Sequential Tests for the Detection of Voice Activity and the Recognition of Cyber Exploits *

Transcription

1 Commuiatios ad Ntwork,, 3, doi:.436/..34 Publishd Oli Novmbr ( Squtial Tsts for th Dttio of Voi Ativity ad th Rogitio of Cybr Exploits * Abstrat Ehab Etllisi, P. Papatoi-Kazakos Dpartmt of Eltrial Egirig, Uivrsity of Colorado Dvr, Dvr, USA {hababdalla.tllisi, Titsa.Papatoi}@udvr.du Rivd Sptmbr 5, ; rvisd Otobr, ; aptd Otobr 9, W osidr th problm of automatd voi ativity dttio (VAD), i th prs of ois. To attai this objtiv, w itrodu a Squtial Dttio of Chag Tst (SDCT), dsigd at th idpdt mixtur of Laplaia ad Gaussia distributios. W aalyz ad umrially valuat th proposd tst for various oisy viromts. I additio, w addrss th problm of fftivly rogizig th possibl prs of ybr xploits i th voi trasmissio hal. W th itrodu aothr squtial tst, dsigd to dtt rapidly ad auratly th prs of suh xploits, amd Cybr Attaks Squtial Dttio of Chag Tst (CA-SDCT). W aalyz ad umrially valuat th lattr tst. Exprimtal rsults ad omparisos with othr proposd mthods ar also prstd. Kywords: Voi Ativity Dttio, Squtial Dttio of Chag Tst, Cybr Exploits. Itrodutio Voi Ativity Dttio (VAD) is dployd xtsivly, iludig th Global Systm for Mobil Commuiatios (GSM), as wll as svral satllit ad radar military ad ivilia appliatios, (s i Figur ). Thus, VAD is a importat ompot of most systms that iorporat digital voi trasmissios. Durig ral tim voi trasmissio, priods of voi ativity ar followd by sil, whr both voi ad sil priods ar imbddd i bakgroud ois. Si voi is grally trasmittd through fixd badwidth liks, th trasmissio of th sil priods idus svr badwidth wast. Voi Ativity Dttio (VAD) allows for th omprssio of th sil priods ad may rsult i up to 3 to 4 prt of badwidth savigs. To dtt voi ativity vrsus sil priods, th startig ad dig poits of otiuous sph ativity must b dttd. Svral rsarh fforts hav b ivstd i this ara [-3]. I this papr, w propos a ovl VAD algorithm, amd Voi Ativity Dttio usig a Squtial Dttio of Chag Tst (SDCT- VAD). Th algorithm is dsigd at a idpdt mixtur of Laplaia ad Gaussia distributios; it is trakig fftivly th boudary poits btw otiuous voi ativity ad sil tim priods, whr * Partially supportd by th US Air For Offi of Sitifi Rsarh udr otrat AFOSR FA durig sil thr is oly ois, whil durig sph thr is sph plus ois. Th ois ad oisy sph ar modld by a Gaussia vrsus Laplaia plus idpdt Gaussia distributios. Rsults ar iludd for th ass whr th SDCT-VAD is applid to dtt voi ativity, i both th prs ad th abs of ois. Th algorithm is also tstd withi a raltim sario, to xhibit its robustss ad low omplxity proprtis. Figur. VAD itgratd i a tlommuiatio systm. Copyright SiRs.

2 86 E. ETELLISI ET AL. Cosidrig th possibility of ybr xploits durig voi trasmissio, w also prst a ovl ybr attaksqutial dttio of hag Tst (CA-SDCT). Th CA-SDCT algorithm is dployd durig voi ativity priods, as dttd by th SDCT-VAD algorithm. Th proposd CA-SDCA algorithm is dsigd at th Additiv Whit Gaussia Nois (AWGN) ybr attak modl ad is fully aalysd ad umrially valuatd i various viromts. Th papr is orgaizd as follows: I Stio, th SDCT-VAD algorithm is prstd. I Stio 3, th CA-SDCT algorithm is dvlopd. I Stio 4, xprimtal rsults ar iludd. I Stio 5, w draw som olusios.. Voi Ativity Dttio Algorithm Th gral opratio flowhart of th VAD algorithm is dpitd by Figur. Th problm to b solvd hr is th fftiv distitio btw ativ ad iativ voi priods. Howvr, th varity of both th ativ voi ad th ambit ois mak this problm quit ompliatd i ral lif. As show i Figur, first th sph sigal is gratd ad is th orruptd by Additiv Whit Gaussia Nois (AWGN). Th AWGN affts th shaps of both th ativ voi ad sil priods. Th SDCT-VAD is th applid to dtt voi ativity priods. As will b furthr disussd i Stio 3, th SDCT-VAD oprats o various Sigal-to-Nois Ratios (SNRs)... Sph ad Nois Probability Distributios Throughout this stio, w osidr two distit probability dsity futios (pdfs) whih rprst th voi ad ois amplitud distributios of th proposd modl. Th two distributios for sph ad ois ar assumd to b Laplaia ad Gaussia, rsptivly, as i [4], whr diffrt sph distributio modls ar show i Figur 3. Figurs 4-5 show oislss ad oisy atual sph sigals, rsptivly. To dras algorithmi dsig omplxity, w assum statistial idpd btw sussiv voi priods, as wll as btw sigal ad ois. W th driv th oisy sph distributio via th ovolutio of th Laplaia ad Gaussia dsitis. Assumig that th orruptig ois is AWGN, th oisy sph sigal is rprstd blow, Y X N () sigal AWGN whr Y dots th oisy sph, X sigal stads for th la sph ad rprsts th ois, ad N AWGN Figur. Th gral opratio flowhart of th VAD algorithm. Figur 3. Distributios voi sigals. X sigal ad N AWGN ar statistially mutually idpdt. Copyright SiRs.

3 E. ETELLISI ET AL. 87 Figur 4. Atual oislss voi sigal sil + ativ voi. f rprsts th AWGN oisy sil. Giv th fiit squ x x i;i ad th dsity futios f x ad f x, th objtiv is to dtt a possibl f to f hag as rliably ad as quikly as possibl. To dtt a possibl suh hag, slt som positiv thrshold δ. Th, obsrv data poits squtially ad did that th f to f hag has ourrd th first tim suh that T x δ, whr Whr ; Tx max,tx gx T g i i x l og f f x x i i x x i i Th abov algorithm oprats squtially via th us of two thrsholds, ad δ, whr rprsts a rfltig barrir ad δ rprsts a absorbig or disio barrir [8]. Wh th two stohasti prosss rprstd by th dsity futios f ad f ar mmorylss, th th oditioig i th log liklihood i () drops ad th algorithmi opratios ar mmorylss as wll. A symmtri algorithm that dtts a shift from f to f, istad, a b asily drivd. I Figur 6, th timvolutio of both algorithms is dpitd. () Figur 5. Atual voi oisy voi sigal... Th Squtial Tst for th Dttio of Chag Th squtial tst for th dttio of hag, i its gral form, was itrodud ad aalyzd i [5-]. It is assumd that a automatd systm will b moitorig th sigal ativity to did wh th voi is ativ vrsus ot, whos dsig is basd o th dttio of hag i th data gratig stohasti pross. Th automatd systm will b implmtd via th dploymt of th SDCT-VAD algorithm whih will b trakig voi to sil ad sil to voi shifts, whr voi ad sil ar modld by two distit stohasti prosss. Blow, w first prst th gral modl osidrd i rfrs [5-]. Lt f x ad f x dot th -dimsioal dsity futios of two wll kow, distit, mutually idpdt disrt-tim stohasti prosss at th vtor poit x x,x,,x. Lt it b kow that th ativ pross is iitially gratd by th dsity futio f [8]. For th problm addrssd, it is assumd that rprsts th oisy voi pross, whil f (a) (b) Figur 6. Makig th fial disio i th first rossig to th thrshold, Dttig hag (a) from f x to f x, (b) from f x. f x to Copyright SiRs.

4 88 E. ETELLISI ET AL..3. Th SDCT-VAD Usig Laplaia ad Gaussia Distributios f x Lt ad f x rprst th dsity futios of a sigl datum x from oisy voi vrsus just ois, rsptivly. Lt it b dsirabl to dtt a possibl hag from f x to f x, whr f x is Gaussia ad f x is Laplaia plus Gaussia. Th assumptio hr is that th obsrvd voi pross is statioary, mmorylss ad Laplaia, whil th ois pross is idpdt from th voi pross ad AWGN. Th, fx fsxyfny dy (3) whr fs x is th Laplaia distributio that rprsts th voi sph, ad fn x is th Gaussia distributio rprstig th AWGN. a fs x xpax (4) x fn x φ (5) whr dots th stadard dviatio of th Gaussia distributio. W ow driv th xprssio f x : a y f x xp a x y φ y d a y f x xp ax y xp dy π Altrativly, th distributio f x a b xprssd as follows, a a f x xp hxh x (6) whr x hxxpax a x hxxpax a W th omput th log liklihood ratio updatig stp i th squtial tst: f log f x x a xp log x φ a hx h x hx h x f x a π a x log I f x x Th algorithmi updatig stp a b writt as: π (7) I Ih h I Figur 7. Sigal-to-Nois Ratio (SNR). g whr xp h Th algorithmi stp may b subsqutly modifid as follows π g I I hh (8) whr x a ; h xp x u du x ad u φu xp π ad whr th Sigal to Nois Ratio (SNR) is: SNR a From th last quatio, it a b rogizd that th Sigal-to-Nois Ratio (SNR) is a futio of both th Laplaia ostat a ad th stadard dviatio of th ois. To dvlop a robust mthod for trakig th ois ad sph sigals, i Stio.4, w will tst th us of diffrt SNRs i th dsig of th algorithm. I Figur 7, w plot th SNR as a futio of, for various valus of th stadard dviatio of th ois. Lt us ow slt som positiv thrshold ad dfi: Copyright SiRs.

5 E. ETELLISI ET AL. 89 δ δ π l W may th modify th algorithm i (), as maifstd by th distributios drivd i this stio, via salig, rsultig i th followig opratio: Obsrv data squtially ad did that th hag from ois to voi ativity has ourrd th first tim istat suh that T x δ, whr xmax,tx g x T ; T x ma π T x max, T x l l () l lhh W ot that th algorithm i () dtts hag from sil to ativ voi. Th algorithm that dtts hag from ativ voi to sil, istad, is similarly drivd, whr its rursivly drivd algorithmi valus ar giv by th xprssio i () blow ad whr its disio thrshold is grally diffrt tha that of th algorithm i (). f log f x x x φ log xp hx ( ) h( x) π Tx max,tx l lhh () () ξ f f x f,i,i S x x/ ξ xdx (3) Th probabilitis β ; rprst a powr st, Th probabilitis α ; rprst a fals alarm st. Th mai objtiv hr is to fid th thrshold that idus low fals alarm ad high powr for small sampl sizs. To omput th powr ad fals alarm urvs, as idud by th probability squs β ; ad α ;, rsptivly, w d to aalys th haratristis of th updatig stp show i Equatio (8). This pross is xplaid i th Appdix, whr th xprssios for th omputatio of th squs β ; ad α ; ar also drivd. Giv thrshold δ, th sil mod to ativ voi mod hag dttig algorithm is basially haratrizd by two tim urvs: th powr ad fals alarm urvs, dotd rsptivly β ad α, rsptivly, whr dots tim istat ad whr, β : Th probability that th sil to ativ voi mod hag dttig algorithm rosss its thrshold bfor or at tim, giv that th opratio mod is ativ voi mod throughout [6]. α : Th probability that th sil to ativ voi mod dttig algorithm rosss its thrshold bfor or at tim, giv that th opratioal mod is sil mod throughout [6]. Wh th algorithm that moitors hag from mod sil to mod voi is osidrd, th thrshold may b sltd basd o th followig priipl: At giv tim, hav th powrs idud by th paralll algorithms b abov a prdtrmid lowr boud, whil th fals alarm idud by ah algorithm rmais blow a prdtrmid uppr boud. Th thrshold for th algorithm that moitors hag from voi to sil, istad, is sltd similarly. I Figur 8, w dpit th β ad α rprstativ.4. Powr ad Fals Alarm Curvs for Thrshold Valus Sltios I this stio, w prst algorithmi prforma ritria ad thir us i th sltio of th disio thrsholds. W spifially valuat powr ad fals alarm urvs idud by th two algorithms i Stio.3 for svral giv disio thrsholds. W th ompar suh urvs for diffrt thrshold valus, to subsqutly did o th valus of th opratioal algorithmi thrsholds. Lt us dfi, fi ξdξ : Th probability that at tim th algorithm has ot rossd th thrshold, δ, ad its valu lis i ξξ, dξ, giv that th atig pdf is f i ; whr, th rursiv xprssio blow a b drivd, Figur 8. Powr ad fals alarm urvs vs diffrt thrsholds. Copyright SiRs.

6 9 E. ETELLISI ET AL. urvs, to obsrv ad disuss qualitativ haratristis. W plot ths urvs for two diffrt thrshold valus. From th figur, w ot that as th valu of th disio thrshold irass, th fals alarm urv drass, but so dos th powr urv. Th thrshold sltio for th sil to ativ voi hag moitorig algorithm may b basd o a rquird lowr boud for th powr ad a rquird uppr boud for th fals alarm, at a giv tim istat. A similar ritrio may b adoptd i th thrshold sltio for th ativ voi to sil moitorig algorithm. 3. A Algorithm for Dttig Cybr Attaks durig Sph Ativity (a) I this stio, w osidr th as whr th voi trasmissio hal may b vulrabl to ybr xploits. W th fous o dvlopig a automatd systm that, i ourr with voi ativity dttio, also dtts ybr xploit ativitis. W thus dvlop a Cybr Attak- Squtial Dttio of Chag Tst (CA-SDCT), dsigd to dtt ybr attaks durig voi ativity priods, as th lattr ar dttd by th SDCT-VAD algorithm i Stio. Th blok diagram of th ovrall systm is dpitd i Figur, Stio. As show i Figur, first th sph sigal is gratd ad is th orruptd by additiv whit Gaussia ois (AWGN). Th SDCT-VAD is th dployd to distiguish btw voi ativity ad sil priods. W fially wish to dtt possibl ybr attaks durig voi ativity priods. As i Stio., lt f(x) ad f(x ) dot th -dimsioal dsity futios of two wll kow, distit, mutually idpdt disrt-tim stohasti prosss at th vtor poit x = {x,x,,x }. For th problm addrssd hr, f rprsts th pross of ybr xploits suprimposd o oisy voi ativity, whil f rprsts th oisy voi ativity pross i th abs of ybr attaks. Giv th ifiit squ x= x i ;i, lt th -dimsioal dsity futios b dotd f( x) ad f( x ). Th objtiv is to dtt a possibl f to f hag as rliably ad as quikly as possibl, utilizig th obsrvd data squs. Th squtial opratio of th two algorithms is dpitd i Figur 9. As i Stio., w first slt som positiv thrshold. Subsqutly, w obsrv oisy voi data squtially, durig voi ativity priods dttd by th SDCT-VAD, ad did that th f to f hag has ourrd, th first tim suh that T x, whr whr T :T x max,t x g x (4) (b) Figur 9. Makig th fial disio i th first rossig to th thrshold. (a) Cybr Exploits Prst, dotd H; (b) Cybr Exploits Abst, dotd H. i i i i i f xi x g x log f x x A similar algorithm may b dvisd for th dttio of shifts from f to f, istad. W modl th prs of ybr xploits by Additiv Whit Gaussia Nois (AWGN) that is suprimposd o th trasmissio hal AWGN, rsultig i rlativly xssiv umulativ whit ois. Wh th two stohasti prosss rprstd by th dsity futios f ad f ar mmorylss, th oditioig i th log liklihood i (4) drops ad th algorithmi opratios ar mmorylss as wll. As dirtly ddud from Stio.3, i th prst as w hav: whr, f f xp (5) x h x h x xp (6) x h x h x h x xp xφ x x : Stadard dviatio of th trasmissio ois, i th abs of ybr xploits. : Stadard dviatio of th umulativ ois wh ybr xploits ar addd to th trasmissio ois. Copyright SiRs.

7 E. ETELLISI ET AL. 9 Th, s i th SDCT-VAD dsig ar th Laplaia paramtr, th stadard dviatio of th Gaussia ois ad th h xh xp x two algorithmi thrsholds: A thrshold δ usd by th f x log l algorithm i (); for th dttio of hag from ois f x h xh xxp to oisy voi ativity, ad a thrshold δ usd by th algorithm i ( ); for th dttio of hag from oisy ativ voi to just ois. W usd th powr ad fals or, alarm urvs disussd i Stio.4, to did o th f h x h x x valus of ths two thrsholds. I partiular, w sltd log l f x (7) h xh x th ( δ, δ, α, ) valus (.3,.5,.98,.53). W usd th dsig paramtr valus (.3,.5,.98, Th implmtatio of th ybr xploits dttio algorithm is th as follows: SDCT-VAD algorithm i th prs of various oisy.53) ad tstd th robustss of th rsultig Durig voi ativity priods, as dttd by th SDCT- viromts. Various oiss wr mixd with th la VAD algorithm, obsrv data squtially ad did sph sigals. Six diffrt oiss wr usd i our that th hag from abs to prs of ybr xploits has ourrd, th first tim istat suh that babbl, flowig traffi ad trai passig. Figur x- valuatios, iludig whit ois, wid, omputr fa, Tx, whr Equatio (8). hibits th various ois typs, whil Figurs ad 3 W ot that th algorithm i (8) dtts a f show th fft of suh oiss wh suprimposd o th to f hag. Th algorithm that dtts a f to f origial oisy sph sigal i Figur. hag, istad (from prs to abs of ybr xploits), is similarly drivd, whr its rursivly drivd algorithmi valus ar giv by th xprssio i (9) blow ad whr its disio thrshold, is grally diffrt tha that of th algorithm i (8), as show i Figur Exprimtal Rsults 4.. Tstig th SDCT-VAD For ompariso, th sam voi ad ois viromts ar also tstd by th approah prstd i [] ad th G.79 VAD algorithm i []. Th rsults ar summarizd i Tabls ad 3. Th ois data ar obtaid from ad ar addd to th la sph sigal at SNRs varyig from 5 db to 5 db. I this stio, w stat th stps ivolvd i th umrial valuatio of th SDCT-VAD algorithm. First, w slt th prtit ivolvd paramtrs ad dploy th rsultig SDCT-VAD algorithm, to dtt ay voi ativity i th ommuiatio lik. Th, th SDCT- VAD is valuatd i various oisy viromts. I our simplifid modl, th sil plus ois mod of opratio is assumd to b rprstd by a Gaussia distributio, whil th oisy voi sigal is rprstd by a mixtur of Laplaia ad Gaussia distributios, as show i Figur. Th prtit paramtrs to b ho- Figur. Origial voi sigal. h x h x Tmax, T l h x h x Tmax, T l h x h x h x h x (8) (9) Copyright SiRs.

8 9 E. ETELLISI ET AL. Figur. Various oisy viromts. Figur. Origial sigal orruptd by AWGN SNR = 5,, 5, ad 5 db. Figur 3. Rsults of addig ois to th origial sph sigal (5 db SNR). (a) Cla sph; (b) Wid ois; () Babbl ois; (d) Computr fa ois; () Flowig traffi; (f) Trai passig ois; (g) Noisy sigal ois: AWGN ; (h) Noisy sigal ois: wid ; (j) Noisy sigal ois: omputr fa ; (k) Noisy sigal ois: flowig traffi ; (l) Noisy sigal ois: trai passig ut. Copyright SiRs.

9 E. ETELLISI ET AL. 93 To mpirially valuat th SDCT-VAD algorithm, may audio mssags wr usd, with diffrt lgths, (3 s ad 5 s), with both mal ad fmal spakrs ad with diffrt SNRs, (5 db - 5 db). Th fft of ths SNRs o th audio mssags is xhibitd i Figur, whr Figur xhibits th origial sph sigal. To mpirially valuat th SDCT-VAD algorithm, may audio mssags wr usd, with diffrt lgths, (3 s ad 5 s), with both mal ad fmal spakrs ad with diffrt SNRs, (5 db - 5 db). Th fft of ths SNRs o th audio mssags is xhibitd i Figur, whr Figur xhibits th origial sph sigal. Figurs 4 ad 5 blow show rsults for th SDCT- VAD algorithm with opratig paramtrs as thos statd i this Stio, wh th SNR is 5 db ad 5 db, rsptivly. Th auray of th rsults dpds o th lvl of th SNRs ad th typ of th ois viromt, as show i Tabls ad. Figur 4. SDCT-VAD rsults origial voi sigal orruptd by AWGN (SNR = 5 db). Figur 5. SDCT-VAD rsults origial voi sigal orruptd by AWGN (SNR = 5 db). Copyright SiRs.

10 94 E. ETELLISI ET AL. Th ffiiy of th SDCT-VAD algorithm was valuatd for various oisy voi sigals. I th first xprimt, w tstd th ffiiy of th proposd mthod usig th sam audio rordig disussd abov, traig th spd ad th auray of th algorithm i dttig th sil mod to ativ mod hag ad vi vrs. To omparativly valuat th prforma of th proposd SDCT-VAD algorithm, w ompard its idud rsults with thos of th maual sgmtatio. Figur xhibits th had-markd rsults of maual sgmtatio. Figurs 4 ad 5 xhibit th automatd sgmtatio idud by th SDCT-VAD proposd algorithm. W valuatd th algorithmi probability of rror ( ), usig th formula blow: P Av P _ AVSPmaual N AVSP maual AVSP RSDC VAD AVEP maual AVEP RSDC VAD _ AVEPmaual () AV: Ativ Voi; AVSP: Ativ Voi Startig Poit; AVEP: Ativ Voi Edig Poit; N: Numbr of Ativ Voi Rgios. Th prforma of th SDCA-VAD is valuatd i trms of probability of fals ad orrt disios, whr P is th probability of orrt sph lassifiatio ad whr P, is th probability of fals sph lassifiatio, omputd as i (). To omput P w start with kow voi ativity ad th startig ad dig poits of voi ativity markd. W th suprimpos AWGN voi otamiatio with various SNRs (5,, 5, ad 5 db) ad dploy th orrspodig SDCT-VAD for various oisy viromts, as show i Figurs -3. Rsults omparig th SDCT-VAD with th maual approah ar show i Tabl. I Figurs 6 ad 7 w plot th P ad P rsults iludd i Tabl. Tabl. P 's ad P 's of th proposd RSDCA-VAD C F for various viromtal oditios. Nois/SNR (db) Whit Wid Computr Fa Babbl Flowig Traffi Trai Passig SNR 5 SNR SNR 5 SNR SNR 5 P (%) P (%) P (%) P (%) P (%) P (%) P (%) P (%) P (%) P (%) P (%) P (%) Tabl. Comparig th startig ad dig dttio tim istas of th oisy ativ voi mssags usig th maual ad proposd mthod. Avrag P (%) P (%) SNR (db) Mssag Mssag 3 Mssag 3 AVSP AVEP AVSP AVEP AVSP AVEP Maual Automati RSDCA -VAD Figur 6. P 's of th proposd RSDCA-VAD i various viromtal oditios. Copyright SiRs.

11 E. ETELLISI ET AL. 95 th proposd algorithm agaist various viromtal oditios ad to ompar it with th ITU stadard G79 Ax B [] ad th proposd i [] approahs. From Tabl 3, it a b rogizd that v with viromtal hallgig oditios, th proposd SDCT- VAD outprformd th G79B VAD ad th mthod i []. 4.. Tstig th CA-SDCT Figur 7. P 's of th proposd RSDCA-VAD i various viromtal oditios. To furthr validat th fftivss of th proposd SDCT-VAD, w ompard its probabilitis of orrt sph ativity dttio with thos of othr approahs. Tabl 3 shows a ompariso btw th SDCT-VAD ad two diffrt VAD approahs: th G.79 i [] ad th proposd mthod i []. Th la sph sigal that has lgth of 5 s, 6.5% sph ad 39.95% sil, was usd to valuat As statd i Stio 3, to dtt shifts from abs to prs of ybr xploits ad vi vrsa usig th CA-SDCT algorithm, two algorithmi disio thrsholds ar dd: A thrshold δ usd by th algorithm i (8); for th dttio of hag from Cybr xploits abst to Cybr xploits prst, ad a thrshold δ usd by th algorithm i (9); for th dttio of hag from Cybr xploits prst to Cybr xploits abst. It is assumd that th ybr attak is rprstd by AWGN. W tstd th origial sigal ad its oisy vrsios, as thos xhibitd i Figur 8. Usig th powr ad fals alarm urvs, as with th SDCT-VAD algorithm, w sltd th prtit thrsholds. I partiular, w sltd th ( δ, δ, α, ) dsig valus (.7,.,.98,.773), whil w tstd th valus (.798,.849,.34), to valuat th robustss of th rsultig CA-SDCT algorithm. Tabl 3. P 's of th proposd RSDCT-VAD, ad diffrt VAD approahs for various viromtal oditios. Eviromt G.79 VAD [,] Proposd Mthod i [] Proposd RSDCA-VAD Nois SNR P (%) P (%) P (%) Whit Vhil Babbl Copyright SiRs.

12 96 E. ETELLISI ET AL. (a) (b) () Figur 8. (a) Origial sigal; (b) Noisy sigal with SNR = 5 db; () Noisy sigal with SNR = db; (d) Noisy sigal with SNR = 5 db. (d) (a) (b) () Figur 9. Cybr dttio durig sph ativity dttd priods usig th CA-SDCT. (a) Squtial tst: SNR = 5; (b) Squtial tst: SNR = ; () Squtial tst: SNR = 5. Copyright SiRs.

13 E. ETELLISI ET AL. 97 (a) (b) () Figur. Cybr dttio durig sph ativity dttd priods usig RSDA-CA. (a) Alarms SNR = 5; (b) Alarms SNR = ; () Alarms SNR = 5. From Figur 9, parts (a), (b) ad (), w may obsrv th volutio of th dployd CA-SDCT algorithm for diffrt SNR valus, whr th lattr valus rflt th umulativ fft of ormal hal ois ad ybr ois. Eah tim th thrshold is rossd, a alarm is ativatd. Figur shows alarm ativatio sarios rgardig ybr attaks, whr i (a) o alarm is ativatd, whr i (b) o alarm is ativatd ad whr i () svral alarms ar ativatd. 5. Colusios A ovl voi ativity dttio (VAD) approah was prstd. Th approah uss th Squtial Dttio of Chag Algorithm (SDCT-VAD), dsigd at th Laplaia-Gaussia distributios additiv mixtur. W aalysd ad valuatd th robust squtial algorithm i th prs of Additiv Whit Gaussia Nois. Svral diffrt sph mssags wr hos for th fftivss valuatio of th SDCT-VAD, rgardig its aurat dttio of hags from voi ativity to sil ad vi vrsa. Th xprimtal rsults hav show that th algorithm is fftiv i various oisy viromts ad outprforms othr xistig voi ativity dttio mthods. A ovl ybr attak-squtial dttio of hag algorithm (CA-SDCA) was also prstd, dployd to dtt ybr attaks durig sph ativity priods. Th proposd algorithm is prdd by th Voi Ativity Dttio algorithm Squtial Dttio of Chag Tst (SDCT-VAD). W osidrd th as whr voi mssags ar trasmittd through th ommuiatios systm, whil a ybr attak may our at ay poit i tim. Th proposd algorithm was aalyzd ad valuatd. Th lattr algorithm dtts ybr attaks fftivly; durig sph ativity priods dttd-by th SDCT-VAD algorithm. W modld th ybr attaks by Copyright SiRs.

14 98 E. ETELLISI ET AL. Additiv Whit Gaussia Nois. Th xprimtal rsults hav show how th algorithm a b implmtd with fftiv dttio rsults, i a varity of diffrt viromts. 6. Rfrs [] J.-W. Shi, H.-J. Kwo, S.-H. Ji ad N. S. Kim, Voi Ativity Dttio Basd o Coditioal MAP Critrio, IEEE Sigal Prossig Lttrs, Vol. 5, 8, pp [] J. Soh, N.-S. Kim ad W.-Y. Sug, A Statistial Modl-Basd Voi Ativity Dttio, IEEE Sigal Prossig Lttrs, Vol. 6, No., 999, pp. -3. [3] J.-W. Shi, J.-H. Chag, H.-S. Yu ad N.-S. Kim, Voi Ativity Dttio Basd o Gralizd Gamm Distributio, Vol., 5, pp [4] S. Gazor ad W. Zhag, Sph Probability Distributio, IEEE Sigal Prossig, Vol., No. 7, 3, pp doi:.9/lsp [5] R. K. Basal ad P. Papatoi-Kazakos, A Algorithm for Dttig a Chag i a Stohasti Pross, IEEE Trasatio o Iformatio Thory, Vol. IT-3, No., 986, pp [6] A. T. Burrll ad P. Papatoi-Kazakos, Extdd Squtial Algorithms for Dttig Chags i Atig Stohasti Prosss, IEEE Trasatio o Systms, Ma, ad Cybrtis, Vol. 8, No. 5, 998, pp doi:.9/ [7] A. T. Burrll ad P. Papatoi-Kazakos, Dttig Softwar Faults i Distributd Systms, IEEE 9 World Cogrss o Computr Si ad Iformatio Egirig, Vol. 7, 9, pp [8] P. Papatoi-Kazakos, Algorithms for-moitorig Chags i Quality of Commuiatio Liks, IEEE Trasatio o Commuiatio, Vol. COM-7, 979, pp [9] D. Kazakos ad P. Papatoi-Kazakos, Dttio ad Estimatio, Computr Si Prss, Nw York, 99. [] P. Papatoi-Kazakos, Algorithms for Moitorig Chags i Quality of Commuiatio Liks, IEEE Trasatios o Commuiatio, Vol. COM-7, 979, pp [] A. Byassi, E. Shlomot, H.-Y. Su, D. Massaloux, C. Lambli ad J.-P. Ptit, ITU-T Rommdatio G.79 Ax B: A Sil Comprssio Shm for Us with G.79 Optimizd for V.7 Digital Simultaous Voi ad Data Appliatios, Commuiatios Magazi, IEEE, Vol. 35, No. 9, 996, pp Appdix From xprssio (8), i Stio.3, w hav: g l lhh I Figur A blow, w plot g() as a futio of. Lt g y ξ ma that is suh that, g ξ y. Th, Figur A. Evaluat th whol updatig stp algorithm gξ. F y P g y F y P g y S S S F y P g y g y F y F g y F g y S ( ) ( ) i i fs y F y F g y F g y y y y Fig ( y) Fig ( y) g g y y whr S i ( ) i ( ) h g y h g y g g y g y h g y h g y h g y xp xp g y Φ( g y ) i fs,i y fi g y f g y g y h g y h g y h g y h g y Copyright SiRs.

15 E. ETELLISI ET AL. 99 From Figur A, it a b oludd that, β π β ξ l lh ξ h ξ ad th, β π g y yl β i,, i x ( ) f f x f x f x i,,i i i x x/ ( ) ( ) ( ) ( ) h x h x ( x) dx h x h x Th followig rursiv xprssios ar usd for th omputatio of th powr urvs: fi x fi x xh xhxh xhx f f x h x hx dx xp.dx f, f, x h x hx dx xh xhxh xhx x Th followig xprssios ar usd for th omputatio of th fals alarm urvs: f( x) fx f, f, x h x hx dx x/ xh xhx[ h xh x] f, ( ) h x hx xh xhx h xhx f, x x x ξ. dx x/ [ ] whr f x xp h xhx x f x x xp x x xp h h x x x Th, β ad α a b xprssd as follows: δσ δσ f d ; α f,ξ β ξ ξ, dξ Copyright SiRs.