Theoretical Modeling and Simulation of a Chaos-Based Physical Layer for WSNs

Transcription

1 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 Theoretal Modelng and Smulaton of a Chaos-Based Physal Layer for WSs Stevan Berer, Shu Feng Astrat In ths paper the theoretal model and smulaton of the physal layer for wreless sensor networks (WSs) applaton s presented. The spreadng sequenes used are generated from the haot generators desgn usng Cheyshev maps that nreases the seurty n sgnal transmsson. Sgnal propagaton n WSs assumes heavy nfluene of fadng and nter-symol nterferene. To mtgate ths fadng nfluene the applaton of hp nterleavng tehnque s appled. For the ase of fadng presene n the hannel and the ase of nterleaver applaton, the theoretal expressons for the t error rate (BER) n losed form are derved. The system smulators are developed that onfrmed theoretal fndngs. The sgnal proessng proedures n the transmtter and reever loks are presented n dsrete tme doman that makes the desgn of deves dretly mplementale n DSP tehnology, whh was one of the ams of ths researh. Keywords Chaos ased systems, fadng hannel, proalty of error, wreless sensor networks, nterleavers. T I. ITRODUCTIO HIS paper presents the ssues n physal layer desgn for applaton n wreless sensor networks (WSs). One of the as requrements n these networks s to desgn network nodes wth mnmum power onsumpton. The man ause for nreased power onsumpton n sgnal transmsson s related to the exstene of fadng n ommunaton hannel. Ths nrease for transmsson power an e tens of deels. It was proved that the fadng an e quantfed through the nrease of BER n the physal layer n respet to the ase when only addtve Gaussan nose (AWG) s present n the hannel. For the desred BER n the wreless networks, the power of nodes needs to nrease n the presene of fadng n order to ommunate at the same dstane []. The am of the network desgner s to redue ths nrease n requred power. Varous tehnques of fadng mtgaton are used to aheve ths am. It was shown that the fadng nfluene n dret sequene spread spetrum and CDMA systems an e redued y usng nterleavng tehnques [, 3, 4, 5, 6]. A wreless sensor network defned n the Standard IEE [7] uses a modfed spread spetrum tehnque. For that reason an analyss of mplementng haot sequenes generated usng Stevan Berer s wth the Department of Eletral and Computer Engneerng, The Unversty of Aukland, Aukland, ew Zealand, (orrespondng author, phone: ; fax: ; e-mal: s.erer@aukland.a.nz). Shu Feng s wth the Department of Communaton Engneerng, EEOT, anjng Unversty of SCI and TECH, anjng, Chna (e-mal: shufeng@mal.njust.edu.n). logst and u maps s presented. To mtgate fadng n the ommunaton hannel a hp nterleavng tehnque s nvestgated. One soluton for the desgn of modulator and demodulator loks for wreless sensor networks applaton s presented n [8]. The paper presented theoretal modelng, smulaton and desgn of the loks n FPGA tehnology and mplementaton n CMOS tehnology. The transever desgn for WSs applatons s presented n [9]. In ontrast to these desgns, ths paper s unque n presentng the theoretal analyss and smulaton of the physal layer of WSs n dsrete tme doman, whh s the frst ontruton of ths paper. Ths presentaton s sutale for use n dret mplementaton of the systems loks n DSP or FPGA tehnology. In the exstng theory these sgnals and ther proessng are represented n ontnuous tme form. The seond ontruton of ths paper s n theoretal analyss of the whole system and dervatons of BER expressons for haot spreadng sequene for oth AWG nose and fadng hannels. The thrd ontruton s n the development of the system s smulator whh onfrmed theoretally expeted sgnal waveforms and BER expressons. The theoretal model of the haos-ased system n presene of nose and fadng s presented n Seton. In partular the as haot maps are explaned and the as propertes of the haot sequenes are presented. Seton 3 presents the as struture of the system and ts mathematal model n the ase when nose and fadng are present n the hannel. The theoretal BER urves are onfrmed y smulaton. In Seton 4 the nterleaver and denterleaver loks are nluded nto the transmtter and reever strutures respetvely. For ths ase the expressons for the BER are derved n losed forms Also, the results of BER smulaton are presented, whh onfrmed the theoretal fndngs. Conlusons are presented n Seton 5. II. THEORETICAL MODEL OF CHAOS-BASED PHYSICAL LAYER A. Defnton of Chaot Sequenes Chaot sequenes are non-nary sequenes. The statstal struture of these sequenes depends on the defned ntal ondtons. These sequenes an e used as spreadng sequenes n dret sequenes spread-spreadng systems DSSS) and n ode-dvson multple aess systems (CDMA) [,, 4, 5]. Due to ther orrelaton propertes, these haot sequenes, generated usng haot maps, an e used n these systems to spread message ts, f the synhronzaton of the 7

2 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 sequenes s aheved [0, ]. The haot mappng alled Cheyshev Degree-L maps s defned y ths reursve equaton - k ( + ) = os[ Los k ( )]. () E{ } = d = 0 π and the average power s. (6) The dsrete random samples n the sequene (k) have the values etween - and +. For L = the logst map s otaned, and the samples for ths map are generated aordng to ths reursve expresson π E{ } = d =.5 (7) x = () + k xk For L = 3 the u map s defned. The samples for ths map are generated aordng to ths reursve expresson x = + x x (3) k 3 k( k).5 f ( ) 0.5 The densty funton for these maps s fc () = (4) Fg.. Densty funton of haot random varale The analytal results and smulatons, whh are presented n ths paper, are ased on the logst map. The dsrete random values n a haot sequene wll represent hps n the spreadng sequenes. The seres of hps an e treated as a dsrete tme stohast proess. The mean value of ths proess s zero and the mean square value, orrespondng to the power of the sequene, s 0.5. In order to ompare haot systems wth the lassal nary system the haot generator needs to produe the haot hps arryng the same average power as the power of the nary sequene. For that reason, n ths paper, the haot samples are generated wth the average power one. Thus the random varale, defnng the samples of the haot sequene, n ths paper denoted y, s defned as a lnear funton of,.e., () k = () k. Usng the fundamental theorem of proalty theory the densty funton of s derved as f C ( ) = π, for -, (5) whh s presented n Fg.. It s symmetr n respet to zero and an have the values etween plus mnus square root of two. The mean value of ths random varale s For the dervatves of BER expresson ths expetaton wll e used 4 4 π 3 E{ } = d =. (8) B. Blok-shemat of the ommunaton system The proposed modulaton shemes n wreless sensor networks are the nary and quadrature phase sht keyng (BPSK and QPSK). Fg. presents a smplfed lok shemat of a system that uses offset QPSK (OQPSK) modulaton and haot spreadng sequenes nstead of the standard nary sequenes proposed for wreless sensor networks [7]. The system wll e, frstly, analyzed for the ase when the Addtve Whte Gaussan ose (AWG) and fadng are present n the hannel. Seondly, the system wll e analyzed for the ase when nterleaver (IL) and denterleaver (DI) loks are norporated nto the lok shemat n Fg.. C. Transmtter operaton The transmtter operates n the followng way. The soure generates message ts j (k), whh are spread y the haot spreadng sequene n (k) and a hp sequene m(k) = j (k) (k) s otaned. A demultplexer lok (DMUX) s used to splt the hp sequene m(k) nto n-phase and 8

3 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 quadrature sequenes as spefed y the Standard for wreless sensor networks [7]. The even-ndexed hp sequene m I (k) modulates the n-phase arrer and odd-ndexed hp sequene m Q (k) modulates the quadrature arrer. The output of the modulator s the QPSK sgnal expressed as s( k) = m ( k) E / M os Ω k+ m ( k) E / M snω k (9) I Q where m I (k) and m Q (k) are n-phase and quadrature hp sequenes respetvely, and Ω s the normalzed frequeny of the arrer. The energy of a t s E = βe, where E s the energy per hp. The numer of nterpolated samples ontaned n one hp nterval s M. It s mportant to see that the system s analyzed for dsrete tme doman sgnal representaton,.e., eah hp and related nose sample are generated one for eah hp nterval and then repeated (nterpolated) M tmes n the hp nterval to allow the dsrete tme modulaton of the arrer. E / M osω k / M osω k j IL m(k) m I (k) DMUX s T (k) s R (k) y I M k= MUX z I z DI β w Deson Crut ' j m Q (k) T / L α E / M sn Ω k T / M k= y Q / M sn Ωk z Q n(k) Sequene Synhronzaton Blok Fg. Blok shemat of ommunaton system D. Channel haraterzaton A nose sample s generated n eah hp nterval and then s repeated M tmes and added to M dental haot samples representng a hp. For M repeated samples of nose n a hp nterval the average energy s E = Mσ, where the varane s σ =B 0 and the andwdth B=/T =/M. Thus, the energy of a nose n a hp nterval s alulated to e E = 0 /. The and-lmted pass-and nose samples are generated n dsrete tme doman aordng to ths expresson n( k) = n ( k) E / M os Ω k n ( k) E / M snω k, (0) I Q whh orresponds to the lok shemat presented n Fg. 3. n I (k) E E n Q (k) / M osω k / M sn Ω k n(k) Fg. 3 Pass-and nose generator The nose omponents n I (k) and n Q (k) are n-phase and quadrature nose samples of zero mean and unt varane. The energy of the nose samples nsde a hp nterval s E and M s the numer of nterpolated samples nsde the hp nterval. Thus, the output of the nose generator n Fg. 3 s the pasand nose wth the frequeny andwdth that orresponds to the andwdth of the generated sgnal. Also, n the system smulaton the power of the nose s ontolled y defnng the value of the nose energy E. If fadng s present n the hannel t s represented y a multpler n Fg.. The nomng transmtted sgnal s multples y a fadng oeffent α whh s a realzaton of a random varale that has Raylegh densty funton defned as f ( α) α α α / = e. () Defned y ths densty funton, the random varale α has the mean value α = (π/4) -/ and varane σ α = (4-π)/4. E. Correlator reever operaton If fadng s present n the hannel, the reeved sgnal s R (k) s [3] jϕ sr ( k) = α e s( k) + n ( k) () 9

4 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 where α s the fadng oeffent and φ s the phase shft. For a slow fadng t s assumed that the fadng oeffent s onstant n a t nterval, It s also assumed that the phase shft φ an e elmnated y the reever s phase loked loop. The reeved sgnal s R (k) an e oherently demodulated usng a orrelator reever whh onssts of a multpler and an adder. The sgnal at the output of the multpler n n-phase ranh s that the powers of all hps are equal, the mean value of W may e alulated as η β w Ew EE α E = { } = { } { } (6) and the varane of n general form as y ( k) = [ αs( k) + n( k)] E / M osω k I (3) σ = E{ w } η = E{( A+ B) } η. (7) w w w The M samples nsde a hp nterval of ths dsrete sgnal are added (orresponds to ntegraton n ontnuous tme systems) resultng n a random sample z n I ranh for even ndex values =, 4,, β. The smlar proessng s performed n the Q ranh for =, 3,,β-. The multplexer (MUX) omnes n-phase and quadrature sequenes ak nto a β-hp sequene of samples that s represented y ths realzaton of a dsrete tme stohast proess Z z α = E + E n (4) where =,, 3, 4,, β and n are samples of the n-phase and quadrature aseand nose. The frst term n ths sample represents the sgnal part and the seond one s the nose part. In order to detet the t values the nomng stream of hps, representng a t, needs to e orrelated wth the loally generated and synhronzed referene hp sequene. Therefore, the reeved stream of dsrete samples z s orrelated wth a loally generated referene hp sequenes (, =,, 3, 4,, β), otaned from the sequenes synhronzaton lok [0, ]. The orrelator onssts of a multpler and an adder. For the sake of smplty, t s assumed that the t sent was +. Then the output of adder wll e a random sample that represents a soft t reeved value and s expressed as β β β = = α + w z E E n = A+ B III. COMMUICATIO SYSTEMS WITH OISE AD FADIG A. Closed form BER dervaton for u map (5) It s assumed that the soure generates nary ts from the alphaet (+, -). The reeved soft t values wll e represented as a dsrete tme stohast proess wth the samples representng realzatons of a random varale W. The mean value of ths random varale s zero. Thus, the threshold value n the deson rut should e defned as z T = 0. Assumng that the t sent s +, the densty funton of random varale W, due to the entral lmt theorem (CLT), an e approxmated y Gaussan funton. Also, assumng It an e found and β E{ A } = α E = = βe{ α } E [ E{ E{ B 4 } + (β ) E{ β } = E E n = } E{ = βe j }] E{ The mean value squared an e expressed n ths form η = E{ w} = βee{ α} E{ } w + β β β EE α E E j + E ( ) { } { } { } { } } (8) (9) (0) The varane an e otaned from (7), (8), (9) and (0) n ths form σ = βe[ E{ α } E { } E{ α} E { }] 4 w β β α α j j= + + E[ E{ } E{ }] E { } E { } + β E E { } () Suppose that the u map s used. Insertng the values from expressons (7) and (8), and the values for the expetatons of the fadng oeffent α, the expresson for the varane an e smplfed as π σ = βe [ + β(4 π) + ]. () 0 w 4 E Havng the mean and varane avalale, the proalty t error an e expressed as / π 4(4 π) 4 E pe = erf + + (3) βπ π π 0 30

5 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 where the energy of a t s E = βe and energy of the nose s E = 0 /. B. System smulaton and omparson wth theory The smulators of the systems, nludng pulse shapng, are developed and smulatons were onduted for varous hannel ondtons. The system s smulated n MATLAB and the resultant BER urves are generated and plotted alongsde wth the theoretal urves. For the ase when anly WG s present n the hannel, the graphs, showng theoretal proalty of error and the smulated BER values, are presented n Fg. 4. The graph otaned y smulaton follows the shape of the graph for theoretal BPSK modulaton as expeted. amely, when fadng nfluene s elmnated, α =, and the nose only s present n the hannel, the theoretal expresson (5) eomes, To larfy ths fat, Fg. 5 presents four smulatons of the BER urves. Ovously they are lose to the theoretal urve, stll eng at dfferent poston n respet to that urve. BER z = E + E n (4) Beause the nfluene of fadng s elmnated, the output of adder, representng a soft t reeved value, an e expressed from (5) as β β β = = + (5) w z E E n = A+ B The densty funton of random varale W s Gaussan. If the powers of all hps are equal, the mean value of W may e alulated from (6) as η = Ew { } = βe { } E = β E. (6) w and the varane (7), for expeted values spefed n (6), an e alulated as 4 σw = βe[ E { } E { }] + βee { } = βe [3 / ] + βe = βe + βe (7) For the mean and varane alulated, the proalty t error an e expressed as p e E = erf + β 0 / (8) where the energy of a t s E = βe and energy of the nose s E = 0 /. The graphs n Fg. 4 and Fg. 5 are losely approxmate the theoretal BER urve. However ths approxmaton s dfferent for the two plots presented. The reason s n that, durng the smulaton, the ntal ondton for haot sequene generaton was dfferent, eause the smulator randomly generates ntal ondton SR Fg. 4 BER urves for the haot reever n presene of AWG: theoretal (lak) and smulaton (green). The theoretal BER (lue) n presene of fadng for nary hp spreadng and transmsson s ompared wth the BER otaned y derved formula () (magenta) for haot hps spreadng and transmsson BER SR Fg. 5 BER urves for the reever n presene of AWG and fadng: theoretal (magenta) and smulaton (magenta yles) for fadng and theoretal for nose only (lak). As expeted, the BER rate n fadng hannel s sgnfantly greater than n the ase when AWG only s present n the hannel (lak urve). For the sake of omparson, the BER for Standard nary sequenes [7] are ompared y the BER for haot sequenes of the same average powers. The BER n 3

6 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 the ase when a haot sequene s used s slghtly worse than n the ase when a nary orthogonal hp sequene defned y the Standard for wreless sensor networks s used. The BER n presene of fadng s sgnfantly worse than n the ase when only AWG s present n the hannel (Blak urve n Fg. 5). Ths degradaton n BER due to fadng an e elmnated y usng one of the dversty methods. In order to elmnate ths degradaton of BER n fadng, a method of fadng mtgaton usng nterleavers s nvestgated n the next seton of ths paper. IV. ITERLEAVER COMMUICATIO SYSTEM In real wreless systems the nfluene of fadng on sgnal transmsson an e very hgh that s manfested as severe attenuaton of the sgnal reeved. Therefore, t s mportant to mtgate ths fadng nfluene. Varous dversty shemes an e used for ths mtgaton []. It was shown that the nterleaver and denterleaver loks at the transmtter and the reever sde, respetvely, an also mtgate Raylegh fadng n dret sequenes spread spetrum systems [4, 3-5]. Therefore, n the ommunaton system defned for wreless sensor networks, t wll e worth to see f ths nterleaver tehnque an e appled. The followng theoretal analyss of the system presented n Fg., the nterleaver (IL) and denterleaver (DI) loks wll e nluded nto the transever struture and theoretally analyzed. It wll e assumed that a smple lok nterleaver of βxβ sze s employed. Aordng to ths nterlaeaver struture, the hps for eah t wll e wrtten nto the lok nterleaver row wse. Thus the frst raw wll ontan all the hps elongng to the frst t. When the nterleaver lok s full the hps wll e taken out olumn wse and appled to the nput of the modulator. Thus, the frst β hps enterng the modulator wll elong to β dfferent ts. The opposte operaton s performed y the denterleaver at the reever sde to re-order the hps. amely, the frst β hps taken out of the denterleaver wll ontan the hps elongng to the fst t ut affeted y dfferent fadng oeffents. By ths operaton the samples of hps z at the output of multplexer (MUX) are pratally affeted wth ndependent fadng oeffents and an e expressed as z = α E + E n. (9) These are soft hp values that are appled at the hp sequene orrelator nput, whh onssts of a multpler and an adder. For the assumed frst t value equal to +, whh s sent at the transmtter sde, the output of the orrelator s a sum of β hp samples, whh an e represented as one realzaton of a random varale W, expressed as β β β = A + w = z = E + E α n B (30) Ths s a t soft value. The mean and varane of ths random varale are η and w Ew E Eα E β = { } = { } { } (3) β β 4 w = E E E E E + β EE { }. (3) σ [ { α } { } { α } { }] If the expetatons (7), (8) and expetaton for Raylegh varale are nserted nto (3) and (3), the mean and the varane of a t soft value an e smplfed to and η = β π /4 E (33) σ w 0 w 4 E 6 π = βe [ + ]. (34) Due to the CL theorem, the random varale representng t soft value has Gaussan dstruton havng the mean (33) and varane (34). Therefore, for the nary message ts and haot spreadng sequenes wth unt average power, the proalty of error an e expressed as p e (6 π ) 4 E = erf + βπ π 0 /. (35) Smulators were developed n MATLAB to nvestgate haraterst of ommunaton systems that nludes the nterleaver/denterleaver struture and the aheved mprovements n BER due to the nterleaver applaton s presented n Fg. 6 (dashed magenta). Ths BER urve s plotted aordng to the theoretal expresson (35). For sgnal to nose rato SR = 8, for example, the theoretal gan n BER rate s from x0 - to.8x0-3. Ths mprovement n BER sustantally nreases when sgnal to nose rato nreases. The theoretal urve wth nterleaver and denterleaver loks, aordng to expresson (35), s plotted n magenta, whle the urve for AWG presene n the hannel s presented n lak olour. For the BER value that s approxmately x0 -, the savng n SR s approxmately 5.5 db, as shown n Fg. 6. Ths savng nreases sgnfantly when the BER dereases. It s nterestng to ompare the theoretally derved expressons for the BER wth the orrespondng graphs otaned y smulaton. The theoretal expresson (35) s onfrmed y the smulaton of the system as the results 3

7 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 presented n Fg. 7 show. Ovously, the theoretal urve, ased on the losed form dervatve (35), s followed y the BER urve otaned y smulaton. The dfferene etween the two urves, eng less than 0. db, s neglgle. BER eomes smlar to the nfluene of the AWG. Consequently, the fadng BER urve omes loser to the urve that s otaned when only AWG nose s present n the hannel. Further mprovements n BER ould e aheved f the spreadng fator β s nreased, as an e seen from theoretal expresson (35). Therefore, the general onluson s that the lok hp nterleavng s an effent tehnque that an e used to mtgate fadng n the physal hannel of wreless sensor networks [7]. Also, further nvestgaton an target the other knd of nterleavers and ther effeny n respet to the fadng mtgaton. To aheve desred auray of BER, n all prevous graphs, estmaton the numer of hps and ts n the smulaton are hosen aordng to the requrements presented n referene [6] SR Fg. 6 BER urves for the system wth nteleaver and denterleaver n AWG and fadng hannel: theoretal for fadng (Blue), theoretal for fadng wth nterleavers (Red) and theoretal for nose only (Blak). 0 0 BER SR Fg. 7 BER urves nteleaver reever n presene of AWG and fadng: theoretal (Blue) for fadng, theoretal derved (Green full lne) theoretal wth nterleavers (Green dashed) followed y the smulaton (Red) for fadng wth nterleavers and theoretal urve for nose only (Blak). We an onlude that, y usng nterleavers the fadng oeffents are de-orrelated and the fadng nfluene V. COCLUSIO In ths paper, the theoretal expressons for the proalty of errors are derved for a ommunaton system representng the physal layer of wreless sensor networks. The system s analyzed n the ase when flat fadng s present n the hannel and n the ase when the nterleaver tehnque s used to mtgate the fadng. It was found that the nterleaver tehnque mtgates the fadng and sgnfantly mproves the BER rate n the system. For example, for SR = 8 db, the theoretal gan n BER rate aheved s from x0 - to.8x0-3. The ommunaton system analyzed has a struture that s defned for the wreless sensor network applatons. In the theoretal analyss and n smulaton, all the sgnals are represented and proessed n dsrete tme doman. In ths way the developed and smulated system model an e easly mplemented n dgtal tehnology, DSP or FPGA. REFERECES [] Lee, S. J. and Mller, L. E., CDMA Systems Engneerng Handook, st edton, Arteh House Pulshers, Boston and London, 998. [] X. Gu, Chp-Interleavng DS SS System over Ran Multpath Fadng Channel, Wreless Communaton and Mole Computng, John Wley & Sons, on-lne, DOI/wm.30, 0. [3] R. H. Mahadevappa and J. G. Proaks, Mtgatng multple aess nterferene and ntersymol nterferene n unoded CDMA systems wth hp-level nterleavng, IEEE Trans. on Wreless Communatons, vol., 00, pp [4] S. M. Berer, R. Val, Fadng Mtgaton n Interleaved Chaos-Based DS-CDMA Systems for Seure Communatons, 5th WSEAS Int. Conf. on Communatons, Corfu, Greee, July 5-7, 0, pp. -6. [5] L. Yu-an and D. W. Ln, ovel analytal results on performane of t-nterleaved and hp-nterleaved DS-CDMA wth onvolutonal odng, IEEE Transatons on Vehular Tehnology, Vol. 54, 005, pp [6] X. Gu and T. S. g, A ovel hp-interleavng DS SS System, IEEE Trans. On Veh. Teh., Vol. 49, January 000, pp. -7. [7] "IEEE Std (Revson of IEEE Std ), Wreless Medum Aess Control (MAC) and Physal Layer (PHY) Spefatons for Low-Rate Wreless Personal Area etworks (WPAs), pp. 0_-305, 006. [8] C. C. Wang, C. C. Huang, J. M. Huang, C. Y. Chang, C. P. L, Zg-Bee 868/95-MHz Modulator/Demodulator for Wreless Personal Area etwork, IEEE Transatons on Very-Large Sale Integraton (VLSI) Systems, Vol. 6, o. 7, July 008,

8 ITERATIOAL JOURAL OF COMMUICATIOS Issue, Volume 7, 03 [9] O. am-jn, L. Sang-Gug, Buldng a.4-ghz rado transever usng IEEE , Cruts and Deves Magazne, IEEE, Vol., 006, pp [0] G. Kaddoum, D. Rovras, P. Charge, and D. Fourner-Prunaret, Roust synhronzaton for asynhronous mult-user haos-ased DS-CDMA, Sgnal Proessng, vol. 89, no. 5, pp , 009. [] M. Bank, Y. Barsh, S. Tapuh, M. Bank, B. Hll, M. Hardm, Phase Dversty Method n Mole Communaton Systems, Internatonal Journal of Communatons, Issue, vol. 6, pp. 64 7, 0. [] R. Val, S. Berer, and S. K. guang, Effet of Raylegh fadng on nonoherent sequene synhronzaton for mult-user haos ased DS- CDMA, Sgnal Proessng, vol. 90, no. 6, pp , 00. [3] H. Tor, M. Satoh, T. Matsumoto, and M. akamura, Quas-Optmal and Optmal Generalzed Mutually Orthogonal ZCZ Sequene Sets Based on an Interleavng Tehnque, Internatonal Journal of Communatons, Issue, vol. 7, pp. 8 5, 03. [4] Stevan M. Berer, Ramn Val, Fadng Mtgaton n Interleaved Chaos-Based DS-CDMA Systems for Seure Communatons, 5th WSEAS Int. Conf. on Communatons, Corfu, Greee, July 5-7, 0, pp. -6. [5] B. K. Upadhyaya, and S. K. Sanyal, ovel desgn of WMAX multmode nterleaver for effent FPGA mplementaton usng fnte state mahne ased address generator, Internatonal Journal of Communatons, Issue, vol. 6, pp. 7 36, 0. [6] S. M. Berer, Bt error rate measurement wth predetermned onfdene, Eletrons Letters, vol. 7, p. 05, 0th June 99. [7] S. Berer, S. Feng, Chaos-Based Physal Layer Desgn for WS Applatons, 7th WSEAS Int. Conf. on Communatons, Rhodos, Greee, July 6-9, 03, pp