Chaos-Based Physical Layer Design for WSN Applications

Transcription

1 Reent Advanes n Teleommunatons Crut Desgn Chaos-Based Physal Layer Desgn for WS Applatons STVA BRBR Department of letral Computer ngneerng The Unversty of Aukl Aukl, ew Zeal s.berber@aukl.a.nz SHU FG Department of Communaton ngneerng, OT, anjng Unversty of SCI TCH, anjng, Chna, mal: shufeng@mal.njust.edu.n Abstrat: - Due to ther orrelaton propertes, haot sequenes an be used n dret sequene spread spetrum systems. In ths paper the applaton of these sequenes for desgn of physal layer n wreless sensor networks s presented. In order to mtgate fadng the hp nterleavng tehnque s nvestgated. Theoretal expressons n losed form for the bt error rate (BR) are derved onfrmed by smulaton. The sgnals n the system all proessng are performed n dsrete tme doman. Smulaton results onfrmed the derved theoretal expressons. Key-Words: - haos based systems, wreless sensor networks, fadng hannel, nterleavers, BR urves. Introduton One of the bas requrements n wreless sensor networks s to desgn network nodes wth mnmum power onsumpton. Also, t was proved that the fadng nreases BR n the physal layer. Therefore, for the desred BR n the network the power of nodes needs to nrease n the presene of fadng n order to ommunate at the same dstane []. It was shown that the fadng nfluene n dret sequene spread spetrum CDMA systems an be redued by usng nterleavng tehnques [, 3, 4, 5, 6]. A wreless network defned n the Stard I [7] uses a modfed spread spetrum tehnque. For that reason, n ths paper, an analyss of mplementng haot sequene hp nterleavng tehnque n these networks s nvestgated. One desgn of modulator demodulator bloks for ths network s presented n [8] whh nluded theoretal modelng, smulaton desgn n FPGA mplementaton n CMOS tehnology. The transever desgn s presented n [9]. In ontrast to those desgns, ths paper presents the theoretal analyss smulaton of the physal layer n dsrete tme doman that s sutable for dret mplementaton n DSP or FPGA tehnology. In the exstng theory these sgnals ther proessng are represented n ontnuous tme form, whh s not sutable for dret mplementaton n dgtal tehnology. The theoretal model of the system n presene of nose fadng s presented n Seton, nludng bas propertes of the haot sequenes. BR expressons are derved n the losed form. Seton 3 presents the mathematal model of the system n the ase when nterleaver denterleaver bloks are used n the transmtter reever respetvely. For ths ase the expresson for the BR s derved I losed form. Seton 4 presents the results of smulaton whh onfrmed the theoretal fndngs. Seton 5 ontans onlusons. Chaos-based system n presene of Gaussan nose fadng In ths paper a haot sequenes wll be used to spread the bts. It was shown that the haot sgnals, generated usng haot maps, an be used n DSSS CDMA systems to spread message bts, due to ther orrelaton propertes, f the synhronzaton of the sequenes s resolved [0.]. The analytal results smulatons, presented n ths paper are based on the haot mappng alled Chebyshev Degree-L maps defned by ths reursve equaton - k ( ) os[ Los k ( )], () where dsrete rom samples n the sequene (k) have the values between - +. If L = the logst map s obtaned, wth L = 3 the ub map s defned. The dsrete rom samples wll be alled hps. The densty funton of these maps s ( k) os[ Los ( k)] () - ISB:

2 Reent Advanes n Teleommunatons Crut Desgn / M os k / M osk b j IL m(k) m I (k) DMUX s T (k) s R (k) y I M k MUX z I z DI w Deson Crut ' b j m Q (k) T / / M sn k T / M k y Q / M sn k z Q n(k) Sequene Synhronzatn Blok Fg. Blok shemat of ommunaton system In order to ompare haot systems wth the lassal bnary system the haot generator needs to produe the haot hps arryng the same power as the power of the bnary sequene. Thus, a new haot varable wll be defned as ( ) ( ) k k whh has the densty funton alulate as shown n the Appendx. Fgure presents a smplfed blok shemat of a system that uses OQPSK modulaton bnary spreadng sequenes proposed by the stard for wreless sensor networks [7]. In ths paper these bnary sequenes are replaed by haot sequenes. The system wll be analyzed for the ase when the Addtve Whte Gaussan ose (AWG) fadng are present n the hannel, for the ase when nterleaver (IL) denterleaver (DI) are nluded nto blok shemat n the Fgure. The soure generates message bts b j (k). The bts are spread by the haot spreadng sequene n (k) a hp sequene m(k) = b j (k) (k) s obtaned. A demultplexer (DMUX) s used to splt the hp sequene m(k) nto n-phase quadrature sequenes n suh a way that the even-ndexed hp sequene m I (k) modulates the n-phase arrer odd-ndexed hp sequene m Q (k) modulates the quadrature arrer, as spefed by the Stard for wreless sensor networks [7]. The energy of a bt s b = β, where s the energy per hp. The number 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 related nose sample are generated one for eah hp nterval then repeated (nterpolated) M tmes n the hp nterval to allow the dsrete tme modulaton of the arrer. For M repeated samples of nose n a hp nterval the average energy s = Mσ, where the varane s σ =B 0 the bwdth B=/T =/M. Thus, the energy of a nose n a hp s alulated to be = 0 /. The output of the modulator s the QPSK sgnal expressed as s() k m () k / M os km () k / M sn k I Q where m I (k) m Q (k) are n-phase quadrature hp sequenes respetvely, Ω s the normalzed frequeny of the arrer. The b-lmted pass-b nose samples are also generated n dsrete tme doman as nk () ni () k / Mos knq() k / M snk. The nose omponents n I (k) n Q (k) are n-phase quadrature nose samples of zero mean unt varane. The energy of the nose samples nsde a hp nterval s M s the number of nterpolated samples nsde the hp nterval. If fadng nose are present n the hannel, the fadng s haraterzed by fadng oeffent, whh has Raylegh densty funton wth the mean value = (πb/4) -/ varane σ = b(4-π)/4. In the presented model smulatons t s assumed that { }=. Thus, the reeved sgnal s R (k) s [3] j sr ( k ) e s( k) n ( k ) (3) where s the fadng oeffent φ s the phase shft. For a slow fadng the fadng oeffent s onstant n a bt nterval the phase shft φ an be elmnated by the reever s phase loked loop. The reeved sgnal s R (k) an be oherently demodulated usng a orrelator reever. The sgnal at the output of the multpler s y ( k) [ s( k) n( k)] / M os k I (4) ISB:

3 Reent Advanes n Teleommunatons Crut Desgn The samples nsde the hp nterval of ths dsrete sgnal are added (orresponds to ntegraton n ontnuous tme systems) resultng n a rom sample z n I branh for =, 4,,, n Q branh for =, 4,,. The multplexer (MUX) ombnes n-phase quadrature sequenes bak nto a β-hp sequene of samples z z n (5) where =,, 3, 4,, n are samples of the n-phase quadrature baseb nose. The frst term n ths sample represents the sgnal part the seond one s the nose part. The reeved stream of samples z s orrelated wth a loally generated referene hp sequenes (, =,, 3, 4,, ), obtaned from the sequenes synhronzaton blok [0, ]. The orrelator s a multpler adder. Assumng that the bt sent was +, the output of adder wll be a rom sample that represents a bt reeved s expressed as w z n AB (6) It s assumed that the soure generates bnary bts from the alphabet (+, -). Thus the threshold value n the deson rut should be defned as z T = 0. The densty funton of rom varable W, due to the entral lmt theorem (CLT), an be approxmated by Gaussan funton. Also, assumng that the powers of all hps are equal, the mean value may be alulated as w w { } { } { } (7) the varane of w n general form s w { } {( AB) } (8) w w w It an be found { A } { } [ { 4 } ( ) { } { j }] (9) { B } n { } (0) The mean value squared an be expressed n ths form { w} { } { } w j ( ) { } { } { } { } () The varane an be obtaned from (8), (9), (0) () n ths form [ { } { } { } { }] 4 w j j [ { } { }] { } { } { } Suppose that the ub map s used. Insertng the values from expressons (A4) (A6), the values for the fadng expetatons, the expresson for the varane an be smplfed as [ (4 ) ]. 0 w 4 Then, the probablty bt error an be expressed as p be 4(4 ) 4 b erf 0 / () where the energy of a bt s b = β energy of the nose s = 0 /. 3 Interleaver ommunaton system It was shown that the nterleaver blok at the transmtter denterleaver blok at the reever an mtgate Raylegh fadng n dret sequenes spread spetrum systems [4]. Therefore, n the system defned for wreless snsor networks, t wll be worth to see f the nterleaver tehnque an mtgate fadng. In the followng analyss the nterleaver (IL) denterleaver (DI) bloks, shown n Fg., wll be nluded nto the transever struture theoretally analyzed. It s assumed that a blok nterleaver of βxβ sze s employed. The hps for eah bt are wrtten nto the blok nterleaver row wse, then taken ISB:

4 Reent Advanes n Teleommunatons Crut Desgn out olumn wse appled to the nput of the modulator. The opposte operaton s performed by the denterleaver at the reever sde to re-order the hps. By ths operaton the samples of hps at the output of multplexer (MUX) are affeted wth ndependent fadng oeffents,.e., z n (3) Ths soft hp values are appled at the hp sequene orrelator nput. The orrelator s a multpler an adder. For the assumed frst bt equal to + sent, the output of the orrelator s a sum of β hp samples, whh an be represented as one realzaton of a rom varable W, expressed as w z n A B The mean varane of ths rom varable are w w (4) { } { } { } (5) 4 w { }. (6) [ { } { } { } { }] If the expetatons (A4), (A6) expetaton for Raylegh varable are nserted nto (5) (6), the expressons for the mean the varane of a hp varable an be smplfed to /4 (5) w 0 w 4 6 [ ] (6) Therefore, f the soure generates bnary bts the spreadng sequene s a haot sequene wth unt power, the probablty of error an be expressed as p be (6 ) 4 b erf 0 /. (8) 4 Smulaton Results dsussons In Fg. 3 the theoretal BR (blue) n presene of fadng for bnary hp transmsson s ompared wth the BR obtaned by derved formula () (magenta) for haot hps transmsson. The system s smulated the resultant BR values are plotted along the blue lne. The number of hps bts n the smulaton are hosen n suh a way to fulfll the ondtons of auray n BR estmaton []. The BR rate n fadng hannel s sgnfantly greater than n the ase when AWG s present n the hannel (blak urve). It s mportant to note that the BR n the ase when haot sequene s used s slghtly worse than n the ase when a bnary orthogonal hp sequene defned by the Stard for wreless sensor networks s used [7]. The BR n presene of fadng s sgnfantly worse than n the ase when only AWG s present n the hannel, whh s represented by the thrd (Blak) urve n Fg. 3. In order to elmnate ths degradaton of BR n fadng, a method of fadng mtgaton usng nterleavers s nvestgated n ths paper BR SR Fg. 3 BR urves for the reever n presene of AWG fadng: theoretal (magenta) smulaton (magenta yles) for fadng theoretal for nose only (blak). The aheved mprovements n BR due to the nterleaver applaton s presented n Fg 4 (dashed magenta). Ths BR urve s plotted aordng to the theoretal expresson (8). For sgnal to nose ISB:

5 Reent Advanes n Teleommunatons Crut Desgn BR 0-3 BR SR Fg. 4 Theoretal BR urves for reever wth nteleavers n presene of AWG fadng: theoretal (Blue) for fadng, theoretal (Red) for fadng wth nterleavers theoretal for nose only (blak). rato SR = 8 db, for example, the theoretal gan n BR rate s from 0 - to x0-3. Ths mprovement n BR nreases when sgnal to nose rato nreases. The theoretal urve wth nterleaver denterleaver bloks, aordng to expresson (8), s plotted n magenta, whle the urve for AWG presene n the hannel s presented n blak olour. For the BR value that s approxmately.6x0 -, the savng n SR s approxmately 5.5 db, as shown n Fg. 4. Ths savng nreases sgnfantly when the BR dereases. The theoretal expresson (8) s onfrmed by the smulaton of the system. The results are presented n Fg. 4. The theoretal urve, based on the losed form dervatve (8) s followed by the BR urve obtaned by smulaton. The dfferene between the two urves n less than 0. db. In summary, by usng nterleavers the fadng oeffents are de-orrelated the fadng BR urve tends to the urve that s obtaned when only AWG nose s present n the hannel. As an be seen from theoretal expresson (8), further mprovements n BR ould be aheved f the spreadng fator s nreased. Therefore, the hp nterleavng s an effent tehnque that an be used to mtgate fadng n the physal hannel of wreless sensor networks SR Fg. 5 Smulated BR urves for reever wth nteleavers n presene of AWG fadng: theoretal (Blue) for fadng, theoretal derved (Green full lne) theoretal wth nterleavers (Green dashed) followed by the smulaton (Red) for fadng wth nterleavers theoretal urve for nose only (Blak). 5 Conlusons In ths paper, the theoretal expressons for the probablty of errors are derved n the ase when flat fadng s present n the hannel n the ase when the nterleaver tehnque s used to mtgate the fadng. It was proved that the nterleaver tehnque mtgates the fadng sgnfantly mproves the BR rate n the system. The ommunaton system analyzed has a struture that s defned for the wreless sensor network applatons. In the theoretal analyss n smulaton all the sgnals are proessed n dsrete tme doman. In ths way the developed system model an be easly mplemented n dgtal tehnology, DSP or FPGA. Referenes: [] Lee, S. J. Mller, L.., CDMA Systems ngneerng Hbook, st edton, Arteh House Publshers, Boston London, 998. [] X. Gu, Chp-Interleavng DS SS System over Ran Multpath Fadng Channel, Wreless Communaton Moble Computng, John Wley & Sons, on-lne, DOI/wm.30, 0. [3] R. H. Mahadevappa J. G. Proaks, Mtgatng multple aess nterferene ntersymbol nterferene n unoded CDMA ISB:

6 Reent Advanes n Teleommunatons Crut Desgn systems wth hp-level nterleavng, I Trans. on Wreless Communatons, vol., 00, pp [4] S. M. Berber, R. Val, Fadng Mtgaton n Interleaved Chaos-Based DS-CDMA Systems for Seure Communatons, 5th WSAS Int. Conf. on Communatons, Corfu, Greee, July 5-7, 0, pp. -6. [5] L. Yu-an D. W. Ln, ovel analytal results on performane of bt-nterleaved hp-nterleaved DS-CDMA wth onvolutonal odng, I Transatons on Vehular Tehnology, Vol. 54, 005, pp [6] X. Gu T. S. g, A ovel hp-interleavng DS SS System, I Trans. On Veh. Teh., Vol. 49, January 000, pp. -7. [7] "I Std (Revson of I Std ), Wreless Medum Aess Control (MAC) 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, I Transatons on Very- Large Sale Integraton (VLSI) Systems, Vol. 6, o. 7, July 008, [9] O. am-jn, L. Sang-Gug, Buldng a.4-ghz rado transever usng I , Cruts Deves Magazne, I, Vol., 006, pp [0] G. Kaddoum, D. Rovras, P. Charge, D. Fourner-Prunaret, Robust synhronzaton for asynhronous mult-user haos-based DS- CDMA, Sgnal Proessng, vol. 89, no. 5, pp , 009. [] R. Val, S. Berber, S. K. guang, ffet of Raylegh fadng on non-oherent sequene synhronzaton for mult-user haos based DS- CDMA, Sgnal Proessng, vol. 90, no. 6, pp , 00. [] S. M. Berber, Bt error rate measurement wth predetermned onfdene, letrons Letters, vol. 7, p. 05, 0th June 99. the power one n order to ompare haot system wth the bnary system. Thus the rom varable defnng the samples of the haot sequene n ths paper s defned as a funton of,.e., =. Usng the fundamental theorem of probablty theory the densty funton of s f C ( ),for -. The expetatons of ths rom varable are (A) { } d 0, (A3) { } d, (A4) { } d. (A6) Appendx The densty funton of haot sequene sample s fc (), for -. (A) The mean value s zero the mean square value, orrespondng to the power of the sequene s 0.5. In ths paper the haot samples are generated wth ISB: