autonomous channel switching: towards efﬁcient...

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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: DOI10.1109/JIOT.2015.2490544, IEEE Internet of Things Journal

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Autonomous Channel Switching: Towards EfficientSpectrum Sharing for Industrial Wireless Sensor

NetworksFeilong 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) arecommitted to bring the industry automation into the era ofIndustry 4.0 by providing the ubiquitous perception to improvethe production efficiency. However, the proliferation of wirelessdevices in industrial applications makes the spectrum sharing inlimited ISM (Industrial, Scientific, and Medical) band a chal-lenging problem. In this paper, it is concerned with the intrinsicimpact of the evenness of spectrum usage on the spectrumsharing performance in terms of channel accessing probability,spectrum utilization, and fairness of spectrum usage. In orderto explore the explicit relationship between the evenness andspectrum sharing performance, a new concept of equilibrium isfirst defined to represent the achievable best evenness of spectrumusage. Then, a set of rules called Local EQuilibrium guidedAutonomous Channel Switching (LEQ-AutoCS) are devised, withwhich each accessed sensor autonomously equalizes the localchannel occupations within its range of spectrum sensing withoutoverhead on exchanging the sensors’ spectrum sensing reports.It is further proved that the equilibrium can be achieved bythis concessive manner. Theoretical analysis and experimentsresults demonstrate that the proposed LEQ-AutoCS rules providehigher utilization and fairness of spectrum usage comparing tothe existing spectrum access approaches. Moreover, it is shownthat LEQ-AutoCS rules assist the system to reduce the spectrumaccess delay to 1/2 of CSMA based systems and 1/50 of TDMAbased systems, respectively.

Index Terms—Industrial wireless sensor networks, spectrumsharing, autonomous channel switching, equilibrium

I. INTRODUCTION

The development of wireless sensor networks in the lastdecades is bringing the Internet of Things (IoT) to the world,which promotes the industry automation entering the ear ofIndustry 4.0. Industrial wireless sensor networks (IWSNs), asthe fundamental element for the realization of IoT in industry,are endowed with the advantages in terms of rapid deploy-ment, 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; acceptedSeptember 28, 2015. This work was supported in part by NSF of Chinaunder the grants 61221003, U1405251, 61371085, 61431008, 61290322 and61273181, 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, ShanghaiJiao Tong University, and Key Laboratory of System Control and InformationProcessing, 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 ComputerEngineering, 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 improvementof productivity and efficiency by using IWSNs [4, 5]. Takingthe hot strip mill of Bao Steel, Shanghai, China shown in Fig. 1as an example, hundreds of sensors are deployed to monitordifferent milling processes including reversing roughers R1and R2, finishing mill, laminar cooling, and down coiler. Inorder to guarantee the quality of alloy steel, hundreds ofsensors can be deployed to monitor the milling process topercept the strip temperature, thickness, milling pressure, andother process data to acquire the precise mathematic modeland improve the precision of process control [6]. IWSNs canalso provide a dedicated temperature evolution monitoring tosupport flexible milling [7]. For the general application ofequipment health monitoring, IWSNs can work continuouslyto reduce the unexpected downtime. It is foreseeable that inthe very near future IWSNs would become a standard featureof smart factory in the era of Industry 4.0.

However, the ever-increasing wireless communication de-mands necessitate efficient spectrum sharing strategies toimprove spectrum efficiency of IWSN in limited ISM band.The existing standardized industrial wireless protocols, suchas WirelessHART [8], ISA100.11a [9], and WIA-PA [10], im-plement the spectrum sharing based on the superframe design.The slotted channels are periodically allocated to the wirelesssensors for data packet delivery, which are efficient for theperiodic data gathering in small-scale networks. To provideefficient spectrum sharing for event-driven data collection inlarge-scale networks, more flexible and powerful spectrumsharing strategies are expected. Recently, many works havebeen done for the efficient spectrum sharing, such as coop-erative spectrum sharing to increase the spectrum utilization[11, 12], or game theory based methods to improve the fairnessof spectrum sharing [13, 14]. However, all these methodsinevitably require frequent exchange of the spectrum sensingreports among entities to obtain a convergence result. Forpractical applications, they would cost considerable networkresource (including spectrum resource and time), which isnot acceptable in IWSNs due to strict timeliness requirement.Contention based spectrum access is an effective way forsmall-scale IWSNs, which provides fast spectrum access.However, for large-scale networks, without global knowledgeof spectrum states and efficient coordination, the channels can-not be fairly used which may lead to the congestion on somecertain channels while some others are relatively vacant. It has



2

Walking Beam Furnaces

Reversing Rougher R1

Reversing Rougher R2

Crop Shear Finishing Mill Laminar Cooling Down Coilers

Hot Metal Detector Pyrometer Width Gauge Multi Function Gauge Velocimeter PH Laser Sensor Vibration Transducer

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

been demonstrated that contention based spectrum access inlarge-scale networks results in long spectrum accessing delayand low network throughput [15, 16].

This paper aims to develop a simple but effective way toimprove the spectrum sharing by the inspiration from thecollective behaviors in biological systems [17], such as lineforming of the flying geese and vortices forming of the fishschool. In the collective biological system, when one agentjoins or leaves the formation, each agent in the system willautonomously adapt its behavior (such as adjustment of posi-tion, direction, and speed) according to the local observationof neighbor agents’ states, and thus the system motion sus-tains the consensus. Based on this observation, a concessionbased spectrum sharing scheme is proposed to approach thecollective spectrum usage by sensors’ autonomous channelswitching. Specifically, the concept of equilibrium of spectrumoccupation is defined to show the best evenness of spectrumusage. A set of rules named Local EQuilibrium guided Au-tonomous Channel Switching (LEQ-AutoCS) are devised, withwhich each accessed sensor switches the channel autonomous-ly based on the self-observation on limited spectrum range,thus to achieve the evenness of channel usage within thisspectrum range. We have preliminarily studied the autonomouschannel switching to improve the evenness of spectrum usagein [18]. In this work, we design the specific consoles foraccessed sensors to conduct autonomous channel switching.The convergence of the equilibrium of the whole spectrumusage based on the proposed spectrum sharing scheme isproved. Finally, the improvement of utilization and fairness ofspectrum usage are evaluated by simulations and experimentsbased on universal software radio peripheral (USRP) and PCIextensions for instrumentation (PXI) platform. We summarizethe main contributions of this paper as follows:• First, inspired by the collective motion, we investigate

that an evener spectrum usage facilitates to improve thespectrum sharing performance in IWSNs, such as spec-trum access delay, utilization and fairness of spectrumusage.

• Then, a new concept of equilibrium is defined to representthe achievable best evenness of spectrum usage. A set ofrules called LEQ-AutoCS are devised for accessed sen-sors to approach the equilibrium by autonomous channelswitching based on local sensing results, which avoid theexchange of spectrum sensing reports.

• Finally, both theoretical and experimental results validate

that with LEQ-AutoCS rules, the equilibrium of spectrumusage is always achievable and thus the spectrum sharingperformance criteria above are improved.

The remainder of this paper is organized as follows. SectionII gives a brief review on existing works. Section III presentsthe network model and performance criteria of spectrumsharing. In Section IV, the so-called LEQ-AutoCS rules areproposed. Theoretical analysis on the network performancebased on the proposed rules is presented in Section V. InSection VI, numerical and experiment results are presented.Conclusion and future works are given in Section VII.

II. RELATED WORKS

As the proliferation of wireless sensor networks in industrialapplications, three standardized protocols have been developedfor efficient coordination of IWSNs, i.e., WirelessHART [8],ISA100.11a [9], and WIA-PA [10]. Based on IEEE 802.15.4standard, the existing standardized protocols implement thespectrum sharing by the design of superframe. In the super-frame, the slotted channels are allocated to network devicesin reservation manner. Then the network devices transmit orreceive the data packets under the superframe repeatedly. Forexample, the superframe scheduler in WirelessHART protocolallocates the guaranteed time slots (GTS) to network devices.The protocol of ISA100.11a introduces the slotted channelhopping mechanism to enhance the communication robust-ness in the interfered radio environment. Similar spectrumsharing mechanism is used in WIA-PA. In order to improvethe transmission reliability, redundant transmission schemeis executed to the reservation based scheduling, which candecrease the spectrum utilization. In addition, to adapt tothe network dynamics (e.g., spectrum dynamics and datatraffic dynamics), the superframe scheduler has to update thesuperframe design frequently. It is time-consuming for large-scale IWSNs. Motivated by the strong demand and tremendoustrend of industrial wireless networking, how to enable the highspectrum utilization in a scalable and cost-effective manner istherefore a key research issue for the development of IWSN.

In order to adapt to spectrum dynamics and improve thespectrum sharing efficiency, many distributed spectrum sharingapproaches have been proposed, either in the contention basedmanner or the cooperative manner. In [19, 20], different carriersense multiple access (CSMA) based opportunistic spectrumsharing schemes are devised using the round-robin or randomspectrum sensing and access approach. However, the authors



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Plant Network

Control Network

Field Network

Industry Ethernet

Field Bus

Running Control

Order Management

FieldNet

Sensor

AP

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

in [15, 16] have proved that for large-scale network, theCSMA based channel access would bring in seriously collisionamong the new spectrum access requests, which results in lowtransmission probability. As a result, the performances in termsof spectrum access delay, network throughput and spectrumutilization are all low.

The cooperative manner is considered to be more efficientfor spectrum sharing since different network utilities canbe achieved by the cooperation. The spectrum utilization ofnetwork and the fairness of sensors’ resource allocation areconsidered in [11, 12, 14]. The authors in [21–23] consideredthe fair spectrum sharing with varying traffics of sensors. In[13], a distributed game based channel allocation algorithmis proposed for spectrum sharing, which leads negotiationsamong the sensors and finally reaches to a Nash Equilibrium.The authors in [24, 25] propose a flexible and fast channelaccess scheme based on multi-agent imitation in mobile WSN.In [26], a biologically-inspired spectrum sharing algorithm isadopted to model the local cooperative spectrum sensing forwireless sensor networks to facilitate the dynamic resourceallocation, and a swarming mechanism is devised for collisionavoidance and spatial reuse of spectrum resource. However,this spectrum sharing algorithm requires that each sensorhas the knowledge of neighboring sensors’ observation onchannel states. All the aforementioned distributed coopera-tive algorithms require sensors to exchange spectrum sensingreports iteratively till a consensus is achieved. By usingthese algorithms, the exchange of spectrum sensing reportsamong the sensors occupies considerable spectrum and timeresource, which inevitably decreases the spectrum efficiency.Moreover, the iteration process is also time-consuming, whichmay result in long access delay and thus is not applicable forthe timeliness requirement in industrial applications.

Therefore, for large-scale IWSNs, a good spectrum sharingmethod should promote the spectrum utilization, improve thefairness of spectrum usage, decrease the spectrum accessdelay, and also be easy to implement with low overhead.

III. IWSN MODEL AND PROBLEM FORMULATION

In this work, we select the hot strip mill process monitoringin BaoSteel, Shanghai, China as our application scenario. Asshown in Fig. 1, the milling process consists of several processsections, such as reversing roughers, finishing mill, laminarcooling, and down coiler. We design a three-layer network asshown in Fig. 2 to cater to the hot rolling production line.Specifically, the plant network is in charge of the configura-tion and management of production. The control network isresponsible for the process control with the monitoring datafrom field network. In the field network, a large amount ofsensors are deployed to perceive the production process andtransmit the reports to the upper layers. As multiple processsections of the production line are naturally laid out one by onein the plant, we group the sensors around one section into aclustered subnetwork named FieldNet as shown in Fig. 2. Foreach FieldNet, one access point (AP) is employed to collectthe data packets from the sensors. In this paper, we focus onthe 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 orthogonalchannels with equal bandwidth, i.e., {Cm},m = 1, 2, ...,Mwith the order from the lowest frequency channel to the highestone. Without ambiguity, let Cm(t) = 0 represent the idle stateand Cm(t) = 1 represent the occupied state at the slot t,respectively. The symbol t is omitted for simplicity for theanalysis within one slot in the following. The AP is withmultiple interfaces which covers the channels assigned to thenetwork.

The sensors transmit data over single channel but cansense a number of consecutive channels. Without loss ofgenerality, we assume that each sensor can simultaneouslysense three consecutive channels. It is noted that the methodto be proposed is easy to be extended to the scenarios ofdifferent sensing ranges. Here, each sensor always aligns theradio central frequency to the transmission channel’s centralfrequency. Hence, one sensor transmitting on channel Cm cansense the states of channels {Cm−1, Cm, Cm+1}. If it switchesits transmission channel to Cm+1, its sensing channels become{Cm, Cm+1, Cm+2}.

Sensors work on event-driven manner. If one sensor has datato transmit, it enters to the accessing state to wait and seekone idle channel for transmission. After it has successfullyaccessed a channel, it switches to the accessed state. At theaccessed state, the sensor also will sense the local spectrumand can switch channel according to some proper rules whichare 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 through-put, channel access delay, network scalability, etc [1, 2].However, the limited radio spectrum resource in industry fieldsmakes 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 thenetwork performance. In this work, we investigate that anevener spectrum usage normally facilitates the traffic loadbalance over the channels and avoids the local congestion ofspectrum access, thus decreases the channel access delay andimproves the utilization and fairness of spectrum usage. Weaim to increase the spectrum sharing efficiency by improvingthe evenness of spectrum usage. Hence, the following threecriteria are considered, i.e., spectrum access probability ofaccessing sensors, spectrum utilization, and fairness, wherea higher spectrum access probability means faster spectrumaccess for accessing sensors.

Assume that an accessing sensor randomly set a centralchannel Cm (2 ≤ m ≤ M − 1) with probability 1

M−2 , andscans the spectrum range {Cm−1, Cm, Cm+1}. Obviously, theaccessing sensor will successfully access a channel only ifnot all the three channels’ states are equal to 1. Therefore,the spectrum access probability Pa for the accessing sensor isdefined as

Pa∆= 1− 1

M − 2

M−1∑m=2

Cm−1CmCm+1. (1)

We quantify the utilization and fairness of spectrum usagefrom the viewpoint of statistics over T time slots. First, wedefine the channel utilization of Cm as the ratio of occupationtime over T time slots, i.e.,

Um∆=

1

T

T∑t=1

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

Then, the system utilization of the all channels is

U∆=

1

M

M∑m=1

Um. (3)

To evaluate the fairness of channels’ usage, the Jain’s fairness[27] is exploited:

Uf∆=

(∑M

m=1 Um)2

M∑M

m=1 U2m

. (4)

This metric identifies underutilized channels. Note that theresult of Jain’s fairness ranges from 1

M (worst fairness) to1 (best fairness). When only one channel is used, it resultsthe worst fairness, and when the channels are used equally, itachieves best fairness.

The objective of this paper is to explore the explicit re-lationship between the evenness of spectrum usage and thespectrum sharing performances mentioned above, and furtherto propose the autonomous channel switching rules to achievethe evenness of spectrum usage.

IV. LOCAL EQUILIBRIUM GUIDED AUTONOMOUSCHANNEL SWITCHING RULES (LEQ-AUTOCS)

In this section, the details of LEQ-AutoCS rules are pre-sented. Note that the collective motion in biological systemscan be achieved by agents’ autonomous actions with localinformation. In such systems, each collective individual in the

system autonomously adjusts its own dynamics to coordinateitself with the neighbors within its scope of observation andavoids collisions with them. In this way, the whole systemexhibits a dynamic formation. Reconsidering the spectrumsharing problem from the perspective of collective motion,we regard the accessed sensors as agents and the desiredcollective motion as the optimal evenness of channels’ oc-cupation. When the collective motion reaches the optimum,the occupied channels are evenly distributed in the givenspectrum range. Considering discretely channelized spectrumand channel sensing model, we give a definition of equilibriumto demonstrate the optimal evenness of spectrum usage in thefollowing.

Definition 1 (Equilibrium): Suppose that N of M channelsare occupied by the sensors. The equilibrium of spectrumusage is defined as the state which satisfies any of thefollowing two conditions:

1) for N ≤ dM/2e, there do not exist any two neighboringoccupied channels, or

2) for N > dM/2e, there do not exist any two neighboringfree channels and both C1 and CM are occupied.

Remark 1: The equilibrium may not be unique. It representsthe state with optimal evenness of spectrum usage. For exam-ple, when M = 7 and N = 4, the equilibrium of spectrum us-age is unique, i.e., {1, 0, 1, 0, 1, 0, 1}. But when N = 5, thereare more than one channel occupation states achieving theequilibrium, 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 thespectrum usage of individual sensors within its sensing range(three channels), and present the definition of local equilibriumof spectrum usage as follows.

Definition 2 (Local equilibrium): Within the sensing range{Cm−1, Cm, Cm+1}, we have the following statement: 1) ifno more than one channel is occupied, any occupation stateis the local equilibrium; 2) if two channels are occupied, thelocal equilibrium is unique, i.e., {1, 0, 1}; 3) if all the threechannels are occupied, i.e., {1, 1, 1}, the local equilibrium isalso achieved.

The key point of autonomous switching rules is to enableeach sensor to achieve the local equilibrium of spectrum usage,thus to achieve the equilibrium of the whole spectrum range. Inthe following, we aim to propose a concession based spectrumsharing scheme for the accessed sensors to switch channelsautonomously. We first define three consoles, and then presentthe so-called LEQ-AutoCS rules.

1) Potential Indicator. The concept of potential is borrowedfrom collective motion in biological systems [17]. It describesthe relationship between the accessed sensor sn using channelCm and its neighboring sensors in the sensing frequency range.Specifically,

Elm

∆=

{0, Cm−1 = 0,1, Cm−1 = 1,

(5)

Erm

∆=

{0, Cm+1 = 0,−1, Cm+1 = 1,

(6)

Evm

∆= El

m + Erm, (7)



5

where Elm represents the potential from the neighboring sensor

at lower channel Cm−1 to the sensor sn at Cm, which propelsthe sensor sn to switch to the channel Cm+1. Er

m has thesimilar effect but with opposite direction from Cm+1 to Cm.Specially, define El

1 = 0 and ErM = 0. Ev

m represents theaggregated potential of sensor sn.

2) Time Regulator. This console is to avoid the collisionswhich may be caused by both accessing and accessed sensorstrying to access the same channel simultaneously. As shownin Fig. 3, a time fraction at the beginning of each slot is set toregulate the sensors’ actions, which is divided into three sub-slots with equal length ts, 0 < ts � 1. The accessing sensoraccesses channel and accessed sensor departs from channelwithin (t, t+ts). The accessed sensor switches to higher neigh-boring channel within (t+ts, t+2ts). The accessed sensorswitches to lower neighboring channel within (t+2ts, t+3ts).This time regulator not only grants the priority to accessingsensors for acquiring the free channels, but also guaranteesthat there are no collisions among the accessing and accessedsensors.

3) Switching Controller. This console is to control thepace of channel switching and prevent sensors from ping-pong switching. Let vm = 0 represent the case that sn onchannel Cm did not switch at the last time slot, and vm = 1represent the case it switched from other channel at the lastslot. For vm = 1, the accessed sensor sn on channel Cm isnot permitted to switch channel at this slot.

Based on the three consoles, each accessed sensor is allowedto adjust the transmission channel according to the sensingresult and equalize the distribution of channels usage amongits sensing range, to reach the local equilibrium of spectrumusage. The LEQ-AutoCS rules are given as follows:

LEQ-AutoCS rules:

Rule I: In sub-slot (t+ts, t+2ts),a) If Ev

m = 0 or vm = 1, the sensor sn keeps onthe incumbent channel Cm and set vm = 0,

b) If Evm = −1 and vm = 0, the sensor sn switch-

es 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 Ev

m = 1 and vm = 0, the sensor sn switchesto the channel Cm+1 and set vm+1 = 1,

Rule III: The sensor using channel C1 or CM does not switchat all circumstances.

For the case of Evm = 0, both of the neighboring channels

of Cm are free or occupied simultaneously, which is at theequilibrium state according to Definition 2. The accessedsensor sn keeps on the incumbent channel in this case. Forthe cases of Ev

m = 1 or Evm = −1, local equilibrium of

spectrum usage has not been achieved, and the accessed sensorsn is regulated to switch channel to reach the local equilibriumwith the channels’ states of {1, 0, 1}. Fig. 4 presents a simple

𝐴𝐴𝑜𝑜,𝑚𝑚 𝐴𝐴𝑚𝑚−1,𝑚𝑚 𝐴𝐴𝑚𝑚+1,𝑚𝑚

𝑡𝑡 𝑡𝑡 + 𝑡𝑡𝑠𝑠 𝑡𝑡 + 2𝑡𝑡𝑠𝑠 𝑡𝑡 + 3𝑡𝑡𝑠𝑠 𝑡𝑡 + 1

𝐷𝐷𝑚𝑚,𝑜𝑜 𝐷𝐷𝑚𝑚,𝑚𝑚+1 𝐷𝐷𝑚𝑚,𝑚𝑚−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 II 𝐶𝑚−1 𝐶𝑚 𝐶𝑚+1

𝑡+2𝑡𝑠 𝑡+3𝑡𝑠

𝑡+𝑡𝑠 𝑡+2𝑡𝑠

… …

… …

Case I 𝐶𝑚−1 𝐶𝑚 𝐶𝑚+1

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

illustration for rules of autonomous channel switching, whereCase I and Case II in Fig. 4 correspond to I.b) and II.b) in theLEQ-AutoCS rules, respectively.

It is worth noting that the rules can be extended to sce-narios of different sensing ranges by set time regulator withdifferent sub-slots to coordinate the sensors’ channel accessand switching.

V. PERFORMANCE ANALYSIS

In this section, the convergence of spectrum usage is dis-cussed and then spectrum sharing performance is analyzed bythe queueing network model.

A. Convergence of the collective channel occupations underthe LEQ-AutoCS rules

We assume that N sensors are initially randomly distributedover M channels at the beginning, and there are no newaccessing requests or departures. In the following, we showhow LEQ-AutoCS rules facilitate to achieve the equilibriumof spectrum usage. First, we introduce the concept of absolutepotential, which describes the potential on the systemic level.

Definition 3 (Absolute Potential): For the accessed sensorsn at the channel Cm, its absolute potential is defined as

Em∆=

{|El

m|+ |Erm|, Cm = 1,

0, Cm = 0,(8)

and the absolute potential of the network system is defined as

Esys =

M∑m=1

Em. (9)

Then, we can obtain the following important properties.



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1 1 1 1 0 0 0 0

1 1 1 0 1 0 0 0

1 1 0 1 1 0 0 0

1 0 1 1 0 1 0 0

1 0 1 0 1 1 0 0

1 0 1 0 1 0 1 0

𝑡𝑡 = 0

𝑡𝑡 = 1

𝑡𝑡 = 2

𝑡𝑡 = 3

𝑡𝑡 = 4

𝑡𝑡 = 5

𝐂𝐂1 𝐂𝐂0

𝐂𝐂1

𝐂𝐂1 𝐂𝐂1

𝐂𝐂0

𝐂𝐂0

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

Lemma 1: Esys is monotonically non-increasing under theLEQ-AutoCS rules.

Proof: According to the time regulation of LEQ-AutoCSrules, 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 switchto Cm+1 and the state of the three channels becomes {1, 0, 1}.According to definitions in (5), (6), and (8), the channelswitching could cause the changing of potentials Em andEm+1, and their neighboring potentials Em−1 and Em+2. Weconsider the following two cases:

1) Cm+2 = 0. Both of Em−1 and Em decrease by 1 andboth 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. Onthe contrary, both of Em+1 and Em+2 increase by 1, thenEsys does not change, but 2 units of the potential transferfrom {Cm−1, Cm} to {Cm+1, Cm+2}.

Hence, Esys is non-increasing. Similarly, we have the non-increasing property of Esys in the sub-slot (t+2ts, t+3ts).Therefore, with the LEQ-AutoCS rules, Esys is monotonicallynon-increasing. The proof is completed.

The following theorem illustrates how the sensor’s collectiveoccupation affects the spectrum usage.

Theorem 1: With the LEQ-AutoCS rules, the spectrum us-age state converges to the equilibrium. Moreover, the followingresults hold:

(1) The convergence time to equilibrium is not longer than

Tmax =

{2N − 3, N ≤ dM/2e,2(M −N)− 1, N > dM/2e. (10)

(2) At the equilibrium state, it yields that

Esys =

{0, N ≤ dM/2e,4N − 2M − 2, N > dM/2e. (11)

(3) The spectrum access probability Pa satisfies that{Pa = 1, N ≤ dM/2e,2(M−N)M−2 ≤ Pa ≤ min{ 3(M−N)

M−2 , 1}, N > dM/2e.(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 spectrumusage, according to Definition 1, there coexist the structure oftwo or more consecutive occupied channels, noted as C1, and

the structure of two or more consecutive free channels, notedas C0, or C1 = 0 or CM = 0 in the case of N > dM/2e. Onone hand, if C1 meets C0, according to case 1) in the proof ofLemma 1, channel switching occurs, Esys decreases by 2, andboth sizes of C1 and C0 decrease by 1, as channel switchingfrom 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 mustexist one or more consecutive structures [0, 1] between C1 andC0. 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 meetand then both the sizes decrease by 1, as evolution from t = 1to t = 2 shown in Fig. 5. Now, we can conclude that C1 andC0 cannot coexist as the system evolves. Similarly, we canprove that C1 = 0, CM = 0 and C1 will not coexist in theevolution under the LEQ-AutoCS rules. When the system isin 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 ofslots needed to achieve the equilibrium, we analyze the worstcase in the following. According to the definition of Esys,it is easy to see that the maximum of Esys is only obtainedin the cases where all N sensors are distributed one by onewith Emax

sys = 2N − 2. In such states, it takes the most stepsfor the sensors to achieve equilibrium. If N ≤ dM/2e, as theexample of system evolution shown in Fig. 5, according tothe proposed channel switching rules, it takes two slots forthe sensor to make a channel switching towards to the sparefrequency region. It can be concluded that the system wouldtake Tmax = 2N−3 slots to reach the equilibrium that avoidsany two neighboring channels occupied. On the other hand, ifN > dM/2e, it can be concluded Tmax = 2(M −N)− 1.

Third, when the system is at the equilibrium state. It is easyto obtain Esys = 0 if N ≤ dM/2e, and Esys = 4N−2M−2if N > dM/2e.

Forth, we analyze Pa at the equilibrium state from thefollowing two cases. 1) For N ≤ dM/2e, the equilibri-um implies that any two neighboring channels will notbe occupied simultaneously in the system. Thus, we haveCm−1CmCm+1 = 0,∀2 ≤ m ≤M − 1, which indicates thatthe accessing sensor can find at least one free channel inits sensing range with probability 1. 2) For N > dM/2e, theequilibrium implies that there are not any two neighboringfree channels and {C1, CM} are occupied. As N channels areoccupied, 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 twoadjacent free channels, the Pa for accessing sensor is mini-mum, which is Pa = 2(M−N)

M−2 . b) When there are more thanone occupied channel between any two adjacent free channels,the spectrum access probability for new accessing sensor isthe maximum, Pa = 3(M−N)

M−2 for N >⌊

2M3

⌋and Pa = 1 for⌊

M2

⌋≤ N ≤

⌊2M3

⌋. Hence, we have Pa = min{ 3(M−N)

M−2 , 1}.

It thus completes the proof.



7

…

𝜇 𝜇 𝜇 𝜇

𝜇1 𝜇2 𝜇3 𝜇𝑀

𝜆1 𝜆2 𝜆3 𝜆𝑀

𝑝2,1 𝑝2,3

𝑝1,2 𝑝3,2 𝑝1 𝑝2 𝑝3 𝑝𝑀

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

B. Performance evaluation of spectrum sharing

In this subsection, the performance analysis of spectrumsharing with LEQ-AutoCS rules is presented to show theimprovement of utilization and fairness of spectrum usage.For simplicity, each accessing sensor is set to wait and accesson its initial channel fixedly. Then, we investigate how theaccessed sensors work under the LEQ-AutoCS rules.

Considering each channel as a queueing server with virtualwaiting room of infinite length and sensors as customers, thesystem can be seen as a discrete time queueing network withmultiple servers as shown in Fig. 6. This queueing networkfeatures that the customer will switch server driven by statesof neighboring servers.

The Bernoulli probability model is applied to model thearrival processes of accessing sensors on each channel. Forexample, at each time slot on channel Cm, there will beone accessing sensor arriving with probability pm, and withprobability (1−pm) there will be no arrival. The distribution oftransmission time of all accessed sensors is in accordance withgeometric distribution. At each slot, for each accessed sensor,it will depart the queueing network with probability µ, andwith probability 1− µ it will stay at least one additional timeslot. Recalling the LEQ-AutoCS rules, whether an accessedsensor switches only depends on the current states of itsneighboring channels. Hence, the network dynamics can beconsidered 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). Sincechannel switching only occurs when the target channel is inidle state, it is impossible that more than one sensors arriveat this channel in one slot. Hence, we have λkm ∈ (0, 1) andµkm ∈ (0, 1). According to Theorem 2.3 in [28], each queueing

process in the queueing network is irreducible and aperiodicand has unique stationary and limiting distribution. Fromthe statistical perspective, let pm,m−1 and pm,m+1 representthe switching probabilities from Cm to Cm−1 and Cm+1,respectively. When the queue length is 0, a sensor arrivingat Cm can be an accessing sensor or the accessed sensor fromthe neighboring channel. When the queue length is larger than0, a sensor arriving at Cm must be the new accessing sensorjoining the queue. As for the departure, one sensor leaving Cm

may leave the network after finishing transmission or switchto the neighboring channel. Therefore, at different states ofqueue length k, the arrival and departure probabilities λkm and

µkm of a sensor on Cm are

λkm =

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

(13)

µkm =

{0, k = 0,µ+ pm,m−1 + pm,m+1, k ≥ 1,

(14)

Denote Pm = (pi,jm ), i = 0, 1, 2, . . . , j = 0, 1, 2, . . . as theone-step matrix of transition probability of queueing process(Markovian process) on Cm. Specifically, p0,1

m = λ0mµ

1m

means the probability that the queue length transits from 0to 1, where µ1

m = 1 − µ1m. Then p0,0

m = 1 − p0,1m is the

probability that the queue length still stays at 0 after one-steptransition. Similarly, pk,k+1

m = λkmµk+1m and pk,k−1

m = λkmµkm

are probabilities that the queue length transits from k to k+ 1and k to k − 1, respectively, where λkm = 1 − λkm andµk+1m = 1 − µk+1

m . Then pk,km = 1 − pk,k+1m − pk,k−1

m is theprobability that queue length still stays at k after one-steptransition. Hence, the one-step matrix of transition probabilityof queueing process on each channel can be obtained as

Pm =

1− λ0mµ

1m λ0

mµ1m 0 0

λ1mµ

1m 1− λ1

mµ1m − λ1

mµ2m λ1

mµ2m 0

0. . . . . . . . .

.(15)

Denote Πm = [π0m, π

1m, . . . , π

km, . . . ] as the probability

distribution of different queue lengthes of Cm at the steadystate. We have the balance equation [28] as follows:

ΠmPm = Πm. (16)

Normalizing (16) by∑∞

k=0 πkm = 1, we obtain

π0m =

1 +

∞∑k=1

k−1∏j=0

λjm(1− µj+1m )

k∏j=1

(1− λjm)µjm

−1

, (17)

πkm =

k−1∏j=0

λjm(1− µj+1m )

k∏j=1

(1− λjm)µjm

π0m, k ≥ 1, (18)

where m = 1, 2, . . . ,M. Since the LEQ-AutoCS rules onlyconcern whether the neighboring channels are idle or not, weuse π+

m to denote the probability that the channel is occupied.Substituting (13) and (14) into (17) and (18), we have

π0m =

(1 + γm

αm

1− αm

)−1

, (19)

π+m = 1− π0

m, (20)

where

αm =pm(1− µ− pm,m−1 − pm,m+1)

(1− pm)(µ+ pm,m−1 + pm,m+1), (21)

γm =pm + pm−1,m + pm+1,m

pm, (22)



8

for all m = 1, 2, . . . ,M.Then, according to the conditions defined in the LEQ-

AutoCS rules, the switching probabilities at the steady statecan be calculated as follows:

pm,m+1 = (1− pm+1)π+m−1π

+mπ

0m+1, (23)

pm,m−1 = (1− pm−1)π0m−1π

+mπ

+m+1. (24)

Theoretically, we can substitute (19) and (20) to solve theequations of (23) and (24) to acquire pm,m+1 and pm,m−1

for all m ∈ {2, . . . ,M − 1}. However, the order of equationwill increase by each iteration, making the explicit solutionintractable. Alternatively, we can use MATLAB to get thenumerical solutions. The numerical examples are presentedin the following section. Then, the performance metrics ofspectrum sharing defined in (2)-(4) in Subsection III-B can bereformulated by the queueing network model, as shown in thefollowing proposition.

Proposition 1: The Um, U and Uf in the queueing networkmodel can be reformulated as

Um = π+m, (25)

U =1

M

M∑m=1

π+m, (26)

Uf =(∑M

m=1 π+m)2

M∑M

m=1 π+m

2 . (27)

Proof: The proof is omitted since it is easy to obtainthe statistical utilization of each channel π+

m, and the systemutilization is the mean of {π+

m},m = 1, 2, . . . ,M .

VI. EXPERIMENT RESULTS

A. Experiment setup

In this work, we focus on the spectrum sharing withinthe FieldNet as shown in Fig. 2. Hence, we build a proto-type system of FieldNet based on USRPs and PXI platformto validate the effectiveness of the proposed LEQ-AutoCSrules. As shown in Fig. 7(a), the FieldNet consists of eightNI USRP 2921 devices (taken as sensors equipped withsoftware-defined wireless transceiver) and a PXI extensionsplatform (taken as the AP). Fig. 7(b) shows the configurationof USRP. With WXB daughter board acting as duplex RFtransceiver front-end, USRP receives RF signal and convertsit to the baseband signal, then passes it to signal processmodule in LabVIEW. This module charges for spectrumsensing and decision making. Conversely, the signal processmodule generates the baseband signal to USRP together withRF transceiver configuration parameters including operatingradio frequency, bandwidth of RF transceiver, and RF gaincontrol. We set of 8 radio channels in the experiments isfrom 2.4GHz to 2.44GHz, with 5MHz bandwidth of eachchannel. Each USRP has 5MHz transmitting bandwidth and15MHz receiving bandwidth, respectively. The PXI platformwith 5663E vector signal analyzer works as the AP with 8 airinterfaces, and it covers 40MHz bandwidth in the experiments.The transmission power of each USRP is 0dBm. Time slotis set to 50ms and sub-slot for channel switching is set to

AP

Sensors Sensors

(a) Prototype system

WBX Daughter

Board

DAC

ADC

TX

RX

USRP

Baseband signal

modulation

Channel decision

LabVIEW

Radio Frequency Configuration

(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 arehomogeneous, and set µ = 0.125. We assume that the arrivalprobabilities of the channels, i.e., {pm},m = 1, 2, · · · , 8,follow the Gauss distribution:

pm =1√2πσ

exp (−(m− M

2 −12 )2

2σ2),

where variance σ is set to 0.5. Normalizing the maximalpm 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 firstcase, where the sensors mainly arrive at channels C4 and C5.Normalizing the maximal pm to 1.5µ, we set another setof {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.

B. LEQ-AutoCS rules vs. dynamic accessing based strategies

We compare the proposed scheme with two existing dy-namic channel accessing methods: round-robin method (RR)[19, 29], and pseudo random sequence based method (PR)[30]. With the round-robin method, accessing sensors performspectrum sensing in a round-robin way from low frequency

1In the analysis of queueing networks, the arrival probability p is set to0 < p < 1. In order to make sense of the accessing sensor arrival modelin queueing networks, here the p1, p2, p7, p8 are chosen as a small positivenumber such as 0.0001.



9

TABLE ISTATISTICS OF NUMBER OF CHANNEL SWITCHINGS.

Case I Case IISwi. Num. Swi. Num. Swi. Num. Swi. Num.S12 0 S21 1243 S12 0 S21 4871S23 93 S32 3397 S23 553 S32 9748S34 435 S43 3221 S34 2181 S43 9887S45 2733 S54 495 S45 5420 S54 1451S56 5257 S65 357 S56 9467 S65 1335S67 3251 S76 60 S67 9125 S76 403S78 1178 S87 0 S78 4323 S87 0

TABLE IITHEORETICAL CHANNEL SWITCHING PROBABILITIES.

Case I Case IIProb. Value Prob. Value Prob. Value Prob. Valuep1,2 0 p2,1 0.0243 p1,2 0 p2,1 0.0373p2,3 0.0111 p3,2 0.0503 p2,3 0.0180 p3,2 0.0806p3,4 0.0141 p4,3 0.0758 p3,4 0.0142 p4,3 0.1281p4,5 0.0310 p5,4 0.0310 p4,5 0.0332 p5,4 0.0332p5,6 0.0758 p6,5 0.0141 p5,6 0.1281 p6,5 0.0142p6,7 0.0503 p7,6 0.0111 p6,7 0.0806 p7,6 0.0180p7,8 0.0246 p8,7 0 p7,8 0.0373 p8,7 0

channel to high frequency channel to search for availablechannels. With the pseudo random sequence based method,accessing sensors carry out spectrum sensing according to thepredefined pseudo random sequence to search for availablechannels. Let ‘LS’ be short for LEQ-AutoCS rules and ‘NS’represent the strategy without spectrum sharing. We investigatesix scenarios with different spectrum sharing strategies: ‘NS’,‘RR’, ‘PR’, ‘LS’, ‘RR+LS’ and ‘PR+LS’, where the latter twostrategies adopt the LEQ-AutoCS rules together with ‘RR’ and‘PR’ access control methods, respectively.

In the experiments, the statistical numbers of channelswitchings between the neighboring channels are provided inTable I, where Sij denotes the channel switching from Ci toCj . The statistical analysis of channel switching probabilitiesis shown in Fig. 8. It can be seen that with LEQ-AutoCS rules,accessed sensors are capable of switching from high crowdedchannels to relatively sparse ones. Specifically, on the lowerchannels C1 ∼ C4, the channel switching probabilities fromhigher channels to lower ones are lager, and on the higherchannels C5 ∼ C8, the channel switching probabilities fromlower channels to higher ones are lager.

The theoretical channel switching probabilities are alsopresented in Table II. From the comparison result shown inFig. 8, it can be seen that the channel switching probabilitiesfrom the experiments are basically consistent to the theoreticalresults.

Then we evaluate metrics: channel utilization Um, systemutilization U and Jain’s fairness Uf . The comparison results ofchannel utilization are shown in Fig. 9. From Fig. 9(a), it canbe seen that in the scenarios ‘NS’, ‘RR’ and ‘PR’, we havesimilar channel utilization, and ‘LS’, ‘RR+LS’ and ‘PR+LS’are similar in case I. However, in the scenarios with LEQ-AutoCS rules, the loads on different channels are effectivelybalanced and thus the channel utilization is more even. FromFig. 9(b), in case II when the arrival rate is increased, C4

and C5 are overloaded; but not surprisingly the LEQ-AutoCSrules effectively alleviate the overcrowded phenomenon bybalancing channel utilization among M channels. The theo-

-0.15 0 0.15-0.15 -0.1 -0.05 0 0.05 0.1 0.15

C7

C6

C5

C4

C3

C2

C1 C2

C8

C7

C6

C5

C4

C3

Experimental

Theoretical

Experimental

Theoretical

(a) Switching probability for case 1

-0.15 0 0.15-0.15 -0.1 -0.05 0 0.05 0.1 0.15

C7

C6

C5

C4

C3

C2

C1 C2

C8

C7

C6

C5

C4

C3

Experimental

Theoretical

Experimental

Theoretical

(b) Switching probability for case 2

Fig. 8. Experiments statistics of switching probability.

retical results according to calculation in equation (25) arealso showed by the dash lines noted by ‘Theo’. Note that inthe theoretical analysis, only the channel switching of accessedsensors with LEQ-autoCS rules is considered; each accessingsensor is set to wait and access on its initial channel fixedly.Hence, the results show that the ‘Theo’ lines for both casesare not as even as the lines of ‘LS’, ‘RR+LS’ and ‘PR+LS’.However, ‘Theo’ lines indicate that even in such scenario, theLEQ-autoCS rules achieve more even channel utilization thanthe scenarios without them.

Fig. 10 shows the statistics of utilization and fairness ofspectrum usage. For case I, the system utilization is similarfor 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 tothe traffic loads, which results in low fairness. On the otherhand, the strategies with ‘LS’ achieve high fairness of channelusage by autonomous channel switching. As the arrival ratesincrease in case II, the system utilization of ‘NS’ is obviously



10

1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

Channel

Util

izat

ion

of e

ach

chan

nel

NSRRPRLSRR+LSPR+LSTheo

(a) Channel utilization of case I

1 2 3 4 5 6 7 80

0.2

0.4

0.6

0.8

1

Channel

Util

izat

ion

of e

ach

chan

nel

NSRRPRLSRR+LSPR+LSTheo

(b) Channel utilization of case II

Fig. 9. Channel utilization of six scenarios for both cases.

TABLE IIIFAILED ACCESSES WITH DIFFERENT STRATEGIES.

NS RR PR LS RR+LS PR+LSCase I 218 0 0 0 0 0Case II 3025 27 43 16 16 10

TABLE IVMEAN ACCESS DELAY OF SENSORS WITH DIFFERENT STRATEGIES.

NS RR PR LS RR+LS PR+LSCase I 0.50 0.09 0.11 0.02 0.01 0.01Case II 2.40 0.33 0.39 0.16 0.11 0.11

lower than other strategies. With other spectrum sharing s-trategies, the congestion is alleviated. Different scenarios leadto different fairness of spectrum usage. The best performancecan be achieved when ‘LS’ works together with ‘RR’ or ‘PR’.

Fig. 11 shows the distribution of the waiting time on thechannels. Both cases confront with unbalanced distributionof the waiting time due to the different loads on differentchannels. Especially for case II, the waiting time for channels

Utilization

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

CASE I CASE II

NS

RR

PR

LS

RR+LS

PR+LS

(a) System utilization

Fairness

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

CASE I CASE II

NS

RR

PR

LS

RR+LS

PR_LS

(b) Fairness of spectrum usage

Fig. 10. System utilization and fairness of spectrum usage of six scenariosfor both cases.

C4 and C5 are even extremely large as the both channels areoverloaded. However, with the spectrum sharing strategies,the traffic loads can be balanced. Then, the waiting time iseffectively reduced and its distribution becomes more even. Italso can be seen that the LEQ-AutoCS rules perform betterthan ‘RR’ and ‘PR’, and the best efforts can be obtainedby ‘LS+RR’ and ‘LS+PR’. Intuitively, congestion on specificchannels would result in low channel access probability. Inthe following, we evaluate the failed accesses and the meanwaiting time of sensors. The results are listed in the TableIII 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 greatlyreduced for both cases (for case I, the failed access is perfectlyavoided). This implies that LEQ-AutoCS rules provide ahigher spectrum access probability for sensors. Although ‘RR’and ‘PR’ can also effectively reduce the failed accesses, theLEQ-AutoCS rules bring lower mean waiting delay for sensorsas shown in Table IV. With the LEQ-AutoCS rules, the meanwaiting delay of sensors is lower than 1/2 of the delay basedon ‘RR’ and ‘PR’, since the LEQ-AutoCS rules promotethe evener channels’ usage and provide lager channel access



11

1 2 3 4 5 6 7 80

1000

2000

3000

4000

5000

6000

Channel

Wai

ting

time

on e

ach

chan

nel

NSRRPRLSRR+LSPR+LS

(a) Waiting time of case I

1 2 3 4 5 6 7 80

2000

4000

6000

8000

10000

Channel

Wai

ting

time

on e

ach

chan

nel

NSRRPRLSRR+LSPR+LS

(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 im-

prove the spectrum utilization, fairness of spectrum usage andthe spectrum access probability. Moreover, the proposed rulesare compatible with other accessing control based schemes tofurther improve the performance.

C. LEQ-AutoCS rules vs. TDMA reservation based strategy

In this subsection, the comparison between LEQ-AutoCSrules and TDMA reservation based strategy for spectrumsharing is studied. The TDMA reservation based strategyemploys contention free scheduling method as used in Wire-lessHART [8]. Specifically, each channel is allocated to thefixed sensors by designing a multi-channel superframe. Thesuperframe consists of several periods named guaranteed timeslots (GTS). The GTSs on one channel are scheduled to thesensors, considering their workloads. For simplicity, we setthe arrival rate at each channel to be equal and the arrival oftransmission tasks of each sensor is a independent Bernoulli

TABLE VMEAN WAITING TIME OF SENSORS ON EACH CHANNEL.

Case I:C1 C2 C3 C4 C5 C6 C7 C8 Ave.

LS 0.05 0.04 0.03 0.01 0.02 0.01 0.02 0.06 0.03TDMA 3.85 3.62 3.73 4.14 3.90 3.76 3.90 3.69 3.82Case II:

C1 C2 C3 C4 C5 C6 C7 C8 Ave.LS 0.23 0.11 0.08 0.06 0.07 0.07 0.09 0.33 0.13

TDMA 6.63 6.27 6.29 6.79 6.88 6.49 6.45 6.34 6.51

random process. In this experiment, we have two sensors oneach channel. The total rates of all sensors are 0.20 for Case Iand 0.38 for Case II, respectively. The packet number of eachtransmission, i.e., 1/µ, is fixed to 8. Under these settings, weobserve the spectrum access delay of the two spectrum sharingstrategies.

The statistical results are presented in Table. V. The spec-trum sharing by LEQ-AutoCS rules achieves a much lowermean access delay than that by TDMA reservation basedstrategy. Particularly, with LEQ-AutoCS rules, the averagedelay of all sensors (noted by ‘Ave.’ in Table. V) is lowerthan 1/50 of that by TDMA reservation based strategy. Thisis because the TMDA reservation based spectrum access isnormally suitable to the periodic data delivery. As for the caseof random data delivery, it is inadequate to quickly response tothe 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 reservationbased strategy on the performance of spectrum access delay.

D. Discussion for the scenarios with interference

If there exists a wide-band interference, it would block thedata transmissions and greatly decrease the performance ofcommunications with different spectrum sharing methods. Inthis subsection, we investigate how LEQ-AutoCS rules work inthe scenarios with narrow-band interference. For example, theinterference signal exists on channel Cm, then transmissionsset up on Cm will be blocked. Since the sensing range of eachsensor covers 3 channels, the sensor on Cm−1 will observethat Cm is occupied, and so will sensor on Cm+1 do. Theywill not switch to Cm according to the rules. As a result,the channels are divided into two segments, C1 ∼ Cm−1 andCm+1 ∼ CM . The sensors in each segment would approachto a new equilibrium of channels’ usage under the LEQ-AutoCS rules. With spectrum sensing ability, each sensorwill autonomously avoid the interfered channel. But when theinterference disappears, the channel will be reused. Then, theLEQ-AutoCS rules would promote the even usage of the wholespectrum and approach to the equilibrium. In other words, theLEQ-AutoCS rules can adapt to the scenarios with narrow-band interference, where the interference is just considered asa stubborn user which does not switch channel.

VII. CONCLUSIONS

An even-spectrum-usage targeted spectrum sharing schemehas been proposed for industrial wireless sensor networksso that the spectrum utilization and fairness of spectrum



12

usage, and probability of spectrum access for new transmissionrequests can be improved compared to standardized industrialwireless protocols. The so-called LEQ-AutoCS rules havebeen devised for accessed sensors to autonomously switchchannels by imitating the behavior of biological agents toachieve collective motion with only local observation andaction. It has been demonstrated that the equilibrium ofspectrum usage can be achieved under the LEQ-AutoCS rules.Moreover, the lower bound of spectrum access probabilityat the equilibrium and the upper bound of the convergencetime to equilibrium have been derived as well. The proposedmethod provides an effective scaling way for large-scaleindustrial wireless applications with limited spectrum resource.The experiment results demonstrate the effectiveness of theproposed spectrum sharing scheme. In our future work, wewill investigate the issue of autonomous channel switchingdesign with the consideration of sensors’ imperfect sensing.

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

Cailian Chen received the B.Eng. and M.Eng. de-grees in automatic control from Yanshan University,China, in 2000 and 2002, respectively, and the Ph.D.degree in control and systems from City Universityof 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 in-dustrial wireless sensor and actuator network, In-ternet of Vehicles for ITS applications, and control

and communication design for cyber-physical systems. She has authoredand/or coauthored two research monograph and over 100 referred internationaljournal and conference papers in these areas. Dr. Chen was one of the FirstPrize Winners of a Natural Science Award from the Ministry of Educationof China in 2007. She was a recipient of the “IEEE Transactions on FuzzySystems Outstanding Paper Award” in 2008. She is on the editorial board ofIEEE Transactions on Vehicular Technology and Peer-to-Peer Networking andApplications (Springer), and serves as a Track TPC co-chair of IEEE VTC2016. Dr. Chen is a New Century Excellent Talent in University of Chinahonored by Ministry of Education of China, “Pujiang Scholar” and “YoungScientific Rising Star” honored by Science and Technology Commission ofShanghai Municipal, China, and SMC Outstanding Young Faculty of ShanghaiJiao Tong University, China..

Ning Zhang received the Ph.D degree from Uni-versity of Waterloo in 2015. He received his B.Sc.degree from Beijing Jiaotong University and theM.Sc. degree from Beijing University of Posts andTelecommunications, Beijing, China, in 2007 and2010, respectively. His current research interestsinclude dynamic spectrum access, 5G, physical layersecurity, and vehicular networks.

Xinping Guan received the Ph.D. degree in controland systems from Harbin Institute of Technology,Harbin, China in 1999. In 2007, he joined theDepartment of Automation, Shanghai Jiao Tong U-niversity, Shanghai, China, where he is currently aChair Professor, the Deputy Director of UniversityResearch Management Office, the Director of theKey Laboratory of Systems Control and InformationProcessing, Ministry of Education of China, andthe Leader of “Design, Control and Optimization ofNetwork System” National Innovation Team. Before

that, he was the Professor and Dean of Electrical Engineering, YanshanUniversity, China.

Dr. Guan’s current research interests include cyber-physical systems,wireless networking and applications in smart city and smart factory, andunderwater sensor networks. He has authored and/or coauthored 3 researchmonographs, more than 160 papers in IEEE Transactions and other peer-reviewed journals, and numerous conference papers. As a Principal Investi-gator, he has finished/been working on many national key projects. He is theleader of the prestigious Innovative Research Team of the National NaturalScience Foundation of China (NSFC). Dr. Guan is a Committee Memberof the Chinese Automation Association Council and the Chinese ArtificialIntelligence Association Council. He was on the editorial board of IEEETrans. System, Man and Cybernetics-Part C and several Chinese journals.He also serves as an IPC/TPC member of a lot of conferences. He receivedthe First Prize of Natural Science Award from the Ministry of Education ofChina in 2006 and the Second Prize of the National Natural Science Awardof China in 2008. He was a recipient of the “IEEE Transactions on FuzzySystems Outstanding Paper Award” in 2008. He is a “National OutstandingYouth” honored by NSF of China, “Changjiang Scholar” by the Ministry ofEducation of China and “State-level Scholar” of “New Century Bai QianwanTalent 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), allin electrical engineering. He is a Professor andUniversity Research Chair, Department of Electricaland Computer Engineering, University of Waterloo,Canada. He was the Associate Chair for GraduateStudies from 2004 to 2008. Dr. Shen’s researchfocuses on resource management in interconnectedwireless/wired networks, wireless network security,

social networks, smart grid, and vehicular ad hoc and sensor networks. He isa co-author/editor of six books, and has published more than 600 papers andbook chapters in wireless communications and networks, control and filtering.Dr. Shen served as the Technical Program Committee Chair/Co-Chair forIEEE 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 TechnicalProgram Committee Chair for IEEE Globecom’07, the General Co-Chair forChinacom’07 and QShine’06, the Chair for IEEE Communications SocietyTechnical Committee on Wireless Communications, and P2P Communicationsand Networking. He also serves/served as the Editor-in-Chief for IEEE Net-work, Peer-to-Peer Networking and Application, and IET Communications; aFounding Area Editor for IEEE Transactions on Wireless Communications; anAssociate Editor for IEEE Transactions on Vehicular Technology, ComputerNetworks, and ACM/Wireless Networks, etc.; and the Guest Editor for IEEEJSAC, IEEE Wireless Communications, IEEE Communications Magazine, andACM Mobile Networks and Applications, etc. Dr. Shen received the ExcellentGraduate Supervision Award in 2006, and the Outstanding Performance Awardin 2004, 2007 and 2010 from the University of Waterloo, the Premier’sResearch Excellence Award (PREA) in 2003 from the Province of Ontario,Canada, and the Distinguished Performance Award in 2002 and 2007 fromthe Faculty of Engineering, University of Waterloo. Dr. Shen is a registeredProfessional Engineer of Ontario, Canada, an IEEE Fellow, an EngineeringInstitute of Canada Fellow, a Canadian Academy of Engineering Fellow,and a Distinguished Lecturer of IEEE Vehicular Technology Society andCommunications Society.

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