Internatona Journa of Computer Scence and Eectroncs Engneerng (IJCSEE) Voume 1, Issue 1 (213) ISSN 232 428 (Onne) Demoduaton of M sgna based on seuenta Monte Caro mode Lun Huang and G. E. Atkn Abstract Demoduaton of the constant-amptude oynoma hase Moduaton (M) sgna [1] Based on oynoma hase ransform () [2] and Hgh-order Ambguty Functon (HAF) [3] generay reures very arge oversampng rate. hey aso dd not consder the mutpath channe envronment and Inter Symbo Interference (ISI). In ths paper, a demoduaton method for M sgna based on Seuenta Monte Caro (SMC) agorthm s proposed. Compared wth the conventona code dvson mutpe access (CDMA) technue, where the spread factor s fxed n one moduaton codng scheme, the proposed SMC M demoduaton method can dynamcay adjust the oversampng rate (correspondng to the spread factor n CDMA) accordng to the avaabe bandwdth and performance reurement. hs s attractve to Cogntve Rado (CR) and Software Defned Rado (SDR) system. he proposed SMC M demoduaton methods can aso cope wth the mutpath channe and ISI. Smuaton resuts under fxed narrow-band channe wth AGN shows that, wth the proposed SMC M demoduaton method, the M can provde sgnfcant performance mprovement over the conventona moduatons, such as QS and 8S. eywords Seuenta Monte Caro (SMC), Inter Symbo Interference, mutpath channe. I. INRODUCION HE oynoma hase Sgnas (S) was frsty ntroduced as a moduaton method for communcaton system n [2]. As shown n [2], S moduaton, aso caed poynoma phase moduaton (M), provdes hgher power effcency than conventona moduaton technues such as QAM and S [3]. On the other hand, M s hgh order tme-varant sgna, whch can be oversamped to obtan better performance [2]. However, the conventona demoduaton approach of M was based on oynoma hase ransform () and hgh-order ambguty functon (HAF) estmaton [3], whch reures very arge oversampng rate to use Fourer ransform to estmate the moduatng data. It makes the demoduaton of M unreastc n practca communcaton systems. Furthermore, ths conventona demoduaton approach dd not consder the mutpath channe envronment and Inter Symbo Interference (ISI), whch s common n communcaton. L. Huang, h.d Canddate s wth the Department of Eectrca & Computer Engneerng, Inos Insttute of echnoogy, Chcago, IL 6616, USA (phone: 1-312-567-3417; e-ma: huang13@t.edu). G. E. Atkn, h.d, Senor Member IEEE, Assocate rofessor s wth the Department of Eectrca & Computer Engneerng, Inos Insttute of echnoogy, Chcago, IL 6616, USA (e-ma: atkn@t.edu). In ths paper, a nove demoduaton approach of a M based on Seuenta Monte Caro (SMC) agorthm s proposed. Accordng to the theory of mted state-space and Compressve Sensng (CS) [4, 5], ths method can sgnfcanty reduce the oversampng rate reured to obtan optmum estmaton of transmtted symbos. It can aso cope wth the mutpath channe and ISI. Smuaton resuts under fxed narrow-band channe wth AGN ndcates that, wth the proposed SMC S demoduaton method, the S moduaton can provde sgnfcant performance mprovement over the conventona moduatons, such as QS and 8S. he rest of the paper s organzed as foows. In Secton II, the system mode for the Seuenta Monte Caro demoduaton probem s presented. In Secton III, the Seuenta Monte Caro demoduaton (SMCD) agorthm for M n condton of fxed narrow-band channe wth AGN s derved. In Secton IV, the smuaton resuts and performance comparson for S wth dfferent demoduaton approaches and parameters are provded. Secton V concudes the paper. II. SYSEM MODEL oynoma phase moduaton refers to a constant enveop moduaton where the nformaton bts are mapped to the coeffcent of a phase poynoma. By augmentng the coeffcent aphabet and poynoma degree, the rate of transmsson can be mproved wth mnmum bandwdth and power. Let φ (t) represents a poynoma phase of order -1 wth duraton of. he poynoma phase n -th sgnang nterva can be expressed as: 1 t a, c, < t φ (t) =, otherwse here c s a normazaton constant, s the duraton of the symbo nterva, the a, takes rea vaues from an aphabet wth C eements, for =,1,..., 1, = 1,2,..., Q, Q s the number of symbos n the transmtted seuence. So the dscrete moduated sgna can be denoted as: (1) 45
Internatona Journa of Computer Scence and Eectroncs Engneerng (IJCSEE) Voume 1, Issue 1 (213) ISSN 232 428 (Onne) = A exp j ( ) = ( ) y n, φ n N A Y n N 25 2 φm 1 ms a, c, < m N =, otherwse Amptude 15 1 5 t where m =, * denotes the functon of roundng to s nearest smaer nteger, s s the sampng perod,, s c N = s the oversampng rate, A s the s amptude, the coeffcents a, n each symbo wth duraton contan the nformaton. In M, the sera nformaton bt stream s converted to parae paths; each of the paths s mapped to a rea vaue for a coeffcent. Assume that the number of eves for each coeffcent a, s C, the aphabet for Y ( m ) s { } = φ m Y m exp j X = [Y 1,,Y N ], =,, C 1, where 1 m s, = c exp j a, < m N Y m, otherwse a,, =,1,, 1 s the phase coeffcent for the -th symbo n the aphabet. hroughout ths paper, C=2 s used. It shoud be noted that X, the eement of the aphabet for Y ( m ), s a vector ncudng the N sampes n one perod. At the recever, f the channe s not tme-dspersve thus consdered to have ony one path, conventona teratve decodng agorthms, such as oynoma hase ransform (), can be used to estmate the coeffcents of the phase poynoma of the receved sgna [2] [6] [7]. However, to obtan accurate estmate of coeffcent wth Fourer transform, Dscrete (D) approach aways reures very arge oversampng rate whch sometmes can be up to a hundred tmes of the order of phase poynoma [8, 9]. Large oversampng rate means arge transmt bandwdth and ower bandwdth effcency. Furthermore, n wreess communcatons, there exst mutpe propagaton paths between the transmtter and the recever n reaty. In ths scenaro, D approach aways fas to offer correct estmatons [9]. If the mpuse response of the tme-nvarant channe that conssts of L deayed paths can be -1 -.8 -.6 -.4 -.2.2.4.6.8 1 (2) Freuency ( x π ) Fg. 1 he hgh-order ambguty functon of M sgna n condton of mut-path channe expressed as [1] gven by [1-12] L 1 h(t) = δ(tτ) h,t L 1, the receved sgna s rn = h,ny(n ) + nw (3) here L s the ength of the channe mpuse response, n w s addtve whte Gaussan nose (AGN). An amptude freuency response of Hgh-order Instantaneous Moment n the procedure of demoduatng M wth D approach s gven n Fg. 1. In can be observed that there are severa peaks n the freuency doman, and the hghest one doesn t gve the correct estmaton of the coeffcent n the poynoma phase. In ths paper, a nove approach of demoduatng M based on Seuenta Monte Caro (SMC) agorthm s proposed. he system dagram for SMC demoduaton of M sgna s descrbed n Fg. 2, where ω c s the carrer freuency, LF denotes ow-pass fterng, whe pre-fterng can whten the nose n the receved seuence [13], channe estmaton w provde the matrx of channe mpuse response for demoduator. Gven the oversampng rate N, every N eements of rn can be put n a vector r, then r = Η y (4) here j c e ω t r = r N, r N + 1,, r + 1N 1, LF A/D converter re-fterng Channe estmaton r (n) y(n) SMC demoduaton Fg. 2 he system dagram of SMC demoduator for M sgna H 46
here h Θ x ' ',, x 2: 1 j,, x 2, x L 1,N,h L 2,N,,h,N = L L + 1 Η= h L 1,N,h + 1 L 2,N, + 1,h,N+ 1 denotes the subseuence contanng from the second to L ' - th eements n h L 1, ( + 1N ) 1,h L 2, ( + 1N ) 1,,h Θ. hus, gven the DFV Θ, and the, ( + 1N ) 1 y = y( N L + 1 ), y( N L + 2 ),, y( ( + 1) N 1), state at tme nterva, x, the dstrbuton of the observed receved vector r s then gven he N ( N + L 1) matrx H can be obtaned wth by: channe estmaton, the ength of the transmtted sgna vector 2 y s N + L 1. he Fg. 3 shows the case of N = 2. p( r Θ, ) exp( Φ x = r H ) (6) Accordng to the theory of Compressve Sensng, M r can be demoduated at a ower oversampng rate sgna wth suffcenty sma Mean Suare Error (MSE). In the next secton, the Seuenta Monte Caro mode for demoduaton of M sgna w be presented. III. SEQUENIAL MONE CARLO DEMODULAION (SMCD) ALGORIHM FOR FIXED NARRO-BAND CHANNEL IH AGN At tme nterva -1, the hdden decson-feedback vector (DFV) of ength ' L can be descrbed by: Θ = x ',, j,, 2, L 1 ' L = ( N + L 1) / N s the normazed ength of channe, "*" denotes the nearest bgger nteger. he assocated transmtted sgna vector of ength N + L 1 can be gven as ( 1) = y( ( 1)N L+ 1,y ( 1)N L+ 2, ),yn ( 1) y X x, X,, L ' x X L ' x + 1 1 As descrbed n Fg. 3, when N = 2, X = [y( 2 2 ), y( 2 1 )]. Y x 1 Internatona Journa of Computer Scence and Eectroncs Engneerng (IJCSEE) Voume 1, Issue 1 (213) ISSN 232 428 (Onne) Let x be the state assocated wth the transmtted symbo ( n ) at tme nterva, x takes vaue from the state space {,1,, C 1} χ =, the possbe transmtted parta seuence can be defned as ' Θ = x ',, x,, 1, Θ ', 1 L j x x x + = 2: L x L' x L'+1 x 1 ( n L +1)... ( n 3) y ( n L 1) y( n L) y y( n L + 2) hl 1 h 2 3 y y( n 2) y ( n 1) y(n) h L h2 h h 1 X X X X X X + x r( n)( r( )). here H s the N ( N + L 1) channe matrx defned n (4), Φ = X ' = X,,,,, Θ x X 1 L ' x X j x X 1 x + hus the nference probem can be put n the way as foows. If the state reazatons up to tme nterva s presented as S = x1, x2,, x, the receved seuences up to tme nterva can be expressed as R = r1, r2,, r, where r s the receved vector wth N eements. aphabet ndex of the transmtted symbo Y receved matrx R, the state reazatons x s the from a fnte aphabet { X}, =,1,, C 1, ths make t necessary to consder a possbe extensons for each partce from tme nterva -1. hus at tme nterva, for each seuence sampe S (5 1, k = 1,,, the assocated weghts for ) a C possbe extensons are evauated. Based on the C weghts acheved, the extensons wth the argest weghts are retaned to update the Θ of the partces and n. Gven the S can be estmated. It can be assumed that there are severa sets of seuence { S, w, k 1,, } sampe and ts assocated weght ( ( k ) ( k ) ) 1 1 = at tme nterva -1 [14, 15]. Each set can be regarded as a partce, thus s the number of partces. At the begnnng, when =1, the partces are ntated wth tranng seuence, and the weghts are set to dentca vaue. hat means S = S = x,, ' x 1, k = 1,, L +, where S = x,, ' x L + 1 s the tranng seuence. Snce the transmtted symbos at tme nterva can be any eement { S, wˆ, k 1,, } obtan ˆ ( ( k ) ( k ) ) =. Gven M sets of extended seuence sampe S and the assocated weght {( S, w ), k 1,, M} can be obtaned as =, the posteror dstrbuton of S Fg. 3 he dagram of deayed-tap channe mode 47
Internatona Journa of Computer Scence and Eectroncs Engneerng (IJCSEE) Voume 1, Issue 1 (213) ISSN 232 428 (Onne) here ( ) ( δ = ) w S S p S R M w k= 1 M k = 1 =, and 1, x = δ(x) =., otherwse ( ) ( ) p S R w = S R (8) S R s caed mportance densty of the sampes n ( k E ) [16]. At tme nterva, f the sampes consttutng an approxmaton to p( S 1 R 1) are avaabe, ( ) be approxmated wth a new set of sampes by δ(s S ) p S R = w p s,r S 1 1 1 1 k = 1 here S 1= s1, s2,, s 1 wthout s. (7) p S R can (9) denotes the subseuence of S As a suboptma approach, (9) can be smpfed to ( S ) = 1 1 p R w p s,r S k = 1 ( ) = w Θ 1 p r x, k = 1 (1) hs dentty can be used for weght update. In the seecton step, the partces wth the hghest weghts are retaned. conventona QS and 8S moduaton respectvey, and the oversampng rate adopted n demoduaton pays an mportant roe n the decdng the performance of M. At BER of 3 1, the oversampng rate N=4 brngs about 1.8 db gan for 4-ary M, and 1.2 db gan for 8-ary M over oversampng rate N=3. For SNR ess than 7dB, 8-ary M even outperforms QS. (a) Bt Error Rate wth respect to dfferent Sgna to Nose power Rato IV. SIMULAION RESULS In ths secton, the performance of seuenta Monte Caro demoduaton agorthm for M sgna transmtted n the fxed narrow-band channe wth AGN w be evauated. he number of partces s eua to the correspondng moduaton eve, so t s eua to 4 and 8 for 4-ary and 8-ary M. a π π, takes vaue from the set {, + }, thus C=2. 2 2 takes vaue of 2 and 3 for 4-ary and 8-ary M respectvey. For oversampng rate N=1, the coeffcents of the narrowband channe used n performance evauaton are gven as h(n) = [ 1.,.1259,.3]. For oversampng rate N>1, the fnte mpuse response of the channe s obtaned by dong nterpoaton on h(n). he performance of dfferent moduaton methods, ncudng QS, 8S, 4-ary M, and 8-ary M are gven n the Fg. 4. In Fg. 4(a), the Bt Error Rate (BER) wth respect to dfferent Sgna to Nose power Rato (SNR) for each moduaton method s presented, and Fg. 4(b) shows the Mean Suare Error (MSE) wth respect to dfferent SNR for each moduaton method. From Fg. 4, t can be observed that the oynoma hase Moduatons, ncudng both 4-ary M and 8-ary M, aways have better BER and MSE performance compared to (b) Mean Suare Error wth respect to dfferent Sgna to Nose power Rato Fg. 4 erformance of dfferent moduaton methods n fxed narrow-band channe V. CONCLUSION In ths paper, demoduaton methods for M sgna based on Seuenta Monte Caro (SMC) agorthm s proposed. he proposed methods can sgnfcanty reduce the oversampng rate reured by conventona approaches, whch are based on oynoma hase ransform () and Hgh-order Ambguty 48
Internatona Journa of Computer Scence and Eectroncs Engneerng (IJCSEE) Voume 1, Issue 1 (213) ISSN 232 428 (Onne) Functon (HAF) [3], to obtan the accurate estmaton of transmtted symbos. he proposed SMC M demoduaton method can dea wth the ISI caused by the fxed mutpath channe wth Addtve hte Gaussan Nose (AGN). Smuaton resuts show that, wth the proposed SMC M demoduaton methods, the M can provde sgnfcant performance mprovement over the conventona moduatons, such as QS and 8S. REFERENCES [1]. Yun, R. Snha, and G. Atkn, "Modfed moduaton formats usng tme-varyng phase functons," reess Communcatons, IEEE ransactons on, vo. 5, pp. 8-11, 26. [2] S. eeg and B. orat, "Estmaton and cassfcaton of poynomaphase sgnas," Informaton heory, IEEE ransactons on, vo. 37, pp. 422-43, 1991. [3] S. eeg and B. Fredander, "Mutcomponent sgna anayss usng the poynoma-phase transform," Aerospace and Eectronc Systems, IEEE ransactons on, vo. 32, pp. 378-387, 1996. [4]. Bajwa, J. Haupt, A. Sayeed, and R. Nowak, "Compressve wreess sensng," n roceedngs of the 5th nternatona conference on Informaton processng n sensor networks, 26, pp. 134-142. [5] A. C. Gurbuz, J. H. McCean, and V. Cevher, "A compressve beamformng method," n Acoustcs, Speech and Sgna rocessng, 28. ICASS 28. IEEE Internatona Conference on, 28, pp. 2617-262. [6] S. eeg and B. Fredander, "he dscrete poynoma-phase transform," Sgna rocessng, IEEE ransactons on, vo. 43, pp. 191-1914, 1995. [7] S. eeg and B. orat, "Lnear FM sgna parameter estmaton from dscrete-tme observatons," Aerospace and Eectronc Systems, IEEE ransactons on, vo. 27, pp. 67-616, 1991. [8] L. amer, "Coarse freuency estmaton usng the dscrete Fourer transform (Corresp.)," Informaton heory, IEEE ransactons on, vo. 2, pp. 14-19, 1974. [9] S. Barbarossa, A. Scagone, and G. B. Gannaks, "roduct hgh-order ambguty functon for mutcomponent poynoma-phase sgna modeng," Sgna rocessng, IEEE ransactons on, vo. 46, pp. 691-78, 1998. [1] X. Huang and H. C. u, "Robust and effcent ntercarrer nterference mtgaton for OFDM systems n tme-varyng fadng channes," Vehcuar echnoogy, IEEE ransactons on, vo. 56, pp. 2517-2528, 27. [11] E. Yakhnch, "Channe estmaton for EGRS modems," n Vehcuar echnoogy Conference, 21. VC 21 Sprng. IEEE VS 53rd, 21, pp. 419-422 vo.1. [12] M. occ, L. Martnot, and Z. Zvonar, "Sgna rocessng echnues for EDGE reess Modem," n Computer as a oo, 25. EUROCON 25.he Internatona Conference on, 25, pp. 131-134. [13]. H. Gerstacker, F. Obernosterer, R. Meyer, and J. B. Huber, "On prefter computaton for reduced-state euazaton," reess Communcatons, IEEE ransactons on, vo. 1, pp. 793-8, 22. [14]. Fearnhead, "artce fters for mxture modes wth an unknown number of components," Statstcs and Computng, vo. 14, pp. 11-21, 24. [15]. Lang, X. ang, and D. Anastassou, "A profe-based determnstc seuenta Monte Caro agorthm for motf dscovery," Bonformatcs, vo. 24, p. 46, 28. [16] M. Sanjeev Aruampaam, S. Maske, N. Gordon, and. Capp, "A tutora on partce fters for onne nonnear/non-gaussan Bayesan trackng," IEEE transactons on sgna processng, vo. 5, pp. 174-188, 22. 49