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Autonomous Channel Switching: Towards Efficient Spectrum Sharing for Industrial Wireless Sensor Networks Feilong Lin, Student Member, IEEE, Cailian Chen, Member, IEEE, Ning Zhang, Member, IEEE, Xinping Guan, Senior Member, IEEE, and Xuemin (Sherman) Shen, Fellow, IEEE

Abstract—Industrial wireless sensor networks (IWSNs) are committed to bring the industry automation into the era of Industry 4.0 by providing the ubiquitous perception to improve the production efficiency. However, the proliferation of wireless devices in industrial applications makes the spectrum sharing in limited ISM (Industrial, Scientific, and Medical) band a challenging problem. In this paper, it is concerned with the intrinsic impact of the evenness of spectrum usage on the spectrum sharing performance in terms of channel accessing probability, spectrum utilization, and fairness of spectrum usage. In order to explore the explicit relationship between the evenness and spectrum sharing performance, a new concept of equilibrium is first defined to represent the achievable best evenness of spectrum usage. Then, a set of rules called Local EQuilibrium guided Autonomous Channel Switching (LEQ-AutoCS) are devised, with which each accessed sensor autonomously equalizes the local channel occupations within its range of spectrum sensing without overhead on exchanging the sensors’ spectrum sensing reports. It is further proved that the equilibrium can be achieved by this concessive manner. Theoretical analysis and experiments results demonstrate that the proposed LEQ-AutoCS rules provide higher utilization and fairness of spectrum usage comparing to the existing spectrum access approaches. Moreover, it is shown that LEQ-AutoCS rules assist the system to reduce the spectrum access delay to 1/2 of CSMA based systems and 1/50 of TDMA based systems, respectively. Index Terms—Industrial wireless sensor networks, spectrum sharing, autonomous channel switching, equilibrium

I. I NTRODUCTION The development of wireless sensor networks in the last decades is bringing the Internet of Things (IoT) to the world, which promotes the industry automation entering the ear of Industry 4.0. Industrial wireless sensor networks (IWSNs), as the fundamental element for the realization of IoT in industry, are endowed with the advantages in terms of rapid deployment, low-cost maintaining, flexibility, and scalability [1, 2]. They are taken as one of the most promising techniques for Manuscript received July 7, 2015; revised September 7, 2015; accepted September 28, 2015. This work was supported in part by NSF of China under the grants 61221003, U1405251, 61371085, 61431008, 61290322 and 61273181, in part by Ministry of Education of China under NCET-13-0358, and in part by Science and Technology Commission of Shanghai Municipality (STCSM), China under 13QA1401900. Corresponding author: Cailian Chen. F. Lin, C. Chen, and X. Guan are with Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, P. R. China (email: bruce [email protected], [email protected], [email protected]). N. Zhang and X. Shen are with Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada (email: [email protected], [email protected]).

Industry 4.0 to ubiquitously perceive the industrial processes [3]. Recent applications in industry witness the improvement of productivity and efficiency by using IWSNs [4, 5]. Taking the hot strip mill of Bao Steel, Shanghai, China shown in Fig. 1 as an example, hundreds of sensors are deployed to monitor different milling processes including reversing roughers R1 and R2, finishing mill, laminar cooling, and down coiler. In order to guarantee the quality of alloy steel, hundreds of sensors can be deployed to monitor the milling process to percept the strip temperature, thickness, milling pressure, and other process data to acquire the precise mathematic model and improve the precision of process control [6]. IWSNs can also provide a dedicated temperature evolution monitoring to support flexible milling [7]. For the general application of equipment health monitoring, IWSNs can work continuously to reduce the unexpected downtime. It is foreseeable that in the very near future IWSNs would become a standard feature of smart factory in the era of Industry 4.0. However, the ever-increasing wireless communication demands necessitate efficient spectrum sharing strategies to improve spectrum efficiency of IWSN in limited ISM band. The existing standardized industrial wireless protocols, such as WirelessHART [8], ISA100.11a [9], and WIA-PA [10], implement the spectrum sharing based on the superframe design. The slotted channels are periodically allocated to the wireless sensors for data packet delivery, which are efficient for the periodic data gathering in small-scale networks. To provide efficient spectrum sharing for event-driven data collection in large-scale networks, more flexible and powerful spectrum sharing strategies are expected. Recently, many works have been done for the efficient spectrum sharing, such as cooperative spectrum sharing to increase the spectrum utilization [11, 12], or game theory based methods to improve the fairness of spectrum sharing [13, 14]. However, all these methods inevitably require frequent exchange of the spectrum sensing reports among entities to obtain a convergence result. For practical applications, they would cost considerable network resource (including spectrum resource and time), which is not acceptable in IWSNs due to strict timeliness requirement. Contention based spectrum access is an effective way for small-scale IWSNs, which provides fast spectrum access. However, for large-scale networks, without global knowledge of spectrum states and efficient coordination, the channels cannot be fairly used which may lead to the congestion on some certain channels while some others are relatively vacant. It has

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Walking Beam Furnaces

Reversing Rougher R1

Hot Metal Detector

Reversing Rougher R2

Pyrometer

Width Gauge

Crop Shear

Multi Function Gauge

Finishing Mill

Velocimeter

Laminar Cooling

PH Laser Sensor

Down Coilers

Vibration Transducer

Fig. 1. An illustration of hot strip milling process.

been demonstrated that contention based spectrum access in large-scale networks results in long spectrum accessing delay and low network throughput [15, 16]. This paper aims to develop a simple but effective way to improve the spectrum sharing by the inspiration from the collective behaviors in biological systems [17], such as line forming of the flying geese and vortices forming of the fish school. In the collective biological system, when one agent joins or leaves the formation, each agent in the system will autonomously adapt its behavior (such as adjustment of position, direction, and speed) according to the local observation of neighbor agents’ states, and thus the system motion sustains the consensus. Based on this observation, a concession based spectrum sharing scheme is proposed to approach the collective spectrum usage by sensors’ autonomous channel switching. Specifically, the concept of equilibrium of spectrum occupation is defined to show the best evenness of spectrum usage. A set of rules named Local EQuilibrium guided Autonomous Channel Switching (LEQ-AutoCS) are devised, with which each accessed sensor switches the channel autonomously based on the self-observation on limited spectrum range, thus to achieve the evenness of channel usage within this spectrum range. We have preliminarily studied the autonomous channel switching to improve the evenness of spectrum usage in [18]. In this work, we design the specific consoles for accessed sensors to conduct autonomous channel switching. The convergence of the equilibrium of the whole spectrum usage based on the proposed spectrum sharing scheme is proved. Finally, the improvement of utilization and fairness of spectrum usage are evaluated by simulations and experiments based on universal software radio peripheral (USRP) and PCI extensions for instrumentation (PXI) platform. We summarize the main contributions of this paper as follows: • First, inspired by the collective motion, we investigate that an evener spectrum usage facilitates to improve the spectrum sharing performance in IWSNs, such as spectrum access delay, utilization and fairness of spectrum usage. • Then, a new concept of equilibrium is defined to represent the achievable best evenness of spectrum usage. A set of rules called LEQ-AutoCS are devised for accessed sensors to approach the equilibrium by autonomous channel switching based on local sensing results, which avoid the exchange of spectrum sensing reports. • Finally, both theoretical and experimental results validate

that with LEQ-AutoCS rules, the equilibrium of spectrum usage is always achievable and thus the spectrum sharing performance criteria above are improved. The remainder of this paper is organized as follows. Section II gives a brief review on existing works. Section III presents the network model and performance criteria of spectrum sharing. In Section IV, the so-called LEQ-AutoCS rules are proposed. Theoretical analysis on the network performance based on the proposed rules is presented in Section V. In Section VI, numerical and experiment results are presented. Conclusion and future works are given in Section VII. II. R ELATED W ORKS As the proliferation of wireless sensor networks in industrial applications, three standardized protocols have been developed for efficient coordination of IWSNs, i.e., WirelessHART [8], ISA100.11a [9], and WIA-PA [10]. Based on IEEE 802.15.4 standard, the existing standardized protocols implement the spectrum sharing by the design of superframe. In the superframe, the slotted channels are allocated to network devices in reservation manner. Then the network devices transmit or receive the data packets under the superframe repeatedly. For example, the superframe scheduler in WirelessHART protocol allocates the guaranteed time slots (GTS) to network devices. The protocol of ISA100.11a introduces the slotted channel hopping mechanism to enhance the communication robustness in the interfered radio environment. Similar spectrum sharing mechanism is used in WIA-PA. In order to improve the transmission reliability, redundant transmission scheme is executed to the reservation based scheduling, which can decrease the spectrum utilization. In addition, to adapt to the network dynamics (e.g., spectrum dynamics and data traffic dynamics), the superframe scheduler has to update the superframe design frequently. It is time-consuming for largescale IWSNs. Motivated by the strong demand and tremendous trend of industrial wireless networking, how to enable the high spectrum utilization in a scalable and cost-effective manner is therefore a key research issue for the development of IWSN. In order to adapt to spectrum dynamics and improve the spectrum sharing efficiency, many distributed spectrum sharing approaches have been proposed, either in the contention based manner or the cooperative manner. In [19, 20], different carrier sense multiple access (CSMA) based opportunistic spectrum sharing schemes are devised using the round-robin or random spectrum sensing and access approach. However, the authors

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III. IWSN M ODEL AND P ROBLEM F ORMULATION Order Management

Plant Network Industry Ethernet Control Network

Running Control Field Bus

Field Network AP

FieldNet

Sensor

Fig. 2. Three-layer topology of industrial wireless sensor networks.

in [15, 16] have proved that for large-scale network, the CSMA based channel access would bring in seriously collision among the new spectrum access requests, which results in low transmission probability. As a result, the performances in terms of spectrum access delay, network throughput and spectrum utilization are all low. The cooperative manner is considered to be more efficient for spectrum sharing since different network utilities can be achieved by the cooperation. The spectrum utilization of network and the fairness of sensors’ resource allocation are considered in [11, 12, 14]. The authors in [21–23] considered the fair spectrum sharing with varying traffics of sensors. In [13], a distributed game based channel allocation algorithm is proposed for spectrum sharing, which leads negotiations among the sensors and finally reaches to a Nash Equilibrium. The authors in [24, 25] propose a flexible and fast channel access scheme based on multi-agent imitation in mobile WSN. In [26], a biologically-inspired spectrum sharing algorithm is adopted to model the local cooperative spectrum sensing for wireless sensor networks to facilitate the dynamic resource allocation, and a swarming mechanism is devised for collision avoidance and spatial reuse of spectrum resource. However, this spectrum sharing algorithm requires that each sensor has the knowledge of neighboring sensors’ observation on channel states. All the aforementioned distributed cooperative algorithms require sensors to exchange spectrum sensing reports iteratively till a consensus is achieved. By using these algorithms, the exchange of spectrum sensing reports among the sensors occupies considerable spectrum and time resource, which inevitably decreases the spectrum efficiency. Moreover, the iteration process is also time-consuming, which may result in long access delay and thus is not applicable for the timeliness requirement in industrial applications. Therefore, for large-scale IWSNs, a good spectrum sharing method should promote the spectrum utilization, improve the fairness of spectrum usage, decrease the spectrum access delay, and also be easy to implement with low overhead.

In this work, we select the hot strip mill process monitoring in BaoSteel, Shanghai, China as our application scenario. As shown in Fig. 1, the milling process consists of several process sections, such as reversing roughers, finishing mill, laminar cooling, and down coiler. We design a three-layer network as shown in Fig. 2 to cater to the hot rolling production line. Specifically, the plant network is in charge of the configuration and management of production. The control network is responsible for the process control with the monitoring data from field network. In the field network, a large amount of sensors are deployed to perceive the production process and transmit the reports to the upper layers. As multiple process sections of the production line are naturally laid out one by one in the plant, we group the sensors around one section into a clustered subnetwork named FieldNet as shown in Fig. 2. For each FieldNet, one access point (AP) is employed to collect the data packets from the sensors. In this paper, we focus on the spectrum sharing problem of the FieldNet. A. Network model Suppose that the FieldNet is time slotted and synchronized. The spectrum is divided into M non-overlapping orthogonal channels with equal bandwidth, i.e., {Cm }, m = 1, 2, ..., M with the order from the lowest frequency channel to the highest one. Without ambiguity, let Cm (t) = 0 represent the idle state and Cm (t) = 1 represent the occupied state at the slot t, respectively. The symbol t is omitted for simplicity for the analysis within one slot in the following. The AP is with multiple interfaces which covers the channels assigned to the network. The sensors transmit data over single channel but can sense a number of consecutive channels. Without loss of generality, we assume that each sensor can simultaneously sense three consecutive channels. It is noted that the method to be proposed is easy to be extended to the scenarios of different sensing ranges. Here, each sensor always aligns the radio central frequency to the transmission channel’s central frequency. Hence, one sensor transmitting on channel Cm can sense the states of channels {Cm−1 , Cm , Cm+1 }. If it switches its transmission channel to Cm+1 , its sensing channels become {Cm , Cm+1 , Cm+2 }. Sensors work on event-driven manner. If one sensor has data to transmit, it enters to the accessing state to wait and seek one idle channel for transmission. After it has successfully accessed a channel, it switches to the accessed state. At the accessed state, the sensor also will sense the local spectrum and can switch channel according to some proper rules which are to be determined in this paper. B. Performance criteria Compared to other applications of wireless sensor networks, IWSNs have higher requirements in terms of network throughput, channel access delay, network scalability, etc [1, 2]. However, the limited radio spectrum resource in industry fields makes the IWSNs more challenging to improve the network

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performance while wireless devices are boosting. Therefore, the spectrum sharing scheme in IWSNs vitally concerns the network performance. In this work, we investigate that an evener spectrum usage normally facilitates the traffic load balance over the channels and avoids the local congestion of spectrum access, thus decreases the channel access delay and improves the utilization and fairness of spectrum usage. We aim to increase the spectrum sharing efficiency by improving the evenness of spectrum usage. Hence, the following three criteria are considered, i.e., spectrum access probability of accessing sensors, spectrum utilization, and fairness, where a higher spectrum access probability means faster spectrum access for accessing sensors. Assume that an accessing sensor randomly set a central channel Cm (2 ≤ m ≤ M − 1) with probability M1−2 , and scans the spectrum range {Cm−1 , Cm , Cm+1 }. Obviously, the accessing sensor will successfully access a channel only if not all the three channels’ states are equal to 1. Therefore, the spectrum access probability Pa for the accessing sensor is defined as ∆

Pa = 1 −

M −1 X 1 Cm−1 Cm Cm+1 . M − 2 m=2

(1)

We quantify the utilization and fairness of spectrum usage from the viewpoint of statistics over T time slots. First, we define the channel utilization of Cm as the ratio of occupation time over T time slots, i.e., ∆

Um =

T 1X Cm (t), m = 1, 2, . . . , M. T t=1

(2)

Then, the system utilization of the all channels is M 1 X U= Um . M m=1 ∆

(3)

To evaluate the fairness of channels’ usage, the Jain’s fairness [27] is exploited: PM 2 ∆ ( m=1 Um ) Uf = . (4) PM 2 M m=1 Um This metric identifies underutilized channels. Note that the 1 (worst fairness) to result of Jain’s fairness ranges from M 1 (best fairness). When only one channel is used, it results the worst fairness, and when the channels are used equally, it achieves best fairness. The objective of this paper is to explore the explicit relationship between the evenness of spectrum usage and the spectrum sharing performances mentioned above, and further to propose the autonomous channel switching rules to achieve the evenness of spectrum usage. IV. L OCAL EQUILIBRIUM GUIDED AUTONOMOUS CHANNEL SWITCHING RULES (LEQ-AUTO CS) In this section, the details of LEQ-AutoCS rules are presented. Note that the collective motion in biological systems can be achieved by agents’ autonomous actions with local information. In such systems, each collective individual in the

system autonomously adjusts its own dynamics to coordinate itself with the neighbors within its scope of observation and avoids collisions with them. In this way, the whole system exhibits a dynamic formation. Reconsidering the spectrum sharing problem from the perspective of collective motion, we regard the accessed sensors as agents and the desired collective motion as the optimal evenness of channels’ occupation. When the collective motion reaches the optimum, the occupied channels are evenly distributed in the given spectrum range. Considering discretely channelized spectrum and channel sensing model, we give a definition of equilibrium to demonstrate the optimal evenness of spectrum usage in the following. Definition 1 (Equilibrium): Suppose that N of M channels are occupied by the sensors. The equilibrium of spectrum usage is defined as the state which satisfies any of the following two conditions: 1) for N ≤ dM/2e, there do not exist any two neighboring occupied channels, or 2) for N > dM/2e, there do not exist any two neighboring free channels and both C1 and CM are occupied. Remark 1: The equilibrium may not be unique. It represents the state with optimal evenness of spectrum usage. For example, when M = 7 and N = 4, the equilibrium of spectrum usage is unique, i.e., {1, 0, 1, 0, 1, 0, 1}. But when N = 5, there are more than one channel occupation states achieving the equilibrium, such as {1, 1, 1, 0, 1, 0, 1} and {1, 0, 1, 1, 1, 0, 1}, according to Definition 1. According to the definition of equilibrium, we concern the spectrum usage of individual sensors within its sensing range (three channels), and present the definition of local equilibrium of spectrum usage as follows. Definition 2 (Local equilibrium): Within the sensing range {Cm−1 , Cm , Cm+1 }, we have the following statement: 1) if no more than one channel is occupied, any occupation state is the local equilibrium; 2) if two channels are occupied, the local equilibrium is unique, i.e., {1, 0, 1}; 3) if all the three channels are occupied, i.e., {1, 1, 1}, the local equilibrium is also achieved. The key point of autonomous switching rules is to enable each sensor to achieve the local equilibrium of spectrum usage, thus to achieve the equilibrium of the whole spectrum range. In the following, we aim to propose a concession based spectrum sharing scheme for the accessed sensors to switch channels autonomously. We first define three consoles, and then present the so-called LEQ-AutoCS rules. 1) Potential Indicator. The concept of potential is borrowed from collective motion in biological systems [17]. It describes the relationship between the accessed sensor sn using channel Cm and its neighboring sensors in the sensing frequency range. Specifically,  0, Cm−1 = 0, ∆ Elm = (5) 1, Cm−1 = 1,  0, Cm+1 = 0, r ∆ Em = (6) −1, Cm+1 = 1, ∆

Evm = Elm + Erm ,

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where Elm represents the potential from the neighboring sensor at lower channel Cm−1 to the sensor sn at Cm , which propels the sensor sn to switch to the channel Cm+1 . Erm has the similar effect but with opposite direction from Cm+1 to Cm . Specially, define El1 = 0 and ErM = 0. Evm represents the aggregated potential of sensor sn . 2) Time Regulator. This console is to avoid the collisions which may be caused by both accessing and accessed sensors trying to access the same channel simultaneously. As shown in Fig. 3, a time fraction at the beginning of each slot is set to regulate the sensors’ actions, which is divided into three subslots with equal length ts , 0 < ts  1. The accessing sensor accesses channel and accessed sensor departs from channel within (t, t+ts ). The accessed sensor switches to higher neighboring channel within (t+ts , t+2ts ). The accessed sensor switches to lower neighboring channel within (t+2ts , t+3ts ). This time regulator not only grants the priority to accessing sensors for acquiring the free channels, but also guarantees that there are no collisions among the accessing and accessed sensors. 3) Switching Controller. This console is to control the pace of channel switching and prevent sensors from pingpong switching. Let vm = 0 represent the case that sn on channel Cm did not switch at the last time slot, and vm = 1 represent the case it switched from other channel at the last slot. For vm = 1, the accessed sensor sn on channel Cm is not permitted to switch channel at this slot. Based on the three consoles, each accessed sensor is allowed to adjust the transmission channel according to the sensing result and equalize the distribution of channels usage among its sensing range, to reach the local equilibrium of spectrum usage. The LEQ-AutoCS rules are given as follows:

𝐴𝐴𝑚𝑚−1,𝑚𝑚 𝐴𝐴𝑚𝑚+1,𝑚𝑚

𝐴𝐴𝑜𝑜,𝑚𝑚 𝑡𝑡

𝐷𝐷𝑚𝑚,𝑜𝑜

𝑡𝑡 + 𝑡𝑡𝑠𝑠

𝑡𝑡 + 2𝑡𝑡𝑠𝑠

𝐷𝐷𝑚𝑚,𝑚𝑚+1

𝑡𝑡 + 3𝑡𝑡𝑠𝑠

𝐷𝐷𝑚𝑚,𝑚𝑚−1

𝑡𝑡 + 1

Fig. 3. Time regulator for actions of sensors, where Am−1,m , Am+1,m , Dm,m+1 , and Dm,m−1 represent accessed sensors’ switching, and Ao,m and Dm,o represents accessing and departing sensors, respectively.

Case I

𝐶𝑚−1

𝐶𝑚

𝐶𝑚+1

… … Case II

𝐶𝑚−1

𝐶𝑚

… …

𝑡 + 𝑡𝑠 𝑡 + 2𝑡𝑠

… …

𝑡 + 2𝑡𝑠 𝑡 + 3𝑡𝑠

𝐶𝑚+1

… …

Fig. 4. Autonomous channel switching: case I, sensor sn switches from channel Cm to channel Cm−1 ; case II, sensor sn switches from channel Cm to channel Cm+1 .

illustration for rules of autonomous channel switching, where Case I and Case II in Fig. 4 correspond to I.b) and II.b) in the LEQ-AutoCS rules, respectively. It is worth noting that the rules can be extended to scenarios of different sensing ranges by set time regulator with different sub-slots to coordinate the sensors’ channel access and switching.

LEQ-AutoCS rules: V. P ERFORMANCE ANALYSIS Rule I: In sub-slot (t+ts , t+2ts ), a) If Evm = 0 or vm = 1, the sensor sn keeps on the incumbent channel Cm and set vm = 0, b) If Evm = −1 and vm = 0, the sensor sn switches to the channel Cm−1 , and set vm−1 = 1, Rule II: In sub-slot (t+2ts , t+3ts ), a) If Evm = 0 or vm = 1, the sensor sn keeps on the incumbent channel Cm and set vm = 0, b) If Evm = 1 and vm = 0, the sensor sn switches to the channel Cm+1 and set vm+1 = 1, Rule III: The sensor using channel C1 or CM does not switch at all circumstances.

For the case of Evm = 0, both of the neighboring channels of Cm are free or occupied simultaneously, which is at the equilibrium state according to Definition 2. The accessed sensor sn keeps on the incumbent channel in this case. For the cases of Evm = 1 or Evm = −1, local equilibrium of spectrum usage has not been achieved, and the accessed sensor sn is regulated to switch channel to reach the local equilibrium with the channels’ states of {1, 0, 1}. Fig. 4 presents a simple

In this section, the convergence of spectrum usage is discussed and then spectrum sharing performance is analyzed by the queueing network model. A. Convergence of the collective channel occupations under the LEQ-AutoCS rules We assume that N sensors are initially randomly distributed over M channels at the beginning, and there are no new accessing requests or departures. In the following, we show how LEQ-AutoCS rules facilitate to achieve the equilibrium of spectrum usage. First, we introduce the concept of absolute potential, which describes the potential on the systemic level. Definition 3 (Absolute Potential): For the accessed sensor sn at the channel Cm , its absolute potential is defined as  |Elm | + |Erm |, Cm = 1, ∆ Em = (8) 0, Cm = 0, and the absolute potential of the network system is defined as Esys =

M X

Em .

m=1

Then, we can obtain the following important properties.

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𝐂𝐂 0

𝐂𝐂1

𝑡𝑡 = 0

1 1 1 1 0 0 0 0

𝑡𝑡 = 1

1 1 1 0 1 0 0 0

𝑡𝑡 = 2

𝐂𝐂1

𝐂𝐂1

𝐂𝐂1

𝐂𝐂 0 𝐂𝐂 0

1 1 0 1 1 0 0 0

𝑡𝑡 = 3 1 0 1 1 0 1 0 0 𝑡𝑡 = 4 1 0 1 0 1 1 0 0

𝑡𝑡 = 5 1 0 1 0 1 0 1 0

Fig. 5. An example to illustrate the channel structures and their evolution.

Lemma 1: Esys is monotonically non-increasing under the LEQ-AutoCS rules. Proof: According to the time regulation of LEQ-AutoCS rules, channel switching occurs in sub-slot (t+ts , t+2ts ) or in sub-slot (t+2ts , t+3ts ). To be specific, in sub-slot (t+ts , t+2ts ), if the state of the channels {Cm−1 , Cm , Cm+1 } is {1, 1, 0} and vm = 0, then the sensor using Cm will switch to Cm+1 and the state of the three channels becomes {1, 0, 1}. According to definitions in (5), (6), and (8), the channel switching could cause the changing of potentials Em and Em+1 , and their neighboring potentials Em−1 and Em+2 . We consider the following two cases: 1) Cm+2 = 0. Both of Em−1 and Em decrease by 1 and both of Em+1 and Em+2 keep 0, then Esys decreases by 2; 2) Cm+2 = 1. Both of Em−1 and Em decrease by 1. On the contrary, both of Em+1 and Em+2 increase by 1, then Esys does not change, but 2 units of the potential transfer from {Cm−1 , Cm } to {Cm+1 , Cm+2 }. Hence, Esys is non-increasing. Similarly, we have the nonincreasing property of Esys in the sub-slot (t+2ts , t+3ts ). Therefore, with the LEQ-AutoCS rules, Esys is monotonically non-increasing. The proof is completed. The following theorem illustrates how the sensor’s collective occupation affects the spectrum usage. Theorem 1: With the LEQ-AutoCS rules, the spectrum usage state converges to the equilibrium. Moreover, the following results hold: (1) The convergence time to equilibrium is not longer than  2N − 3, N ≤ dM/2e, Tmax = (10) 2(M − N ) − 1, N > dM/2e. (2) At the equilibrium state, it yields that  0, N ≤ dM/2e, Esys = 4N − 2M − 2, N > dM/2e. (3) The spectrum access probability Pa satisfies that  Pa = 1, N ≤ dM/2e, 2(M −N ) 3(M −N ) ≤ P ≤ min{ , 1}, N > dM/2e. a M −2 M −2

(11)

(12) Proof: The proof consists of four steps as follows. First, the proof by contradiction is taken to demonstrate that the equilibrium is achievable. As the example shown in Fig. 5, if the system has not reached the equilibrium of spectrum usage, according to Definition 1, there coexist the structure of two or more consecutive occupied channels, noted as C1 , and

the structure of two or more consecutive free channels, noted as C0 , or C1 = 0 or CM = 0 in the case of N > dM/2e. On one hand, if C1 meets C0 , according to case 1) in the proof of Lemma 1, channel switching occurs, Esys decreases by 2, and both sizes of C1 and C0 decrease by 1, as channel switching from t = 0 to t = 1 shown in Fig. 5. On the other hand, if C1 and C0 coexist, they will meet eventually. Assuming that C1 and C0 are the closest pair but have not met yet, there must exist one or more consecutive structures [0, 1] between C1 and C0 . Then, as described by case 2) in the proof of Lemma 1, the potential will transit from low channels to high channels, so does the structure C1 , until the closest C1 and C0 meet and then both the sizes decrease by 1, as evolution from t = 1 to t = 2 shown in Fig. 5. Now, we can conclude that C1 and C0 cannot coexist as the system evolves. Similarly, we can prove that C1 = 0, CM = 0 and C1 will not coexist in the evolution under the LEQ-AutoCS rules. When the system is in such states, the equilibrium of spectrum usage is achieved, as defined in Definition 1. Second, in order to find the upper bound of the number of slots needed to achieve the equilibrium, we analyze the worst case in the following. According to the definition of Esys , it is easy to see that the maximum of Esys is only obtained in the cases where all N sensors are distributed one by one with Emax sys = 2N − 2. In such states, it takes the most steps for the sensors to achieve equilibrium. If N ≤ dM/2e, as the example of system evolution shown in Fig. 5, according to the proposed channel switching rules, it takes two slots for the sensor to make a channel switching towards to the spare frequency region. It can be concluded that the system would take Tmax = 2N −3 slots to reach the equilibrium that avoids any two neighboring channels occupied. On the other hand, if N > dM/2e, it can be concluded Tmax = 2(M − N ) − 1. Third, when the system is at the equilibrium state. It is easy to obtain Esys = 0 if N ≤ dM/2e, and Esys = 4N − 2M − 2 if N > dM/2e. Forth, we analyze Pa at the equilibrium state from the following two cases. 1) For N ≤ dM/2e, the equilibrium implies that any two neighboring channels will not be occupied simultaneously in the system. Thus, we have Cm−1 Cm Cm+1 = 0, ∀2 ≤ m ≤ M − 1, which indicates that the accessing sensor can find at least one free channel in its sensing range with probability 1. 2) For N > dM/2e, the equilibrium implies that there are not any two neighboring free channels and {C1 , CM } are occupied. As N channels are occupied, there are (M − N ) free channels. In the following, we analyze the worst and best cases for Pa , respectively. a) When there is only one occupied channel between any two adjacent free channels, the Pa for accessing sensor is mini−N ) mum, which is Pa = 2(M M −2 . b) When there are more than one occupied channel between any two adjacent free channels, the spectrum access probability for new accessing sensor is  2M  3(M −N ) the maximum, Pa = M −2 for N > 3 and Pa = 1 for M    3(M −N ) ≤ N ≤ 2M 2 3 . Hence, we have Pa = min{ M −2 , 1}. It thus completes the proof.

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𝑝1 𝜆1 𝜇1

𝜇

𝑝2

𝑝1,2 𝑝3,2

𝜆2 𝜇2 𝑝2,1 𝑝2,3

𝜇

𝑝3 𝜆3

𝑝𝑀

…

𝜇3

𝜇

𝜆𝑀 𝜇𝑀

𝜇

Fig. 6. Queueing network model of FieldNet with LEQ-AutoCS rules.

B. Performance evaluation of spectrum sharing In this subsection, the performance analysis of spectrum sharing with LEQ-AutoCS rules is presented to show the improvement of utilization and fairness of spectrum usage. For simplicity, each accessing sensor is set to wait and access on its initial channel fixedly. Then, we investigate how the accessed sensors work under the LEQ-AutoCS rules. Considering each channel as a queueing server with virtual waiting room of infinite length and sensors as customers, the system can be seen as a discrete time queueing network with multiple servers as shown in Fig. 6. This queueing network features that the customer will switch server driven by states of neighboring servers. The Bernoulli probability model is applied to model the arrival processes of accessing sensors on each channel. For example, at each time slot on channel Cm , there will be one accessing sensor arriving with probability pm , and with probability (1−pm ) there will be no arrival. The distribution of transmission time of all accessed sensors is in accordance with geometric distribution. At each slot, for each accessed sensor, it will depart the queueing network with probability µ, and with probability 1 − µ it will stay at least one additional time slot. Recalling the LEQ-AutoCS rules, whether an accessed sensor switches only depends on the current states of its neighboring channels. Hence, the network dynamics can be considered as a Markovian process. Denote λkm and µkm as the arrival and departure probability of channel Cm when its queue length is k (k ≥ 0). Since channel switching only occurs when the target channel is in idle state, it is impossible that more than one sensors arrive at this channel in one slot. Hence, we have λkm ∈ (0, 1) and µkm ∈ (0, 1). According to Theorem 2.3 in [28], each queueing process in the queueing network is irreducible and aperiodic and has unique stationary and limiting distribution. From the statistical perspective, let pm,m−1 and pm,m+1 represent the switching probabilities from Cm to Cm−1 and Cm+1 , respectively. When the queue length is 0, a sensor arriving at Cm can be an accessing sensor or the accessed sensor from the neighboring channel. When the queue length is larger than 0, a sensor arriving at Cm must be the new accessing sensor joining the queue. As for the departure, one sensor leaving Cm may leave the network after finishing transmission or switch to the neighboring channel. Therefore, at different states of queue length k, the arrival and departure probabilities λkm and

µkm of a sensor on Cm are λkm

 =

µkm =



pm + pm−1,m + pm+1,m , k = 0, pm , k ≥ 1,

(13)

0, µ + pm,m−1 + pm,m+1 ,

(14)

k = 0, k ≥ 1,

Denote Pm = (pi,j m ), i = 0, 1, 2, . . . , j = 0, 1, 2, . . . as the one-step matrix of transition probability of queueing process 0,1 (Markovian process) on Cm . Specifically, pm = λ0m µ ¯1m means the probability that the queue length transits from 0 0,0 to 1, where µ ¯1m = 1 − µ1m . Then pm = 1 − p0,1 m is the probability that the queue length still stays at 0 after one-step ¯ k µk transition. Similarly, pk,k+1 = λkm µ ¯k+1 and pk,k−1 =λ m m m m m are probabilities that the queue length transits from k to k + 1 ¯ k = 1 − λk and and k to k − 1, respectively, where λ m m k+1 k+1 k,k k,k+1 µ ¯m = 1 − µm . Then pm = 1 − pm − pk,k−1 is the m probability that queue length still stays at k after one-step transition. Hence, the one-step matrix of transition probability of queueing process on each channel can be obtained as 1 − λ0m µ ¯1m 1 1  ¯ =  λm µm 0

λ0m µ ¯1m 1 1 2 ¯ µ − λ1 µ 1−λ m m m ¯m .. .

 0 0  Pm . .. . (15) 0 1 k Denote Πm = [πm , πm , . . . , πm , . . . ] as the probability distribution of different queue lengthes of Cm at the steady state. We have the balance equation [28] as follows: 

0 λ1m µ ¯2m .. .

Π m Pm = Π m . P∞ k Normalizing (16) by k=0 πm = 1, we obtain 

k−1 Q

∞  X j=0  0 πm = 1 + k Q 

λjm (1

k=1

(1 −

−

−1 j+1 µm )    

λjm )µjm

(16)

,

(17)

j=1 k−1 Q k πm =

λjm (1 − µj+1 m )

j=0 k Q

0 πm ,

(1 −

k ≥ 1,

(18)

λjm )µjm

j=1

where m = 1, 2, . . . , M. Since the LEQ-AutoCS rules only concern whether the neighboring channels are idle or not, we + use πm to denote the probability that the channel is occupied. Substituting (13) and (14) into (17) and (18), we have 0 πm + πm



αm = 1 + γm 1 − αm 0 = 1 − πm ,

−1 ,

(19) (20)

where pm (1 − µ − pm,m−1 − pm,m+1 ) , (1 − pm )(µ + pm,m−1 + pm,m+1 ) pm + pm−1,m + pm+1,m = , pm

αm =

(21)

γm

(22)

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for all m = 1, 2, . . . , M. Then, according to the conditions defined in the LEQAutoCS rules, the switching probabilities at the steady state can be calculated as follows: + + 0 pm,m+1 = (1 − pm+1 )πm−1 πm πm+1 ,

(23)

0 + + pm,m−1 = (1 − pm−1 )πm−1 πm πm+1 .

(24)

Theoretically, we can substitute (19) and (20) to solve the equations of (23) and (24) to acquire pm,m+1 and pm,m−1 for all m ∈ {2, . . . , M − 1}. However, the order of equation will increase by each iteration, making the explicit solution intractable. Alternatively, we can use MATLAB to get the numerical solutions. The numerical examples are presented in the following section. Then, the performance metrics of spectrum sharing defined in (2)-(4) in Subsection III-B can be reformulated by the queueing network model, as shown in the following proposition. Proposition 1: The Um , U and Uf in the queueing network model can be reformulated as + Um = πm , M 1 X + π , M m=1 m PM + 2 ( m=1 πm ) Uf = . PM +2 M m=1 πm

U=

(25) (26) (27)

Proof: The proof is omitted since it is easy to obtain + , and the system the statistical utilization of each channel πm + utilization is the mean of {πm }, m = 1, 2, . . . , M . VI. E XPERIMENT RESULTS A. Experiment setup In this work, we focus on the spectrum sharing within the FieldNet as shown in Fig. 2. Hence, we build a prototype system of FieldNet based on USRPs and PXI platform to validate the effectiveness of the proposed LEQ-AutoCS rules. As shown in Fig. 7(a), the FieldNet consists of eight NI USRP 2921 devices (taken as sensors equipped with software-defined wireless transceiver) and a PXI extensions platform (taken as the AP). Fig. 7(b) shows the configuration of USRP. With WXB daughter board acting as duplex RF transceiver front-end, USRP receives RF signal and converts it to the baseband signal, then passes it to signal process module in LabVIEW. This module charges for spectrum sensing and decision making. Conversely, the signal process module generates the baseband signal to USRP together with RF transceiver configuration parameters including operating radio frequency, bandwidth of RF transceiver, and RF gain control. We set of 8 radio channels in the experiments is from 2.4GHz to 2.44GHz, with 5MHz bandwidth of each channel. Each USRP has 5MHz transmitting bandwidth and 15MHz receiving bandwidth, respectively. The PXI platform with 5663E vector signal analyzer works as the AP with 8 air interfaces, and it covers 40MHz bandwidth in the experiments. The transmission power of each USRP is 0dBm. Time slot is set to 50ms and sub-slot for channel switching is set to

AP

Sensors

Sensors

(a) Prototype system

TX

RX

WBX Daughter Board

DAC

Baseband signal modulation

ADC

Channel decision

Radio Frequency Configuration

USRP

LabVIEW (b) USRP configuration

Fig. 7. Experiment Platform.

5ms. The period of each experiment is 100, 000 time slots. An accessing sensor will give up the accessing after 10 tries. The departure probability is identical since that channels are homogeneous, and set µ = 0.125. We assume that the arrival probabilities of the channels, i.e., {pm }, m = 1, 2, · · · , 8, follow the Gauss distribution: 1 2 (m − M 1 2 − 2) exp (− ), 2 2σ 2πσ where variance σ is set to 0.5. Normalizing the maximal pm to 0.8µ, we obtain a set of values of {pm } = {0.0001, 0.0001, 0.0018, 0.1, 0.1, 0.0018, 0.0001, 0.0001}1 for the first case, where the sensors mainly arrive at channels C4 and C5 . Normalizing the maximal pm to 1.5µ, we set another set of {pm } = {0.0001, 0.0001, 0.0034, 0.1875, 0.1875, 0.0034, 0.0001, 0.0001} for the second case, where both p4 and p5 are larger than µ, implying that C4 and C5 are overloaded.

pm = √

B. LEQ-AutoCS rules vs. dynamic accessing based strategies We compare the proposed scheme with two existing dynamic channel accessing methods: round-robin method (RR) [19, 29], and pseudo random sequence based method (PR) [30]. With the round-robin method, accessing sensors perform spectrum sensing in a round-robin way from low frequency 1 In the analysis of queueing networks, the arrival probability p is set to 0 < p < 1. In order to make sense of the accessing sensor arrival model in queueing networks, here the p1 , p2 , p7 , p8 are chosen as a small positive number such as 0.0001.

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TABLE I S TATISTICS OF NUMBER OF CHANNEL SWITCHINGS . Swi. S12 S23 S34 S45 S56 S67 S78

Case I Num. Swi. 0 S21 93 S32 435 S43 2733 S54 5257 S65 3251 S76 1178 S87

Num. 1243 3397 3221 495 357 60 0

Swi. S12 S23 S34 S45 S56 S67 S78

Case Num. 0 553 2181 5420 9467 9125 4323

II Swi. S21 S32 S43 S54 S65 S76 S87

Num. 4871 9748 9887 1451 1335 403 0

TABLE II Case I Value Prob. 0 p2,1 0.0111 p3,2 0.0141 p4,3 0.0310 p5,4 0.0758 p6,5 0.0503 p7,6 0.0246 p8,7

Value 0.0243 0.0503 0.0758 0.0310 0.0141 0.0111 0

Prob. p1,2 p2,3 p3,4 p4,5 p5,6 p6,7 p7,8

Case Value 0 0.0180 0.0142 0.0332 0.1281 0.0806 0.0373

II Prob. p2,1 p3,2 p4,3 p5,4 p6,5 p7,6 p8,7

C8

C6

C7

C5

C6

C4

C5

C3

C4

C2

C3

C1

C2

-0.15 -0.15

T HEORETICAL CHANNEL SWITCHING PROBABILITIES . Prob. p1,2 p2,3 p3,4 p4,5 p5,6 p6,7 p7,8

C7

Value 0.0373 0.0806 0.1281 0.0332 0.0142 0.0180 0

channel to high frequency channel to search for available channels. With the pseudo random sequence based method, accessing sensors carry out spectrum sensing according to the predefined pseudo random sequence to search for available channels. Let ‘LS’ be short for LEQ-AutoCS rules and ‘NS’ represent the strategy without spectrum sharing. We investigate six scenarios with different spectrum sharing strategies: ‘NS’, ‘RR’, ‘PR’, ‘LS’, ‘RR+LS’ and ‘PR+LS’, where the latter two strategies adopt the LEQ-AutoCS rules together with ‘RR’ and ‘PR’ access control methods, respectively. In the experiments, the statistical numbers of channel switchings between the neighboring channels are provided in Table I, where Sij denotes the channel switching from Ci to Cj . The statistical analysis of channel switching probabilities is shown in Fig. 8. It can be seen that with LEQ-AutoCS rules, accessed sensors are capable of switching from high crowded channels to relatively sparse ones. Specifically, on the lower channels C1 ∼ C4 , the channel switching probabilities from higher channels to lower ones are lager, and on the higher channels C5 ∼ C8 , the channel switching probabilities from lower channels to higher ones are lager. The theoretical channel switching probabilities are also presented in Table II. From the comparison result shown in Fig. 8, it can be seen that the channel switching probabilities from the experiments are basically consistent to the theoretical results. Then we evaluate metrics: channel utilization Um , system utilization U and Jain’s fairness Uf . The comparison results of channel utilization are shown in Fig. 9. From Fig. 9(a), it can be seen that in the scenarios ‘NS’, ‘RR’ and ‘PR’, we have similar channel utilization, and ‘LS’, ‘RR+LS’ and ‘PR+LS’ are similar in case I. However, in the scenarios with LEQAutoCS rules, the loads on different channels are effectively balanced and thus the channel utilization is more even. From Fig. 9(b), in case II when the arrival rate is increased, C4 and C5 are overloaded; but not surprisingly the LEQ-AutoCS rules effectively alleviate the overcrowded phenomenon by balancing channel utilization among M channels. The theo-

-0.1

-0.05

0 0

0.05

0.1

Theoretical

Theoretical

Experimental

Experimental

0.15 0.15

(a) Switching probability for case 1

C7

C8

C6

C7

C5

C6

C4

C5

C3

C4

C2

C3

C1

C2

-0.15 -0.15

-0.1

-0.05

0 0

0.05

0.1

Theoretical

Theoretical

Experimental

Experimental

0.15 0.15

(b) Switching probability for case 2 Fig. 8. Experiments statistics of switching probability.

retical results according to calculation in equation (25) are also showed by the dash lines noted by ‘Theo’. Note that in the theoretical analysis, only the channel switching of accessed sensors with LEQ-autoCS rules is considered; each accessing sensor is set to wait and access on its initial channel fixedly. Hence, the results show that the ‘Theo’ lines for both cases are not as even as the lines of ‘LS’, ‘RR+LS’ and ‘PR+LS’. However, ‘Theo’ lines indicate that even in such scenario, the LEQ-autoCS rules achieve more even channel utilization than the scenarios without them. Fig. 10 shows the statistics of utilization and fairness of spectrum usage. For case I, the system utilization is similar for different scenarios because there are few lost packets. However, as sensors mainly arrive at channels C4 and C5 , the strategies ‘NS’, ‘RR’ and ‘PR’ cannot rapidly response to the traffic loads, which results in low fairness. On the other hand, the strategies with ‘LS’ achieve high fairness of channel usage by autonomous channel switching. As the arrival rates increase in case II, the system utilization of ‘NS’ is obviously

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Utilization of each channel

1

NS RR PR LS RR+LS PR+LS Theo

0.8 0.6 0.4 0.2 0 1

5

4

3

2

Channel

7

6

Utilization of each channel

0.6

RR PR LS RR+LS PR+LS

0.4 0.2

Fairness NS RR PR LS RR+LS PR_LS CASE I

0 1

5

4

3

2

Channel

7

6

8

CASE II (a) System utilization

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

NS RR PR LS RR+LS PR+LS Theo

0.8

NS

CASE I

8

(a) Channel utilization of case I

1

Utilization

0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0

CASE II

(b) Fairness of spectrum usage Fig. 10. System utilization and fairness of spectrum usage of six scenarios for both cases.

(b) Channel utilization of case II Fig. 9. Channel utilization of six scenarios for both cases. TABLE III FAILED ACCESSES WITH DIFFERENT STRATEGIES . Case I Case II

NS 218 3025

RR 0 27

PR 0 43

LS 0 16

RR+LS 0 16

PR+LS 0 10

TABLE IV M EAN ACCESS DELAY OF SENSORS WITH DIFFERENT STRATEGIES . Case I Case II

NS 0.50 2.40

RR 0.09 0.33

PR 0.11 0.39

LS 0.02 0.16

RR+LS 0.01 0.11

PR+LS 0.01 0.11

lower than other strategies. With other spectrum sharing strategies, the congestion is alleviated. Different scenarios lead to different fairness of spectrum usage. The best performance can be achieved when ‘LS’ works together with ‘RR’ or ‘PR’. Fig. 11 shows the distribution of the waiting time on the channels. Both cases confront with unbalanced distribution of the waiting time due to the different loads on different channels. Especially for case II, the waiting time for channels

C4 and C5 are even extremely large as the both channels are overloaded. However, with the spectrum sharing strategies, the traffic loads can be balanced. Then, the waiting time is effectively reduced and its distribution becomes more even. It also can be seen that the LEQ-AutoCS rules perform better than ‘RR’ and ‘PR’, and the best efforts can be obtained by ‘LS+RR’ and ‘LS+PR’. Intuitively, congestion on specific channels would result in low channel access probability. In the following, we evaluate the failed accesses and the mean waiting time of sensors. The results are listed in the Table III and Table IV. There are lots of failed accesses in the ‘NS’ since the congestion occurs. With LEQ-AutoCS rules, the congestion is relieved and the failed accesses are greatly reduced for both cases (for case I, the failed access is perfectly avoided). This implies that LEQ-AutoCS rules provide a higher spectrum access probability for sensors. Although ‘RR’ and ‘PR’ can also effectively reduce the failed accesses, the LEQ-AutoCS rules bring lower mean waiting delay for sensors as shown in Table IV. With the LEQ-AutoCS rules, the mean waiting delay of sensors is lower than 1/2 of the delay based on ‘RR’ and ‘PR’, since the LEQ-AutoCS rules promote the evener channels’ usage and provide lager channel access

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TABLE V M EAN WAITING TIME OF SENSORS ON EACH CHANNEL .

Waiting time on each channel

6000

NS RR PR LS RR+LS PR+LS

5000 4000 3000

Case I: LS TDMA Case II: LS TDMA

2000 1000 0 1

3

2

4

5

Channel

6

7

8

(a) Waiting time of case I

Waiting time on each channel

10000

NS RR PR LS RR+LS PR+LS

8000 6000 4000 2000

C1 0.05 3.85

C2 0.04 3.62

C3 0.03 3.73

C4 0.01 4.14

C5 0.02 3.90

C6 0.01 3.76

C7 0.02 3.90

C8 0.06 3.69

Ave. 0.03 3.82

C1 0.23 6.63

C2 0.11 6.27

C3 0.08 6.29

C4 0.06 6.79

C5 0.07 6.88

C6 0.07 6.49

C7 0.09 6.45

C8 0.33 6.34

Ave. 0.13 6.51

random process. In this experiment, we have two sensors on each channel. The total rates of all sensors are 0.20 for Case I and 0.38 for Case II, respectively. The packet number of each transmission, i.e., 1/µ, is fixed to 8. Under these settings, we observe the spectrum access delay of the two spectrum sharing strategies. The statistical results are presented in Table. V. The spectrum sharing by LEQ-AutoCS rules achieves a much lower mean access delay than that by TDMA reservation based strategy. Particularly, with LEQ-AutoCS rules, the average delay of all sensors (noted by ‘Ave.’ in Table. V) is lower than 1/50 of that by TDMA reservation based strategy. This is because the TMDA reservation based spectrum access is normally suitable to the periodic data delivery. As for the case of random data delivery, it is inadequate to quickly response to the random arrival of transmission task by the TDMA strategy, as the GTSs are scheduled periodically and statically. Hence, the LEQ-AutoCS rules outperform the TMDA reservation based strategy on the performance of spectrum access delay. D. Discussion for the scenarios with interference

0 1

2

3

4

5

Channel

6

7

8

(b) Waiting time of case II Fig. 11. Waiting time of six scenarios for both cases.

probability. In summary, the LEQ-AutoCS rules can be applied to improve the spectrum utilization, fairness of spectrum usage and the spectrum access probability. Moreover, the proposed rules are compatible with other accessing control based schemes to further improve the performance. C. LEQ-AutoCS rules vs. TDMA reservation based strategy In this subsection, the comparison between LEQ-AutoCS rules and TDMA reservation based strategy for spectrum sharing is studied. The TDMA reservation based strategy employs contention free scheduling method as used in WirelessHART [8]. Specifically, each channel is allocated to the fixed sensors by designing a multi-channel superframe. The superframe consists of several periods named guaranteed time slots (GTS). The GTSs on one channel are scheduled to the sensors, considering their workloads. For simplicity, we set the arrival rate at each channel to be equal and the arrival of transmission tasks of each sensor is a independent Bernoulli

If there exists a wide-band interference, it would block the data transmissions and greatly decrease the performance of communications with different spectrum sharing methods. In this subsection, we investigate how LEQ-AutoCS rules work in the scenarios with narrow-band interference. For example, the interference signal exists on channel Cm , then transmissions set up on Cm will be blocked. Since the sensing range of each sensor covers 3 channels, the sensor on Cm−1 will observe that Cm is occupied, and so will sensor on Cm+1 do. They will not switch to Cm according to the rules. As a result, the channels are divided into two segments, C1 ∼ Cm−1 and Cm+1 ∼ CM . The sensors in each segment would approach to a new equilibrium of channels’ usage under the LEQAutoCS rules. With spectrum sensing ability, each sensor will autonomously avoid the interfered channel. But when the interference disappears, the channel will be reused. Then, the LEQ-AutoCS rules would promote the even usage of the whole spectrum and approach to the equilibrium. In other words, the LEQ-AutoCS rules can adapt to the scenarios with narrowband interference, where the interference is just considered as a stubborn user which does not switch channel. VII. C ONCLUSIONS An even-spectrum-usage targeted spectrum sharing scheme has been proposed for industrial wireless sensor networks so that the spectrum utilization and fairness of spectrum

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usage, and probability of spectrum access for new transmission requests can be improved compared to standardized industrial wireless protocols. The so-called LEQ-AutoCS rules have been devised for accessed sensors to autonomously switch channels by imitating the behavior of biological agents to achieve collective motion with only local observation and action. It has been demonstrated that the equilibrium of spectrum usage can be achieved under the LEQ-AutoCS rules. Moreover, the lower bound of spectrum access probability at the equilibrium and the upper bound of the convergence time to equilibrium have been derived as well. The proposed method provides an effective scaling way for large-scale industrial wireless applications with limited spectrum resource. The experiment results demonstrate the effectiveness of the proposed spectrum sharing scheme. In our future work, we will investigate the issue of autonomous channel switching design with the consideration of sensors’ imperfect sensing.

[15]

[16]

[17] [18]

[19]

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JIOT.2015.2490544, IEEE Internet of Things Journal 13

Feilong Lin received the B.Sc. degree in 2004 and the M.Sc. degree in 2007, both in electronic and information engineering from Xidian University, Xi’an, China. He is currently working towards the Ph.D. degree at the Department of Automation, Shanghai Jiao Tong University, Shanghai, China. His research interests include industrial wireless sensor networks, spectrum resource allocation, and multichannel transmission scheduling for industrial wireless applications.

Cailian Chen received the B.Eng. and M.Eng. degrees in automatic control from Yanshan University, China, in 2000 and 2002, respectively, and the Ph.D. degree in control and systems from City University of Hong Kong, Hong Kong SAR, China, in 2006. In 2008, she joined the Department of Automation, Shanghai Jiao Tong University, Shanghai, China, where she is a Full Professor. Dr. Chen’s current research interests include industrial wireless sensor and actuator network, Internet of Vehicles for ITS applications, and control and communication design for cyber-physical systems. She has authored and/or coauthored two research monograph and over 100 referred international journal and conference papers in these areas. Dr. Chen was one of the First Prize Winners of a Natural Science Award from the Ministry of Education of China in 2007. She was a recipient of the “IEEE Transactions on Fuzzy Systems Outstanding Paper Award” in 2008. She is on the editorial board of IEEE Transactions on Vehicular Technology and Peer-to-Peer Networking and Applications (Springer), and serves as a Track TPC co-chair of IEEE VTC 2016. Dr. Chen is a New Century Excellent Talent in University of China honored by Ministry of Education of China, “Pujiang Scholar” and “Young Scientific Rising Star” honored by Science and Technology Commission of Shanghai Municipal, China, and SMC Outstanding Young Faculty of Shanghai Jiao Tong University, China..

Ning Zhang received the Ph.D degree from University of Waterloo in 2015. He received his B.Sc. degree from Beijing Jiaotong University and the M.Sc. degree from Beijing University of Posts and Telecommunications, Beijing, China, in 2007 and 2010, respectively. His current research interests include dynamic spectrum access, 5G, physical layer security, and vehicular networks.

Xinping Guan received the Ph.D. degree in control and systems from Harbin Institute of Technology, Harbin, China in 1999. In 2007, he joined the Department of Automation, Shanghai Jiao Tong University, Shanghai, China, where he is currently a Chair Professor, the Deputy Director of University Research Management Office, the Director of the Key Laboratory of Systems Control and Information Processing, Ministry of Education of China, and the Leader of “Design, Control and Optimization of Network System” National Innovation Team. Before that, he was the Professor and Dean of Electrical Engineering, Yanshan University, China. Dr. Guan’s current research interests include cyber-physical systems, wireless networking and applications in smart city and smart factory, and underwater sensor networks. He has authored and/or coauthored 3 research monographs, more than 160 papers in IEEE Transactions and other peerreviewed journals, and numerous conference papers. As a Principal Investigator, he has finished/been working on many national key projects. He is the leader of the prestigious Innovative Research Team of the National Natural Science Foundation of China (NSFC). Dr. Guan is a Committee Member of the Chinese Automation Association Council and the Chinese Artificial Intelligence Association Council. He was on the editorial board of IEEE Trans. System, Man and Cybernetics-Part C and several Chinese journals. He also serves as an IPC/TPC member of a lot of conferences. He received the First Prize of Natural Science Award from the Ministry of Education of China in 2006 and the Second Prize of the National Natural Science Award of China in 2008. He was a recipient of the “IEEE Transactions on Fuzzy Systems Outstanding Paper Award” in 2008. He is a “National Outstanding Youth” honored by NSF of China, “Changjiang Scholar” by the Ministry of Education of China and “State-level Scholar” of “New Century Bai Qianwan Talent Program” of China.

Xuemin(Sherman) Shen received the B.Sc.(1982) degree from Dalian Maritime University (China) and the M.Sc. (1987) and Ph.D. degrees (1990) from Rutgers University, New Jersey (USA), all in electrical engineering. He is a Professor and University Research Chair, Department of Electrical and Computer Engineering, University of Waterloo, Canada. He was the Associate Chair for Graduate Studies from 2004 to 2008. Dr. Shen’s research focuses on resource management in interconnected wireless/wired networks, wireless network security, social networks, smart grid, and vehicular ad hoc and sensor networks. He is a co-author/editor of six books, and has published more than 600 papers and book chapters in wireless communications and networks, control and filtering. Dr. Shen served as the Technical Program Committee Chair/Co-Chair for IEEE Infocom’14, IEEE VTC’10 Fall, the Symposia Chair for IEEE ICC’10, the Tutorial Chair for IEEE VTC’11 Spring and IEEE ICC’08, the Technical Program Committee Chair for IEEE Globecom’07, the General Co-Chair for Chinacom’07 and QShine’06, the Chair for IEEE Communications Society Technical Committee on Wireless Communications, and P2P Communications and Networking. He also serves/served as the Editor-in-Chief for IEEE Network, Peer-to-Peer Networking and Application, and IET Communications; a Founding Area Editor for IEEE Transactions on Wireless Communications; an Associate Editor for IEEE Transactions on Vehicular Technology, Computer Networks, and ACM/Wireless Networks, etc.; and the Guest Editor for IEEE JSAC, IEEE Wireless Communications, IEEE Communications Magazine, and ACM Mobile Networks and Applications, etc. Dr. Shen received the Excellent Graduate Supervision Award in 2006, and the Outstanding Performance Award in 2004, 2007 and 2010 from the University of Waterloo, the Premier’s Research Excellence Award (PREA) in 2003 from the Province of Ontario, Canada, and the Distinguished Performance Award in 2002 and 2007 from the Faculty of Engineering, University of Waterloo. Dr. Shen is a registered Professional Engineer of Ontario, Canada, an IEEE Fellow, an Engineering Institute of Canada Fellow, a Canadian Academy of Engineering Fellow, and a Distinguished Lecturer of IEEE Vehicular Technology Society and Communications Society.

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