Value β Path loss constant 1 α Path loss exponent 2 n Number of sensors per cluster 10 d Transmission distance 100 m r c Cluster range 10 m σ 2 Noise power 5 μw P ct,max Maximum of P ct 200 mw P ct,min Minimum of P ct 0mW π 0 Initial step in PC algorithm 10 mw P cir Circuit power consumption 10 mw L T Capacity Requirement 1 bps/hz λ 1, λ 2, λ 3 0.1, 0.15, 0.75 First, we investigate the PC algorithm. We set M =20 and π 0 =10mW. Given different n = v, the simulation results in Fig. 2 show that P ct v converges to its optimal value Pct v with sufficiently small difference in a limited number of iterations I max =30. Note that the optimal cooperative ansmission power Pct n is inversely proportional to the number of cooperative sensors n. In Fig. 3 we show that under the QoS requirement, there exists the optimal outage probability p out that can maximize the average outage capacity C out.givenn =6, Fig. 3 shows that Cout reaches its maximum value C out = 1 bps/hz at p out = We also see that the approximation algorithm gives a similar result to that for the actual channel. In this case, the approximate average outage capacity C out reaches its maximum value C out =0.998 bps/hz at p out =0.178.

6 Fig. 3. Average outage capacity with different p out for n = 6 and P ct n =53mW Fig. 5. Performance of the dynamic power conol algorithm with different values of n Fig. 4. Optimal outage probability with different n We give the optimal outage probability p out for various values of n in Fig. 4. It shows that p out is inversely proportional to n. We also note that the approximation algorithm gives a similar result. The relation of P t and n is given in Fig. 5. From 15 and taking into account the reansmissions, we define the average total power consumption as P t n = P t n 1 p out n 34 where p out n is the optimal outage probability corresponding to n. From Fig. 5, we see that P t and P t reach their minimum value at n = 2 and n = 3 respectively. We choose n = 3 as the optimal solution according to the definition in 16 and 34. Note that for the optimal n, the optimal outage probability p out n should fulfill the QoS requirement p out n 1 N 1T.Ifp out n is out of range p out n > 1 N 1T, the new optimal value ˆn should be the smallest n n,n] that fulfills the QoS requirement, since P t monotonically increases with n n,n] and p out n is inversely proportional to n. V. CONCLUSION In this paper, we investigated the power consumption and optimization in a multi-hop QoS-consained cooperative WSN in a fading environment. We showed that there is no closed form solution for the power optimization problem with certain QoS consaints in the fading environment. For each singlehop ansmission, we proposed a three-phase ansmission scheme. We then proposed the PCO scheme to optimize the power consumption. By using PCO scheme, cooperative diversity is utilized and the power consumption of the multi-hop ansmission is minimized. We further proposed a channel approximation algorithm to reduce the computational complexity of PCO scheme. The simulation results showed the efficiency of the PCO scheme. REFERENCES [1] V. Gungor and G. Hancke, Indusial wireless sensor networks: Challenges, design principles, and technical approaches, Indusial Eleconics, IEEE Transactions on, vol. 56, no. 10, pp , Oct [2] A. Paulraj, R. Nabar, and. Gore, Inoduction to Space-Time Wireless Communications, 1st ed. New York, NY, USA: Cambridge University Press, [3] S. Cui, A. Goldsmith, and A. Bahai, Energy-efficiency of mimo and cooperative mimo techniques in sensor networks, Selected Areas in Communications, IEEE Journal on, vol. 22, no. 6, pp , Aug [4] S. Jayaweera, Virtual mimo-based cooperative communication for energy-consained wireless sensor networks, Wireless Communications, IEEE Transactions on, vol. 5, no. 5, pp , May [5] A. el Coso, U. Spagnolini, and C. Ibars, Cooperative disibuted mimo channels in wireless sensor networks, Selected Areas in Communications, IEEE Journal on, vol. 25, no. 2, pp , February [6] A. Goldsmith, Wireless Communications. New York, NY, USA: Cambridge University Press, [7] O. Younis and S. Fahmy, Heed: a hybrid, energy-efficient, disibuted clustering approach for ad hoc sensor networks, Mobile Computing, IEEE Transactions on, vol. 3, no. 4, pp , Oct [8] W. Heinzelman, A. Chandrakasan, and H. Balakrishnan, Energyefficient communication protocol for wireless microsensor networks, in System Sciences, Proceedings of the 33rd Annual Hawaii International Conference on, Jan 2000, pp. 10 pp. vol.2. [9] J. Perez, J. Ibanez, L. Vielva, and I. Santamaria, Closed-form approximation for the outage capacity of orthogonal stbc, Communications Letters, IEEE, vol. 9, no. 11, pp , Nov 2005.