Ling Lyu, Cailian Chen, Yao Li, Feilong Lin, Lingya Liu, and Xinping Guan. Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of ...
Cognitive Radio Enabled Transmission for State Estimation in Industrial Cyber-physical Systems Ling Lyu, Cailian Chen, Yao Li, Feilong Lin, Lingya Liu, and Xinping Guan Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai 200240, P. R. China Email:{sjtulvling, cailianchen, kobetomli, bruce lin, spar, xpguan}@sjtu.edu.cn
Abstract—State estimation, which computes the best possible approximation for the system state based on the perceived information transmitted from sensors to the estimators, is vital for control system performance in industrial cyber-physical systems (ICPSs) with the integrated techniques of control, communication and computing. Thus the performance of state estimation relies on the communication reliability. In order to improve the reliability, redundant channels/slots are reserved for the data transmission in industrial wireless techniques, such as WirelessHART. However, the redundancy scheme burdens the increasingly over-crowded ISM spectrum band due to the envisioned emerging ubiquitous industrial wireless monitoring in the architecture of ICPS in the near future. The cognitive radio (CR) technology can intelligently explore the available spectrum opportunities on licensed channels, and it motivates this paper to consider the redundant transmission through the opportunistically available licensed channels to guarantee the transmission reliability for state estimation. Unfortunately, spectrum sensing takes extra energy consumption, thus it is necessary to take into account the energy efficiency for the battery-powered IWSN. Then a CR enabled energy-efficiency maximization problem is formulated by regarding the convergence of state estimation as a constraint of the resource allocation problem. In order to solve the non-convex and mixed integer programming, the Dinkelbach and Lagrangian relaxation techniques are adopted to transform the problem into a convex programming and furthermore reduce the computational complexity. Numerical results demonstrate that the CR technology can significantly release the spectrum for the redundancy design from the ISM band while guarantee the reliability for the effective state estimation.
I. INTRODUCTION In industrial cyber-physical systems (ICPSs), the system state is estimated based on the information which is perceived by sensors and then transmitted to the estimators through the industrial wireless sensor networks (IWSNs) [1][2]. Thus the performance of estimation heavily relies on the communication reliability of IWSNs [3][4]. However, as the packets may loss sometimes due to the severe electromagnetic interference and radio-frequency interference, the estimator has to update the current state estimate of the physical process based on the previously collected information, which deteriorates the performance of state estimation. To overcome the packet loss problem in IWSNs, one effective way is to reserve redundant Industrial Scientific Medical (ISM) channels or slots for the data redundant transmission, such as the redundancy scheme in the standardized protocol
WirelessHART [5]. However, the redundancy scheme burdens the over-crowded ISM spectrum band in the circumstance that the industrial monitoring data are increasingly growing up in the near future. Furthermore, it is challenging to efficiently allocate the limited spectrum resource in ISM band. In order to offload the redundancy data from ISM spectrum, the Cognitive Radio (CR) technology is introduced to opportunistically use the licensed channels for redundancy data retransmission, because it can provide an intelligent and adaptive way to explore the available spectrum opportunities on licensed channels (CR channels). The introduction of CR technology will significantly release the spectrum for the redundancy design from the ISM band and thus alleviate the spectrum crisis for the ISM band. Furthermore, the communication reliability requirements of the convergence of state estimation is satisfied. Unfortunately, the spectrum sensing will consume extra energy which deteriorates the energy crisis of the battery-powered sensor nodes, so the energy efficiency should be considered [6][7]. The performance of the state estimation and the energy efficiency are tightly coupled. Specifically, the redundancy and retransmission can improve the communication reliability and the performance of state estimation, but they will cost extra energy and spectrum, which will reduce the energy efficiency. In real ICPSs, if the communication reliability surpasses a threshold, the state estimation is convergent. Thus, it is unnecessary to pursue the quite high communication reliability. In this paper, firstly the sufficient and necessary condition for the convergence of state estimation is established with the packet loss rate according to the physical process dynamics, and the maximum allowable packet loss rate is derived by using the Kalman filter approach. Secondly, in order to guarantee the estimation convergence and improve the energy efficiency, a CR-enabled energy-efficiency maximization problem is proposed by regarding the convergence of state estimation as a constraint of the resource allocation problem. Specifically, the convergence of state estimation is guaranteed by allocating redundant channels to ensure the communication reliability, i.e., assigning ISM channels for the first transmission and reserving CR channels for the retransmission. Finally, the optimization problem is transformed from a non-convex and mixed integer programming into
978-1-4799-5952-5/15/$31.00 ©2015 IEEE
a convex programming by the Dinkelbach and Lagrangian relaxation technologies. We consider the hot rolling process as a typical example of ICPSs. As shown in Fig. 1, the hot rolling process consists of several sub-processes, such as furnaces, the first and second reversing roughers, finishing millings, laminar cooling, down coilers. The sensor network for each sub-process is called FieldNet, which is composed of a group of sensors and one access point (AP) [8]. The dynamical hot rolling process is monitored by the sensors in the FieldNet and the raw measurements are transmitted from the sensors to the state estimator via the AP. According to the sensors’ roles in the FieldNet, the ones in charge of sensing the licensed channels are called CR sensors, and the others in charge of providing physical state information for the estimator are called NCR sensors, which have strict requirements for the communication reliability. The system description and network model are detailed below. |·| denotes the number of the elements of a set. Tr (·) is the trace of a matrix. ρ (·) is the maximum eigenvalue of a matrix. E (·) is the expectation operator. TABLE I NOTATIONS
pbi,m,n pcj,k,n ps ai,k,n bi,m,n cj,k,n C γi,k,n M γi,m,n C γj,k,n
Estimator
Access Point CR Sensor
Controller
NCR Sensor Ethernet Wired Communication Wireless Communication
࢚࠰1
Furnaces
Reversing Rougher R1
Reversing Rougher R2
Laminar Cooling
Finishing Mill
Fig. 1. Hot Rolling Process and FieldNet Transmission time
Channel Sensing time
Down Coilers
One time slot
CR3
L-4
L-9
L-6
H-1
L-13
L-11
L-10
CR2
L-5
H-1
H-2
L-7
H-4
L-12
H-4
CR1
L-3
L-1
H-3
H-2
L-8
H-3
L-2
ISM2
H-1
H-2
H-4
H-4
H-2
H-4
H-1
ISM1
H-2
H-3
H-1
H-3
H-3
H-1
H-2
1
2
3
4
5
6
H-i
First transmission of NCR sensor i
H-i
Retransmission of NCR sensor i
L-j
Transmission of CR sensor j
7
Time/slots
Fig. 2. Joint Allocation of ISM and CR Channels
the set of available CR channels the set of ISM channels the set of NCR sensors the set of CR sensors the transmission power of NCR sensor i transmitting on the CR channel k at slot n the transmission power of NCR sensor i transmitting on the ISM channel m at slot n the transmission power of CR sensor j transmitting on the CR channel k at slot n the sensing power of each CR sensor the channel allocation variable for NCR sensor i on CR channel k at slot n the channel allocation variable for NCR sensor i on ISM channel m at slot n the channel allocation variable for CR sensor j on CR channel k at slot n the SNR of CR channel k for NCR sensor i at slot n the SNR of ISM channel m for NCR sensor i at slot n the SNR of CR channel k for CR sensor j at slot n
A. System Description According to the heat transfer law and by using the 2D finite volume scheme [3], the slabs’ temperature distribution can be described by the following discrete time dynamical model (1) xl+1 = Axl + wl , where xl ∈ n1 is the temperature state vector of the slab in the direction of thickness at the time step l, wl ∈ n1 is the system modeling error and noise; A ∈ n1 ×n1 is the state transition matrix. The measurement is given by yl = Cxl + vl ,
Gateway Collected Information
Remote Controller
II. SYSTEM DESCRIPTION AND NETWORK MODEL
FC FM Nh Nl pa i,k,n
Local Controller
FieldNet
(2)
where yl ∈ n3 is the output vector, vl ∈ n3 is the measurement noise, and C ∈ n3 ×n1 is the measurement matrix. wl and vl are assumed to be zero-mean white noise. Since both the rolling force and the metallurgical and mechanical
properties of the products are closely related to the slab temperature, the state estimation of temperature is vital for the hot rolling The estimation problem is to achieve process. < ∞, where xl|l xl − xl|l xl − xl|l supl≥0 E Tr is the estimation of the slab temperature. Here, the wireless sensors are used to measure the temperature of the slab. B. Network Model In this paper, the FieldNet is based on the time division multiple access (TDMA) technology. The duration of one frame, i.e., one sampling interval of the estimator, is T , which includes several slots. The duration of one slot is Δt. The CR and ISM channels are assumed to be Rayleigh fading channels and the corresponding signal-to-noise ratios (SNRs) C and follow the exponential distribution with mean value γi,k M γi,m , respectively. AP gathers the sensing results from the CR sensors and then calculates the idle probability Pkd of the CR channel k. Then AP jointly allocates the CR and ISM channels to the two kinds of sensors. Therefore, the available transmission time of the CR and ISM channels is (Δt − ts ) in one slot, where ts is the sensing time. To ensure the transmission reliability of the NCR sensors, ISM channels are assigned to them for the first transmission and CR channels are reserved for the retransmission. For the CR sensors, the CR channels are allocated to them without reserving any redundant channels for the retransmission as shown in Fig. 2. The objective of combining the ISM and CR channels allocation with power control is to improve the energy efficiency while guarantee the estimation performance. We define ai,k,n ∈ {0, 1}, bi,m,n ∈ {0, 1}, and cj,k,n ∈ {0, 1} for the resource allocation of sensors, as shown in Table
I. Each NCR or CR sensor is allowed to transmit data on a single channel such that
bi,m,n +
m∈FM
ai,k,n ≤ 1, ∀i ∈ Nh ,
(3)
k∈FC
and
cj,k,n +
and
ai,k,n ≤ 1, ∀k ∈ FC ,
(5)
i∈Nh
bi,m,n ≤ 1, ∀m ∈ FM .
(6)
i∈Nh
The lower bound of the throughput required by each CR sensor is Rmin such that
ts C Pkd 1 − cj,k,n log2 1 + pcj,k,n γj,k,n ≥ Rmin , ∀j ∈ Nl . Δt k∈FC (7)
Since each sensor is battery-powered, the maximum transmission power constraint of each NCR sensor and each CR sensor are defined as
k∈FC
ai,k,n pai,k,n +
∀i ∈ Nh ,
m∈FM
bi,m,n pbi,m,n
1−
ts Δt
≤ pm i ,
and ts ps t s c ≤ pm cj,k,n pj,k,n 1 − + j , ∀j ∈ Nl , Δt Δt
(8) (9)
k∈FC
m where pm i (i ∈ Nh ) and pj (j ∈ Nl ) are the maximum transmission power of NCR and CR sensors, respectively. The total power consumption is defined as E = ts + Es , where Ea , Eb , and Ec are [Ea + Eb + Ec ] 1 − Δt the power consumptions for data transmission and Es is the power consumption for sensing on licensed channels, which are defined as
Ea = Ec =
i∈Nh k∈FC
j∈Nl k∈FC
ai,k,n pai,k,n , Eb = cj,k,n pcj,k,n , Es =
Wl|l
(4)
k∈FC
i∈Nh m∈FM
ts p s . Δt j∈Nl
bi,m,n pbi,m,n ,
(10) III. COGNITIVE RADIO ENABLED TRANSMISSION FOR STATE ESTIMATION
A. State Estimation Based on Kalman Filter The Kalman filter based estimator is used to estimate the temperature distribution in the hot rolling systems [1]. The arrival of the estimator’s observation values is modeled as a random process which is related to the packet loss rate Pl . At time step l, we define a random variable rl ∈ {0, 1} to model the communication reliability [9]. Specifically, if the current state information is successfully received by the estimator, rl = 1. Otherwise, rl = 0. The prediction and xl|l , estimation values of the system state are xl|l−1 and respectively. For simplicity, we assume that the system noise wl , the measurement noise vl , and the initial state x0 are mutually independent. The means of Gaussian noises wl , vl , and initial state x0 are 0, 0, and x0 , respectively, and the corresponding covariance matrices are Q√ >0, D > 0, and W0|0 > 0, respectively. We assume A, Q is controllable and (A, C) is observable. It implies that the unknown state x can be estimated by the measurement y [3]. The predicted
xl − xl|l−1 xl − xl|l−1 = E xl − xl|l xl − xl|l .
Wl|l−1 = E
and
cj,k,n ≤ 1, ∀j ∈ Nl .
Each ISM or CR channel can only be assigned to one sensor such that j∈Nl
error covariance Wl|l−1 and estimated error covariance Wl|l are defined as ,
(11) (12)
Then the Kalman filter under packets loss runs recursively as follows [10] ⎧ Δ ⎪ xl|l−1 = A xl−1|l−1 ⎪ ⎪ ⎪ ⎪ ⎨ Wl|l−1 = AWl−1|l−1 A + Q xl|l = xl−1|l−1 + rl Kl yl − C xl|l−1 (13) ⎪ −1 Δ ⎪ ⎪ K CW = W C C + D ⎪ l l|l−1 l|l−1 ⎪ ⎩ Wl|l = (I − rl Kl ) Wl|l−1 According to (13), the predicted error covariance should satisfy the following modified Algebraic Riccati Equation.
−1 Wl = APl−1 A − rl AWl−1 C CWl−1 C + D CWl−1 A + Q. (14)
If supl≥0 E [Tr (Wl )] < ∞ , the estimation process is MSE stable. Lemma 1. [10] If matrix C is of full column rank, the sufficient and necessary condition for the MSE stability of the estimation (14) is 1 Δ , Pl < P , P = 2 (15) ρ (A) where P is the maximum allowable packet loss rate of each NCR sensor under the condition of estimation convergence. B. CR-Enabled Channel Allocation and Power Control In this subsection, the joint allocation of the ISM and CR channels combining with power control is proposed to meet the MSE stability condition in Lemma 1 and improve the energy efficiency of ICPSs. The probability density function of SNR for each CR channel k is defined C γi,k,n 1 C . The outage probability is as fi,k,n = C exp − C γi,k
given by
C Pi,k,n
γi,k
γ Cth
Cth = 1 − exp(− γ Ci,k ), where γi,k is the i,k,n
M threshold of the SNR. The probability density function fi,m,n M and the outage probability function Pi,m,n for each ISM channel m are defined similarly. In order to guarantee the estimation performance, the outage probability of the NCR sensors should satisfy the following condition T
M Pi,m,n
T bi,m,n
m∈FM n=1
C Pi,k,n
ai,k,n
< P , ∀i ∈ Nh .
k∈FC n=1
(16)
Taking logarithm operation on both sides of (16), it yields T
C ai,k,n log Pi,k,n +
n=1 k∈FC
M bi,m,n log Pi,m,n < log P .
m∈FM
(17)
In order to avoid the congestion caused by unlimited retransmission, the retransmission times of each NCR sensor are constrained by T
n=1 k∈FC
ai,k,n +
T
n=1 m∈FM
bi,m,n ≤ N r , ∀i ∈ Nh ,
(18)
where N r is a constant denoting the maximal retransmission times. The achievable throughput is defined as R = Ra + Rb + Rc , where C C ts 1 − Δt , ai,k,n Xi,k,n Pkd 1 − Pi,k,n i∈Nh k∈FC
M M ts Rb = 1 − Pi,m,n 1 − Δt , bi,m,n Xi,m,n i∈Nh m∈FM
C d ts cj,k,n Xj,k,n Pk 1 − Δt , Rc =
Ra =
with
=
log2 1 +
C pai,k,n γi,k,n
k∈FC
C8 : [
=
The optimization problem constrained by the convergence of state estimation is formulated as follows max R/E a, b, c, pa , pb , pc s.t.C1 ∼ C9 : (3) ∼ (9), (17), (18), C10 : ai,k,n = {0, 1} , bi,m,n = {0, 1} , cj,k,n = {0, 1} ,
(19)
C11 : pai,k,n ≥ 0, pbi,m,n ≥ 0, pcj,k,n ≥ 0.
(20)
P1 is a non-convex and mixed integer programming problem. In order to reduce the computational complexity, we focus on the sub-optimal solution of P1 in the next subsections. C. Channel and Power Allocation Algorithm In this subsection, we will present how to solve the optimization problem P1. The detailed process is shown in Algorithm 1. 1) Transformation of the Objective Function: The fractionform objective function of P1 is not concave. With the Dinkelbach method [11], the maximum energy efficiency q ∗ can be transformed to polynomial form by using iterative method such that q ∗ = max R/E. q ∗ is achieved, if and only if max {R − q ∗ E} = R∗ − q ∗ E ∗ = 0, R ≥ 0, and E > 0. For a fixed q, the problem P 1 is equivalent to the problem P2. The proof is omitted due to the space limit. P2 :
max
a,b,c,pa ,pb ,pc
pa i,k,n +
k∈FC
M , Xi,m,n
M C C . log2 1+pbi,m,n γi,m,n , Xj,k,n = log2 1 + pcj,k,n γj,k,n
P1 :
max R − qE a, b, c,pa , pb , pc s.t.C1 ∼ C6 : (3) ∼ (6), (17), (18), C C7 : cj,k,n Xj,k,n Pkd [1 − ts /Δt] ≥ Rmin ,
j∈Nl k∈FC
C Xi,k,n
P3 :
R − qE
s.t.(3) ∼ (9), (17) ∼ (20).
2) Relaxation of Problem P2: As P2 is a mixed integer programming problem, the Lagrangian relaxation method can be used to relax the binary integers in P2 to continuous variables between 0 and 1. Each relaxed continuous variable can be regarded as the portion of time in one slot assigned to each corresponding sensor. We define that pa i,k,n = ai,k,n pai,k,n , pb i,m,n = bi,m,n pbi,m,n , pc j,k,n = cj,k,n pcj,k,n . Then we can obtain the convex optimization problem P3, which can be proved by checking the properties of the objective function and the feasible set.
C9 :
k∈FC
pb i,m,n ] [1 − ts /Δt] ≤ pm i ,
m∈FM
pc j,k,n [1 − ts /Δt] +
ps ts ≤ pm j , Δt
C10 : 0 ≤ ai,k,n ≤ 1, 0 ≤ bi,m,n ≤ 1, 0 ≤ cj,k,n ≤ 1, C11 : pa i,k,n ≥ 0, pb i,m,n ≥ 0, pc j,k,n ≥ 0.
Algorithm 1 Channel and Power Allocation Algorithm 1: Initialize the maximum number of iterations Nmax , the error bound ε, q = 0 and n = 1; 2: while n ≤ Nmax and f lag = 0 do 3: Relax the binary integers in P2, and give the Lagrangian function; 4: Adopt the Lagrangian dual decomposition method, and calculate the variables with (22) ∼ (27); 5: Obtain the values of variables, and calculate R and E; 6: Δ = R − qE; 7: if Δ ≤ ε then 8: f lag = 1; q ∗ = R/E; 9: return q, R, E and the values of variables; 10: else 11: q = R/E; n = n + 1; f lag = 0; 12: end if 13: end while 3) Sub-optimal Solution: Since P3 is convex, there is no duality gap between P3 and its dual problem. We obtain one master problem and T (|FM | + |FC |) sub-problems by the Lagrangian dual decomposition method as shown in (21). Let the Lagrangian multipliers α, β, μ, ν, ψ, ϕ, φ, , ξ, η 0 , η 1 , θ0 , θ1 , δ 0 , δ 1 , ϑa , ϑb , ϑc > 0. By taking the first-order derivative of the Lagrangian function of each sub-problem, the sub-optimal solutions can be obtained based on the Karush-Kuhn-Tucker (KKT) conditions [12]. C ts 1 − Δt ai,k,n Pkd 1 − Pi,k,n 1 − C , t s γi,k,n ϕi − ϑai,k + ai,k,n q 1 − Δt M ts 1 − Δt bi,m,n 1 − Pi,m,n 1 b − M , pi,m,n = ts b γ bi,m,n q 1 − Δt + ϕi − ϑi,m i,m,n d ts cj,k,n (1 + ψ) Pk 1 − Δt 1 − C , pcj,k,n = ts γj,k,n φj − ϑcj,k + cj,k,n q 1 − Δt 1, i = arg max LC k,n , ai,k,n = 0, others, 1, i = arg max LM m,n , bi,m,n = 0, others,
pai,k,n =
(22)
(23)
(24)
(25) (26)
C
a pa γi,k,n C ts ts 1 − Δt −q ai,k,n log 1+ i,k,n p i,k,n 1 − Δt Pkd 1 − Pi,k,n ai,k,n i∈Nh i∈N h
C C
pc j,k,n γj,k,n pc j,k,n γj,k,n d ts d ts cj,k,n log 1 + + Pk 1 − Δt + ψi,n cj,k,n log 1 + Pk 1 − Δt cj,k,n cj,k,n j∈Nl j∈Nl
0
1 ηi,k,n ai,k,n + ηi,k,n cj,k,n − ai,k,n − ϕi,n pa i,k,n + (1 − ai,k,n ) +μk,n 1 − j∈Nl i∈Nh i∈Nh i∈Nh
0
c 1 c δi,k,n cj,k,n + δi,k,n (1 − cj,k,n ) − ϑj,k,n p j,k,n + βi,n ai,k,n − ξi ai,k,n − j,n cj,k,n + j∈Nl j∈Nl i∈Nh i∈Nh j∈Nl
a
c
ts C a c −q p j,k,n 1 − Δt + ϑi,k,n p i,k,n − αi,n ai,k,n log Pi,k,n − φj,n p j,k,n , j∈Nl i∈Nh j∈Nl i∈Nh M
b
pb γi,m,n M ts ts 1 − Pi,m,n 1 − Δt −q bi,m,n log 1+ i,m,n p i,m,n 1 − Δt LM m,n = bi,m,n i∈Nh i∈Nh 0
1 θi,m,n bi,m,n + θi,m,n − βi,n bi,m,n − νm,n 1 − bi,m,n − ϕi,n pb i,m,n + (1 − bi,m,n ) i∈Nh i∈Nh i∈Nh i∈Nh
b M ϑi,m,n pb i,m,n − ξi bi,m,n − αi bi,m,n log Pi,m,n . +
i∈Nh
1, if j = arg max LC k,n 0, others.
and
ai,k,n = 0, (27)
IV. PERFORMANCE EVALUATION AND DISCUSSION A. Estimation Performance Based on Kalman Filter In this subsection, the estimation performance is evaluated. The slab is divided into strips to reduce the computational complexity. The grid in strip s is labeled as xsw,r , where w and r are the thickness and length numbers, respectively. According to [3], the state transition matrix of the temperature estimation defined as A = I + is T T · · · , FuTs with Gr = diag {G 1 O, ·s · · Gus O},u = s F1 , Tλ Tλ , diag Δh2 ς s1,rC s , · · · , Δh2 ς s w,rC s 1,r
w,r
1,r
⎡
−2 ⎢ ⎢ 1 ⎢ ⎢ O=⎢ 0 ⎢ ⎢ . ⎣ . . 0
than the P , the estimation diverges, i.e., the estimator cannot obtain the temperature state. Therefore, if the packet loss rate is less than P , the Kalman filter based estimator can obtain the temperature state. Furthermore, the smaller the packet loss rate, the better the estimation performance. 200 100 0 -100 packet loss rate =0.3 packet loss rate =0.18 packet loss rate =0.1
-200 -300
0
5
10
2
0
2 .. . .. . ···
1 .. .
··· .. . .. .
1 0
2 2
⎤ 0 .. ⎥ . ⎥ ⎥ ⎥ . 0 ⎥ ⎥ ⎥ ⎦ 1 −2
Define I as the unit matrix. The parameters are set as follows: B = −I, H = I, Q = W = 10I, the initial error covariance matrix P0 = 10I, us = 1, v = 3, w = 1, and r = 1, TABLE II VALUES OF PARAMETERS
Values 0.1s 1/2m 40W/mK 7.85kg/m3 0.46 × 103J/kg · K
Therefore, the maximum allowable packet loss rate under estimation convergence is obtained as P = 0.183. Fig. 3 shows that when the packet loss rate is 0.1, the MSE of state estimation converges to zero with small fluctuations. When the packet loss rate is 0.18, which is close to the bound P , the state estimation still converges though the fluctuation is large at the beginning. When the packet loss rate is 0.3, larger
15
20 Time step
25
30
35
40
Fig. 3. Estimation performance under different packet loss rates AVE-C
CRSE
w,r
Parameters Sampling interval of the estimator T Slab thickness of one grid Δh Slab thermal conductivity λ Slab density ς Slab specific heat capacity C
(21)
ISE
AVE-I
1600 1500 1400 1300 1200 1100 1000 900 800
210 200 190 180 170 160 150 140 130 0
10
20
30
40
50
60
70
80
90
Energy Efficiency (bit/Joule)
cj,k,n =
i∈Nh
Mean squared error (MSE)
i∈Nh
Energy Efficiency (bit/Joule)
LC k,n =
100
Ordinal Number of Simulation
Fig. 4. Energy efficiency of CRSE and ISE (AVE-C and AVE-I denote the average energy efficiency for CRSE approach and ISE approach, respectively)
B. Energy Efficiency Based on the CRSE Approach In this subsection, the energy efficiency of the proposed CRSE approach is evaluated under the condition of estimation convergence. The transmission in ISM band for state estimation (ISE) approach is also introduced as a comparison to verify the effectiveness and superiority of the CRSE approach. The CRSE approach assigns both ISM and CR channels to sensors while the ISE approach only assigns ISM channels to sensors. The influence of SNR on the energy efficiency is evaluated by the ratio of the mean SNR value of the CR channel to that of the ISM channel, abbreviated as RSNR for simplicity. The sense of opportunistically available licensed channels consumes extra energy and time, whose influence is
evaluated by the ratio of energy consumption that is defined s . as REC= ppms tΔt The simulation environment is set as follows: the energy consumption ratio is 1% and the mean SNRs of CR channels and ISM channels are 17.5 dB and 7.5dB, respectively. We run the simulation randomly 100 times and use the average energy efficiency to evaluate performance. As shown in Fig. 4, the energy efficiency of CRSE approach is better than that of ISE approach, increasing by more than 580% in this case. 1500
RSNR-C=1 RSNR-I=1 RSNR-C=2 RSNR-I=2 RSNR-C=3 RSNR-I=3 RSNR-C=4 RSNR-I=4 RSNR-C=5 RSNR-I=5
Energy Efficiency (bit/Joule)
200 195 1000
ISE
190
185
CRSE 0.055
500
0.06
0.065
CRSE
ISE 0 0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Energy Consumption Ratio
Fig. 5. Influence of REC and RSNR (RSNR-C and RSNR-I denote the RSNR for CRSE approach and ISE approach, respectively)
As shown in Fig. 5, the CRSE approach is influenced by the RSNR and REC while the ISE approach is not. Comparatively, the energy efficiency of CRSE approach outweighs that of ISE approach when REC< 6%. Although the advantage of the CRSE approach over the ISE approach narrows as the REC increases, it is rare for REC to surpass 6% in practice. Therefore, the CRSE approach has better energy efficiency under the condition of reasonable energy consumption of sensing, which significantly alleviates the energy crisis for ICPSs. 800 750
750 700
700
650 600
650
550 16 10
14 8
12
Number of CR Sensors
600
Energy Efficiency (bit/Joule)
Energy Efficiency (bit/Joule)
220 800
850
250
200
200
180
150
160
100
140 120
50 16
4
Number of NCR Sensors
Number of CR Sensors
100
8
12
6 10
10
14
80
6 10
4
Number of NCR Sensors
Fig. 6. Energy efficiency of CRSEFig. 7. Energy efficiency of ISE apapproach with the various numbers ofproach with the various numbers of NCR and CR sensors NCR and CR sensors
Since CRSE approach reserves channels in the CR band which has adequate channels, the increase of the number of NCR sensors has no influence on the channel capacities of CR sensors. Therefore, the energy efficiency of CRSE approach increases with the number of NCR sensors as shown in Fig. 6. Comparatively, as the ISE approach reserves channels in the ISM band which has scarce channels, the channel capacities of CR sensors decrease with the number of NCR sensors. Consequently, the energy efficiency of ISE approach decreases, as shown in Fig. 7. The energy efficiency of the two approaches increases as the number of CR sensors grows. In summary, the CRSE approach allows to deploy more sensors in the FieldNet to gather more perceived information, which benefits releasing more spectrum requests in ISM band.
V. CONCLUSIONS The explicit relationship between the convergence of state estimation and the maximum allowable packet loss rate is presented in this paper. The so-called CRSE approach is proposed for offloading redundancy data transmission in ISM band by exploring more spectrum opportunities in licensed band. By jointly assigning the ISM channels and harvested licensed channels with power control, the transmission reliability of the perceived data transmission is improved and the convergence of state estimation is guaranteed with energy efficiency. Comparing with the traditional transmission in ISM band for state estimation, simulation results show that: (1) CRSE guarantees the state estimation performance with energy-efficiency even with the extra energy consumption in spectrum sensing, and (2) CRSE improves the network scalability for ubiquitous monitoring in future ICPSs, since it releases more spectrum requests in ISM band by offloading the redundancy data. In conclusion, the proposed CRSE approach provides more possibility for the application of the large-scale IWSN in the energy- and spectrum-limited ICPSs. ACKNOWLEDGMENT
This work was partially supported by NSF of China under the grants 61371085, 61431008, 61221003, 61290322 and 61273181, and by STCSM under the grant 13QA1401900. R EFERENCES [1] C. Chen, S. Zhu, X. Guan, and X. S. Shen, Wireless Sensor Networks: Distributed Consensus Estimation. Springer, 2014. [2] S. Zhu, C. Chen, X. Ma, B. Yang, and X. Guan, “Consensus based estimation over relay assisted sensor networks for situation monitoring,” IEEE Journal of Selected Topics in Signal Processing, vol. 9, no. 2, pp. 1–14, 2014. [3] C. Chen, J. Yan, N. Lu, Y. Wang, X. Yang, and X. Guan, “Ubiquitous monitoring for industrial cyber-physical systemsover relay assisted wireless sensor networks,” IEEE Transactions on Emerging Topics in Computing, DOI: 10.1109/TETC.2014.2386615, 2015. [4] X. Cao, P. Cheng, J. Chen, and Y. Sun, “An online optimization approach for control and communication codesign in networked cyberphysical systems,” IEEE Transactions on Industrial Informatics, vol. 9, no. 1, pp. 439–450, 2013. [5] A. Saifullah, Y. Xu, C. Lu, and Y. Chen, “End-to-end communication delay analysis in industrial wireless networks,” IEEE Transactions on Computers, DOI: 10.1109/TC.2014.2322609, 2013. [6] S. Wang, M. Ge, and W. Zhao, “Energy-efficient resource allocation for OFDM-based cognitive radio networks,” IEEE Transactions on Communications, vol. 61, no. 8, pp. 3181–3191, 2013. [7] L. Liu, C. Hua, C. Chen, and X. Guan, “Power allocation for virtual MIMO-based three-stage relaying in wireless Ad Hoc networks,” IEEE Transactions on Wireless Communications, vol. 13, no. 12, pp. 6528– 6541, 2014. [8] F. Lin, C. Chen, L. Li, H. Xu, and X. Guan, “A novel spectrum sharing scheme for industrial cognitive radio networks: from collective motion perspective,” in Proc. IEEE International Conference on Communications (ICC’14), Sydney, Australia, Jun. 10-14, 2014. [9] X. Cao, P. Cheng, J. Chen, S. S. Ge, Y. Cheng, and Y. Sun, “Cognitive radio based state estimation in cyber-physical systems,” IEEE Journal on Selected Areas in Communications, vol. 32, no. 3, pp. 489–502, 2014. [10] B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan, and S. S. Sastry, “Kalman filtering with intermittent observations,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1453–1464, 2004. [11] W. Dinkelbach, “On nonlinear fractional programming,” Management Science, vol. 13, no. 7, pp. 492–498, 1967. [12] D. P. Bertsekas, Constrained optimization and Lagrange multiplier methods. Academic press, 2014.
