Evaluation of Kolmogorov - Smirnov Test and Energy Detector Techniques for Cooperative Spectrum Sensing in Real Channel Conditions

Transcription

1 Tefor Journa Vo. 7 No Evauaton of Komogorov - Smrnov Test and Energy Detector Technques for Cooperatve Spectrum Sensng n Rea Channe Condtons Deman Lekomtcev Student ember IEEE and Roman arsaek ember IEEE Abstract The cogntve rado technoogy aows sovng one of the man ssues of current wreess communcaton technooges namey a defct of vacant spectrum. A dynamc spectrum access used n the cogntve rado networks (CRN) gves an abty to access an unused spectrum n rea tme. Cooperatve spectrum sensng s the most effectve method for spectrum hoes detectng. It combnes sensng nformaton of mutpe cogntve rado users. In ths paper an expermenta evauaton of spectrum sensng methods based on the Komogorov - Smrnov statstca test and Energy Detector usng the Unversa Software Rado erphera (USR) devces synchronzed through a IO cabe and wth further processng n the GNU Rado and atab software are presented. Three hard decson fuson schemes are anayzed. Smuaton comparson between these rues s presented va Recever Operatng Characterstc (ROC) curves. The nfuence of rea channe wth nterferences s compared n contrast to commony assumed AWGN channe mode of vacant channe nose. Keywords Spectrum sensng K-S test Energy Detector Fuson Rues Recever Operatng Characterstc (ROC) GNU Rado USR IO. I. INTRODUCTION ARLIER ths year the IEEE Standards Assocaton Eannounced the creaton of IEEE forms study group to expore standardzaton for spectrum occupancy sensng technoogy []. The man objectve for ths workng group s optmzng usage of rado spectrum for wreess broadband servces for the IEEE 80. standard. That s why despte the ct that there are many nvestgatons amed at studyng the spectrum sensng ths queston s aper receved Apr 05; revsed June 5 05; accepted June 05. Date of pubcaton Juy The assocate edtor coordnatng the revew of ths manuscrpt and approvng t for pubcaton was rof. Branmr Rejn. Ths paper s a revsed and expanded verson of the paper presented at the th Teecommuncatons Forum TELFOR 04. Ths research has been supported by the EYS of the Czech Repubc project LD006 wth the correspondng COST acton IC004. Thanks aso for parta support of the BUT Interna project FEKT-S-4-77 (EKOS). The measurements were performed n the aboratores of the SIX center regstraton number CZ..05/..00/ the operatona program Research and Deveopment for Innovaton but wth the hep of a project CZ..07/.3.00/ WICOT. D. Lekomtcev s wth the Department of Rado Eectroncs Brno Unversty of Technoogy Techncka 6600 Brno Czech Repubc (phone: ; e-ma: xekom00@stud.feec.vutbr.cz). R. arsaek s now wth the Department of Rado Eectroncs Brno Unversty of Technoogy Techncka 6600 Brno Czech Repubc (phone: ; e-ma: marsaer@feec.vutbr.cz). st open. The smpest and the most common method of spectrum sensng s the Energy Detector (ED). oreover the sensng devces do not need any knowedge about the rmary User (U) sgnas. The Komogorov-Smrnov (K-S) test [] used n statstcs to compare two random dstrbutons s one of the promsng approaches to spectrum sensng. Its appcaton to ths doman s based on the dea of testng the measured sgna dstrbuton over the nose dstrbuton (usuay AWGN). In ths paper we want to perform an extended anayss of K-S test and ED n more reastc condtons e.g. to test what s the nfuence of rea vacant channe nose wth nterferences and to evauate the nfuence of the precson of cumuatve dstrbuton functon estmaton. oreover we are aso focusng on few smpe hard decson methods for cooperatve sensng because these technooges are effectve smpe and owcost to be mpemented. The evauaton s based on the expermenta data from the Unversa Software Rado perphera (USR) devces controed by GNU Rado software wth subsequent anayss n atab. It s aso mportant to note that most of the research efforts on dfferent fuson rues for cooperatve sensng are anaytca and/or atab smuatons based [3]-[5]. Recenty a few measurement-based studes on cooperatve sensng can be found n [6]-[8]. In [] [9] and [0] the authors nvestgate an ndvdua sensng based on K-S test. These works provde the bass for our paper. The rest of ths paper s organzed as foows. In Sectons II and III we ntroduce K-S test-based and ED based spectrum sensng agorthms respectvey. Secton IV brefy presents three most common hard fuson rues for cooperatve sensng. In Secton V we provde a descrpton of the expermenta setup. Secton VI presents smuaton resuts whe Secton VII concudes the paper. II. SECTRU SENSING BASED ON KOLOGOROV- SIRNOV TEST The detecton of a sgna wthn a nosy measure over a specfc frequency band s the key probem assocated wth spectrum sensng. The essence of ths probem s to dstngush between the foowng two hypotheses: n( t) H 0 r ( t) () s( t) + n( t) H do:0.5937/tefor5003l

2 3 Tefor Journa Vo. 7 No. 05. where r(t) s the receved sgna at Secondary User (SU) ocaton s(t) represents the transmtted sgna of the U observed at SU and n(t) s a nose (n the smpest case the AWGN or other nose mode). In the case of K-S test a decson between one or the other hypothess s performed as descrbed beow. Ths test checks the accordance between the emprca (measured) and the theoretca dstrbuton functons whereas the dstrbuton parameters of the theoretca dstrbuton are known n advance. Fg. ustrates the prncpe of ths method. Fg.. Vsua descrpton of K-S test. The nu hypothess H 0 s assumed to be vad when the emprca and theoretca probabty dstrbutons are not statstcay sgnfcanty dfferent and the aternatve hypothess H s assumed when these dstrbuton are sgnfcanty dfferent. Frst the emprca Cumuatve Dstrbuton Functon (CDF).e. CDF of the receved sgna s estmated. Ths functon s defned by: N F ( x) J ( x( n) x) () N n where J denotes the ndcator functon whch takes on a vaue f the nput s true and a vaue 0 otherwse N denotes the number of data sampes from each gven sgna segment. The argest absoute dfference between the emprca and the theoretca CDFs s used as the goodness-of-ft statstc gven by []: T sup { F( x) G( x) } (3) KS x R where G(x) s the known (expected) theoretca CDF. In accordance wth [] ths equaton can be expressed as: T max{ F( x ) G( x )} (4) KS where F(x ) denotes the vaue of CDF evauated at the pont x. To cacuate the theoretca CDF for the absoute vaue of compex sgna and addtve whte nose wth rea and magnary parts havng norma dstrbuton the ch-square dstrbuton wth two degrees of freedom s used []. In atab ths can be mpemented by cang the functon: G ( x ) chcdf ( x v) (5) that computes the ch-square CDF at each of the vaues n x usng the correspondng degrees of freedom v (n our case v). The hypothess H s accepted at the sgnfcance eve α (the se aarm probabty) when the vaue of the test statstc T KS s ower than a crtca vaue k(αn). There are tabes for the vaues of k(αn) for 5 N 50 n the terature. As n our nvestgaton N 50 the crtca vaues can be approxmated as []: k( α N ) n. (6) N α The motvaton for ths paper was to nvestgate what s the nfuence of nose havng the dstrbuton dfferent from the exact Gaussan (.e. rea measured nose) to expore the nfuence of CDF approxmaton by fnte (and sma) numbers of ponts (mportant for the effcent mpementaton) and to check the potenta of cooperaton between severa (at east two) sensng nodes. III. SECTRU SENSING BASED ON ENERGY DETECTOR In the case of ED technque spectrum sensng s performed as foows. Frst N sampes of the receved sgna from the nvestgated channe are receved by SU. Then the sgna s dvded nto N segments. Then the sgna energy for each segment s estmated e.g. as: N Y ( r( t)) (7) N n where Y represents the output of the energy detector whch serves as the test statstc. To make a decson about the presence or absence of a sgna we ntroduce γ as the threshod that vares dependng on the nose varance σ n. The probabty of se aarm ( ) and detecton probabty ( d ) for ED s gven as foows: [3]. γ σ ( Y > γ H ) Q n (8) 0 σ n / N γ σ ( SNR) ( > H ) n d Y γ Q (9) σ n / N SNR + where Q(x) s defned by the compementary dstrbuton functon of the standard Gaussan and s gven as u Q( x) e / du (0) π x SNR s a sgna to nose rato whch can be defned n terms of the sgna and nose varance (σ s and σ n ) as σ SNR s. () σ n Therefore for a constant se aarm rate ( ) the threshod s gven by [3] Q ( ) δ n γ δn +. () N

3 Lekomtcev and arsaek: Cooperatve Spectrum Sensng n Rea Channe Condtons 33 IV. COOERATIVE SENSING FUSION RULES To mprove sgna detecton the cooperatve spectrum sensng can be used [4] [5]. In the prospectve scenaro there are SUs that sense one U. Each of the SUs makes ts own decson regardng the presence or absence of the U and forwards the bnary decson ( or 0) to a fuson center (FC) for further processng. SUs are ocated at a neggbe dstance from each other compared to the dstance from them to U. Thus from a ong-term perspectve the prmary sgna receved by a the SUs has the same oca mean sgna power. For smpcty we have frst assumed that the nose dng statstcs and average SNR are the same for each SU and the channes between SUs and FC are dea (.e. there s no oss of nformaton). A fna decson on the presence of U s made by k out of SUs and can be descrbed by a bnoma dstrbuton based on the Bernou tras where each tra represents the decson process of each SU. The generazed formua for the probabty of detecton at the fuson center s gven by [4] [5]: d k d d k (4) (5) where d and are the probabtes of detecton and se aarm respectvey for each SU. In ths paper three rues of the hard combnaton scheme are dscussed. A. Logca OR-Rue In ths rue a decson that the U s present s made f any of the SUs detects the U. The cooperatve probabty of detecton (se aarm) usng OR fuson rue can be evauated by settng k n eq. (4 5): ( ) ( ) (6) d d. (7) B. Logca AND-Rue In ths rue a decson that the U s present s made f a SUs have detected the U. The cooperatve probabty of detecton (se aarm) usng AND fuson rue can be evauated by settng k n eq. (4 5): d d (8). (9) C. Logca AJORITY-Rue In ths rue a decson that the U s present s made f haf or more of the SUs detect the U. The cooperatve probabty of detecton (se aarm) usng AJORITY fuson rue can be evauated by settng k/ n eq. (4 5): / (0) d d d. () / V. TESTBED DESCRITION We use a smar measurement setup as the one used n our prevous paper [6]. Fg. depcts ths setup. It conssts of one persona computer (C) and two USR devces. One of the USR s carryng out SU as we as U roes and s connected to the C through a Ggabt Ethernet port. Fg.. Expermenta setup workng n TV whtespaces. The second USR (whch s carryng out a SU roe) s connected to the frst USR through a IO cabe to synchronze the system. Note that the precse synchronzaton between the SUs must be reazed n order to reaze the cooperatve scheme. Optona GSdscpned oscators provde the capabty to synchronze devces to the GS standard over a arge geographc area [7]. In the setup the frst USR mpementng the SU and U empoys the WBX daughter board (front-end) whe the SBX front-end s used n SU devce. One SU had an antenna behnd the wndow and t was connected wth an ampfer to enhance the receved sgna the other had t on the aboratory tabe and the dstance between them was about 4 meters. Wth such a scenaro two receved-sgna repcas were created. Both USRs work n the TV whtespace. The prmary user sgna whch was transmtted by the frst USR s an 8SK sgna wth a bandwdth of 00 khz (bandwdth correspondng to wreess mcrophones bandwdth athough the moduatons are dfferent) centered at 6 Hz carrer frequency whch corresponds to one of the TV channes (n our experment the 38 th channe). A pror we know that n the measurement ocaton ths channe s vacant. Each SU scans two channes the frst one s a free channe at 60 Hz frequency (ths channe s vacant throughout the experment) the second one s a channe where U transmts. Note that athough the channe s vacant t s possbe to suppose that the character of receved sgna s not exacty whte Gaussan as t can contan nterferences from neghborng bands. The C s runnng Fedora 6 the sgna processng appcaton s done usng an open-source GNU Rado verson Each of SUs sensed the channe of nterest. By appyng the GNU Rado the sensng resuts are recorded nto the data fes for subsequent processng. After that based on the recorded data fes the vaues of d

4 34 Tefor Journa Vo. 7 No. 05. and are cacuated for each SU n atab n order to estmate correspondng ROC curves. The equatons to estmate these quanttes are as foows: Number of segments that havey > γ H d () Number of observed segments Number of segments that havey < γ H.(3) Number of observed segments In accordance wth fuson rues for cooperatve sensng a fna decson about a vacant channe s made. The most mportant resuts are presented beow. VI. EXERIENTAL RESULTS To evauate the performance of a partcuar method of (cooperatve) spectrum sensng technques the key characterstcs as d and are used [3]. The ROC curve graph vsuay shows the dependence between these two parameters. A cacuatons for constructng dagrams are performed n atab. Frst we anayzed the dependence of d and on the SNR vaues. Fg. 3 demonstrates a hgher detecton reabty for ncreased SNR vaues. Fg. 4 s reated to the practca mpementaton of K-S testng devce and descrbes ROC curves for dfferent numbers of ponts used for emprca and theoretca CDF approxmaton (N CDF ). Fg. 4. ROC curves for 8SK sgna for dfferent N CDF SNR0.5 db 000 segments wth 00 data sampes. Note here that ROC curve evauaton has been done for one hundred sampes per segment ony. Ths reatvey sma vaue of the number of sampes per segment (n comparson wth e.g sampes n []) resuts n a ower SNR performance. Fg. 3. ROC curves for 8SK sgna for dfferent SNR 000 segments wth 00 data sampes. It can be observed that aso the vaue of N CDF 7 provdes suffcent reabty ony sghty degraded than n the case of a hgher number of ponts for approxmaton. Note that n ths case the number of ponts n each sgna segment and SNR vaue s fxed. To ustrate the meanng of N CDF and ts nfuence on the emprca CDF we present Fg. 5. It can be seen that wth ncreasng N CDF the emprca CDF becomes smoother and coser to the theoretca one (n the case of vad hypothess H 0 ). Fg. 6 shows smuaton resuts for dfferent channes t compares the theoretca AWGN case wth the rea measured channe n TV band. As expected and evdent from the fgure the pure AWGN channe resuts n a hgher detecton probabty d than the rea dng channe. Fg. 5. Emprca (bue ne) and theoretca (red ne) CDFs for dfferent N CDF (top N CDF 7 n the mdde N CDF 50 bottom N CDF 00). Fnay we compared the snge spectrum sensng by each SU wth ther cooperatve verson n accordance wth

5 Lekomtcev and arsaek: Cooperatve Spectrum Sensng n Rea Channe Condtons 35 three most-used fuson rues. Fg. 7 and Fg. 8 ustrate these comparsons for K-S test and ED respectvey. Fg. 6. ROC curves for 8SK sgna for dfferent channe SNR9 db 000 segments wth 00 data sampes. Fg. 7. ROC curves for KS test for 8SK sgna for three fuson rues SNR0.5 db 000 segments wth 00 data sampes. Fg. 8. ROC curves for ED for 8SK sgna for three fuson rues SNR0.5 db 000 segments wth 00 data sampes. As can be seen from Fgs. 7 and 8 a cooperatve fuson rues gave a better detecton performance than the ndvdua sensng. The AND rue has a better detecton performance than the OR and AJORITY rues at ow. Ths s due to the ct that for OR rue the FC decdes whether a U s present when at east one SU detects t. Whe n the AND rue a SUs must detect a U sgna. Aso worth notng s the ct that K-S test has a better detecton performance than ED as for ndvdua sensng as we as for a cooperatve fuson rues. As t s known [8] for the IEEE 80. standard d shoud be 90% or hgher at 0.. In our experment a fuson rues and each SU for K-S test meet ths requrement whereas ED cannot reach t for the same SNR vaues. VII. CONCLUSION In ths paper we present a performance evauaton of Komogorov-Smrnov test-based and energy detectonbased spectrum sensng methods n cose-to-rea channe condtons. We have compared the nfuence of rea channe nose and nterferences on the sensng performance expressed by the Recever Operatona Characterstcs and the effect of cumuatve functon approxmatons by a fnte number of sampes. Fnay the hard (bnary) fuson rues for cooperatve sensng were used to demonstrate ther mprovement on the decson process. Usng an exampe of the sensed 8SK sgna wth dfferent SNR vaues t s frst checked that the performance of ndvdua sensng mproves wth an ncreased SNR. It was aso demonstrated that the probabty of detecton for rea channe deterorates n comparson wth AWGN usuay assumed n theoretca anayss. On the contrary the effect of fnte approxmaton of dstrbuton functons seems to be margna. In our future work we w use the nvestgated sensors for TV and wreess mcrophones sgnas cooperatve sensng n a cty area on severa vacant TV channes. REFERENCES [] IEEE 80. Workng Group on Wreess Regona Area Networks. Enabng Rura Broadband Wreess Access Usng Cogntve Rado Technoogy n TV Whtespaces. Recpent of the IEEE SA Emergng Technoogy Award. [Onne] Avaabe: (ay 3 04). [] R. arsaek K. ovaac Komogorov Smrnov test for spectrum sensng: from the statstca test to energy detecton IEEE Workshop on Sgna rocessng Systems pp [3] D. Tegug B. Scheers and V. Le Nr Data fuson schemes for cooperatve spectrum sensng n cogntve rado networks tary Communcatons and Informaton Systems Conference (CC) pp [4] d. Shamm Hossan et. a. Hard Combnaton Data Fuson for Cooperatve Spectrum Sensng n Cogntve Rado n Internatona Journa of of Eektrca and Computer Engneerng (IJECE) vo. No.6 December 0 pp [5] H. Du et. a. Hybrd Cooperatve Spectrum Sensng Scheme Usng Doube-Fuson n Cogntve Rado Networks n Journa of Computatona Informaton Systems vo. 7 0 pp [6] S. Chaudhar et a. easurement Campagn for Coaboratve Sensng usng Cycostatonary Based obe Sensors IEEE Internatona Symposum on Dynamc Spectrum Access Networks (DYSAN) pp [7] S. Kyperountas et a. A Comparson of Fuson Rues for Cooperatve Spectrum Sensng n Fadng Channes Vrgna Tech Symposum on Wreess ersona Communcatons pp [8] A. Gamero et. a. Seectve reportng - a haf sgnang oad agorthm for dstrbuted sensng n EURASI Journa on Wreess Communcatons and Networkng vo pp. -4.

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