Robust Cooperative Spectrum Sensing for Disaster Relief Networks in Correlated Environments

Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 1 Abstract — Di saster relief netw orks are d esig ned t o be adapt abl e an d resilient so to encom pass the de mands of t he emergency s ervice. Cog nitive Ra dio enhanc ed ad - hoc architect ure ha s been p ut for w ard as a candi date t o ena ble s uch ne tw or ks. Spect ru m sens ing , t he cor ner st one of th e Cog nit ive Radi o para dig m, h as be en t he fo cus of intensi ve rese arch, f rom whi ch the ma in c oncl usi on w as t hat i ts perfor mance c an be grea tly enha nced t hr oug h the us e of coo pera tiv e se nsi ng sc he mes. T o apply the C og niti ve Ra dio para dig m to A d-h oc disaster r eli ef netw orks, the design of effect ive coop erative spect rum sensi ng sc he me s is essential. In this pa per w e propose a cluster based o rchestrati on coope rati ve s ensi ng sc he me, whi ch ad apt s to th e cluster nodes surr oundi ng radi o en viro n ment state as w ell as to the d egree of correlatio n obse rv ed betw een th ose nodes . The prop ose d sche me is given both in a cent rali zed as well as in a decentralized approa ch . I n t he c entr aliz ed a ppro ach , t he cluster head cont rols and a dapts the di stri buti on of the cl uste r se nsing nod es acc ord ing to the monit ored s pectru m state . While i n t he decentrali zed appr oach, each of the cl uster no de s deci des w hich spect rum it shoul d monit or, acc ordi ng t o the pas t l ocal s ensi ng deci sio ns of the cl uste r nodes . T he ce ntra lize d a nd dec ent ra lized schem es can be co mbi ned t o ac hie ve a more rob ust cooper ative s pectr um sensing sch eme. Th e pro pos ed sc hem e per form anc e is eval uate d t hroug h a framew or k, whi ch all ow s mea suri ng the acc uracy of the spectru m sensing coo perative s cheme by meas uring the error in the estimation of the monit ored spect rum stat e. Thro ugh t h is eval uati on i t is s how n that the pro pose d sc he me outpe rfo r ms the case w here the choice of w hich sp ectrum to se nse is do ne w it hout usi ng t he kn ow ledge o btai ne d in pr evi ous se nsi ng iteratio ns, i.e. a imple mentati on of a bl ind R ou nd Ro bin s che me. Index Terms — Coope rativ e S pectr um S ensi ng , Ad - hoc , Disaster R elief, Orc hestratio n Scheme , Ad apt ive C ount ing R ule . I. I NTRODUCTION disaster, according to [1] , can be loosely defin ed as an event, which over a relativ ely short time period, causes a large number of casualties and infrastructure damage s . In a M anus cri pt subm it ted o n Dec embe r 1, 200 9 to the Jo urnal of S ele cted Are as in Comm unicat ions, s pecial i ssue o n “ Advances in Cogniti ve Radio Networki ng and C ommunicati ons ”. 1 Center for TeleInFra struktu r Aalborg Universit y, Denmark 2 IT/IST, Tec hnic al Universi ty of Lisbon , Portuga l Contac t E - mail: {nup, n m, np}@es.aau.d k scenario where the breakdown of the communication infrastructure o ccurs, it is vital that the co mmunicatio ns bet ween the rel ief gr oup s, up on net wor k de plo yment , are established as quickly and as easily as po ssib le. T his rai ses the need for specifi cally tailored infrastructure - less mobil e netw orks with the ability to d ynamically acces s the availa ble radio spe ctrum . To accom plis h this , it can be con sidere d to combi ne i n one net wor k the Mo bile Ad - hoc architec ture and Cogni tive Radi o (CR) paradigm s [2,3] . The co rner stone of such ne t work is its ability to ada pt to th e su rroundin g environment, which can only be accomplished if accur ate information o f it is made available. In t his p ape r we foc us on t he sp ect ru m sens in g par t o f environment awareness. Spectrum sensing, covered extensively in literature [4 - 5], falls in to what is known as detect ion th eory, pr esented i n detail in [6]. Spectrum s ensing is realized as a physical and MAC layer mechanism. The physical la yer se nsing focu se s on d etec ting si gnals , a nd the detection methods put in place can be classif ied into two grou ps, eith er cohere nt (pri or inf ormation needed, e .g. Pi lot Detection , [4]) or non - coh erent (no prior inf ormation n eeded, e.g. Energy Detector, [7]). The MAC layer part of the spectr um se nsing - the target of this paper - f ocuse s on when to sen se and which spectrum to sense. Cons ider ing t hat t he sen sing req uire ments are s et by t he chann el condit ions, w hich depen d on th e path los s, multip ath, shado win g and local int erference, the combinatio n of the se pheno mena can result in regimes where the signal SNR is below the detection th reshold of the sensor. To overcome this limitation, in [8 – 11] it w as proposed th e us e of cooper ation in the spectrum se ns ing. Sin ce t he signal s trength varies wit h the sensor location , th e worst fading conditi ons can be avoi ded if multiple sensor s in differe nt spatial lo cations s hare their sensing measurements, i.e. take advantage of the spatial divers ity . Most of these proposed coo perative m ethods are based on data fus ion techn iques to perf orm th e decision on what is the actual state of the spectrum. Recently, in [12], it has been proposed the use of a scheduling scheme to select which channels to sense based on the channel statisti cs, altho ugh t he a uthor s ass umed that they ha d p rio r infor mat io n on the correct channel oc cupation s tatistics. On [ 1 3 ] the authors did a com prehensive study on the effect of correlation on coopera tive spectrum sensing , besi des providi ng a theoretical fra me wo rk bas ed on Bayesian inference, the Robust Cooperative Spectrum Sensing for Disaster Rel ief Networks in Correla ted Environments Nuno Pratas 1,2 , Nicola Mar chetti 1 , Neel i Rashm i Prasad 1 , António Rodrig ues 2 and Ram jee Pras a d 1 A Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 2 paper ' s main c onc lus ion was that under certain correlation condit ions the use of cooperat ion is not w orthwhil e. In this paper a cooperative spectrum sensing scheme is propose d for an Ad - hoc based scenario. The proposed scheme works under th e assumptio n that all t he nodes in this ad - hoc netwo rk ar e gr oup ed in c lu ste rs. T he proposed scheme allows assign ing a channel to sense to each of the cluster node s. This assign ment i s done accor ding to prev iously estimat ed chann el oc cupation st atistics. The proposed scheme is accomplished following both a cen tralized and a decentralized approach. In the centrali zed approach, the cluster head is respons ible f or collecting and fusi ng the local decisions of each of the cluster nodes, wit h t he p urp ose o f es ti matin g the moni tored ch annel s occupancy . The esti mated c hannel occ upations stati stics ar e then used by the cluster head to assig n to eac h cluster node which channel to sense. In the cluster decentralized approach, each o ne of the clust er nodes gat hers and fuse s t he lo ca l decisions of the oth er cluster nodes and from there it e stima tes the monitored channels occupancy. Using the estimated information the cl uster nod e decide s which channel to sense in the ne xt se nsin g se ssio n. The remaind er of this paper i s organi zed as fol lows. In Section II it is given the pro blem definition toget her with a short descri ption of th e methodolog y used to s olve i t , and i n Section III the syste m de sig n is discus sed . In Section IV one studie s the da ta fusio n s chem e un der certain correlation conditions for the cooperativ e spectrum sensing , while in Section V two chann el state estimators are considered . In Section VI o ne propose s and d iscusse s in d etail s the sensi ng orchestration schemes, whereas, in Section VII a comparative perform ance evaluati on of the in tegrat ed proposed s chemes is presented . Finally, Sectio n V III concludes the paper with a recap of the con tribu tion and of th e main obtained results, as well a s an o utlo ok o n furt her d evel op ment. II. P ROBL EM D EFIN IT ION AND M ETHODOLO GY A. Problem De finition The prob lem we tackle in this paper is the follo wing: Consid er a n Ad - hoc C ognitive R adio disas ter r elief ne twork, composed of networ k nodes , organiz ed in clus ters, and capable of ope rating o n and sensi ng any narrow band channel of a targe ted range of spectr um. How s hould the se cluster nodes cooper ate, s o that at any given ti me all the clus ter nodes have accurate statistics of the targ eted spectru m ? To tackle this pro blem we present a MAC la yer distribute d spectr um se ns in g mec hani sm . T he mechanism was developed following a ce ntralized as well as a decentralized approach , both elaborated in th e later sections of the paper. The proposed distributed mechanis m , in both appr oaches , allow s for each of the sensing nodes to sens e a n y cha nnel of the monitored spectrum while ensuring that at cluster level a detection , a s accurate as poss ible, of the available spectrum is achieved in all no des . B. Methodology The m ethodol ogy followed mirrors the article structure, and is the followin g: f irst we describe the sys te m desi gn a nd s cenario assumpti ons , t hen we identify from the syste m de sign the three topics that are treated in this paper , be ing the se : Spectrum Se nsin g Res ults Fusi on, Cha nne l Sta te E sti matio n and Se nsi ng O rche stra tion. E ach o f these topics is analyzed in depth in a dedicated section. The stud y then co nc ludes wit h the int egrat io n of the analyzed topics in a distribu ted spectr um s ensing sch em e and a performance comparison between the centralized and decentralized approaches . C. Eva lua tion Metrics The goal of spe ctrum sens ing, cooperat ive or n ot, is to fi nd out wha t is th e state of th e channe l being s ensed. This pr ocess, illustrated in Fi gur e 1 , can be described as a m echanism which correspon ds to an imperf ect and simplified mapping of the real rad io e nviron ment to a r epr esenta tio n in t he se nsin g no de. Therefore a metric or a set of metri cs that can gauge how imperfect/accurate a spectrum sen sing method is needed . Figure 1 - Spect ru m sensing as a mappi ng mech anis m. The Root Mean Square Error ( RMS E ) is fre quen tl y used to measure the diff erences between values predicted by a model or a n estimator and the values actually observed from the pheno meno n being mode lled or est im ated ; th erefore RMSE is a measure of accuracy . While considerin g that    ,  represents the c hanne l’s m estimated mean un - occup anc y in se ns ing sessio n i a nd   i s the cha nnel’ s m real mean un - o ccupa ncy. The n the individ ual accounted d iff erence s ,    ,     , ar e called residuals , and the RM SE aggr ega te s these indi vidual residuals into a single measure of predicti on . Here we extend the RMSE to measure th e accuracy of the propose d sens ing sch eme, by applyi ng it t o the es timated mean chan nel un - occupancy. T he RMSE of th e channel m estimated un - occup anc y is given b y,  (    ) =      ,     2   =1  (1) where N is the numb er o f se nsing sess ion s. This metric is used to gauge the performance of the n channels with the greater un - occupancy, being incorporated in the Multi - Chan nel Effective Root Mean Square Error, RMSE ME , which is defined as,   (  ) =   (    )    (2) where Ω is the set o f n c han nels wit h gre ater un - occupancy. The RMSE ME (n) m etric allows to gauge how accurate is the estimation of the channel mean un - oc cupa ncy i n the n top un - occupied channels. Frequency Channels Time Radio Environment Sensing Frequency Channels Time Sensed Radio Environment Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 3 III. S YSTEM D E SI GN A. Preliminaries It is assu med that the targeted spectrum for sensing is divid ed i n cha nnel s of equa l b and width, and that eac h o f the netwo rk no de s is a ble to se nse o nl y one o f th e se channels . Furt her more, it is assumed t hat the ne t wor k nodes are already organized in clust ers. Each no de of t he net work i s as sumed to have ava i lable t wo logical types of channel, the Control Channel (CCH) where all contr ol i nfor matio n i s exc han ged and t he Da ta C ha nnel (D CH) thro ugh whic h all use r s data are exchanged. For the physical implementatio n of these chan nels it is assumed that the y have i ndependent transceivers associated. Figure 2 - (a) CCH Con trol Frame, (b) DCH Data Frame. The CCH method of access is CSMA/CA. The spectrum channel allocated to th e CCH is assumed to be cluster - dedicated, i.e., the chann el contenders are the other cluster nodes; the CCH associated transmission time is divided as depicted in Figure 2- (a). The control exchanges are f ully dedicate d to control function s (transmit and receive contr ol data), while the se nsing e xchanges are dedicated to the report of the sensing as well as of the orchestration decis ions (in the case of the centrali zed scheme). The DCH access method is ou t of scope. The only assumption is that par t of the re ception/trans mission time is dedicated p eriod ically to sp ectrum sens ing, as de picted in Figur e 2- (b). T he DCH is able to operate and sen se dynamically in differen t spectrum channels, one for each sensing session, whereas these channels are assumed to have the same bandw idth. We consider that each cluster node performs the sensing through the use of a En ergy Detector (ED) [7 - 8] , an no n - coherent sensing scheme. The ED was chosen since the condit ions of the radio spec trum environm ent an d of its incumb e nt signa ls str uctur e a r e unkno wn t o our ne twor k , therefore onl y non - coherent schemes are considered, since due to lack of prior inf orma tion coh erent spe ctrum sensi ng schemes are rendered usel ess. B. Common System Desi gn The purpos e of t he dis tribu ted spect rum sensing mechanism is to ensur e tha t all of the cluster nodes have updated and synchronized information about th e state of the targ eted spectrum. Figure 3 - Dis tribut ed s pectr u m sensi ng mecha nis m fl ow . The distributed spectrum sensing mechanism flow i s depicted in Figur e 3 in different steps: • Spectru m Sensing - Each c luster node performs the sensing through the use of a Energy Detector, therefore at the end of the spectrum sensing a binary decision rega rding the stat us o f the sense d c hanne l i s tak en b y each node . The sensi ng o ccurs in the DCH in t he "Sens ing" period depicte d in Figure 2- (b) ; • Br oadcast R esult t o Clust er - E ach clu ster node shares t he re sult of the binar y de cis ion r eac hed in t he spectrum sensi ng. T he sh aring i s do ne t hroug h broadcast , whic h is done through t he C CH dur in g the Sensing Ex change s pe riod dep icted in Fi gure 2- (a); • Cl uster Results Reception - Each cluster node receives the resu lts broadcasted by the rem ain ing cluster n odes thro ug h the CCH ; • Sensing R esult s Fusi on - At this po int, t he nod e fuse s together the sensing results received from the other cluste r no des . N ote t hat t he fusio n p roc ess i s d one separately for each sensed channel. The data fusion scheme u sed is classifi ed as a synchronous hard decision, and th erefore the result is a binary decision ; • Channel St ate Estim ation - T he e stimat ion o f the channel s st ate is don e based on past observ ations and curr ent obser vati on s , when available, i.e. if th e chann el in q uestio n was se nsed . T hr ough t his pro cess it is possi ble to obta in updat ed statis tics of th e network targeted channels; • Choose Spectru m to Sense - T his step depen ds on the approach chosen to implement the mechanism, i.e. if the me cha nis m is centraliz ed or decentralized coordina tion . In the centralized approach one of the cluster n odes decide s whic h chan nel s hould be sensed by each of the cluster nodes, while in the decentralized approach , th e decision on which cha nne l to se nse is done in depende ntly by each of the clus ter node s. Both approaches perform this choice according to the channels oc cupation statistic s. The flo ws of the centralized and decentralized mechanism imple menta ti on have in common all the steps except f or the "Choose Spect rum to Sens e" step . T he differen ces of each implementatio n will be d epicted in the following s ub - sec tio ns. C. Cen tralize d Syst em De sign The centralized distributed s pectrum sensin g mechanis m steps are depicted in Figure 4 , and in Fi gur e 5 are depicted the "Se nsing E xcha nge s " i n the CCH . Control Frame Control Exchanges Sensing Exchanges Data Frame Data Sensing (a) (b) Common Steps Sense Spectrum Broadcast Result to Cluster Cluster Results Reception Sensing Results Fusion Choose Spectrum to Sense Channel State Estimation Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 4 Figure 4 - Centralized M echani sm . The C om m on S teps were the ones described in the previous section , t he re maini ng one s ar e: • Compute Sensing Orchest rat ion - In thi s ste p t he coordinating node, i.e. the cluster head, computes what will b e t he di strib uti on o f the sens ing nod es i n the follo wing se nsing sessio ns , a process which we call orchestration. This process is impleme nt ed thr ough a resource scheduler , which will be presented in a later section of the paper . T his step o ccur s d urin g the "Pr oce ssing" period depicted in Figur e 5. • Rep ort Sensing Orchestrat ion - After the orchestratio n h as been comp uted, the cluster head repor ts it to the clust er nodes . T his report is broadcast ed t hrough t he C CH in the "Orc hestration Reporti ng" peri od depic ted in Figur e 5. Figure 5 - Centr alize d M echa nis m "Se nsi ng Ex cha nges" peri od of Fig ure 2-(a),. D. Decentralized System Design The decentralized distributed spectrum sensing mechanism steps are depicted in Figure 6 . Since in the decen tralized case the ne xt c hanne l to be s ense d i s chose n b y the nod e itse lf, t he n the " Sen sing E xc hange s" period of the C CH depicted in Figur e 2- (a) is used only by th e cluster n odes to repor t their sensin g res ults. Figure 6 - Decentralize d Mecha nism. The choice o f which c hanne l the cluster nod e should se nse in the next sensi ng se ssion is don e follo wing t he sa me approach as the centralized mechanism, i.e. it is based on a resource scheduler, which will be presented in a later section of the paper. E. Conside rations The distrib uted spectr u m mechanism st eps were described for both the centralized and the decentralized approach. The first rem ark is that the centralized schem e requires more radio resou rces du e to the orch estration reporting . But th e tradeoff of the decentralized scheme is tha t the resource d istributio n, i.e. the no des se nsin g the c ha nnels in next sen sing se ssi on, might no t be as optimal as in the centralized scheme. So the choice between these sch em es is be twe en opt im ali ty of resource allocation, and consequ entially energy and ra dio resources sp ent d ue to e xtra s ignal in g, or sub - optimal resource allocation. From the system description were identified three task s whi ch will be foc used in this paper , being t ho se : • S pectrum Sensing Result s Fusion - T he dat a fusion scheme considered is the s ync hrono us ha rd de cisio n , which uses predefined fusion rules to achieve the data fusi on . In thi s paper we will derive a data fusion rule which will take in to account the properties of the phen omenon bei ng observ ed, i.e. of the radio c hann el, and t he correlation observed bet w een the cluster nodes ; • Channel State Estim ation - The estimation of channel stat e is don e based on pas t observ ation s wh en available. In this paper we will derive an estimator which accomplishes this; • S ensing Orchestration - The sensing orch estrati on scheme which dis tribut es the cluster n odes across the targeted spec trum is derived. This will be extende d to accomplish the orchestration in the centralized approach as well as in decen tralized appro ach. These three tasks will be disc u ssed in the next se ct ions. IV. S PECT RUM S EN SIN G R ES ULTS F US ION A. Introduct ion to d ata fus ion Cooperative s ensi ng is a distributed detectio n system specialized in detecting the sta te of the monitor ed spectru m. In this paper we consider a t wo - level distributed de tecti on syste m , as de picted in F igur e 7. This syste m co nsist s of a number of local detectors and a fusion cent er. The local dete cto rs make a d ecis io n of t he under lyin g bi nar y hyp othe sis test ing probl em bas ed on their o wn ob serva tio ns a nd t hen transmit t heir decision s to the fusion center where the global decision is derived. In this paper we consider that the local detectors were already designed to achiev e a certain detection performance, i.e. we assume that the y are Energy Detect o rs designed to detect signals above a certain SNR. We also consider that these detectors have an homoge neo us performance, i.e. all the detectors were designed to detect the same le vel of S NR. Figure 7 - Tw o - level dis tributed detection sy ste m . In the fusion center the local decisions need to be combined so that a global d ecision is achieved. In this section we describe the design of such fusion rule. In t he fusion center a Common Steps Compute Sensing Orchestration Report Sensing Orchestration Sensing Reporting Processing Orchestration Reporting Common Steps Compute Next Sensing Channel Detector 1 Detector 2 Detector n Fusion Center u 2 u 1 u n u f y 1 y 2 y n Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 5 binary hypot hesis testing is don e, and it is thro ugh th is testing that t he fus io n rule i s def ined. In t he literature two approaches to model this pr oblem are co mm only followed , [6] , t he Bayesian approach ( were the conditio nal densitie s under the two hy poth esis h ave to be priory kno w n as well as the cost of the ac tion t hat c an be follo we d, whic h in a two h ypo thes es problem is four ), a nd t he Ne yman - Pearson (N - P) test wh ere such i nfor mati on is no t nee ded . Here we f ollow the N-P test formulation , since we assume that we do not hav e access to any prior kn owledg e about the signals that w e are trying to detect . B. Data fusi on formul ation Consi der the binary hy pothe sis tes ting problem with hypoth esis H 0 and H 1 , which correspond respectively to the case s where the sensed channel is v acant and occupied . T he fusi on center im ple ments the N - P test by usi ng all the decisions that the indivi dual sensors have communicated. The N- P test , Λ( u ) , is for mulat ed as the follo wi ng Likeli hoo d Ra tio (LR) test:  (  ) =  (  1 ,  2 ,  ,   |  1 )  (  1 ,  2 ,  ,   |  0 )  1   0  (3) where u = [ u 1 ...u n ] T , is the vector formed by the set of local decisions ( u i take s t he va lue 0 when t he se nso r i decides H 0 , and u i = 1 w hen t he se nsor i decides H 1 ) cor respondi ng t o the n local detectors , and λ i s t he threshold determined by setting an u pper boun d to the probab ility of fa lse al arm at th e fusion center , [6] . Considering the case were al l the local detectors/sensors have the same performance and that there i s a qua ntifiab le degree of correlation betw ee n their de cisions, then accor ding to [1 4 ] , the L ikelihood R atio T est (LRT ) to that case can be defined as,  ( u ) = P ( u | H 1 ) P ( u | H 0 ) =  ( m ) (4) where m out of n d etectors are in f avor of H 0 (i.e. there are m 0's i n the ve cto r u ). Elaborating further  (  ) , [1 4] we get,  (  ) =  (  1 )         1 (  + 1    ) +   1 +   1   +   2  =0   =0  (  1 )         0  + 1     +   1 +   0   +   2  =0   =0 , 0      2 (5) where P d and P fa , are respectively the prob ability of detection and proba bili ty of false alarm , and the cor relation indice s  0 and  1 , whe re 0   0  1 and 0   1  1 , are defined by,   =      |    [   |   ]    |      [(    [   ]) 2 |   ]  󰇣      2 |   󰇤 ,   ,     ,  = 0 ,1 (6)  (  ) for the case wh en m = n -1 and m = n wa s no t explicitly cons idered in [1 4 ], but were d eri ved i n [1 5 ]. The op timum rule, i.e. t he o ne ma ximizing the global probabil ity of dete ction, for a giv en upper boun d of the global prob ability of false alarm is o btained b y the LRT, given b y,   (  ) =   (  ) = 󰇱  1 ,   (  ) >   1    ,   (  ) =   0 ,   (  ) <   (7) whe re  is a randomization constant , and  > 0 a nd  > 0 a re defined according to th e global probability of false alarm upper bou nd. Considering t hat the implem entation of the LRT leads to complex iterati ve algorithms, a nd that in [1 4 ] it w as sh own that the LRT can be expressed as a funct ion of m , i.e. t he number of detectors that decide in favor of H 0 , i n [15 ] wa s propose d the us e of a counting rule, i.e . a rule th at counts m , and decide H 1 whe n m is small er tha n a gi ve n inte ger threshold. Therefore a counti ng rul e ca n be define d b y,   (  ) =   (  ) = 󰇱  1 ,   <  0  1    ,   =  0  0 ,   >  0  (8) The equiva lenc e bet wee n the LRT and the co unt ing r ule, i.e.,  (  )       0 (  ) is only valid if  (  ) is a dec reas ing f uncti on of m , whi ch was t horo ughl y de monstr at ed in [1 5 ], i.e. it was sho wn that for p roper ly operating lo cal detectors ( P d >>P fa ) the counting rule is a l mos t a U nifo rml y M ost P o we r f ul (UMP) t est , [15 ] . The choic e of t he co unti ng r ule thre sho ld, m 0 , depends on the local detectors performance, th e correlation between the decisions o f these de tectors and finally on the upper boun d set for th e global probabi lity of fals e alarm. Bu t consideri ng tha t the correlation betw een the decisions change over time, when the detector s are mobile, t hen there shou ld a mechanism w hich adapts the m 0 to th e se changing condit ions. We propose such a mecha nis m in t he ne xt sub - sectio n. C. Data fusion t hrough a daptive c oun ting r ule mec hanism The need for an adaptive counting rule can be motivated by the exa mpl e give n in Fi gur e 8 and Figure 9 , wher e it is depicted the RMSE of t he decision at the fusio n center compared to th e real stat e of the signal, according to k , the decision thre shold and k = n - m 0 . Fro m the fig ure s we observe that the opti mum k depends on the average correlation index between the local detectors. Therefore the re mus t be a mecha ni sm whi ch allo ws selecti ng the optimum k according to the correlatio n ind ex . N ote that the optimum k depends als o o n the sensors performance as well as the number of sensors put in place to sens e the channel. Here we propose a mech anism which adapts continuously the k according t o the f eedback f rom th e previous global decisions, i.e. if the sensed channel is dee med available then Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 6 the cl ust er nod es tr y to use th e cha nne l, a nd t he re sult of that action is used as feedback to tu ne the k . If the c han nel is occ upied the n it means tha t there was a misdetection, and therefore it means the k s hould be decreased, increasing the prob ability of detection. At t he same time there s hould be an opposite mechanism which increases k , so to ens ure tha t the upper bou nd of the gl obal fal se alarm proba bility is respected. Figure 8 - RM SE vs k a ccording t o correlatio n index, with 10 local detectors . Figure 9 - RMS E vs k accor ding to corre lati on in dex , wit h 5 local detectors . The propos ed al gorithm ma kes use of the following quantities : • MD C - The Misdetection Counter cou nts e ver y ti me t he cluster decides that the ch annel is free, and the network tries to use the ch annel but the channel is occupied ; • OC C - The Occupied Detection Counter cou nts every ti me the cluster decides the channel is occupied; • O W - T he Ob ser vatio n Wi ndo w is the time i nterva l o f the observation s used to make the decisions , i.e. it is the mem ory of what occ urred in the previous sensing sessio ns; • MD Thrs - The Misdetection T hreshold refe rs to the amoun t of misdete ction perm itt ed during th e observ ation win dow . When this val ue is o verc o me t rigger s the k needs to be decrease d . T his t hres hold is obtain ed by mult iplying the upper boun d of the global prob ability of false alarm with O W ; • OC Thrs - T he Occupied Detection Threshold refers to the a mou nt of occupied det ections occurri ng dur ing the O W , whi ch if overcome triggers t he increase of the needed po sitive detections to decid e a global positive detection. I t is obtained b y multiplyin g the O W wi t h the upper bound of the allowed global false alarm probabil ity . The algorith m which imple ments the ada ptable co unting rule is dep icted in Algor ithm 1 . T his algorith m adapts the decision thre shold k , so t hat for a detection to occur there have to be at lea st k local detec tions out of the n local detector. % After the Fusion Centr e receiv ing the loc al dec isions Compute current dec ision, U F If ( U F is H 1 ) Increment OC C Else If (Channel state is not H 0 ) Increment MD C If ( MD C > MD Thrs ) Decrease k If ( OC C > OC Thrs ) Increase k Update MD C and OC C %discard obser vations outside t he O W %End of Adaptive Counti ng Rule Algorithm 1 - Ada ptiv e co unti ng rule mecha nis m. D. Adaptive co unting r ule per form ance compari son To illust rate the perfor mance of the adaptive counting rule mechanism, we compare it with t wo extreme cases, the OR rule ( 1 - out - of - n ) and the AN D rule ( n - out - of - n ), while consi der ing t he s ame scenario it was used to obtain the resu lts sho wn in Figur e 8 a nd Fig ure 9. Figure 10 - RMSE ac cordi ng t o fus ion r ule. The RMSE o bta ined whil e usi ng t he d iffer ent rule s is depicted in Figure 10 . A s expected the adaptive rul e RMSE is close to the one obt ained w ith th e optimum rule, whi le outperf ormin g both th e OR and AND rul e, except for the c ase where correlation is 0.3 w ith C=5. In this cas e the performance of the adaptive rule was worse than the optimum/OR rule b ecause it i s unable to maintain the k , due to its d yna mic nat ure , eq ual to the val ue o f the l ower bo und ( k=1 ) o r uppe r bound ( k=n ). The p roposed adap tive fusion rule algorith m allows achieving a l mo s t the same performance as the optimum rule, witho ut nee di ng as inp ut the co rrelation between the local detectors . 0% 10% 20% 30% 40% 50% 60% 1 2 3 4 5 6 7 8 9 10 RMSE Cor r e lat ion = 0 .3 Cor r e lat ion = 0 .9 0% 10% 20% 30% 40% 50% 60% 1 2 3 4 5 RMSE Cor r e lat ion = 0 .3 Cor r e lat ion = 0 .9 0% 10% 20% 30% 40% 50% 60% OR Ru le A ND R u le Optim um R ule Adapt ive Rule RMSE Co rrela t io n = 0.3 ( C =10) Co rrela t io n = 0.9 ( C =10) Cor re lat ion = 0 .3 (C= 5) Cor re lat ion 0 .9 (C=5 ) Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 7 V. C HANNEL S TATE E STIMAT ION A. Introduct ion After the s ensi ng o f the channel is done and its current state determined, it is ti me to combine the cur rent ob served state with past obs ervations : t hro ugh t his pr oce ss it is t hen p ossib le to obtain upd ated statistics of the sensed c hannel state, e.g. average occupation, free period, etc. The us e of these sta tisti cs can the n allo w fo r a more adequate decision on when to use the cha n nel fo r data transmission. Here we consider the estimation of the channel ’s m mean un - occ upa nc y , denoted as s m , whic h is est i mated cont inuo usl y during the netw ork lifet ime. This e stimati on is based on pre vious o bse rvati ons, whe n ava ilab le, while ta ki ng in a cco unt whe n a cha nnel ha s not bee n ob ser ve d in a long ti me. T he s m is the estimatio n of P(H 0 ) . To e stimate s m we st udy t wo metho ds, whi ch ca n be classi fied a s a n exp one ntial mo ving aver age and a linear movi ng ave ra ge , respectively . B oth include a reset mechanism which allo ws updating the s m , altho ugh i ntro duc ing an error, even whe n the c hanne l wa s not sensed. The need for this mecha nis m , is that since the s m i s used as a bid in the orc hestr atio n sche me, then t here needs to be a feedback mechanism which enables a controlled distributio n of the sensi n g nod es b y usin g the    as the c hanne l bid , i. e. w m . Thi s will be made clear er in S ectio n VI. B. Exponential Movi ng Average Es timat or The exp onent ial m oving average with reset factor c hanne l un - occ upa nc y estimator i s giv en b y,    = 󰇫 ( 1  )    ,  +    ,  , if  sen sed ( 1  )    ,  +    , if  not sen sed  (9) whe re   is the estimated un - oc cupa ncy of t he cha nnel m ,    ,  is the estimated un - occupancy from the last s pectru m sensin g s essio n ,   ,  is the ins tant ane ous o ccup anc y obtain ed from the se nsi ng of t he chan nel m in the p revio us sensin g sessio n,   is t he term that is used to r eset the channel un - occ upa ncy estimation when the channel has no t been sensed i n the p revio us se nsin g sess ion a nd fi nall y α is the forgetting factor used t o t une the e xpo nent ial movi ng a vera ge smoot hness . C. Linear Mov ing Aver age Esti mator The linear moving average with reset factor channel un - occ upanc y est imat or is give n b y,    =       ,      =1 +   ,    ,       ,      =1 +     ,      (10 ) w here   i s the estimated un - oc cup anc y of the c han nel m is ,   ,   is the observed un - occ up anc y i n the i th previ ous spectr um se nsing se ssio n ,   ,  is t he ins tant ane ous occupancy obtained from the se nsin g o f the c han nel m in t he previo us sensi ng sessi on,   is the term that is u sed to reset the cha nne l un - occupancy es timati on when t he cha n nel ha s not b een sense d in the previo us sensi ng sessio n , a nd O W i s the obs ervat ion windo w le ngth. D. Implement ation Iss ues an d Per formance Compari son The linear estim ator achieves the minimum RMSE if th e observ ation window is the s ame as the num ber of obs ervat ions, alt houg h ne ed ing to ha ve all t he p re vious observ ation s stor ed. The exponential average can offer similar perform ance, depending on the dis tribu tion of the s amples , but it only needs to s t ore the previous estim ation. Therefore from an implementatio n point of view the exp onential estimato r is the one to choose. In F igure 11 it is depicte d the obtain ed RMS E while using both estimat ors for each of the channels. Tw o sc e nario s are considered, one wh ere the channel is sensed each session , i.e. all samples are considered, and the case where the channel is sensed every second sensing session, i.e. half of the available sa mp l e s ar e taken into account . s reset was set to 0.5, α wa s s e t to 0.01 a nd th e O W was se t to 40. Fr o m Fi gur e 11 it can be observed, as expected, that both estimators have similar performance, except in the Ch 2 duri ng the i nter rup ted s en sing, whe re the RMS E wa s substa ntia ll y hig her for the exp onent ial e sti mato r. T his was caused by the s reset value whic h was set as 0 .5. Altho ug h it c an be a rgued that b y ta king o ut the s reset the RMSE wo uld b e minimized, it needs to be considered since the estimation is used a s cha nnel bid for the sc he dule r and therefore needs to be updated in every sensing cycle. T his will be fur the r moti vate d in Section VI. Figure 11 - Estima tors co mparis on thr oug h RM SE . VI. S E NS IN G O RC HESTRATION S CHE ME A. Foundati ons of the Schedul ing Sche me In th is section i t is introduc ed the orc hestrating sc heme which distri butes th e sensing nodes across the spectr um along consec utive sen sing sess ions. The proposed scheme is based on the Kelly scheme [1 6 ], here described according to [1 7 ], as follo ws . Consider t he case where M u sers are bidding for a share of a f inite resource denoted as C . Here the sch eme users are the ch annels being targeted for the sensing , while the resources to distribute are 0% 5% 10% 15% 20% 25% CH 1 (s 1=0.44) CH 2 (s 2=0.86) CH 3 (s 3=0.61) RMSE E xpone nt ia l Li nea r E xpone nt ia l (I nt er rupted Sensing) Line ar (I nt er rupted Sensing) Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 8 the se nsin g no des . Eac h us er m has associated a utilit y functi on, A m (d m ) , w hich determines the m onetary value of any resource allocation, d m , to user m . Let us con sider the tr iple (C , M, A ) , where C > 0 , M > 1 , and A = [A 1 ,..., A M ] , as the utility system. T he utility is measured in monetary units; therefore, if the user m receives a resource allocation d m , it must pay a price w m , thus receiving a net pay off N PO , given by,   =   (   )    ( 11 ) Give n a ny vec tor of ut ili ty func tio ns A the maximizatio n problem ca n be expressed as the ma ximization of the aggre gate util ity, and can be defined as the triple (C , M, A ) such t hat:     (   )   =1          =1    0 (12) where d m are the components of the n on - ne gati ve vec tor of resource allocation d . This vect o r d can be computed, by considering that each user m submi ts a bid, denoted a s w m , to the resource manager, i.e. the cluster head. T hen given the vector w , defined as w = [ w 1 ,..., w M ] , the resource m anager chooses and allocates d , according to,   (   ) = 󰇫        =1  ,    > 0 0 ,    = 0  (13) Cons ider ing t hat t he use rs c hoo se the b id b ased on t he maximization of t he N PO , then according to [1 7 ], the allocatio n of the reso ur ces i s full y e ffici ent, rea chin g the maxi mu m possi ble aggregate utilit y . The challenge presented in this paper is to apply this scheduler both in a cen tralized and decentralized approach. In the centralized approach the cluster head is the one res ponsible for the o rche strat io n, but w hen we follow a dece ntralized app roa ch, t here i s not a n enti ty/sc hed uler which comput es and then a ssi gns t he re sour ces to t he cha nne ls acco rdingly. Therefore, to apply this scheduler to the decentralized case the Eq. (13 ) needs to be obtained indirectly, i.e. each o f the sensing nodes w ill select which channel to sense based on the bids, and in the e nd the resourc e distribution will follow (13 ) , altho ugh wit h some d eviation . B. Centr alize d Orchestr ation Schem e Implem entation In Algor ithm 2 it is sho wn t he algori thm us ed to im plement the centralized se nsi ng or che str atio n sc heme. To initialize t he syste m the nod es se nse a ra ndo m cha nnel in the fir st sen si ng session and from th ere one sta rt s to e stimate the s m . %Start S ensin g Orchest ration Sessi on Receive Sensing Results from C luster Nodes For (every channel) %Fin d expected a llocated resour ces If (channel m has been sensed) Compute   according with fusion rule Compute   and obtain   Co mpute   (   ) Allocate resources to next sensing session a ccording to   End %End Sen sing Orc hest ration Session Algorithm 2 – Centr alized Orc hestratio n Scheme. C. Decentral ized Or chestr ation Sc heme Imple mentati on In Algorithm 3 it is s ho wn the algorithm which accomplishes t he dis tribu tion of th e sensi ng nodes a cross t he monitored channels in the decentralized case . T he pro posed algori thm oc curs with in each node after the period when the nodes re por t the se nsin g res ults, gi ven i n Fi gure 1 - (a), and before the nodes perform the channel sensi ng, depic ted in Figur e 1 - (b ). To initialize t he syste m the nodes sense a random channel in the first sensi ng sessio n . B y running t his alg orithm o n all o f t he cluster nodes it is poss ible to obta in an approxim ation of Eq. ( 11 ). %Start S ensin g Orchest ration Sessi on Receive Sensing Results from C luster Nodes For (every channel) %Com pute the channel bids If (channel m has been sensed) Compute   .  acco rding to fusion rule Compute   , i.e. obta in    End Normalize the cha nnel bids, i.e.     =         Compute C DF, i.e.      =     +     1   Generate random variable, r ~ Unifo rm(0 ,1) Select the mi nim al m for which tru e that  <      Select channel to sen se with i ndex m %End Sen sing Orc hest ration Session Algorithm 3 - Dece ntralize d Orchestrati on Sche me. D. Implement ation Iss ues Comparison Bo th of the pr oposed a lgorithms are impleme ntable, although with some constraints, especially i n the case of the decentralized algorithm. In deed in the decentralized algorithm since it is not pos sible to kno w for certain what will be the numbe r of sensi ng nodes whi ch w ill be se nsing a chann el then it is n ot possibl e to apply the adapti ve coun ting rul e scheme for the data fusion. Therefore we only apply it i n the centralized algorithm . The centralized schem e will of course achieve a better performance than the decentralized, as expected. But the advantage of using the decentralized scheme is to give a higher robustness to the cooperative s pectrum sensing scheme, since if in the centralized the scheme the central node stops wor kin g the n the spec trum se nsing also colla pses, while in the decentralized in the case that some of the nodes wi thd ra ws fr o m t h e c luster it will still b e possible to continue the sen sing. The centralized and decentralized schemes complement each other, i.e. a possible way to increase the robustness of the cooperati ve spe ctrum sensing is to combin e both sch emes. So whe n the c entr al no de, b y any re aso n, s top s wor king the cluster can start working following the decentral ized scheme, until another cluster h ead i s elected. Th rough this is possible to achieve uninterru pted cooperative spectrum sensing. Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 9 VII. P ERFORMA NCE E VALUATION Here we evaluate the perform ance of the propos ed orchestratio n a lgorithm s , while compar ing t he m wit h the Round R obin schem e performance , using o f course the sam e data fusio n sc he me a nd cha nnel est ima tor . I n T able 1 are depicted the relevant simu lation values. Table 1 - Rel evant si mul atio n para meters . Parameter Value Estimation Method Exponent ial Mean Cor relation I ndex 0.5  0.01   0.5 M 20 Channel Occupa ncy Model Poisso n On - Off Model   0.05 Sensing Sessio ns 10000 Local Detector Model Energy detec tor Note that all th e results presented, except f or the theoretical ones, wher e ob tai ned t hrou gh the si mulator developed for this study which imple ments the syste m de sign de fine d i n Sec tio n II I. In Fi gur e 12 and Fi gure 13 are depicted the RMSE ME (5) achieved by each of th e orchestration schemes according to the num ber of local dete ctors an d underly ing data fusi on rule . As expected the cen tralized scheme achieves a lower RMSE ME (5) si nce it allo ws for a more co ntrolled distr ibution of the sensing users. Also in the decent ralized scheme evalua tio n it was not considered th e adapti ve coun ting fus ion rule due to a lack of not being able to control exactly the number of nodes to sense a ch annel, as explained in the sub - section VI.D. Figure 12 - Centralized sc heme RMS E ME (5) evaluati on. VIII. C ONC LUSION In this paper it w e propose d a robust cluster based cooperative spectrum sensing scheme to be used in an Ad- hoc cluster network in a disaster relief context. The pro posed sch eme allow s the dist ribut ion of th e sensing nodes t o be adapted according to t he cha nnel mut ati ng co nditi ons, therefore maximizing the correct identification of spectrum holes . The proposed scheme system des ig n was fully described and its underlying st eps explained. We explained the sign aling flo w to a chie ve the p ro pose d sche me . We gave special focus on three steps of the proposed scheme, i.e. data fusion, channel state estimati on, and sensing orchestration. Figure 13 - Decentralized sc heme RMS E ME (5) evaluat ion. As per d ata fusi on me tho d , we propose d a n adapt ive counti ng r ule . T his allo ws adap ting the decisio n threshold dyna mical ly ac cor ding t o t he correlation experienced by the unde rlying sensors, w hile not havi ng impl icit inf ormation about the correlation, i.e. acting therefore as an adaptive feedback mecha nis m. As per channel state estimat ion we evaluated two schemes, the Exponential Moving Average and the Li near Movi ng Average estimator. It was concluded that the exponential estimator allo ws for a simple r imple mentation while achievin g almost t he sa m e performance as the li near movi ng aver age esti mato r, which i s more expe nsi ve to i mple me nt. As pe r the spectrum sensing orchestration scheme, we proposed a centralized an d decentralized orchestration schemes. From the perf ormance evaluation it was con clude d that the centrali zed scheme achieves a lo we r RMS E ME (5 ) than the decentralized. From a system design perspective the decentralized scheme is more robust since in the case one of that any of the cluster nodes leaves the cluster the decentralized scheme con tinue s to work , while i n t he centralized s cheme, if th e cluster head withd ra ws fr o m the cluster the cooperative spectrum sensing collapses immediately . So i t was propos ed in the fut ure to combin e both of the schemes which will potentiall y allow for a more robust cooperative sensing sch eme. The fu ture s teps of this w ork will be to ext end th e proposed orchestrating mechanism t o a multi cluster scenario , where it will be st udie d ho w to suppor t m obility between clusters as wel l continua tion of th e knowledg e bas e cont inui ty o f t he estimated stati stics in the network. A lso it sh ould be studied the effect on the performance of the proposed schemes when the Control Cha nnel is imperf ect. ACKNOWLEDGMENT The author s would lik e to than k Profe ssor K wa n g - Cheng Chen , fro m the Depar t ment of Electrical Engineering National Ta iwan U niver sit y , for the fruit ful discus sion about his mo re recent research results o n cooperative spec trum se nsin g . 0% 5% 10% 15% 20% 25% 30% OR Ru le Adapt ive Rule A ND R u l e RMSE ME (5 ) Round R obin (C=5) Central ized Orc he st rat ion (C=5) Round R obin (C=10 ) Central ized Orc he st rat ion (C=10 ) 19% 20% 21% 22% 23% 24% 25% 26% OR Ru le A ND R u l e RMSE ME (5 ) Round R obin (C=5) Dec entrali zed Or che st rat ion (C=5 ) Round R obin (C=10 ) Dec entrali zed Or che st rat ion (C=1 0) Journal of Selected Areas in Comm unications - Advanc es in Cogn itive R adio Netw orking and Comm unicat ions ” 10 R EFERENCES [1] P. Gave r, Patricia A . Jacobs, “Plan ning S ervice to Pro vide Disaste r Reli ef: Gen eri c “ Command & Co n tro l” Mode ls”. T he Hastil y Fo rmed Networks (HFN) Researc h Group.) [2] Q. Zhang , F. W . 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