Bit-error rate analysis for hybrid PIM-CDMA optical wireless. communication systems

Transcription

1 Bt-error rate analyss for hybrd IM-CDMA optal wreless ommunaton systems Z. Ghassemlooy, C. K See, J. M. Holdng and C. Lu 2 Optal Communatons Researh Group, Shool of Engneerng, Sheffeld Hallam Unersty, ond Street, Sheffeld, S WB, U.K. Tel: , Fax: Emal: z.f.ghassemlooy@shu.a.uk for the orrespondng authors. 2 Shool of Eletral and Eletrons Engneerng, anyang Tehnologal Unersty, anyang Ae., Sngapore ABSTRACT: A hybrd pulse nteral modulaton ode dson multple aess (IM-CDMA) s proposed. Expresson for bt error rate (BER) s gen. umeral results presented are ompared wth hybrd M-CDMA and OOK-CDMA shemes. For a low number of users IM-CDMA ahees smlar and margnally lower BER performane ompared wth M-CDMA and OOK-CDMA, respetely. For large number users t offers better performane ompared wth OOK. Key words: ulse modulaton; CDMA; IM; optal wreless; Strt-OOC

2 . ITRODUCTIO There hae been a growng number of researh nterests n usng optal wreless for future ndoor ommunaton systems. It offers larger bandwdth, free from spetrum regulaton, ablty to re-use the same frequeny (or waelength) wthn a large room or adjaent rooms, and mmunty to rado frequeny nterferene [-2]. Optal wreless hannel, just lke optal fbre, has pratally unlmted resoures whh an support mage-based and multmeda applatons, and multple aess. To mplement the latter, there are seeral multplexng shemes aalable, namely, tme-dson multple-aess (TDMA), waelength-dson multple-aess (WDMA) and ode-dson multple-aess (CDMA). Compared wth the others, CDMA offers numerous adantages, namely, the tme-frequeny doman s fully utlsed wth no need for tme synhronsaton and frequeny management between eah transmtter and reeer, flexblty n network desgn, and seurty aganst nterepton. Howeer, CDMA offers less transmsson apaty than TDMA [3]. In CDMA, eah user s assgned a length of unque sgnature sequene or address ode, whh s enoded on eah nddual user s nformaton. At the reeer, the nformaton s reoered by orrelatng the nomng CDMA sgnature sequenes wth the same assgned sgnature sequene as n the transmtter [4]. Therefore, the pattern of eah unque sgnature sequene s rual sne t arres the ntended reeer address and helps to aod the nformaton beng oerlapped when arryng out orrelaton at the reeer. Wong et al [5] hae shown that use of a sgnature sequene an mtgates the effet of mult-path dsperson and artfal lght nterferene. There are two man famles of sgnature sequenes, of unpolar (0,), that has been proposed for optal systems. They are () optal orthogonal ode (OOC) [4,6,7] and () rme ode (C)

3 [8,9]. OOC, whh offers unque orrelaton propertes, ahees mproed bt-error-rate (BER) performane ompared wth C [0]. Howeer, the algorthm used for generatng OOC [7] s more omplex ompared wth C [8]. Both famles are desgned for use n a onstant-bt-rate (CBR) system. Zhang has shown that OOC an be used n a arable-bt-rate (VBR) system, but the drawbak s that ts orrelaton propertes are olated thus resultng n an nreased BER [,2]. In order to aod orrelaton propertes olaton, guard slots must be nserted between any two suesse sgnature sequenes pror to transmsson. Howeer, ths wll result n nreased sgnature length, whh n turn results n nreased modulaton bandwdth, and system omplexty. eertheless a new OOC famly, known as strt-ooc [,2], was proposed that s sutable for arable-bt/multrate and een onstant-bt-rate applatons, where the orrelaton propertes are guaranteed presered. Strt-OOC ahees ths wthout the need for bandwdth expanson and nrease n the system omplexty, ompared wth the onentonal OOC. Strt- OOC an also be used n optal wreless CDMA system, sne no synhronsaton s requred between the users. In ths paper, we use strt-ooc n onjunton wth a hybrd CDMA system. In dffuse optal wreless system M-CDMA has been reported, whh offers mproed power effeny ompared wth OOK-CDMA [3,4,5] but lower bt rate enhanement fator (BEF) [5]. A hybrd M-CDMA [6,5] proposed s more power effent offerng hgher BEF, and effent utlsaton of the modulaton bandwdth ompared wth the OOK-CDMA. ulse nteral modulaton (IM) has also been proposed for optal wreless ommunaton systems due to ts bandwdth and power effenes and bult n slot and frame synhronsaton ompared wth M and OOK [7]. In ths paper, a hybrd IM-CDMA employng strt-ooc address ode s proposed for wreless network, whh offers hgher BEF ompared wth both the hybrd M-

4 CDMA and OOK-CDMA shemes. For a large number of users, t also offers lower bt error rate and margnally hgher error rate ompared wth OOK-CDMA and hybrd M-CDMA, respetely. Before ntrodung hybrd IM-CDMA and ts bt rate analyss, a bref dsusson on reported CDMA shemes are presented n the followng seton. 2. CDMA SCHEMES OOK-CDMA was the frst CDMA sheme proposed for fbre opt ommunaton systems of users usng (n, w, a, ) OOC as sgnature sequenes [4,6], where n s the sequene length of w weght and, a and are the auto- and ross-orrelaton onstrants, respetely. Both a and are usually set to one to ahee the optmum BER performane [4]. The sgnature sequene C for the th user an be represented n bnary format as ( a a,..., a ) ( 0,), 2 n, where,2,, and a s the bnary patterns n the j th slot that haraterses C. The number of a s equal j to w. ote that a s always equal to n order to ntalse the start of sgnature sequene. On the other hand, the sequene an be represented n short as a set of odeword gen as: C j, j,..., j }, () { 2 w j where q j denotes the slot poston of the q th bnary pattern a. In ths system, a sgnature j sequene of length n, for the th transmtter, s transmtted to represent the bt, and where an empty sequene, also of length n, to represent the bt 0. As an example, Fg. shows OOK data stream (0), and ts orrespondng OOK-CDMA symbol struture for the frst transmtter. The sgnature sequene C {,2 } s obtaned from a (7, 2,, ) strt-ooc famly and s used throughout ths paper.

5 Hybrd M-CDMA was proposed to enhane the data rate for a gen fxed bt rate R b [6,5]. M It maps M bts of nformaton onto a fxed frame of duraton T f ( 2 + n )T, representng one of 2 M dstnt symbols. In eah symbol, the a of the frst transmtter s sgnature sequene s b loated at a poston orrespondng to the demal alue Sk of M bts data, where M S {0,,2,...,2 } s for the k th symbol. Fgure 2b shows an example of two hybrd M- k CDMA symbols mappng two bts of the nformaton for the frst transmtter. Both OOK-CDMA and hybrd M-CDMA shemes hae fxed symbol length and thus requre frame synhronsaton. When S k s less than ts maxmum alue (2 M -), hybrd M-CDMA frames wll hae a number of unused (empty) tme slot, (( + + M x k 2 n ) ( n S k )) T b followng the sgnature sequene arryng no nformaton. Whereas, hybrd pulse nteral modulaton (IM)-CDMA sheme s a fully asynhronous system offerng self-synhronsaton [7] and mproement n the data rate by elmnatng the unused tme slots x k (see Fg. 2). In the followng seton, hybrd IM-CDMA haratersts, ts BEF mproement and ts mplementaton are dsussed. Fnally, the bt-error rate analyss s presented n seton 3., followed by dsusson and onludng remarks. 3. HYBRID IM-CDMA 3.. THEORY As wth L-M, L-IM maps ndependent, dentally dstrbuted nput bts of the th user nto one of L2 M possble symbols. A symbol s omposed of a pulse of one slot of duraton, T b, followed by m empty slots, where 0 m L-. Howeer, unlke L-M, symbol duraton s

6 arable and determned by the nformaton ontent S k, whh s the alue of m for the k th symbol. In order to aod symbols that hae no slots between adjaent pulses (.e. m0), a guard slot may be added to eah symbol mmedately followng the pulse [7]. Howeer, wth hybrd IM-CDMA sheme employng strt-ooc, the addtonal guard slot s unneessary, and ths ondton has been explaned n [8]. Eah hybrd IM-CDMA symbol frame s omposed of a sgnature sequene C ( a, a2,..., an ) of fxed length nt b loated at the start of the symbol, followed by S k T b number of empty nformaton slots. Eah enoded symbol has arable duraton of ( n + ) T b. Fgure 2 shows an enoded hybrd IM-CDMA symbol frames format mappng 2 bts of the nformaton. S k Assumng that symbols transmtted by eah user s equal lkely, then eah aerage hybrd IM- CDMA data rate s R 2MR /(2n + L ), and ts BEF normalsed to OOK and M are pm b BEFpm ook 2nM /(2n + L ), and BEFpm ppm 2( n + L ) /(2n + L ), respetely. For a / / gen alue of n and for M 8 the BEF pm/ook M and BEF pm/ppm. Howeer, for 8 < M < 0 the BEF pm/ook < M, and dereasng rapdly for M >0, whereas, BEF pm/ppm mproes by about 5% for M >8. Inreasng n wll nrease further the BEF, by about 0-5%, for M > 8. For hybrd IM-CDMA the optmum BEF s at 2 M n / 2, see [8]. Suppose that a system s omposed of pars of transmtter and reeer (.e. one user) eah transmttng ndependently and asynhronously. Sne eah par s dental, therefore only the th

7 par s shown n Fg. 3a. The only dfferene between pars s the assgned sgnature sequenes, whh are obtaned from a (n, w, a, ) S-OOC famly. As shown n Fg. 3a, an M bts data s frst onerted nto a IM symbol hang a arable length of ( n + S T k ) b. A pulse, g(t) of duraton T b, s loated at the start of eah symbol to ndate both the start of the symbol and the frst pulse, a, of the sgnature sequene. The CDMA enoder, omposed of tapped delay lnes, then spreads out the rest of C,.e. a 2, a 3, a n, wth referene to IM symbol stream and hybrd IM-CDMA symbol stream are gen by: a n eah frame. The nfnte d pm ( t τ pm) g t τ k pm + nk + k l Sl Tb, (2) e pm n ( t τ pm ) a j g t τ k j pm jt b nk + k l Sl Tb, (3) where l denotes the (k-) th symbol and 0 τ pm < (2 M + n )T b s the delay. The reeer blok dagram s shown n Fg. 3b, where the reeed hybrd IM-CDMA sgnals, r r e pm, s frst orrelated wth the same sgnature sequene C as that of the th transmtter. The orrelator generates an autoorrelaton waeform hang a domnant peak equal to the ode weght of C when t reees the rght sequene (.e. C n e ). Howeer, when t reees dfferent ode sequene C y, where y,2,, and y, t generates a ross-orrelaton waeform. The ross-orrelaton onstrant,, s equal to the number of ondene of 's n all tmeshfted sequene of the C and C y. The output at the orrelator s gen by:

8 h ( t) w n j r k wg( t ) + I a e j g t τ r pm ( t pm r ( t τ ( n ) T ) + I pm ( t 2 ) jt ) b b + nk + k l Sl Tb + I ( t), (4) where t {tme slots where a sgnal pulse ours} and, - < t 2 < and t 2 t. The frst term n (4) represents the IM symbol stream wth an offset of (n-)t b whh s due to orrelaton proess, and the remanng two terms represent the nterferng sgnal due to self-nterferene and other smultaneous users nterferene, whh s gen by: I n n y y ( t) a jepm ( t τ pm jtb ) + a jepm ( t τ pm jtb ) wg( t ) j j y. (5) The mnmum sgnal ampltude s gen by wg( t ) and t may be larger than ths due to the present of I ( ) t,.e. the OMAI that falls at the same tme slot t. The output of the orrelator s then passed through a mathed flter and a sampler. The sampled alues, taken at t T b, are then passed through a threshold detetor, whh s set at the optmum leel w-. The IM symbol stream wll then be extrated from the nterferene, ( t ) I 2. At detetng a pulse at the start of the k th symbol, the IM demodulator wll gnores (n-)t b tme slots, and then start ountng the number of empty slots there after untl the next pulse from the k+ th symbol s deteted (refer to Fg. 4a). The ount number, whh orresponds to the nformaton, S k, s then onerted nto the desred M bt data sequene.

9 3.2. ROBABILITY OF BIT ERROR RATE For the BER analyss, we hae made the followng assumptons: () eah of users s asynhronously transmttng the k th symbol, () the man soure of nterferene s the sgnal reeed from the others users,, that are transmttng smultaneously, better known as the optal multple aess nterferene (OMAI), () the transmtter and reeer s synhronsed at hp (or slot) leel T b, () the hannel s deal and non-dsperse and the normalzed mpulse response s a delta funton δ(t), () nose due to the optal reeer and nterferene from fluoresent lght are assumed to be neglgble ompared wth the OMAI, and therefore are M gnored, and () the nformaton S k s onsdered up to 2 n / 2. Wth referene to Fg. 4b, a false alarm pulse, due to OMAI, ourrng wthn the (n-)t b duraton, whh s preously ouped by the sgnature sequene, wll result n no error beng deteted at all, one of the unque features of ths sheme. Ths s beause the demodulator on detetng the header pulse wll gnore all the remanng (n-)t b slots, as outlned n seton 3. Howeer, an error wll our only f a false alarm pulse falls wthn the nformaton band S k. The affet would be generaton of two new symbols of shorter length for the k th symbol and longer length for the k+ th symbol, whh the IM demodulator wll onert them bak nto two new data bts. In the example shown, the nformaton at the output of CDMA deoder wth no false alarm pulse wll be demodulated as S 2 and S 3 (referred to the orret demod k k + shown as [.]). Wth a false alarm pulse ourrng n the k th symbol, the nformaton wll be demodulated as S 0 and S 5 (referred to the wrong demod ). Hene, n hybrd IM- k k + CDMA system, an error n one symbol wll affet two symbols, a haraterst, whh does not exst n the hybrd M-CDMA due to ts fxed frame struture. As seen from (5), at the CDMA

10 deoder, eah reeng sgnal r e IM s orrelated wth ts desred sgnature sequene. Sne (n, w,, ) strt-ooc s desgned suh that other user sgnature has only one bt mathed to the desred sgnature [], then the probablty of nterferene, also known as the ross-orrelaton onstrants, due to only one other user s gen by: 2w 2 2n + L pm. (6) Whereas the probablty of self-nterferene, also known as the auto-orrelaton onstrants a, due to the target user e pm s gen by: w( w ) a. n (7) M Equ. 7 s true only for 2 n / 2, s also equally applable to hybrd M-CDMA. Therefore, there are two probabltes that false alarm pulse/s may our due to () selfnterferene and OMAI, and () OMAI only, as outlned below SELF-ITERFERECE AD OMAI The probablty that a sgnal leel due to both OMAI and the self-nterferene wll exeed the threshold s gen by: self γ a th ( ) pm, (8) where the threshold leel th w-, and γ s the number of nformaton slots. In addton, t s possble that more than one false alarm pulse wll our n one or more frames, whh may affet any two onseute symbols. Sne we hae assumed that symbols transmtted are equal lkely, then (8) may be wrtten as:

11 ( ) L pm pm a M self th n γ γ γ. (9) 3.4. OLY OMAI The probablty that a sgnal leel, n the presene of OMAI, wll exeed the threshold leel s gen by: ( ) ( ) L pm pm a M OMAI th n γ γ γ. (0) The probablty of false alarm error s just the summatons of (9) and (0). For hybrd IM- CDMA t s gen by OMAI self pm fe +. Thus, ( ) ( ) + + γ γ γ pm pm a pm pm L M a pm fe th th n 0 ) ) (( 2. () For omparson, the probablty of false alarm for the hybrd M-CDMA s also gen as: ( ) ( ) + + γ γ ppm ppm a ppm ppm L M a ppm fe th th L n 0 ) ) (( 2, (2) where 2 + L n w ppm. (3) The probablty of bt error rate s obtaned usng the followng expresson [9]: ( ) ( ) fe b L L 2. (4)

12 Usng () and (4), the BER for hybrd IM-CDMA s alulated and the results ersus number of user for dfferent alues of w, and M 5 are shown n Fg. 5. In addton, for omparson the results are shown for hybrd M-CDMA and OOK-CDMA. All three shemes dsplay mproed BER performane as w nreases. For a gen alue of w, the BER for OOK-CDMA nreases exponentally as nreases. Whereas n hybrd IM-CDMA and M-CDMA the BER nreases as nreases, reahng a peak alue and then dereasng as nreases further. For hybrd IM-CDMA, the maxmum BER s reorded at 30 for w 9, whh are margnally lower than both the M and OOK. Howeer, at a muh larger alues of t dsplays better performane than OOK. Fg. 8 shows the BER ersus for dfferent alues of M. The BER performane mproes as M dereases. At > 20 both M and IM dsplay better performane than OOK. For BER 0-9, the number users for IM and M s less than 0, whereas for OOK t s about COCLUSIOS A hybrd IM-CDMA modulaton sheme for optal wreless ommunaton systems has been presented. We hae shown that the proposed sheme an nrease the system transmsson rate beyond the lmt due to a fxed bt rate ondton, and requres no frame synhronsaton. Analyss for BER takng nto aount the effets of self-nterferene for both hybrd systems were presented and the results were ompared wth hybrd M-CDMA and OOK-CDMA. Hybrd IM-CDMA dsplays a BER performane smlar to hybrd M-CDMA and only margnally hgher than OOK-CDMA at a low number of users. Howeer, at hgh number users hybrd IM-CDMA outperforms OOK-CDMA. Hybrd IM-CDMA s an alternate anddate

13 for a fully asynhronous multple aess system whh prodes hgher transmsson rate, and low BER. REFERECES A.M. Street,.. Starnou, D.C. O Bren and D.J. Edwards, Indoor optal wreless systems a reew, Optal and Quantum Eletrons, ol. 29, no. 3, (997), J.M. Khan and J.R. Barry, Wreless nfrared ommunatons, roeedng of the IEEE, Vol. 85, o.2, (997), H.M.H. Shalaby, A performane analyss of optal oerlappng M-CDMA ommunaton systems, IEEE. J. of Lghtwae Teh., Vol. 7, o.3, (999), J.A. Saleh, Code dson multple-aess tehnques n optal fber networks art I: fundamental prnples, IEEE Trans. On Comm., Vol. 37, o.8, (989), K.K. Wong, T.O Farrell and M. Katweerasakul, The performane of optal wreless OOK, 2-M and spread spetrum under the effets of multpath dsperson and artfal lght Interferene, Intern. J. of Communaton Systems, Vol. 3, o.7-8, (2000), J.A. Saleh, and C.A. Brakett, Code dson multple-aess tehnques n optal fber networks art II: systems performane analyss, IEEE Trans. On Comm., Vol. 37, (989), F.R.K. Chung, J.A. Saleh and Vtor K. We, Optal orthogonal odes: desgn, analyss, and applatons, IEEE Trans. On Informaton Theory, Vol. 35, (989), A.A. Shaar and.a. Daes, rme sequenes: quas-optmal sequenes for hannel ode dson multplexng, Eletrons Letters, Vol. 9, (983),

14 9 A.S. Holmes and R.R.A. Syms, All-optal CDMA usng quas-prme odes, IEEE J. of Lghtwae Teh., Vol. 0, (992), S.W. Lee and D.H. Green, erformane analyss of optal orthogonal odes n CDMA LAs, IEE ro. Commun., Vol. 45, o. 4, (998), J.G. Zhang, Flexble optal fber CDMA networks usng strt optal orthogonal odes for multmeda broadastng and dstrbuton applatons, IEEE Trans. On Broadastng, Vol. 45, o., (999), J.G. Zhang, Desgn of a speal famly of optal CDMA address odes for fully asynhronous data ommunatons, IEEE Trans. On Commun., Vol. 47, o. 7, (999), O. Tomoak, S. Iwao and M. Shnsaku, Effets of Hard-Lmter and Error Correton Codng on erformane of Dret-Deteton Optal CDMA Systems wth M Sgnalng, IEICE Trans. Fundamentals, Vol. E78-A, o. 9, (995), S.S. Hwang, C. ark and J.H. Lee, Asynhronous multrate optal wreless M-CDMA n an ndoor non-dreted dffuse hannel, Eletrons Letters, Vol. 33, o. 8, (997), H.H. Chan, J.M.H. Elmrghan and R.A. Cryan, Optal wreless M CDMA networks employng OC and C sgnature odes, J. of Optal Commun., Vol. 20, o. 3, (999), J.M.H. Elmrghan and R.A. Cryan, Indoor Infrared Wreless etworks Utlsng M CDMA, Sngapore ICCS Conferene roeedngs, Vol., (994), Z. Ghassemlooy, A.R. Hayes,.L. Seed, and E.D. Kaluarahh, Dgtal pulse nteral modulaton for optal ommunatons, IEEE Commun. Mag., Vol. 35, o.2, (998),

15 8 C.K.See, Z. Ghassemlooy and J.M. Holdng, Hybrd IM-CDMA for Optal Wreless etworks, GET 2000, st Annual ostgraduate Symposum on the Conergene of Teleommunatons, etworkng and Broadastng, Shool of Computng and Mathematal Senes, John Moores Unersty, Lerpool, (2000), R.M. Gaglard and S. Karp, Optal Communatons, 2 nd edton, Wley, ew York, (995).

16 Lst of fgures Fg. : Fg. 2: Frame sequene for: (a) OOK, and (b) OOK-CDMA. Frame formats for M 2 bts: (a) OOK-CDMA, (b) hybrd M-CDMA, and () hybrd IM-CDMA. Fg. 3: Fg. 4: Hybrd IM-CDMA system blok dagram, (a) transmtter, and (b) reeer. Output of CDMA deoder for k th and k+ th symbols. (a) error free, and (b) wth false alarm. [.] represents the demodulated data at output IM demodulator. Fg. 5: Fg. 6: BER ersus number user for arous w and M5 bts. BER ersus number user for arous M bts and w9.

17 (a) T b (b) T b 7 T b Fg. (a) T b 7 T b (b) 7 T b x k () 7 T b Fg. 2

18 OOK M IM Enoder d IM CDMA enoder IM-CDMA e IM Optal Tx Sgnature (a) Optal Rx e IM Correlator h (t) Mathed flter ttb Threshold detetor IM deoder OOK M bts OMAI Sgnature CDMA deoder (b) Fg. 3

19 Symbol Symbol 2 S k S k+ (n-)t b (n-)t b 3Tb 2Tb (a) Wrong demod. [0T b ] False pulse (n -)T b 6 T b [5T b ] Corret demod. 6 T b (n -)T b [2T b ] [3T b ] (b) Fg. 4

20 w6 BER w7 w w9 IM M - - OOK Fg IM 0-7 BER M IM --- M - OOK lnes M2 M3 M4 OOK ο M5 - CDM 0 A Fg. 6