CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY

Transcription

1 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY Wag Shuwag, Hu Guobig Shool of Eletroi Iformatio Egieerig Najig College of Iformatio Tehology, Najig, Jiagsu 223, Chia s: Submitted: Marh 4, 26 Aepted: Ot.6, 26 Published: De., 26 Abstrat- A redibility test method based o the features of frequey domai etropy of a phase is proposed to evaluate the blid proessig results of a BPSK sigal. Iitially, a referee sigal was ostruted depedig o the ertai idetified modulatio results. By aalyzig the differees of the phase of the orrelatio series betwee the observed sigal ad the referee sigal, a reliability test problem for the BPSK sigal is performed by alulatig the phase spetrum etropy ad omparig it with a ertai threshold. Simulatio results show that the proposed method a be used to verify the reliability of the blid proessig results of a BPSK sigal at a low sigal-to-oise ratio ad without a priori kowledge of the sigal parameters. Idex terms: blid sigal proessig; redibility test; phase spetrum etropy. 9

2 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY I. INTRODUCTION Sigal detetio, modulatio reogitio, ad parameter estimatio are the importat operatios of sigal proessig i eletroi surveillae ad ogitive radio uder the oditio of lakig a priori iformatio ad low sigal-to-oise ratio (SNR). These three operatios diretly affet the results of suessive sigal proessig parts. I eletroi surveillae, the results of froted sigal proessig will affet the suessive sigal sortig, loatig, trakig, iterferee, ad emitter reogitio. I ogitive radio (CR), the reliable results of frot-ed spetrum sesig ad aalysis are the premise ad foudatio of operatios suh as spetrum sesig ad maagemet. Geerally, modulatio reogitio, parameter estimatio, ad other sigal proessig results are oly blid treatmets beause of a lak of a priori iformatio i the sigal proessig domai of eletroi surveillae ad CR. Judgig the auray of the proessig result has beome a ew issue i CR ad eletroi surveillae. The IEEE P99.6 stadard (about CR) [], reports that a redibility evaluatio for modulatio reogitio of part of a ivilia wireless sigal sesig devie has bee osidered as a output parameter. Referee [2] shows that the redibility evaluatio has bee regarded as a idepedet ew operatio of modulatio reogitio i military sigal proessig systems uder oditios of oooperatio that a be used to judge a ukow sigal. Reetly, some researhers aalyzed the redibility of sigal detetio (or spetrum sesig) or modulatio reogitio, but oly a few of them disussed the redibility test about sigal blid proessig results. Referees [3 6] aalyzed the redibility of the sesig results for eah sigle ode to judge whether there are maliious users i ooperatio spetrum sesig. This proedure will improve the reliability of the sesig system. However, the researhers aalyzed oly the biary detetio redibility of the primary user sigal, ad did ot aalyze the estimatio redibility of sigal modulatio iformatio ad subtle parameters. Referee [7] disussed the redibility of a modulatio reogitio lassifier i CR. Half of the differee betwee the maximum ad the seodary output value of a MLP eural etwork lassifier was used to measure the ofidee of the lassifier. This method requires may traiig samples, ad is diffiult to ahieve this uder o-ooperatio oditios. Referee [8] proposed a redibility aalysis method based o etropy whe BPSK, QPSK, 8PSK, ad QAM modulated sigals i SISO ad MIMO systems were reogized. This method used the differees betwee likelihood 9

3 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 ratios uder differet hypotheses to measure the redibility. However, it is also diffiult to alulate the likelihood futios without a priori iformatio. Referee [9] proposed a redibility assessmet method of sigal blid proessig based o a lak-of-fit test of liear regressio for a BPSK sigal. However, the lak-of-fit test for the regressio depeded o lusterig to ahieve dupliate samples. Thus, the luster method ad the umber of lusters will affet the performae of this method. This paper first ostruted a referee sigal, ad subsequetly alulated the orrelatios betwee the referee sigal ad the observatio sigal. The, the phases of spetrums of the orrelatios were alulated. The redibility assessmet of the BPSK sigal blid proessig results a be obtaied by testig the etropy of the phase spetrum. The simulatio showed that this method a test the redibility of BPSK sigal blid proessig at a low sigal-to-oise ratio ad without a priori kowledge for the sigal parameters, ad that the algorithm is simple. II. SIGNAL MODEL The omplex BPSK sigal model i a limited observatio time a be desribed as N j (2 π ft ( ) + θ ) π j k T ( ), k = s t = Ae e Π t kt t < T () where A is the amplitude, f is the arrier, q is the iitial phase, N is the umber of symbols,t is the observatio period, T is the duratio of the symbol, k is the biary k-th symbol, ad P is the gate futio defied as, b< a P a ( b ) = (2), others The disrete sample sequees of the BPSK sigal added oise a be desribed as N π + θ π j(2 fdt ) j k k = x ( ) = s ( ) + w ( ) = Ae e P ( Dt kt) + w ( ), < N (3) where Dt is the samplig iterval, ad w ( ) is the omplex zero-mea bad-limited white Gaussia oise with a variae 2 σ 2 of whih the real part ad the imagiary part are idepedet. N is the umber of samples, ad the sigal-to-oise ratio a be defied as SNR = A 2 /2σ 2. T 92

4 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY III. ALGORITHM DESCRIPTION The blid proessig of the BPSK sigal osists of modulatio reogitio, arrier estimatio, ode-width estimatio, deodig. The premise of deodig orretly lies i orretly reogizig the modulatio mode ad orretly estimatig the other sigal parameters (suh as arrier frequey ad ode width). Therefore, the redibility evaluatio for blid proessig results of the BPSK sigal a be desribed as the followig hypothesis test: H : Both the modulatio reogitio ad the deodig results are orret; H : The modulatio reogitio result is iorret or the deodig result otais at least a sigle bit error. (4) A. Feature Aalysis Assumig H, the idetifiatio result of the BPSK modulatio mode is orret, ad there are o deodig errors. The estimatios of the arrier, the legth of ode, ode width, ad iitial phase are, respetively, f ˆ, ˆ, N, Tˆ ˆ, θ the referee sigal a be strutured as k Nˆ j( 2π ˆfD t+ θ) jπˆ k y ( ) = e e P ( Dt ktˆ ), N (5) k = The orrelatios betwee the observed sigal x ( ) ad referee sigal y ( ) a be give as Tˆ where z ( ) = xy ( ) ( ) = s( ) + w( ), N (6) Nˆ N j(2 πdfdt + Dθ) jπˆ π P ˆ j k k ˆ D P D T T k= k= s ( ) = Ae e [ t ( k ) T ] e [ t ( k ) T ] (7) where Df = f ˆf is the frequey estimatio error, ad w( ) = wy ( ) ( ) is the oise part of equatio (6). Uder hypothesis H, if are moderate, we a obtai N = N ˆ, T = T T ˆ, Df = f ˆf, ad the SNRs D z ( ) = s ( ) + w ( ) π + + θ where ( ) j[2 DfDt Dd( t) ] s = Ae. Geerally, D dt () is the equivalet error owig to estimatio errors of other parameters suh as the ode width ad iitial phase. It a be igored. Rewrite w ( ) as ( ) j b w = be ϕ, where b ad ϕ b are the modulus ad agle of w ( ), respetively. Beause the real part ad the imagiary part follow a Gauss distributio, the b follows a 93

5 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 Rayleigh distributio, ad ϕ b is a radom phase i the rage of [ ππ, ). Let a = A ad ϕa 2 π f t d() t θ = + +. It follows that This a be further derived as jϕ ( ) ( ) ( ) e a jϕ b z = s + w = a + be (8) jϕ a z ( ) = a e + be jϕb 2 2 jϕ b a ( ) e jφ a a e jϕ b e b j ϕ os si e + β b b φ φ osφ siφ a a a a a = a + = a + + j = a + + (9) b / asiφ where φ = ϕb ϕ, arta a β = ( + b / a os φ ). The phase of z ( ) a be obtaied by ρ = ϕ + β = 2 π f t + d( ) + θ + β () a Cosiderig the assumptio of H, f, d ( ),so ρ θ + β. This a be regarded as the determiisti iitial phase perturbed by a radom ompoet. Figure (a) shows the istataeous phase urve of orrelatio series z ( ) whe H is assumed. Its probability desity a be writte as γ e γ 2 γ si ( ρ θ) p( ρ θ, H) = + os( ρ θ) e Q [ 2γ os( ρ θ)] () 2π π 2 2 y where ρ θ < π, γ = 2,ad 2 Q( x) = e dy. Figure 2(a) shows a statistial histogram x 2A σ 2π of the istataeous phase sequee after removig the diret urret part uder H assumptio. There are probably two ases whe H is assumed: () H A : Modulatio reogitio is orret, but there exists iorretly deodig beause of the large estimatio error of the parameters. Figure (b) shows the istataeous phase urve of orrelatio series z ( ) whe the BPSK is orretly idetified while there is bit error deodig. From the figure, we a fid that the phase of orrelatio series z ( ) will jump i the error deodig iterval beause of the error aumulatio i parameter estimatio, while the phase sequees show radom haraters i orretly deoded itervals. So the etire phase sequees r do ot satisfy the probability distributio of formula (9). Figure 2(b) shows the statisti histogram of phase sequees r i this ase. The figure shows that the statisti histogram uder H is sigifiatly differet from 94

6 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY that uder H. Whe H A is assumed, the statisti histogram is heavier i the left tail. If the umber of deodig errors ireases, the phase jump will irease, ad the phase probability distributio urve will show a greater differee from that uder the hypothesis H. (2) H B :Modulatio reogitio is iorret If the badwidth of the BPSK sigal is small, or the sigal is distorted beause of iterferee, the sigal may be regarded as a ormal sigal (NS) or other modulatio sigal o the reeiver side. Assumig the sigal is reogized as a NS, the referee sigal is strutured as a siusoid j(2 π ˆfD t) y = e N. The the orrelatios betwee the referee sigal ad the observed ( ), sigal a be obtaied: z( ) = xy ( ) ( ) = s( ) + w( ), N (2) where j[2 π f t + ϕ( ) + θ] s = Ae is the sigal part, ad ( ) ( ) D D D w is the equivalet omplex zero-mea 2 bad-limited white Gaussia oise with a variae of 2s. The phase of z ( ) a be alulated as ρ = 2 πdfdt + Dϕ( ) + θ + β (3) From formula (3), we fid that the phase-error futio N π = j k e t kt leads to a T k = Dϕ( ) P ( D ) obvious phase offset ad jump i the urve of the orrelatio betwee the referee sigal ad the origial sigal beause of sigal model mismathig. O the other had, sigal model mismathig may lead to errors of arrier frequey estimatio ireasig, ad 2pDfD t will beome larger ad show slope harateristis. Figure () shows the istataeous phase urve of orrelatios z ( ) whe the BPSK is iorretly idetified as a NS sigal. From the figure, we fid that i this ase the ode sequee is equivalet to a all- sequee. The simulated sequee is a 3-bit Barker ode, ad the first five sequees are all, therefore the error maily arises from arrier estimatio. I this ase, the phase-error futio is i this iterval, so the phase sequee is maily determied by 2pDf D t ad appears as a straight lie with a slope of 2pDfD. t The suessive 7 bits are all deoded to. If the origial ode is ot, a error is produed ad the jump of phase will our. Figure 2() shows a statisti histogram of the phase sequees i this ase. The figure shows that the phase distributio is flat ad there are greater differees betwee the phase probability distributios ompared with those uder hypothesis H. 95

7 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 I olusio, uder the hypotheses H ad H, the istataeous phase urves of orrelatio betwee the referee sigal ad the origial sigal are obviously differet. Uder hypothesis H, the phase of z ( ) a be regarded as a approximate radom series aroud the iitial phase of the observed sigal, ad whose probability distributio a be desribed by formula (). Uder hypothesis H, the phase sequee is ombied with a radom phase ompoet ad determied phase ompoet, ad the probability distributio aot be desribed by formula (). 2 phase phase (a) phase (b) () Figure. Istataeous phase urve of orrelatio series uder differet hypotheses (3-bit Barker ode, SNR is 3 db) (a)bpsk is orretly idetified, ad there is o deodig error (b) BPSK is orretly idetified, but there is oe deodig error () BPSK is iorretly idetified as NS 96

8 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY 25 2 frequey frequey (a) frequey phase Figure 2. Statisti histogram of orrelatios phase uder differet hypotheses (3-bit Barker ode, SNR is 3 db) (a) BPSK is orretly idetified, ad there is o deodig error (b) BPSK is orretly idetified, but there is oe deodig error () BPSK is iorretly idetified as NS B. Properties of Phase Spetrum Etropy From the above aalysis, we fid that the istataeous phase urves of the orrelatio series are differet uder differet hypotheses. The differee maily demostrates the radomess of the (b) () 97

9 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 phase sequee. Therefore the problem is how to judge whether the phase sequee is radom. The phase spetrum etropy a be used as the riterio. Cosiderig the orrelatio series z, ( ) the phase spetrum a be ahieved by DFT: N k Z( k) = z( W ) N, k=,,..., N (4) = Figure 3 shows the smoothig filtered phase spetrum of orrelatio series uder differet hypotheses. From the figure, we a see that the phase spetrum is a radom series uder hypothesis H. There are obvious peaks i the phase spetrum, whih has a ertai badwidth uder hypothesis H beause there are aperiodi retagular-futio or ramp-futio ompoets i the orrelatio istataeous phase sequee. Aordig to referee [-], the module of the phase spetrum Zk ( ) a be divided i to L segmets. The width of eah segmet is defied as W = Zm / L, where Z m idiates the maximum of Zk ( ). k i is the umber of the samples of Zk ( ) setio, ad L i= k i = N. The probability p i is defied as pi = ki / N ad phase spetrum etropy a be alulated by the suessive formula: i= whih are loated i the i th L i= p =. Thus the L ki ki T( Z) = log (5) N N Figure 4 shows a statisti histogram of the orrelatio series phase spetrum etropy uder differet hypotheses. From the figure, we fid a obvious differee i the respetive statisti histograms uder differet hypotheses. Uder hypothesis H, the phase spetrum etropy is greater tha.8 ad is maily loated aroud with a smaller variae. Uder hypothesis H, if the modulatio mode is orretly reogized but there is oe bit error, oly a few phase spetrum etropy values distribute i the iterval [.6,.2]. If the modulatio mode is iorretly reogized, most of the phase spetrum etropy values distribute i the iterval [.,.5]. Thus the phase spetrum etropy a be used to distiguish two differet hypotheses. I additio, the mea value of the radom oise phase spetrum etropy is rarely affeted by oise variae. Figure 5 shows the mea values of the orrelatio series phase spetrum etropy uder differet hypotheses with a SNR i the rage [-8 db, db]. The umber of simulatios is i eah ase. From the figure, we fid that the phase spetrum of the orrelatio series is i 98

10 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY radom uder hypothesis H, ad its etropy almost does ot hage whe the SNR hages. By otrast, uder hypothesis H, the phase spetrum otais ertai varyig otets i the two ases, ad its etropy dereases whe the SNR ireases. Whe the SNR higher tha -8 db, the appearae is obviously differet from that for hypothesis H. spetrum of the phase spetrum of the phase spetrum of the phase k (a) k (b) k () Figure 3. Phase spetrum of orrelatios uder differet hypotheses (3-bit Barker ode, SNR is 3 db) (a) BPSK is orretly idetified, ad there is o deodig error (b) BPSK is orretly idetified, but there is oe deodig error () BPSK is iorretly idetified as NS 99

11 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 2 frequey (a) 2 frequey (b) 2 frequey () Etropy of the phase spetrum Figure 4. Statisti histograms of the phase spetrum etropy of orrelatios uder differet hypotheses (3-bit Barker ode, SNR is 3 db) (a) BPSK is orretly idetified, ad there is o deodig error (b) BPSK is orretly idetified, but there is oe deodig error () BPSK is iorretly idetified as NS 9

12 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY spetrum of phase HA.35 HB.3 H SNR(dB) Figure 5. Mea values of phase spetrum etropy of orrelatios uder differet hypotheses C. Algorithm Desriptio Observed sigal Modulatio reogitio Parameter estimatio Referee sigal ostrutio Correlatio ad phase extratio Phase spetrum etropy alulatio T( Z) Y N H H Figure 6. Algorithm proedure 9

13 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 The algorithm flow proposed by this paper is show i Figure 6. The key steps are desribed as follows: () Parameter estimatio ad referee sigal ostrutio: Reogize the modulatio type, the estimate the orrespodig parameters ad ostrut the referee sigal. (2) Feature extratio: Extrat the phase of the orrelatio series betwee the referee sigal ad the reeived sigal, ad the alulate the phase spetrum etropy after removig the mea. (3) Judgmet: If T( Z) ³ l, H is hose; otherwise H is hose. l is a threshold. IV. PERFORMANCE SIMULATION AND ANALYSIS Assume the reeived sigal x ( ) is the BPSK sigal polluted by additive white Gaussia oise, the arrier is 29.8 MHz, the symbol width is m s, the ode series is [,,,] (whih is a 3-bit Barker ode), the samplig frequey f = MHz, ad the sample legth is 3. Experimet : Suppose 3 proessig results satisfy the H hypothesis (the modulatio reogitio is orret ad there are o deodig errors), 2 proessig results satisfy hypothesis H (the umbers of H A ad H B are respetively).the the redibility of 5 proessig results is deteted by this method. Experimet 2: Co-Simulatio. The itrapulse modulatio reogitio algorithm used the method i referees [2,3], ad the parameter estimatio algorithm used the method i referee [4]. A total of 5 simulatios were exeuted. Table ad Table 2 list the performae statistis of the reliability test for the BPSK sigal blid proessig result uder the oditios of experimet ad experimet 2, respetively. I the tables, idiates the umber of times that H is orretly reogized as H, idiates the umber of times that H is orretly reogized as H, idiates the umber of times that H is iorretly reogized as H, ad idiates the umber of times whe H is orretly reogized as H. P = ( + ) / 5 is osidered to be the estimated probabilities of the two e errors. Here the first error meas that H is iorretly reogized as H, ad the seod error s 92

14 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY meas that H is iorretly reogized as H. P = /( + ) is used to measure the d algorithm disrimiatio ability. Table. Statistial performae for experimet SNR( db ) λ P e P d

15 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 Uder the oditios of experimet, ay modulatio reogitio methods a be used. From Table, we fid that the statistial performae of the ispetio method based o phase spetrum etropy proposed by this paper depeds o the SNR ad the threshold value. Whe the threshold is determied, two type error probabilities derease ad false detetio probability ireases with the asets of SNR. Whe the threshold is ertai, two type error probabilities derease, the ratio of error detetio ireases as the SNR ireases. Whe the threshold is.9 ad the SNR is greater tha -5 db, two type error probabilities are less tha 9%, ad the ratio of error detetio is higher tha 88%. The performae of the redibility evaluatio will worse whe the SNR is less tha -5 db. The threshold will affet the detetio performae whe the SNR is ertai. Whe the threshold is higher, two type error probabilities are lower ad the detetio probability is higher. However, two type error probabilities will ot beome lower at the same time. I pratie, the threshold is usually approximately.9. Table 2. Statistial performae for experimet 2 SNR( db ) λ P e P d /.85 5 / /.8 5 /.85 5 / /

16 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY From Table 2, uder experimet 2, the algorithm proposed by this artile a effetively odut a reliability test of BPSK blid sigal proessig whe the SNR ad the threshold are moderate. If the SNR is ot less tha db, the algorithm a detet more tha 4983 ases from 5 simulatios where the modulatio mode a be orretly reogized ad there is o deode error, ad two type error probabilities are very small. Whe the SNR is i the rage of [-3 db,-4 db], the errors of modulatio reogitio ad deodig will irease as the SNR dereases. Whe the SNR is i the rage of [-5 db,-6 db], the errors of modulatio reogitio ad deodig will further irease as the SNR dereases, while most of them a be idetified by the algorithm proposed i this artile. For example, suppose the SNR is -5 db ad the threshold λ is.85. There are 85 errors of modulatio reogitio ad deodig. Whe 7 errors a be idetified, the ratio of error detetio is higher tha 84.3%. However, two type error probabilities will irease as the SNR dereases. Whe the SNR is less tha -7 db, the performae of the BPSK blid sigal proessig method will dramatially worse. Thus the errors of modulatio reogitio ad deodig will further irease. Eve i this ase, if the threshold λ is.9, the ratio of error detetio is higher tha 83.8%. From the simulatio results, we fid that the redibility test method for blid proessig results of a BPSK sigal has a preferable apaity for error detetio uder oditios with a small SNR. This method eeds o a priori iformatio of the sigal ad has low probabilities of two type errors. 95

17 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL.9, NO.4, DECEMBER 26 V. CONCLUSION By ivestigatig the redibility of blid proessig results for a BPSK sigal, the phase of orrelatios betwee the referee sigal ad observed sigal was obtaied. The harateristis of phase spetrum etropy are used to assess the redibility of blid sigal proessig results. The simulatio shows that the method a effetively assess the redibility of blid proessig results for a BPSK sigal. This method eeds o a priori iformatio ad is simple ad effetive. The method a improve the reliability ad the validity of blid proessig results for radar ad ogitive radio sigals, whih are valuable i the theoretial ad pratial domais. AKNOWLEDGEMENT Top-oth Aademi Programs Projet of Jiagsu Higher Eduatio Istitutios (PPZY25C 242). REFERENCES [] Puker L. Review of Cotemporary Spetrum Sesig Tehologies (for IEEE-SA P9.6 Stadards Group). Sesor_Survey.pdf. 29. [2] W. Su J. A. K., Y. Mig, "Dual-use of modulatio reogitio tehiques for digital ommuiatio sigal", Systems, Appliatios ad Tehology Coferee, 26, pp [3] Hiep V.-V., Isoo K., "Cooperative spetrum sesig with ollaborative users usig idividual sesig redibility for ogitive radio etwork", Cosumer Eletrois, IEEE Trasatios o, Vol.57, No.2, 2, pp [4] Chi-Liag W., Ha-Wei C., Yu-Re C., "A redibility-based ooperative spetrum sesig tehique for ogitive radio systems", Vehiular Tehology Coferee (VTC Sprig), 2 IEEE 73rd, 2, pp. -5. [5] Nam Tua Nguye R. Z., ZhuHa, "O idetifyig primary user emulatio attaks i ogitive radio systems usig oparametri bayesia lassifiatio", IEEE Trasatios o Sigal Proessig, Vol.6, No.3, 22, pp

18 Wag Shuwag, Hu Guobi, CREDIBILITY EVALUATION FOR BLIND PROCESSING RESULTS OF BPSK SIGNALS BY USING PHASE SPECTRAL ENTROPY [6] Cheg Zegpig, "TARGET RECOGNITION BASED ON ROUGH SET WITH MULTI- SOURCE INFORMATION", INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 8, NO. 2, 25, pp [7] Fehske A., Gaeddert J., Reed J. H., "A ew approah to sigal lassifiatio usig spetral orrelatio ad eural etworks", 25 First IEEE Iteratioal Symposium o New Frotiers i Dyami Spetrum Aess Networks, 25. DySPAN 25, 25, pp [8] Li W. S., Liu K. J. R., "Modulatio foresis for wireless digital ommuiatios", IEEE Iteratioal Coferee o Aoustis, Speeh ad Sigal Proessig, 28. ICASSP 28., 28, [9] Hu Guobig, Liu Yu, "Reliability test for blid proessig results of BPSK sigal, " Joural of Data Aquisitio & Proessig, Vol.26, No.6, 2, pp [] Zhag Y., Zhag Q. ad Wu S., Etropy-based robust spetrum sesig i ogitive radio", IET Commuiatios, Vol.4, No.4, 2, pp [] Migxi Yag, "OPTIMAL CLUSTER HEAD NUMBER BASED ON ENTROPY FOR DATA AGGREGATION IN WIRELESS SENSOR NETWORKS," INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL. 8, NO. 4, DECEMBER 25, pp [2] Hu Guobig ad Liu Yu, "Sigal itrapulse modulatio reogitio algorithm based o sie wave extratio", Computer Egieerig, Vol.36, No.3, 2, pp [3] Che Yitao, "Study o ofidee of radar sigal modulatio type idetifyig", Najig: Master dissertatio of Najig Uiversity of Aeroautis ad Astroautis, 28, pp [4] Xu Jiajia, "Study o key algorithms of sigal proessig i eletroi reoaissae ad subsamplig widebad digital reeiver", Najig: Dotoral dissertatio of Najig Uiversity of Aeroautis ad Astroautis, 2, pp