RAPID advances in processing capability, memory capacity,

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1 IEEE SENSORS JOURNAL, VOL. 13, NO. 11, NOVEMBER Spectrum Sensng n Opportunty-Heterogeneous Cogntve Sensor Networks: How to Cooperate? Guoru Dng, Student Member, IEEE, Jnlong Wang, Senor Member, IEEE, Qhu Wu, Senor Member, IEEE, Fe Song, and Yngyng Chen, Senor Member, IEEE Abstract Cogntve sensor network (CSN) s a promsng paradgm to address the spectrum scarcty problem n tradtonal wreless sensor networks. Relable spectrum sensng s essental to enable the normal operaton of a CSN. Exstng researches showed that by explotng spatal dversty, cooperatve sensng can greatly mprove the detecton performance over noncooperatve sensng n opportunty-homogeneous envronment. At a gven tme, cogntve sensors at dfferent locatons, however, may experence heterogeneous spectrum opportuntes makng the cooperaton among cogntve sensors ntractable. In ths paper, we show the lmtatons and drawbacks of merely usng temporal-doman detecton performance metrcs and ntroduce novel spato-temporal detecton performance metrcs to gude the desgn of jont spato-temporal spectrum sensng. An effcent one-bt hard decson based three-phase (.e., a global cooperaton phase, a local cooperaton phase, and a jont decson phase) spato-temporal sensng algorthm s proposed and numercal results demonstrates the effectveness of the proposed algorthm. Index Terms Cogntve sensor network, spectrum sensng, heterogeneous opportunty, cooperaton. I. INTRODUCTION RAPID advances n processng capablty, memory capacty, and rado technology have enabled the development of wreless sensor networks (WSNs) wth small and nexpensve communcaton sensors [1]. WSNs are capable of montorng physcal and envronmental nformaton for varous hgh-level applcatons. We envson that the wde deployment of WSNs wll mpact our daly lfe dramatcally. Current WSN sensors usually operate on lcense-exempt Industral, Scentfc and Medcal (ISM) frequency bands, whch are shared wth many other popular wreless technologes (e.g., W-F and Bluetooth) and become more and more crowded [2]. To deal wth the spectrum scarcty problem, a new sensor networkng paradgm, cogntve sensor network (CSN), whch Manuscrpt receved May 12, 2013; accepted May 15, Date of publcaton May 20, 2013; date of current verson September 25, Ths work was supported n part by the Natonal Natural Scence Foundaton of Chna under Grant and Grant , the Natonal Basc Research Program of Chna under Grant 2009CB320400, and by the Jangsu Provnce Natural Scence Foundaton under Grant SBK The assocate edtor coordnatng the revew of ths paper and approvng t for publcaton was Prof. Elena Gaura. (Correspondng author: Q. Wu.) G. Dng, J. Wang, Q. Wu, and F. Song are wth the College of Communcatons Engneerng, PLA Unversty of Scence and Technology, Nanjng Chna (e-mal: dngguoru@gmal.com; wjl543@sna.com; wqhtxdk@yahoo.cn; aroucan@163.com). Y. Chen s wth the Electrcal and Computer Engneerng Department, Stevens Insttute of Technology, Hoboken, NJ USA (e-mal: yngyng.chen@stevens.edu). Color versons of one or more of the fgures n ths paper are avalable onlne at Dgtal Object Identfer /JSEN X 2013 IEEE ncorporates cogntve rado [3] capablty on the bass of tradtonal WSNs has been studed recently [4] [7]. In CSNs, cogntve sensors explot frequency bands that are lcensed to prmary users (PUs) but are not used by them at a specfc tme and/or n a specfc area. Snce cogntve sensors can operate on lcensed frequency bands of the PUs n an opportunstc or nterference-free manner, they need to have the capablty to dentfy the avalablty of spatal and/or temporal access opportuntes va spectrum sensng pror to transmsson. Thus, spectrum sensng s one of the major functonaltes dstngushng CSNs from tradtonal WSNs. For a frequency band of nterest, the problem of spectrum sensng s generally formulated as a bnary hypothess testng: s there an access opportunty or not? The access opportunty can be characterzed as temporal or spatal. A temporal access opportunty s a tme perod when the prmary transmsson s absent whle a spatal access opportunty s a geographcal area where the cogntve sensor s far away from the PU [8]. Relable spectrum sensng s a challengng task due to hdden node problem [9], shadowng effect, mult-path fadng and tme-varyng natures of wreless channels [10]. To address these problems, cooperatve sensng (CS) among multple spatally dstrbuted spectrum sensors s a promsng drecton [11] [13], whch can acheve much better detecton performance than non-cooperatve sensng (NCS) by explotng multuser dversty [14]. Although the problem of spectrum sensng has been extensvely studed, there are stll some crtcal ssues needed to be addressed. Frst of all, a more general system model s needed. Majorty of the exstng studes (e.g., see [15] [19]) consder an opportunty-homogeneous CSN, whch conssts of a large-scale PU network (e.g., a Dgtal TV system) and a small-scale SU network (e.g., a WLAN-lke CSN system). In ths knd of network scenaro, the dstances between any cogntve sensors are very small compared wth the dstance from any cogntve sensor to the prmary transmtter, and thus the average receved sgnal-to-nose ratos (SNRs) at cogntve sensors are approxmately equal. Hence, the problem of cooperatve sensng n the lterature s usually modeled as a common bnary hypothess testng among all cogntve sensors. However, when we consder an opportunty-heterogeneous CSN, where the network scales of the prmary system (e.g., a Wreless Mcrophone system) and the cogntve system are comparable, at a gven tme cogntve sensors at dfferent locatons may experence dfferent spectrum opportuntes, n whch case the common hypothess does not hold any more.

2 4248 IEEE SENSORS JOURNAL, VOL. 13, NO. 11, NOVEMBER 2013 Furthermore, mproved detecton performance metrcs are needed. Tradtonally, a pure temporal sensng senstvty s used to evaluate the detecton performance of dfferent schemes. For example, n IEEE standard [20], for a fxed sensng tme, a detecton probablty no less than 0.9 and a false alarm probablty no larger than 0.1 are requred when the average receved SNR s 1 db for analog TVs, 21dB for dgtal TVs, and 12dB for wreless mcrophones. Ths temporal sensng senstvty s very conservatve and usually leads to a over-large spatal margn [8]. In ths paper, we study the problem of spectrum sensng n opportunty-heterogeneous CSNs. We ntroduce a novel network model that can characterze opportunty-heterogenety among dfferent cogntve sensors and redefne the problem of spectrum sensng n CSNs from a jont spato-temporal twodmensonal detecton perspectve. We show the lmtatons and drawbacks when only temporal-doman detecton performance metrcs are used by revewng the tradtonal spectrum sensng schemes (.e., both NCS and decson fuson-based CS), and derve novel two-dmensonal detecton performance metrcs to gude the desgn of jont spato-temporal spectrum sensng. The fact that nether NCS nor CS performs well n opportunty-heterogeneous CSNs motvates us to further propose an effcent three-phase spato-temporal sensng (TP-STS) algorthm: a global cooperaton phase to dentfy the common temporal opportunty for all cogntve sensors by explotng multuser dversty, a local cooperaton phase to dentfy the heterogeneous spatal opportuntes for ndvdual cogntve sensors by effectvely fusng non-cooperatve bnary decsons among neghborng sensors, and fnally a jont decson phase to determne the avalablty of the spato-temporal opportunty at each ndvdual cogntve sensor. Numercal results are provded to demonstrate the effectveness of the proposed algorthm. The rest of ths paper s organzed as follows. Secton II descrbes the system model and problem formulaton. Secton III presents the performance comparsons of the exstng NCS and CS schemes. Secton IV presents the techncal challenges ahead and develops a novel sensng algorthm. Secton V provdes numercal results, Secton VI revews the related works, and Secton VII concludes ths paper. II. SYSTEM MODEL AND PROBLEM FORMULATION We consder a CSN that shares a common frequency band wth a prmary user system. Of nterest n ths paper s to determne the avalablty of a spatal and/or temporal spectrum opportunty for each cogntve sensor n CSN. A. Opportunty-Heterogeneous Network Model As shown n Fg. 1, we consder a CSN wth one prmary transmtter (PT) and N cogntve sensors dstrbuted n the gven geographcal area. The PT has a PER wth a radus D p [26]. Insde the PER, no cogntve sensor may transmt f the prmary transmsson s detected, n order to guarantee any potental prmary receptons wthn. Outsde the PER, cogntve sensors can share the common frequency band wth the PT n a spatal reuse manner. Fg. 1. An opportunty-heterogeneous CSN. D p s the radus of prmary exclusve regon (PER) and D s s the sensng range of a cogntve sensor. We further consder that N cogntve sensors randomly dstrbute n a crcular area wth a radus D s, whch s closely related to the sensng senstvty of cogntve sensors. Any cogntve sensor outsde ths area wll not be able to detect the presence of the prmary sgnal. Typcally, D s > D p holds snce cogntve sensors must have a hgher sensng senstvty than the prmary recever senstvty n order to avod nterferng wth PRs [27]. In ths case, some cogntve sensors can be located nsde the PER and only temporal opportuntes could be exploted, whle others can be located outsde the PER and both temporal and spatal opportuntes for them are avalable. Consequently, at a gven tme dfferent cogntve sensors n CSN wll experence heterogeneous spectrum opportuntes. We consder that the cogntve sensors postons follow a two-dmensonal unform dstrbuton wth densty ρ,.e., N = ρπds 2.1 Due to the lack of cooperaton from the prmary user system, we consder that any cogntve sensor n the CSN does not have the pror locaton nformaton of the PT and performs opportunty detecton based only on the receved prmary sgnal strength: P (d ) = P t φ (d ) ψ ϕ, (1) where P t s the transmsson power of PT, d s the dstance between the PT and cogntve sensor, φ (d ) s the path-loss component, ψ and ϕ are respectvely the shadowng fadng and mult-path fadng components [28]. B. Spatal and Temporal Opportunty Model Ths secton formulates a spatal and temporal opportunty model and maps the opportunty to a two-dmensonal coordnate system as shown n Fg. 2. Jont spato-temporal sensng can be regarded as a bnary decson between O 1 (the frst quadrant) and O 0 (the second-thrd-fourth quadrants), where O 0 denotes that a spato-temporal opportunty s avalable and O 1 represents otherwse. 1 x corresponds an operaton that rounds x to the nearest ntegers less than or equal to x.

3 DING et al.: SPECTRUM SENSING IN OPPORTUNITY-HETEROGENEOUS COGNITIVE SENSOR NETWORKS 4249 Fg. 2. An llustratve graph for two-dmensonal opportunty model. For a gven cogntve sensor, an access opportunty exsts (O 0 ) when the prmary sgnal s temporally absent (H 0 ) or the sensor s outsde the PER (S 0 ); no access opportunty exsts (O 1 ) when the prmary sgnal s temporally present (H 1 ) and the sensor s located nsde the PER (S 1 ). Fg. 3. Comparsons of spato-temporal detecton performance between non-cooperatve sensng (NCS) and OR-rule based cooperatve sensng (CS) schemes. The detaled sensng parameter confguraton s gven n Secton V. The pure temporal sensng can be consdered as a bnary decson between left plane and rght plane (Fg. 2) and descrbed as the followng bnary hypothess testng problem [16]: H 0 : x [m] =w [m] H 1 : x [m] = (2) P (d ) s[m]+w [m], where null hypothess H 0 represents the absence of the prmary sgnal and hypothess H 1 denotes the presence of the prmary sgnal. x [m] s the receved sgnal by cogntve sensor at tme nstant m = 1, 2,..., M, where M s the number of collected samples durng one samplng process. w [m] N (0,σn, 2 ) s the addtve whte Gaussan nose sample, and s[m] s the unattenuated sample (normalzed to have unt power) of the prmary transmt sgnal. Smlarly, the pure spatal sensng can be consdered as a bnary decson between upper plane and lower plane (Fg. 2) and modeled as another hypothess testng problem [29]: S 0 : D p < d D s (3) S 1 : 0 d D p, where S 0 denotes the case that cogntve sensor s located outsde the PER and a spatal opportunty s avalable for t. S 1 denotes the case that cogntve sensor s located nsde the PER and no spatal opportunty can be exploted. Therefore, from a two-dmensonal detecton perspectve, we model the problem of spato-temporal spectrum sensng for each cogntve sensor as a new hypothess testng: O 0 : H 0 S 0 (4) O 1 : H 1 S 1, where O 0 denotes the case that a spato-temporal opportunty s avalable, ether because of the absence of the prmary sgnal (H 0 ) or the cogntve sensor s located outsde the PER (S 0 ). O 1 represents the case that no spato-temporal opportunty can be utlzed, whch means that the cogntve sensor s located nsde the PER (S 1 ) and the PT s transmttng (H 1 )atthe same tme. Apparently, (4) s a straghtforward combnaton of (2) and (3), whle t s more general n opportunty-heterogeneous CSNs due to the ntegral consderaton of prmary user s traffc varatons n both tme and space domans. Moreover, t brngs new techncal challenges, e.g., the desgn of proper performance metrcs and effcent sensng algorthms. III. SPATIO-TEMPORAL DETECTION PERFORMANCE METRICS In ths secton, we ntroduce new detecton performance metrcs to gude the jont detecton of spato-temporal opportuntes. The probabltes of spato-temporal false alarm and detecton for ndvdual cogntve sensor are respectvely gven by P f, ST (d ) Prδ ST (d )=O 1 O = O 0 } Prδ ST (d ) = O 1 H 0 }, 0 d D p = P 1 Prδ ST (d ) = O 1 H 1 } (5) +P 0 Prδ ST (d )=O 1 H 0 }, D p <d D s Pd, ST (d ) Prδ ST (d ) = O 1 O =O 1 } = Prδ ST (d ) = O 1 H 1 }, 0 d D p, (6) where O s the actual hypothess of cogntve sensor wth a dstance d from the PT and δ ST (d ) denotes ts bnary decson result. P 1 (P 0 ) denotes the probablty that the prmary transmsson s present (absent). Please refer to our pror works n [30] for detaled dervatons of (5) and (6). In terms of spato-temporal detecton performance metrcs, Fg. 3 compares detecton performance between between noncooperatve sensng (NCS) and OR-rule based cooperatve sensng (CS) schemes. It s shown n Fg. 3 that for a gven temporal false alarm probablty as 0.1, when cogntve sensor s located nsde the PER (.e., d D p ), CS scheme obtans a much hgher detecton probablty than NCS scheme. However, when cogntve sensor s located outsde the PER,

4 4250 IEEE SENSORS JOURNAL, VOL. 13, NO. 11, NOVEMBER 2013 CS scheme brngs a much hgher false alarm probablty than NCS scheme. Ths s manly due to the fact that, n CS scheme, the temporal detecton probablty of a cogntve sensor located far away from the PT (e.g, d = 2D p ) has been greatly mproved, whch actually results n severe spatal false alarms. Moreover, t s shown that the spato-temporal false alarms are hghly related to the prmary actvty level P 1,whchs consstent wth the analytcal results n (5) and (6). Nether NCS nor CS performs well n opportuntyheterogeneous CSNs. In NCS scheme, the cogntve sensor nsde the PER has a low spato-temporal detecton relablty due to the random channel fadng, whch cannot provde enough protecton for the potental prmary recevers. In CS scheme, however, the cogntve sensor outsde the PER has a very hgh spato-temporal false alarm probablty due to the blnd multuser cooperaton dversty, whch provdes overprotecton for the potental prmary recevers and results n severe access opportunty loss for the cogntve sensors. These drawbacks motvate us to desgn an effectve spato-temporal sensng framework. IV. THREE-PHASE SPATIO-TEMPORAL SENSING A. Challenges and Desgn Ratonale In consderng spato-temporal sensng n opportuntyheterogeneous CSNs, many crtcal challenges arse. Frst of all, jont optmzaton of spatal and temporal spectrum sensng s needed, to maxmze the utlzaton of both spatal and temporal access opportuntes for cogntve sensors, whle satsfyng the strct protecton requrement from the prmary users. Secondly, accurate locaton nformaton of the prmary transmtter s vtal to mtgate spatal false alarms, whle n practce t s unavalable for cogntve sensors due to the lack of cooperaton from the prmary transmtter. Furthermore, the random topology dstrbuton of cogntve sensors and the opportunty-heterogenety among them make t ntractable to obtan a close-form optmal sensng scheme. However, there are some nsghtful observatons as follows that can gude us to desgn suboptmal but effectve sensng schemes: For a gven tme nstant, the temporal access opportunty (.e., the absence of the prmary sgnal) s n common for all cogntve sensors and, a global cooperaton among multple cogntve sensors can sgnfcantly mprove the temporal detecton performance by explotng multuser dversty as compared wth a non-cooperatve approach. For a gven topology dstrbuton, the spatal access opportuntes may vary for cogntve sensors located at dfferent postons, whch makes blnd global cooperaton unusable. However, there typcally exst smlar spatal opportuntes among neghborng cogntve sensors, whch wll beneft the spatal opportunty detecton. B. Algorthm Framework The observatons above gude us n proposng a three-phase spato-temporal sensng (TP-STS) framework, whch conssts of the followng sequental phases: Phase 1-Global Cooperaton for Temporal Opportunty Detecton: In ths phase, the prmary sgnal s presence (H 1 )or Fg. 4. Illustraton of spatal opportunty detecton. D p s the radus of prmary exclusve regon (PER), D c s the radus of cogntve cooperatve regon (CCR), and d s the dstance between the prmary transmtter and cogntve sensor. A I (d, D p, D c ) denotes the common area of PER and CCR. absence (H 0 ) s detected through cooperatve sensng among all cogntve sensors. 2 Here we use the classcal OR logcbased decson fuson rule for ts smplcty and superor performance over other schemes n temporal opportunty detecton [33]. Specfcally, n ths phase a common recever collects and fuses the bnary decsons from each cogntve sensor and decdes on the presence of a temporal access opportunty based on the followng decson rule: N T T H 1 = B 1, (7) =1 H 0 where B s the non-cooperatve bnary decson of cogntve sensor. As shown n Fg. 3, for a gven temporal false alarm probablty, the temporal detecton probablty can be mantaned at a very hgh level by usng OR rule. On the other hand, the man drawback of the global cooperaton s the severe spatal false alarm phenomena as also shown n Fg. 3, whch wll be processed n the followng phase. Phase 2-Local Cooperaton for Spatal Opportunty Detecton: Dfferent from exstng studes, ths s a vtal phase to tackle the spatal false alarms resulted from the global cooperaton n Phase 1. In ths phase, each cogntve sensor performs a bnary hypothess testng on whether t s located nsde (S 1 ) or outsde (S 0 ) the PER through effectvely fusng the non-cooperatve bnary decsons of ts one-hop neghbors. As shown n Fg. 4, we consder the case that all one-hop neghbors of cogntve sensor are unformly dstrbuted n a dsc area, named cogntve cooperatve regon (CCR), wth cogntve sensor located at the center and a radus as D c. Specfcally, denote N as the neghbor set of cogntve sensor and N = ρπdc 2 as the total number of neghbors of cogntve sensor. The decson rule at cogntve sensor 2 To further consder the ssue of energy-effcency n spectrum sensng, proper sensor selecton and/or censorng schemes as those proposed n [35] and [36] could be ntegrated n ths phase, whch s not the focus of ths paper.

5 DING et al.: SPECTRUM SENSING IN OPPORTUNITY-HETEROGENEOUS COGNITIVE SENSOR NETWORKS 4251 s gven as: T S = k N B k S 1 S 0 β, = 1,...,N, (8) where β s the spatal detecton threshold. It s noted that the decson rule n (8) s n essence a spatal β-out-of- N rule. That s, f the number of ts neghbors whch make non-cooperatve decsons as no opportunty (.e., B k = 1, k N ) s larger than β, cogntve sensor wll declare tself as located nsde the PER; otherwse, cogntve sensor wll declare tself as located outsde the PER. Notably, the spatal detecton threshold β s a vtal parameter to balance the tradeoff between the protecton for the prmary users and the spatal opportunty utlzaton of the cogntve sensors. If β s much too small, more cogntve sensors located outsde the PER (S 0 ) wll potentally declare as nsde (S 1 ), and f β s much too large, more cogntve sensors located nsde the PER (S 0 ) wll potentally declare as outsde (S 0 ). Generally, for any cogntve sensor, the optmal spatal threshold can be obtaned through solvng the followng optmzaton problems: or OP1: OP2: mn β mn β PrT S β S = S 0 } Subject to PrT S β S = S 1 } P S md (9) Pr(S = S 0 ) PrT S β S = S 0 } +Pr(S = S 1 ) PrT S β S = S 1 }, (10) where OP1 and OP2 are respectvely gven accordng to the classcal Neyman-Pearson crteron and Bayesan crteron n dstrbuted detecton problems [37]. P md S n (9) s the maxmum tolerant probablty of spatal mss detecton requred by the prmary users. Due to the random topology dstrbuton of cogntve sensors, n practce t s ntractable to derve a close-form optmal soluton to ether (9) or (10). In ths paper we propose two heurstc but effectve spatal detecton thresholds as follows = β 1 = N π D 2 ( p arccos 1 D2 Dc 2 c 2D 2 p N AI (d,d p,d c ) π D 2 c D 2 p Dc 2 d =D p } ) ( ) +arccos Dc 2D p 1 4 }, (11) β 2 = k N n 1 PrB k = 1 S k = S 1 } + k N out 1 PrB k = 1 S k = S 0 } d =D p N PrB = 1 S = S 1 } (12) d =D p where A I (d, D p, D c ) denotes the common area of PER and CCR (See Appendx B for general results on A I (d, D p, D c )). N n and N out respectvely denote the sets of cogntve sensor s neghbors that are located nsde and outsde the PER. For any cogntve sensor n the CSN, the desgn prncples of the spatal thresholds β 1 and β 2 are summarzed as follows: As shown n (3), the task of spatal opportunty detectonnessencestodetermnethe relatve relatonshp between d and D p, whch means that the desgn of any proper spatal threshold should drectly relate to D p. Therefore, n desgnng both β 1 and β 2, we focus the study on the cogntve sensor located just at the edge of PER (.e., d = D p ). AsshownnFg.4,thecommonareaA I (d, D p, D c ) of PER and CCR corresponds to the neghbors of cogntve sensor that are located nsde the PER. In the case of unform sensor dstrbuton, β 1 represents the number of cogntve sensor s neghbors that are located nsde the PER. Intutvely, f cogntve sensor tself s located nsde the PER, more than β 1 neghbors n the CCR wll be located nsde the PER, and vce versa. The spatal threshold β 2 s proposed to further ntegrate the mpact of mperfect non-cooperatve decsons. That s, a neghbor located nsde the PER may declare B k = 0, k N n ; and a neghbor located outsde the PER may declare B k = 1, k N out. The frst term on the rght sde of Eq. (12) represents the average number of neghbors that are located nsde the PER and correctly make local ther decsons as nsde the PER and the second term represents the average number of the neghbors that are located outsde the PER and falsely make local decsons as nsde the PER. In practce, due to the lack of the relatve locaton nformaton of the prmary transmtter and ts neghbors, cogntve sensor cannot obtan the non-cooperatve detecton performance of ts neghbors,.e., PrB k = 1 S k = S 1 }, for k N n or PrB k = 1 S k = S 0 }, for k N out. Consequently, an approxmaton s made by only usng the local detecton probablty of the cogntve sensor located at the edge of the PER to obtan β 2. The effectveness of ths approxmaton wll be demonstrated n the followng secton. Phase 3-Jont Decson for spato-temporal Opportunty: In ths phase, a fnal decson on the avalablty of the spatotemporal opportunty s obtaned as follows: If T T < 1orT S <β, then δ ST (d ) = O 0 If T T > 1andT S >β, then δ ST (d ) = O 1. (13) V. NUMERICAL RESULTS AND DISCUSSIONS In ths secton, we present numercal smulatons to demonstrate the effectveness of the proposed TP-STS. The transmsson power of the PT s assumed to be 25 mw. The bandwdth B s 200 KHz and the sensng duraton T s s 1 ms. The recever nose power spectral densty s 174 dbm/hz and the recever nose fgure s 11 db. The path-loss exponent s 4, the shadow fadng db-spread s 5.5 db, and the average multpath Raylegh fadng gan s 1. At the edge of the PER, the average receved sgnal power s 114 dbm, whch amounts to a D p of 1.58 km. The cogntve sensors are randomly located around the prmary transmtter and the average sensor densty s set to ρ = 40/Km 2. The smulaton results are

6 4252 IEEE SENSORS JOURNAL, VOL. 13, NO. 11, NOVEMBER 2013 Fg. 5. Comparsons of the two-dmensonal detecton performance of NCS, CS and the proposed TP-STS (D c = D p /4). (a) For the proposed TP-STS, spatal threshold s set as β = β 1. (b) For the proposed TP-STS, spatal threshold s set as β = β 2. Fg. 6. Comparsons of the two-dmensonal detecton performance of NCS, CS and the proposed TP-STS (D c = D p /2). (a) For the proposed TP-STS, spatal threshold s set as β = β 1. (b) For the proposed TP-STS, spatal threshold s set as β = β 2. obtaned by averagng the results of 100 randomly-generated topologes and 10 4 random channel realzatons. To make a far comparson, the temporal false alarm probabltes for all schemes are set as 0.1. Fg. 5 and Fg. 6 presents the comparson of NCS scheme, CS scheme and the proposed TP-STS scheme, n terms of the spato-temporal detecton performance. It s shown n both Fg. 5 and Fg. 6 that: () The spato-temporal false alarm probablty of the proposed TP-STS scheme declnes to almost zero when d /Dp < 1andd /Dp > 2, whch greatly decreases the amount of access opportunty loss and mproves the spectrum utlzaton for cogntve sensors. The reason behnd s that n TP-STS scheme, most of the potental false alarms resulted from the global cooperaton phase can be corrected n the sequental local cooperaton phase, here we call ths performance gan as mult-phase dversty gan. () The spato-temporal detecton probablty of the proposed TP-STS scheme, usng ether β 1 or β 2, s worse than CS scheme but sgnfcantly better than NCS scheme. Specfcally, usng β 1 provdes a hgher detecton probablty and thus more protecton for the prmary users, whle usng β 2 results n a smaller spato-temporal false alarm probablty and thus hgher spectrum utlzaton for cogntve sensors. By comparng the results n Fg. 5 and Fg. 6, t s observed that the range of CCR,.e., D c, has an mportant mpact on the detecton performance of the proposed TP-STS. Apparently, when the dstance between the cogntve sensor and the PT satsfes d /D p [1, 1.5], the spato-temporal false alarm probabltes of the proposed TP-STS scheme n Fg. 6 wth D c = D p /2 are smaller than those n Fg. 5 wth D c = D p /4. VI. RELATED WORK The subject of opportunty-heterogenety among dfferent cogntve sensors has been studed n the exstng body of research on dynamc spectrum access strateges n terms of

7 DING et al.: SPECTRUM SENSING IN OPPORTUNITY-HETEROGENEOUS COGNITIVE SENSOR NETWORKS 4253 overlay and underlay [9]. In overlay strategy, cogntve sensors can only explot the temporal opportunty n the absence of the prmary transmsson. However, n underlay strategy, cogntve sensors can always access the lcensed spectrum subject to an nterference temperature constrant from the prmary use. Mxed access strategy of overlay and underlay has also been recently studed to explot temporal and spatal opportuntes jontly [21]. The problem of cooperatve sensng among opportunty-heterogeneous cogntve sensors has been frst formulated n [22] and an extenson to wdeband sensng has been presented n [23]. Dfferently, n ths paper we nvestgate the ssue of spectrum sensng n opportuntyheterogeneous CSNs from a perspectve of jont exploraton of spato-temporal opportuntes, whch remans a sgnfcant challenge due to the requrement of ntegratng the spatal and temporal nformaton wth spectrum sensng. The topc of desgnng proper performance metrcs to evaluate the effectveness of spectrum sensng algorthms has also receved growng attenton. As mentoned n Secton I, tradtonally, a probablty of detecton (.e., the probablty of correctly determnng that the prmary transmsson s present) as a functon of a probablty of false alarm (.e., the probablty of ncorrectly determnng that the prmary transmsson s present) s used for temporal sensng [9]. In [24], the ssue of spatal false alarm problem nvolved n the pure temporal performance metrcs s hghlghted to characterze the access opportunty loss n spatal doman. In [25], the authors ntroduce space-tme detecton metrcs to characterze the tradeoff between the safety to prmary users and the spectrum utlzaton of a sngle cogntve sensor, whch may be located ether nsde or outsde a prmary exclusve regon (PER) (see Fg.1). The safety s measured n terms of the harmful nterference caused by a cogntve sensor located at the worst-case locaton,.e., the edge of the PER. The spectrum utlzaton s measured by a weghted (wth respect to all possble locatons of the cogntve sensor) probablty of spectrum holes recovered by the cogntve sensor. Dfferently, the unque features of the presented metrcs n ths paper are two-folds. The frst s that the presented metrcs can characterze the spato-temporal detecton performance of cogntve sensors under a more general locaton assumpton. The second s that the presented metrcs can effectvely evaluate both NCS algorthms and CS algorthms, whle the metrcs n [25] are not yet easly to be extended to mult-sensor CS algorthms. More mportantly, the presented metrcs can be used to gude the desgn of effcent sensng algorthms for opportuntyheterogeneous CSNs, whch are not consdered n [25]. VII. CONCLUSION The spectrum access opportuntes for cogntve sensors exst not only n tme doman but also n space doman. In ths paper we ntroduced a novel opportunty-heterogeneous cogntve sensor network (CSN) model and redefned the problem of spectrum sensng n opportunty-heterogeneous CSNs from a jont spato-temporal two-dmensonal detecton perspectve. We showed the lmtatons and orgnal drawbacks of pure temporal-doman detecton performance metrcs, whch motvated us to derve novel spato-temporal detecton performance metrcs and to further propose an effcent threephase spato-temporal sensng (TP-STS) algorthm to tackle the problem of spectrum sensng n opportunty-heterogeneous CSNs by explotng the mult-phase dversty gan. Numercal results were also provded to demonstrate the effectveness of the proposed algorthm. APPENDIX A CALCULATION OF COMMON AREA OF PER AND CCR As shown n Fg. 5, D p and D c respectvely denote the radus of PER and CCR, d denotes the dstance between the prmarytransmtterand cogntvesensor, the ntersectng area of PER and CCR can be calculated as follows: Case I: for 0 d D p D c, A I (d, D p, D c ) = π mnd 2 p, D2 c }. (14) Case II: for D p D c < d < D p + D c, ( D 2 A I (d, D p, D c ) =D 2 p arccos p + d 2 Dc 2 ) 2D p d ( D 2 + Dc 2 arccos c + d 2 D 2 ) p 2D c d ( D 2 d Dc 2 c + d 2 D 2 ) p 2. (15) 2d Case III: for d D p + D c, A I (d, D p, D c ) = 0. ACKNOWLEDGMENT The authors would lke to thank the anonymous revewers and the Assocate Edtor for ther constructve comments and Dr. Xan Zhang and Dr. Zongsheng Zhang for ther valuable nput. REFERENCES [1] D. Puccnell and M. Haengg, Wreless sensor networks: Applcatons and challenges of ubqutous sensng, IEEE Crcuts Syst. Mag., vol. 5, no. 3, pp , Sep [2] G. Zhou, J. A. Stankovc, and S. H. 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Zhang, Cooperatve communcatons for cogntve rado networks, Proc. IEEE, vol. 97, no. 5, pp , May [35] S. Malek, A. Pandharpande, and G. Leus, Energy-effcent dstrbuted spectrum sensng for cogntve sensor networks, IEEE Sensors J., vol. 11, no. 3, pp , Mar [36] G. Dng, Q. Wu, F. Song, and J. Wang, Decentralzed sensor selecton for cooperatve spectrum sensng usng unsupervsed learnng, n Proc IEEE Int. Conf. Commun. (ICC), Jun. 2012, pp [37] P. K. Varshney, Dstrbuted Detecton and Data Fuson. NewYork, NY, USA: Sprnger-Verlag, Guoru Dng (S 10) receved the B.S. degree (Hons.) n electrcal engneerng from Xdan Unversty, X an, Chna, n 2008, and the M.S. degree from the Insttute of Communcatons Engneerng, PLA Unversty of Scence and Technology, Nanjng, Chna, n He s currently pursung the Ph.D. degree n communcatons and nformaton systems wth the College of Communcatons Engneerng, PLA Unversty of Scence and Technology. Hs current research nterests nclude wreless sensor networks, cogntve rado networks, spatotemporal sgnal processng, dstrbuted optmzaton theory, and statstcal learnng. He currently serves as a Revewer for the IEEE SIGNAL PROCESS- ING MAGAZINE, the IEEE TRANSACTIONS ON COMMUNICATIONS, the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, and the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY. He was a recpent of the Best Paper Awards from the IEEE WCSP n He s currently a votng member of IEEE Whte Space Rado Workng Group. Jnlong Wang (SM 13) receved the B.S. degree n wreless communcatons, and the M.S. and Ph.D. degrees n communcatons and electronc systems from the Insttute of Communcatons Engneerng, Nanjng, Chna, n 1983, 1986, and 1992, respectvely. He s currently a Char Professor wth the PLA Unversty of Scence and Technology, Nanjng. He s the Co-Char of IEEE Nanjng Secton. He has publshed wdely n the areas of sgnal processng for wreless communcatons and networkng. Hs current research nterests nclude soft defned rado, cogntve rado, and green wreless communcaton systems. Qhu Wu (SM 12) receved the B.S. degree n communcatons engneerng, and the M.S. and Ph.D. degrees n communcatons and nformaton systems from the Insttute of Communcatons Engneerng, Nanjng, Chna, n 1994, 1997, and 2000, respectvely. From 2003 to 2005, he was a Postdoctoral Research Assocate wth Southeast Unversty, Nanjng. From 2005 to 2007, he was an Assocate Professor wth the Insttute of Communcatons Engneerng, PLA Unversty of Scence and Technology, Nanjng, where he s currently a Full Professor. From March 2011 to September 2011, he was an Advanced Vstng Scholar wth the Stevens Insttute of Technology, Hoboken, NJ, USA. Hs current research nterests nclude wreless communcatons and statstcal sgnal processng, wth emphass on system desgn of software defned rado, cogntve rado, and smart rado. Fe Song receved the B.S. degree n communcatons engneerng and the Ph.D. degree n communcatons and nformaton system from the Insttute of Communcatons Engneerng, PLA Unversty of Scence and Technology, Nanjng, Chna, n 2002 and 2007, respectvely. She s currently a Lecturer wth the PLA Unversty of Scence and Technology. Her current research nterests nclude cogntve rado networks, MIMO, and statstcal sgnal processng.

9 DING et al.: SPECTRUM SENSING IN OPPORTUNITY-HETEROGENEOUS COGNITIVE SENSOR NETWORKS 4255 Yngyng Chen (SM 11) s an Assocate Professor wth the Department of Electrcal and Computer Engneerng, Stevens Insttute of Technology, Hoboken, NJ, USA. Pror to jonng Stevens Insttute of Technology, she was wth Alcatel-Lucent, Murray Hll, NJ, USA. Her work has nvolved a combnaton of research and development of new technologes and real systems. She was an Instructor wth the Computer Scence Department, Rutgers Unversty. She was a recpent of the NSF CAREER Award n 2010 and Google Research Award n She receved the Stevens Board of Trustees Award for Scholarly Excellence n She s a recpent of the Best Paper Awards from ACM MobCom n 2011 and WONS n 2009, as well as the Best Technologcal Innovaton Award from the Internatonal TnyOS Technology Exchange n She receved the IEEE Outstandng Contrbuton Award from the IEEE New Jersey Coast Secton from 2005 to She receved the Ph.D. degree n computer scence from Rutgers Unversty, the M.S. degree n computer scence from North Carolna State Unversty, and the B.S. degree n physcs from Nanjng Unversty, Nanjng, Chna. Her current research nterests nclude cyber securty and prvacy, wreless embedded systems, wreless and sensor networks and moblty, moble socal networks, and pervasve computng. She has co-authored Securng Emergng Wreless Systems and he has publshed extensvely n journal and conference papers. Her research has been reported n numerous meda outlets, ncludng the Wall Street Journal, MIT Technology Revew, Insde Scence, NPR, and CNET.