Ad Hoc Networks. Opportunistic reliability for cognitive radio sensor actor networks in smart grid. Ozgur Ergul, A. Ozan Bicen, Ozgur B.

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1 Ad Hoc Networks 41 (2016) 5 14 Contents lists available at ScienceDirect Ad Hoc Networks journal hoepage: Opportunistic reliability for cognitive radio sensor actor networks in sart grid Ozgur Ergul, A. Ozan Bicen, Ozgur B. Akan Next-generation and Wireless Counications Laboratory, Departent of Electrical and Electronics Engineering, Koc University, Istanbul 34450, Turkey a r t i c l e i n f o a b s t r a c t Article history: Received 15 June 2015 Revised 3 October 2015 Accepted 6 October 2015 Available online 19 October 2015 Keywords: Sart Grid counications Cognitive radio sensor networks Distributed sensing Spectru sharing Reliability is one of the ost iportant requireents in Sart Grid counications. Reliable detection of an eergency event enables tiely response. Within the autoated nature of Sart Grid, such detection and response are carried out by sensor and actuator nodes. Therefore, it is iportant to study the capabilities of wireless sensor actor networks. In this paper, we first present an analysis of reliability in sensor actor networks, and lay out the factors that affect reliability. We then propose a schee, where actor nodes cooperate to reach a global estiate under interruptions due to licensed user interference, i.e., consensus. We show that consensus iproves reliability copared to local estiation of event features. We further show that convergence rate depends on connectivity of actors. Our analyses are generic and can be applied to inhoogeneous licensed user activity and interference on channels. A siulation study is presented to support our analyses and deonstrate the perforance of proposed schee in achieving consensus and itigating disagreeent aong actor nodes Elsevier B.V. All rights reserved. 1. Introduction Wireless sensor networks [1] and sensor actor networks [2] are expected to watch over expensive equipent in Sart Grid, with sensors onitoring the environent for possible eergency events and counicating with actuators to take proper action when the event occurs. Failure in detection of an eergency event ay result in break down of expensive equipent, and in soe extree cases, ay even cost lives. Therefore, reliability is considered to be one of the ost iportant issues in Sart Grid counications. To avoid such losses reliable and tiely coordination of sensing results ust be addressed. One of the biggest probles in wireless counications is spectru scarcity [3]. The deand for wireless spectru Corresponding author. Tel.: E-ail addresses: ozergul@ku.edu.tr (O. Ergul), abicen@ku.edu.tr (A.O. Bicen), akan@ku.edu.tr (O.B. Akan). is growing rapidly and new paradigs such as Internet-of- Things and Device-to Device counications, which are expected to have assive spectru deand are eerging. In Sart Grid counications, the situation is exacerbated by electroagnetic interference of the devices and harsh environental conditions. Cognitive radio sensor networks (CRSN) are proposed to itigate spectru scarcity specifically in dense deployed sensor networks and enable distributed sensing over teporally unoccupied portions of the licensed spectru [4]. Incorporation of cognitive radio (CR) into distributed sensing requires sharing of spectru opportunities aong CRSN nodes while addressing event specific sensing requireents, while adhering to the inherited collaborative and energyconstrained nature of sensor networks. Furtherore, cognitive radio actor nodes can collect observations of CRSN nodes and cooperate to reach a global estiate, i.e., consensus [5]. Reaching consensus in a decision, i.e., estiation, interval requires efficient and adaptive sharing of spectru opportunities aong cognitive radio sensor and actor nodes, such / 2015 Elsevier B.V. All rights reserved.

2 6 O. Ergul et al. / Ad Hoc Networks 41 (2016) 5 14 that desired aount of saples can be collected fro sensors with iniu spectru access and actors can reach a consensus during an estiation interval. Due to liited battery sizes, energy efficiency has been the ain consideration for counication algorith design for CRSN. Energy-efficient channel anageent is studied in [6]. Residual energy aware channel assignent is investigated in [7]. Energy-efficient spectru sensing algorith for CRSN is proposed in [8]. However, these works ainly lack in incorporating collaborative nature of sensor networks, and application specific reliability, i.e., estiation distortion and interval, requireents are disregarded. Solutions that take correlations between sensor readings have been proposed to take advantage of sensor collaboration [9 11] in WSN. These solutions should be odified to address opportunistic operation in a CRSN, taking spectru conditions into account. Spectru sharing proble for cognitive radio networks (CRN) are investigated in [12 16]. Main drawback of these schees is issing consideration of detection and onitoring requireents of sensor networks. In our design, we specifically target to exploit collaborative effort of sensor nodes on the sae event and achieve reliability opportunistically while reaching consensus aong actor nodes in an estiation interval. Spectru sharing solutions in other CRN ainly focus on throughput axiization and are proposed to efficiently utilize the scarce spectru opportunities. In [12], spectru sharing for ulti-hop cognitive radio networks is studied. In [13 16] spectru sharing schees for ultiple input ultiple output systes have been proposed. The priary reason for their inapplicability in CRSN is their notion of rate axiization. Furtherore, reliable estiation of event features, collaborative nature of CRSN nodes, coordination requireents of CR actor nodes and spectru efficiency ust be addressed while designing spectru anageent algoriths for large scale distributed sensing networks. Hence, there is a need for a novel spectru access echanis in CRSN that ephasizes on collective reliability, spectru efficiency and siplicity. CR based counication in Sart Grid has been investigated in various fronts, such as quaity-of-service (QoS) or priority based access schees [17,18], network infrastructure proposals [19], investigation of iportant paraeters in CR based network design [20], ultiedia counications [21], and green counications [22]. However, reliability is not investigated thoroughly, even though it is one of the ost iportant requireents. In this paper, first, we analyze reliability in event estiation by defining a distortion etric. We characterize required spectru opportunity to attain desired estiation distortion level while iniu aount of channels are accessed, based on spectru obility paraeters, i.e., licensed user activity, interference, spectru sensing and handoff durations, as well as real-tie distributed sensing paraeters, i.e., observation noise, delay-bound on reaching consensus, and energy consuption liitation per estiation interval. Then, we study required duration for reaching consensus aong actor nodes after collection of saples fro sensors and generating local estiate based on the interruption probability due to licensed user interference. Two regies are identified: one in which sufficient spectru opportunity exists and consensus can be achieved aong actor nodes, and another in which actor nodes try to iniize the disagreeent as uch as they can support, i.e., provide opportunistic consensus, due to liited spectru availability. The regie of operation depends on the licensed user activity on channels, and the early regie is desirable but achievable only for sparse licensed user existence on the spectru. It is concluded that in certain environents under sparse spectru occupancy by licensed users, spectru access duration of sensor nodes can be adaptively reduced to enable convergence to consensus for actors in an estiation interval. Contribution of this paper can be outlined as follows: 1. Analyze reliability in event detection : local estiation distortion at actor node is odelled with respect to sensing signal-to-noise ratio (SNR), reporting rate and channel error rate. 2. Opportunistic consensus : a cooperative schee is proposed, where actor nodes share their local event estiations through opportunistic access of licensed channels to reach a global consensus about the event signal. We show that our schee increases reliability. 3. Consensus convergence : ipact of interruptions due to licensed user arrivals, is-detection of licensed users, and wireless channel errors on reaching consensus is forulated. Prolongation in the consensus convergence tie is studied under opportunistic spectru access (OSA). The reainder of the paper is organized as follows. In Section 2, distributed sensing architecture coposed of cognitive radio sensor and actor nodes is elaborated. Proble forulation and reliability analysis is presented in Section 3. Factors that effect reliability are discussed in Section 4. Opportunistic consensus is analyzed in Section 5. Siulation results are presented in Section 6, and paper is concluded in Section Network setup We assue that the network in question consists of ultiple wireless sensor nodes, each equipped with a cognitive radio (CR) and an actuator node with ultiple CR transceivers. These nodes counicate aong each other via opportunistic spectru access (OSA) to perfor reote onitoring and actuation tasks. Collected saples s by sensor node on event signal θ are delivered to the actor node during the reporting interval τ r over assigned channel c within spectru access duration τ a to satisfy reliability requireent D o of distributed event observations. Reliability easure for estiation of the actor node is defined in ters of distortion D (ean square-error) of the estiated event signal over a τ a. Sensor nodes occupy a single CR transceiver with capability of adjusting its operating frequency to any channel c in designated spectru band by the actor node, i.e., channel set C of the actor node. Channels are shared between selected sensor nodes participating in event data delivery. Sensor node behavior in a channel c consists of data transission τ t, spectru sensing τ s and spectru handoff τ h periods. We assue each sensor node is assigned to a specific channel for periodic spectru sensing by the actor node, such that in

3 O. Ergul et al. / Ad Hoc Networks 41 (2016) spectru sensing intervals τ s all sensor nodes perfor spectru sensing to detect spectru holes, i.e., vacant channels. With detection of licensed user, sensor node using that channel perfors spectru handoff and traverses channels provided by actor node to find a spectru opportunity. Spectru handoff duration τ h includes durations of consecutive channel switching τ cs and spectru sensing τ s at the new channel, until a vacant channel is found, i.e., duration between the instant where event reporting stopped due to licensed user detection and the instant when counication is resued in a vacant channel. To achieve desired distortion level D o in an estiation interval τ e, sensors are assigned to channels by the actor node, such that they coplete their transission in spectru access interval τ a. Since τ e includes τ a as well as delays due to cognitive cycle functionality durations, we have τ e > τ a. Channels assigned by the actor node, i.e., c C, are taken to be hoogeneous in ters of licensed user activity and interference. Energy constraints for sensor nodes liit the energy that can be spent for event reporting in an estiation interval. These constraints are taken to be non-equal due to heterogeneous event arrivals in the field and reaining energy of sensor nodes. This energy variation brings liitation to event reporting duration τ r of sensor nodes, and hence, causes heterogeneities for nuber of saples reported by each sensor. 3. Reliable distributed sensing In this section, we lay out the proble forulation and present initial arguents of our analysis on reliability. We define a so called distortion etric D, which is the ean squared error (MSE) of our estiation of the event signal. We show how reliability depends on spectru utilization of priary users (PU) as well as channel conditions. Sensor nodes receive the event signal with varying power levels due to certain factors such as their distance fro the event, device iperfections and noise. Furtherore, each sensor node has different aount of energy left in their battery. It is also possible that the sensor nodes utilize energy harvesting, in which case, the aount of energy harvested per unit tie ay vary fro sensor to sensor. As a result, the aount of energy that can be consued during the reporting of events e, differ aong the sensors. There are also external influences on sensor event data reports such as varying wireless channel conditions, changes in PU channel utilization patterns, etc. Our ai is to incorporate all of these effects into a single etric that serves as a good indicator for reliability in event estiation. We assue that the event signal at tie t, i.e., θ( t ), is received at sensor node, with dispersion loss γ ( t ) and added noise η( t ) as s (t) = γ (t) θ(t) + η (t) (1) For estiation of event signal fro received saples fro sensor nodes, actors use the best linear unbiased estiator (BLUE) [29] for local estiation. For a linear estiation type given above, where saples of η are zero-ean, uncorrelated and have equal variances, BLUE is iniu-variance unbiased estiator. This allows us to ake no assuptions on sensing noise distribution as long as noise power ξ 2 is known. Therefore, we do not assue any specific distribution for sensed signal and noise. Each sensor sends easured signal s ( t ) to the actor node, where θ is estiated fro the received version of s ( t ). We take both θ ( t ) and η ( t ) are i.i.d. over tie. We also assue that θ ( t ), and η ( t ) have zero ean with power σ 2 and ξ 2 θ, respectively. Sensors counicate with actor via op- portunistic spectru access. Actor generates an estiate of the event at the end of each event estiation interval. Under independence over tie and space assuption, indices are ignored for all variables. This delay bounded distributed sensing schee can also be seen as real-tie, since it put tieliness constraint on event reports. Received saple vector by the actor at the end of each event estiation interval τ e, i.e., r, is cobination of sensing noise and sensed signal as r = γ θ + η, where r = [ r 1,..., r ] T, γ = [ γ 1,..., γ ] T, and η = [ η 1,..., η ] T, where is the nuber of sensor nodes selected by actor node. Estiate of event signal using BLUE is forulated as follows [29] : ˆ θ = [ γ T R 1 s γ ] 1 γ T R s 1 r (2) Saple covariance atrix R s for received saples at actor is a diensional rectangular diagonal atrix whose diagonal entries are ξ 2, and other entries are 0. We define a distortion etric D, as the ean square error for BLUE can be deterined as [29] D = E[ ( θ ˆ θ) 2 ] = [ γ T 1 R s γ] 1 ( ) 1 γ 2 = ξ 2 (3) =1 Taking into account the fact that nuber of saples provided by each sensor ζ, will be different due to various factors such as spectru handoff and packet errors, we define a corresponding distortion etric D as follows: ( ) 1 (4) D = =1 ζ γ 2 ξ 2 Naturally, ζ depends on factors such as packet error rate e, and nuber of encountered spectru handoffs. The nuber of packets that are correctly received by the actor can be expressed as ζ = r ( ) 1 e (5) where, r is the aount of packets that node was able to send within a reporting interval, while avoiding the PU by perforing spectru handoff whenever necessary. In the following section, we analyze the effects of these factors on ζ, and consequently on distortion. 4. Analysis of factors that effect reliability In this section, we present an analysis of factors that effect reliability, such as spectru handoff and packet errors Ipact of spectru obility Incorporation of cognitive radio capability into sensor and actor nodes enables reporting of event data over licensed

4 8 O. Ergul et al. / Ad Hoc Networks 41 (2016) 5 14 bands to itigate crowded spectru proble. However, interittent counications due to opportunistic spectru access and interruptions due to licensed user interference ust be addressed. To this end, actual spectru access tie of sensors, based on spectru sensing and spectru handoff functionalities is found., i.e., the experienced nuber of packets sent by node while utilizing licensed spectru bands opportunistically is obtained. First, we derive the ean data counication duration E { τ data } before licensed user arrival in channels C assigned by the actor node. Under exponential inter-arrival and inter-departure durations assuption for PU traffic [23 26], average data counication duration E { τ data }, i.e., average duration fro starting counication in channel C until a licensed user is detected is found as Here, r E{ τ data } = E{ I} τ t (6) where E { I } is the ean nuber of (τ s + τ t ) durations before licensed user arrives at a channel in C. To calculate E { I }, we define the probability of having i intervals without licensed user arrival at the accessed channel as Pr [ I = i ] = (P hole ) i 1 (1 P hole ) (7) where P hole is vacancy probability of a channel in C. Mean of I can be found as 1 E{ I} = i Pr [ I = i ] =. (8) 1 P hole i =1 To find the ean of spectru handoff duration E { τ h }, i.e., the ean of total channel switching and spectru sensing durations until data transission can be started in a vacant channel, we define probability of finding a vacant channel via l consecutive handoffs Pr [ L = l] as Pr [ L = l ] = P hole (1 P hole ) l 1 (9) where we assue licensed user arrivals at different channels of C are independent fro each other. When a licensed user counication is detected at any of accessed channels sensor nodes accessing that channel traverses channels provided by the actor to find a vacant channel, where licensed user detected channel corresponds to c = 0. Tie spent while perforing l consecutive handoffs can be found as τ h (l) = l (τ cs + τ s ) (10) where τ cs is channel switching tie when oving between channels. As a result, E { τ h } can be obtained as E{ τ h } = τ h (l)pr[ L = l] l=1 = l (τ cs + τ s )P hole (1 P hole ) l 1 l=1 = (τ cs + τ s ) 1 P hole (11) To find the nuber of packets sent by sensor node, i.e., r, we use the fact that the total tie spent by a node in spectru sensing, data transission and spectru handoff ust not exceed the reporting period τ r. With this restriction, we can find the expected nuber of handoffs experienced by sensor, i.e., h. We require E{ I} (τ s + τ t ) + h (E{ τ h } + E{ I} (τ s + τ t )) (12) Therefore, we need the axiu value of h that satisfies h τ r E{ I} (τ s + τ t ) E{ τ h } + E{ I} (τ s + τ t ) If we define such h as h, (13) r = h E{ τ data } ν 8 l p (14) where l p is the packet size in bytes and ν is the transission rate in bits/sec. Instantanepus throughput can be defined as T = r /τ r 4.2. Packet error rate Each sensor counicates with the actor node over orthogonal channels that experience independent shadowing and zero-ean AWGN. We use the log-noral channel for received power calculations, which is experientally shown as the accurate odel for low power counication in sensor networks [27]. In this odel, the received power at a receiver at distance d fro a transitter is given by P r (d) = P t PL (d 0 ) 10 η log 10 ( d d 0 ) + X σ, (15) where P t is the transit power in db, PL( d 0 ) is the path loss at the reference distance d 0 in db, η is the path loss exponent, and X σ is the shadow fading coponent with X σ N (0, σ). We denote the counication signal-to-noise ratio (SNR) at the actor with and without licensed user interference as w, and l, respectively. SNR at the receiver without licensed user interference w is given by w = P r (d) P n in db, where P n is the counication noise power in db. On the other hand, SINR at the receiver due to licensed user activity is given by l = P r (d) P n P (k) in db, where P (k) l l is the interference caused by licensed user activity at actor node k. To obtain bit error rate P b to use in analytical derivations, the non-coherent frequency shift keying (FSK) odulation schee is selected. The bit error rate of this schee is given by [28] P b = 1 2 exp ( (E b /N 0 )/ 2 ), E b /N 0 = B N R (16) where B N is the noise bandwidth, and R is the data rate. Finally, packet error rate ( P p ) for packet length l p becoes P p = 1 (1 P b ) l p (17) To deterine average packet error rate e incorporat- ing licensed user interference due to opportunistic spectru access, we propose an error odel based on false-alar P f and detection P d probabilities, and licensed user state transition, i.e., birth β and death α rates. False-alar, i.e., detection of licensed user counication when licensed user is actually not counicating, probability is represented by P f and detection probability when licensed user is counicating P d. Licensed user activity odelled using two state discrete Markov chain odel with ON and OFF states [23 26]. Licensed user being active (1 P hole ) and being inactive P hole probabilities are equal to β/(β + α) and α/(β + α), respectively. Before finding e, we describe two different cases in which licensed user interference occurs as follows:

5 a b O. Ergul et al. / Ad Hoc Networks 41 (2016) ((1 e ατt ) βp p l + αp p w α + β + e ατt P l p ) (18) Fig. 1. Licensed user interference patterns when is-detection occurs, no state change in (a) and state transition occurs in (b). a Fig. 2. Licensed user interference patterns when licensed user is initially OFF while spectru sensing, no state change in (a) and state transition occurs in (b). 1. Although licensed user is active, it ay not be detected, i.e., is-detection can occur, with probability (1 P hole )(1 P d ). In this case, nodes continue to counicate, though there is ongoing licensed user counication. Hence, they get exposed to licensed user interference, which is illustrated in Fig A spectru band can be identified as vacant and eployed by sensor nodes with probability P hole (1 P f ). However, licensed users ay start counication during the nodes transission period. Thereby, until the next spectru sensing period, sensor nodes are unaware of the licensed user presence and continue to counicate under licensed user interference, which is illustrated in Fig. 2. Licensed user ay change its state during τ t, or it can keep its state along whole τ t duration. Having τ t is relatively sall with respect to average active and inactive durations of licensed user, e.g., 1/ α and 1/ β, respectively, is a ore realistic assuption than having large τ t that is longer than licensed user transission duration. Thus, we assue τ t is saller than both 1/ α and 1/ β. Interference due to is-detection exhibits two different patterns according to τ t as in Fig. 1 (a) and (b). It can be through whole τ t period as in Fig. 1 (a) or licensed user state ay change to inactive fro active as in Fig. 1 (b). The probability that the licensed user is transitting during the entire τ t can be obtained as e ατ t, and the probability that licensed user goes inactive state fro active during τ t can be found as 1 e ατ t. If the licensed user state does not change during the τ t, the licensed user interference persists over the entire transission period and in which error rate is P p l. However, if state transition between active and inactive states occurs during τ t, average error rate converges to (1 P hole )P p l + P hole P p w. Thus, average packet error rate for the is-detection case P p 1 can be expressed as p = (1 P β d ) α + β P 1 b Siilarly, if licensed user is inactive and there is no falsealar, interference only happens when licensed user state transition occurs during τ t, as illustrated in Fig. 2 (b). Average packet error rate converges to again approxiately to (1 P hole )P p l + P hole P p w with probability 1 e βτ t. Average packet error rate in this case P p 2 becoes P p 2 = (1 P α f ) α + β ) ((1 e βτt ) βp p l + αp p w + e α + β βτt P p w (19) Then, to find overall packet error rate e in opportunistic spectru access incorporating licensed user interference, we add and noralize P p 1 and P p 2 as e = P p 1 + P p 2 β(1 P d ) + α(1 P f ) α + β 4.3. Spectru access duration and sensor scheduling order (20) The analysis presented in the previous sections provides us with the following expression for distortion etric: ( D = =1 = =1 = σ 2 θ = ζ γ 2 ξ 2 ) 1 ( (1 e =1 σ 2 θ 8 l p E{ τ data } ) r γ 2 ξ 2 ) 1 ( (1 ) ) 1 e r =1 ( h ν ( 1 e ) ) 1 (21) Miniu nuber of sensor nodes satisfying distortion constraint can be reached via ordering sensors in the descending sensing SNR ( ) order, i.e., = 1 is the largest SNR sensor node, and using in (3) with axiu allowed τ () r until distortion constraint is satisfied. According to this forulation, instead of using all sensors, only the right group of sensor nodes can be deterined and still the distortion threshold D 0 can be achieved. In this section, we analyze the contribution of data carried at each channel to distortion. The event observation distortion at an actor node is discretized into contribution of each channel D c, i.e., total distortion is expressed as the addition of saples belonging to different channels, addressing the reduction in the reported saples over a channel by the spectru access duration τ a during estiation interval τ e. Sensor nodes can ove aong spectru holes via spectru handoff as a licensed user arrives at current accessed channel. However, sensor nodes counication is interrupted by periodic spectru sensing as well as spectru handoff triggered by licensed user arrival. Therefore, effect of opportunistic spectru availability on event sensing reliability is investigated

6 10 O. Ergul et al. / Ad Hoc Networks 41 (2016) 5 14 analytically according to proposed distributed sensing distortion odel. To this end, we define M (c) as the source sensors of the actor assigned to c th channel for sharing during τ a. D for proposed distributed sensing schee can be expressed as ( ) 1 D = D 1 c (22) c where D c is the distortion resulted by observations of sensors at channel c. It is dependent on the accessible duration τ a of a channel assigned by the actor during an estiation in- sharing the sae channel. τ a s are independent and identically distributed (i.i.d.) rando variables with ean μ representing data counication duration in an estiation interval for channels of the actor node. D c is the distortion achieved when spectru access duration τ a in an estiation interval is allowing ωth sensor starting fro = 1 to share that channel for event reporting, and it can be expressed as 1 terval and required reporting duration of sensors τ () r ω 1 D c = for =1 + D 1 ω D 1 ω 1 τ () r =1 ω τ a ω 1 τ a =1 =1 τ (ω) r τ () r τ () r, M, ω M, (23) where ω is the last sensor node that was reporting using the channel c at the instant of licensed user arrival, and D is distortion solely depending on saples fro sensor, which can be obtained using forulation in Section 4.3 as σθ 2 ( ) 1 h 8 l p E{ τ data } ν (1 e ) (24) Furtherore, it is deduced that D c is equal to ( M (c) =1 D 1 ) 1 for τ a M (c) τ () =1 r. When τ a M (c) τ () =1 r sensors assigned to channel c are able to find an opportunity to copletely transit their observations to actor during the estiation interval, and desired D c will be achieved. However, when τ a μ, reporting of sensors assigned to a channel are liited by spectru access duration ( τ a M (c) τ () =1 r ), and contribution to total estiation distortion D c is calculated using (23) via replacing τ a with its realization. Latest reporting sensor ω at accessed channels can be deterined via ω 1 τ () =1 r τ a ω =1 τ () r, and its unfinished reporting duration can be found as τ a ω 1 τ () =1 r. Each channel s contribution to distortion of total estiation at actor varies based on sensing SNR of assigned sensors to a channel. Therefore, another iportant issue is the scheduling order of source nodes assigned to sae channel. Addressing the interruptions due to opportunistic counication, and hence, rando τ a duration in an estiation interval τ e, scheduling spectru access of source nodes with respect to their observation SNR in descending order, i.e., highest SNR having node ( = 1 ) accesses first at designated channel, is found favorable. 5. Opportunistic consensus In this section, based on the previous analysis, we propose a consensus schee to increase reliability of event estiation. We assue a case where there are ultiple actor nodes, each with its own set of sensors. Each sensor-actor group of nodes operate as described in previous sections. However, after actor nodes ake a local estiation of the event signal, they counicate their local estiate with other actors to itigate disagreeent and reach a global agreed state. We, first, present an overview of used consensus odel, and then, investigate consensus convergence duration with respect to different algebraic connectivity of actor network for various licensed user arrival β and interference P l values. While reaching a consensus is trivial for sall scale actor networks, for a large scale actor network coputing the global estiate based on local estiates θ ˆ k requires ultiple iterations and packet exchanges aong actors. Interactor counication is subject to licensed user interference. This can either be in the for of licensed user arrival during transission or is-detection of licensed user presence during spectru sensing period. In case of transission errors, iteration is stopped and this failed step is repeated via autoatic repeat request. The exchange of inforation aong actors is perfored via a slotted and collision-free ediu access control (MAC) schee. Consensus convergence tie τ c is deterined as the ultiplication of nuber of required iterations Y to reach consensus and iteration duration τ i, i.e., τ c = ϒ τ i Overview of consensus odel We use a cognitive radio actor network coposed of K actor nodes. Actor k can counicate with actor l if l is a neighbor of k on a graph G = (V, E), where V denotes the set of vertices, i.e., actor nodes, and E V V denotes set of the edges between vertices, i.e., links between actor nodes. The adjacency atrix A of the graph G is coposed of binary-valued entries a k, l that indicates existence of a link between actor k and l. Value of a k, l is equal to 1 if actor k and l are connected, and a k,l = 0 if there is no link between actor k and l. We assue the links E are bidirectional, and hence, the graph G is undirected. Furtherore, A is a syetric atrix with 0 diagonal entries, and since k = l a k,l = l = k a l,k, the undirected graph G is called balanced. The degree atrix D of G is a diagonal atrix with entries d k,k = N k and zero off-diagonal eleents, where N k = k = l a k,l is the nuber of nodes in the neighborhood set N k of actor k. Let L be the Laplacian atrix of the graph G, which is defined as L := D A. Entries l k, l of L are as l k,l = l l,k = { N k if k = l a k,l if k = l (25) Ai of consensus algorith is to ake each actor node reach a globally optial estiate θ ˆ fro a set of easureents, i.e., local estiates θ ˆ k of actor nodes in our syste odel. This is achieved via exchange of local estiates aong nearby actors without utilization of a fusion center. By definition of L su of all coluns or rows is equal to 0, which iplies that L has an eigenvalue of 0. Accordingly, associated eigenvector is 1 since L1 = 0, or 1 T L = 0 T. There-

7 O. Ergul et al. / Ad Hoc Networks 41 (2016) fore, reached final estiate is of the for α1, and consensus value α is equal to average of local estiates of actors. If G is a connected balanced and undirected graph, a consensus is asyptotically reached with = ˆ k (0)/K (26) k Since iniization of the difference between states of actors is the ai of consensus algorith, the disagreeent, i.e., error, function is defined as J( ) ˆ = 1 ˆ T L ˆ = 1 K L 2 4 k =1 l=1 a k,l ( ˆ k ˆ l ) 2 (27) Using steepest descent technique the iniu of J ( ) can be achieved in discrete tie as ˆ k (t + 1 ) = ˆ k (t) + ϑ l N k a k,l ( ˆ k (t) ˆ l (t)) (28) where ϑ is the step-size. In atrix for, dynaics of the actor network can be expressed as (t ˆ + 1 ) = P (t) ˆ (29) where I is the identity atrix, and P = I ϑl. Value of ϑ is selected appropriately to ensure all eigenvalues of P are less than 1. The consensus algorith is initialized with local estiates of actor nodes, i.e., ˆ k (0) = θ ˆ k. In the next section, the described inter-actor distributed estiation fraework is used for assessing consensus convergence duration under opportunistic spectru access Algebraic connectivity and consensus convergence While the perforance of consensus algorith is characterized by its convergence rate, i.e., tie elapsed to reach consensus, convergence speed is lower bounded by the lowest non-zero eigenvalue of P, i.e., λ 2, which is also called algebraic connectivity of the graph. Consensus is reached exponentially in discrete-tie for connected graphs [5] such that (t) ˆ (0 ˆ ) O (e (1 ϑλ 2 (L ))τ c ) (30) We state the reaching consensus condition as θ(t) θ θ(0 ) θ ε. Therefore, the tie elapses until convergence τ c can be defined as the tie needed to sallest eigenvalue of the dynaical syste can be reduced by a factor ε 1. A step of iteration fails if licensed user arrives or in case of isdetection during counication of local estiate. Then, a new vacant channel is oved and failed step is repeated there. Failed step is detected after the end of iteration, hence, iteration is re-started. Instead of trying to know when exactly pu arrived during iteration. To itigate disagreeent for a unit aount 1 /(1 P p ) 1 /(1 ϑλ 2 (L )) iterations are needed, and hence, τ c is found as τ c = 1 log (ε) 1 P p 1 ϑλ 2 (L) E { τ i } (31) where τ i is the tie required for a single iteration, i.e., duration in which all actor nodes counicate their local state once with their neighbor actors. We elaborate calculation of ean of τ i in the following Estiation interval partitioning for consensus Estiation interval ust be partitioned adaptively addressing varying spectru paraeters with spectru obility. Objective of our schee is to provide sufficient duration for counication of local states aong actor nodes after copletion of local estiation. We first describe MAC for inter-actor counication and forulate ean iteration duration E { i }. Then, estiation interval partitioning is introduced. Actor nodes eploy a ρ-persistent carrier sense ultiple access (CSMA) echanis for MAC such that they access channel during slot intervals with a probability of ρ if channel is no other actor node is sensed to be transitting. Expected nuber of actor nodes that will transit when channel becoes idle is given by N k ρ. If N k ρ > 1, then a collision is expected to occur. To prevent collisions and resultant retransissions, ρ should be chosen accordingly, i.e., ρ < 1 / N k. For this schee, successful transission probability of actor node k can be found as ς k = ρ(1 ρ) N k 1 (32) Using ς k, ean nuber of channel access trials ϕ k before gaining access to channel is found as E{ ϕ k } = lς k (1 ς k ) l 1 (33) l=0 Finally, ean duration of an iteration can be found as K E{ τ i } = τ slot E { ϕ k } (34) k =1 where τ slot is the channel access duration of an actor node while broadcasting its local state to neighbor actors. Found E { τ i } is incorporated into (31), to find τ c. Spectru access duration for sensor nodes is adjusted to allow convergence of consensus algorith. To this end, although, higher available spectru access τ a duration is possible, τ a is reduced at the expense of increased nuber of required channels during local estiation. Reduced spectru access duration τa is deterined as τ a = in k { μ k } τ c (35) where τa ax τ () r. Using developed schee, α and β values are found. Instantaneous throughput values, T k, for channels C k of actor node k under opportunistic spectru access are deterined and updated according to spectru opportunities. We now provide perforance assessent of our schee.

8 12 O. Ergul et al. / Ad Hoc Networks 41 (2016) Perforance evaluation In this section, we provide siulation results related to the provided analysis and the proposed consensus schee Instantaneous throughput Perforance of proposed instantaneous throughput deterination odel is shown in Fig. 3. Analytically calculated instantaneous throughput is shown to be closely following siulations. τ s and τ cs are set to 0.02 and s, respectively. P hole is varied fro 0.1 to 0.9. Calculated instantaneous throughputs for τ t = 0.1, 0.08, 0.06, and 0.03 s overshoot the achieved ones after a critical value of P hole, e.g., after P hole = 0. 3 calculated instantaneous throughput exceeds the achieved one for τ t = s, and siilar relationship between siulated and analytic results is observed for other τ t values, as well. Therefore, in our design of consensus algorith, we introduce safety factor κ to reduce calculated throughput by a little aount to copensate for possible overshoots. We use developed fraework to evaluate the instantaneous throughput values, T k, and calculate the ean of the spectru access duration μ k in an event estiation interval for sensor nodes connected to actor node k, i.e., M k, as μ k = T k τ e Error rate Accuracy of proposed analytical packet error rate calculation schee is presented in Fig. 4. For received power calculations, transission power P t is set to 5 db, noise power P n is set to 90 db, path loss exponent η is set to 3, shadowing standard deviance σ is set to 3.8, distance is taken to be 5, reference distance d 0 is taken to be 1, reference path loss PL ( d 0 ) is taken as 40 db, and B N / R ratio is taken Fig. 3. Coparision of calculated and achieved instantaneous throughput due to opportunistic spectru access for τ t = 0. 1, τ t = 0. 08, τ t = 0. 06, τ t = s Fig. 4. Coparison of analytically calculated packet error rate and siulation results with respect to licensed user arrival rate β for SNR values under licensed user interference of P l = 5 and 15 db. to be unity. Value of τ t is taken to be 0.05 s, P d is equal to 0.9, P f is equal to 0.1, and α is equal to 10. Siulations are repeated ties and results are averaged. It is shown in Fig. 4, the analytic forulation follows the siulation values closely. While packet error rate is in the order of 10 5 when the licensed user interference P l is 5 db, packet error rate becoes in the order of 10 2 when P l increases to 15 db Consensus convergence duration Nuerical results are provided to display the consensus convergence duration with respect to algebraic connectivity λ 2 ( L ) and available spectru opportunity in ters of licensed user interference and channels errors. The prolongation of consensus convergence duration with respect to various algebraic connectivity values of actor graph G, i.e., fro 1 to 20, is discussed. Value of ε is set to 40 db. Value of E { τ i } is set to 0.05 s. To investigate effect of spectru obility, effect of licensed user interference P l is assessed for 5 10 db, and effect of birth rate of licensed user β is assessed for In Fig. 5, we show that as the instantaneous throughput decreases, required nuber of channels to schedule sensors increases. However, this decrease becoes arginal after a certain point, e.g., T k = This fact also suggests that it is possible to decrease spectru access duration for sensor-toactor counication, τ a, to provide sufficient tie opportunity to reach consensus aong actor nodes without increasing spectru efficiency by increasing required nuber of channels under sparse licensed user activity. For consensus convergence duration τ c, it has been shown in Fig. 6 that as the algebraic connectivity λ 2 increases, effect of spectru obility, i.e., P l and β, decreases. Effect of increasing λ 2 becoes arginal after a certain point, e.g., τ c reduces to its half value when λ 2 increases fro 1 to 2, however, when λ 2 is increased fro 9 to 10, this increase does not iply any significant reduction of τ c. For P l = 5 db, τ c follows the sae pattern for β = 10 and 20. It is deduced that for low licensed user interference, β value

9 O. Ergul et al. / Ad Hoc Networks 41 (2016) Fig. 5. Required nuber of channels with respect to instantaneous throughput T k for τ e = 1 s and distortion constraint D o of 50 db. does not affect the τ c. However, for P l = 10 db, experienced τ c increases with β. Sufficient tie opportunity to reach consensus aong actor nodes should be provided to reach consensus before end of the estiation interval. Therefore, we incorporate analytically forulated consensus duration to liit spectru access duration for local estiation of actors, i.e., τ a Adaptive spectru sharing for consensus In this section, we present siulation results on the perforance of proposed sensing fraework. In Fig. 7, consensus reaching perforance is presented with respect to algebraic connectivity for different T k values. P l is set to 15 db. It is shown that for different λ 2 values, consensus is reached irrespective of algebraic connectivity. Our schee achieves higher consensus reaching rate perforance with high instantaneous throughput values, i.e., consensus reaching rate Fig. 7. Consensus reaching rate of actor nodes. decreases with decreasing in { T k } fro 0.6 to 0.2. Reducing spectru access duration of sensor nodes in local estiation, provides this perforance gain in channels having high licensed user activity spectru bands. Proposed estiation interval partitioning schee strictly reduces spectru access interval in accordance with sparse spectru availability and high licensed user interference. Reduction of local estiation duration is benefited in high licensed user interference scenarios, and for low instantaneous throughput case, higher duration for consensus convergence is left. In Fig. 8, disagreeent aong actors at the end of estiation interval is presented. With increasing algebraic connectivity λ 2, left duration for consensus decreases. Therefore, higher nuber of incoplete consensus phases yields higher disagreeent than desired disagreeent ε, which is set to Since the predicted τ c decreases with increased λ 2, spectru access interval for local estiation increases, as well. Due to randoness in licensed user activity, this reduction in τ c results in increase of disagreeent aong actor Fig. 6. Consensus duration with respect to algebraic connectivity for various P l and β values. Fig. 8. Consensus disagreeent of actor nodes.

10 14 O. Ergul et al. / Ad Hoc Networks 41 (2016) 5 14 nodes. However, as it is shown in Fig. 8, disagreeent is still very close to and in the order of the objective value. 7. Conclusions In this paper, reliable spectru access and reaching consensus with cognitive radio sensor and actor nodes are discussed. Furtherore, a consensus schee is proposed to increase reliability by enabling consensus convergence of actor nodes with iniu spectru access. Effects of licensed user in ters of both interruption and interference are odeled, and iplications on design and perforance are highlighted. Proposed schee is shown to be satisfying consensus convergence requireents, especially in dense licensed user activity and high interference scenarios which can be encountered in various portions of the Sart Grid. Soe of the future research directions can be listed as investigation of the effects PU obility on opportunistic consensus and coparison of consensus results under different PU channel occupancy odels. References [1] I.F. Akyildiz, W. Su, Y. Sankarasubraania, E. Cayirci, A survey on sensor networks, IEEE Coun. Mag. 40 (8) (2002) [2] I.F. Akyildiz, I.H. Kasioglu, Wireless sensor and actor networks: research challenges, Ad Hoc Netw. 2 (4) (2004) [3] I.F. Akyildiz, W.Y. Lee, M.C. Vuran, S. Mohanty, NeXt generation/dynaic spectru access/cognitive radio wireless networks: a survey, Coput. Netw. J. 50 (13) (2006) [4] O.B. Akan, O.B. Karli, O. Ergul, Cognitive radio sensor networks, IEEE Netw. 23 (4) (2009) [5] R. Oflati-Saber, J.A. Fax, R.M. Murray, Consensus and cooperation in networked ulti-agent systes, Proc. IEEE 95 (1) (2007) [6] J.A. Han, W.S. Jeon, D.G. Jeong, Energy-efficient channel anageent schee for cognitive radio sensor networks, IEEE Trans. Veh. Technol. 60 (4) (2011) [7] X. 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Ding, Opportunistic spectru access in cognitive radio networks, in: Proceedings of IEEE INFOCOM, 2008, pp [26] W.Y. Lee, I.F. Akyildiz, Optial spectru sensing fraework for cognitive radio networks, IEEE Trans. Wirel. Coun. 7 (10) (2008) [27] M. Zuniga, B. Krishnaachari, Analyzing the transitional region in low power wireless links, in: Proceedings of IEEE Sensor and Ad Hoc Counications and Networks, SECON, 2004, pp [28] S. Lin, D.J. Costello Jr., Error Control Coding: Fundaentals and Applications, Prentice-Hall, Englewood Cliffs, NJ, [29] J.M. Mendel, Lessons in Estiation Theory for Signal Processing, Counications, and Control, Prentice-Hall, Englewood Cliffs, NJ, OZGUR ERGUL [S 11] received his M.S. degree in electrical and electronics engineering fro Middle East Technical University, Turkey, in He is currently pursuing his Ph.D. degree as a research assistant in the Next-generation and Wireless Counications Laboratory, Koc University. His current research interests include cognitive radio networks, wireless sensor networks, 5G obile networks, Internet-of-things, Terahertz counications. A. OZAN BICEN [S 08] received the B.Sc. degree in electrical and electronics engineering fro Middle East Technical University, Ankara, Turkey, in 2010 and the M.Sc. degree in electrical and electronics engineering fro Koc University, Istanbul, Turkey, in He is currently working toward the Ph.D. degree in the School of Electrical and Coputer Engineering, Georgia Institute of Technology, Atlanta, GA, USA. He is currently a Graduate Research Assistant with the Broadband Wireless Networking Laboratory, School of Electrical and Coputer Engineering, Georgia Institute of Technology. His current research interests include design and analysis of olecular counication systes, cognitive radio networks, and wireless sensor networks. OZGUR B. AKAN [M 00-SM 07] received his Ph.D. degree in electrical and coputer engineering fro the Broadband and Wireless Networking Laboratory, School of Electrical and Coputer Engineering, Georgia Institute of Technology in He is currently a full professor with the Departent of Electrical and Electronics Engineering, Koc University, and director of the NWCL. His current research interests are in wireless counications, nano-scale and olecular counications, and inforation theory. He is an Associate Editor of IEEE Transactions on Counications, IEEE Transactions on Vehicular Technology, the International Journal of Counication Systes (Wiley), the NanoCounication Networks Journal (Elsevier), and European Transactions on Technology.