FOR upstream communication in a Passive Optical Network

Transcription

1 Comparison of OTDMA and Synchronous OCDMA ith Optical and Electrical Decoding Robert Fritsch, Joachim Speidel Institut für Nachrichtenübertragung, Universität Stuttgart, Pfaffenaldring 47, D-7469 Stuttgart Abstract For upstream digital communication in a Passive Optical Netork PON three synchronous multiple access schemes are investigated: Optical TDMA OTDMA and optical CDMA OCDMA ith Walsh Hadamard Codes and Perfect Difference Codes We propose an improved scheme for OCDMA hich employs dedicated signature sequences for bit and bit alloing for differential decoding at the receiver ith minimum multi user interference MUI in the optical signal The performance of these methods in the presence of additive hite Gaussian noise is compared ith respect to bit error probability and number of users Both, optical and electrical decoders are considered As a result, OTDMA is superior to the other solutions ith optical decoders This also holds, if electrical decoders are used Our proposed Walsh Hadamard Code outperforms the Perfect Difference Code in case of a small number of transmitters Keyords OCDMA, OTDMA, Performance Analysis I INTRODUCTION FOR upstream communication in a Passive Optical Netork PON in Fig the access can be done by Time Division Multiple Access TDMA, Code Division Multiple Access CDMA or Wavelength Division Multiple Access WDMA In case of CDMA synchronous or asynchronous transmission is possible [], [], [3] In this paper e focus on bit synchronous CDMA In the folloing the optical netork units ONU are called transmitter tx Each bit a ν,k {, } of transmitter ν at time k is spread into a chip pattern c ν,i = c ν,i,, c ν,i,,, c ν,i,n T, ith i = a ν,k {, }, c ν,i,m {, }, ν and m =,,, n The chip pattern is often called signature sequence or CDMA codeord n is the number of transmitters hich is in this paper equal to the number of chips of the CDMA codeords n = T b is also called spreading factor, here T b and is the bit and chip duration, resp b ν t is the output of tx ν The received signal at the input of the head end is ut For simplicity reasons e assume, that the fiber connection from the output of tx ν to the input of the head end is characterized only by the attenuation PON,ν So, dispersion effects are assumed to be a,k a ν,k a n,k ONU tx tx ν tx n b t b ν t b n t PON ut head end rx ut rx ν rx n â,k â ν,k â n,k Fig Principal communication system tx transmitter, rx receiver properly compensated It is important to note, that the poer of each transmitter signal b ν t ν =,,, n is adjusted such that it arrives ith the same poer P n at the head end This means, that the near-far-problem [4] is solved by compensation of PON,ν individually for each tx ν The average poer of ut at the input of the head end then is n P n = P The optical poer signal ut is split into n parts, hich provide the same input signal ut for each receiver rx ν ν =,,, n In Fig, = n holds The receiver detects the input signal and outputs an estimate â ν,k of the transmitted bit sequence a ν,k O/E-conversion is done in each rx The principal structure of the νth transmitter is depicted in Fig and consists of to paths, hich spread bit and bit into different codeords to allo for differential decoding at the receiver This is done to overcome the problem, that to the codeords for bit and bit no negative impulses can be allocated to, as for electrical CDMA, because the optical poer signal can only be positive In the upper path bits a ν,k = are coded ith the codeord c ν, Therefore the value a ν,k is mapped to an impulse g ν, t kt b, if a ν,k = At the loer path bits a ν,k = are coded ith the codeord c ν, Therefore bit a ν,k is negated to a ν,k = a ν,k at the beginning of the loer path and mapped to the impulse g ν, t kt b Thus, the optical output poer signal of the νth transmitter is b ν t = PON,νP g ν,aν,k t kt b Mean output poer of each tx depends on the number of -chips ithin a spreading code As e ould like to compare different codes on a fair basis, a factor hich depends on the selected code ensures the same mean transmit poer for all codes The bit impulses g ν,i t, i =, consist of delayed chip impulses gt For simplicity, gt is a rectangular impulse ith gt = for < t < and gt = outside a ν,k g ν,i t = a ν,k c ν,i,j gt j 3 j= g ν,t gν,t poer control + b ν t PON,νP Fig Principal structure of transmitter tx ν

2 Thus, the input signal ut of the head end is ut = P µ= j= c µ,aµ,k,j gtj kt b 4 Note, if all tx in Fig transmit bits a ν,k ith equal probability, ut exhibits the mean poer P This assumption is made throughout this paper In Fig 3 the principal structure of the νth receiver is shon As mentioned earlier, is the attenuation of the splitter at the beginning of the head end The differential optical receiver ν splits its optical input signal ut into to branches Thus, an additional attenuation is introduced The total attenuation is = Obviously, rx ν is a correlation receiver Its structure is very convenient as a mathematical model Normally, it cannot be implemented directly ith optical components, because multiplication is not very feasible Hoever, as is ell knon from theory, a correlation receiver can be replaced by an equivalent matched filter receiver Such a solution ill be given later in Fig 5 The signal d ν t at the input of the sampler is d ν t = ξ=tt b ξ=tt b = P S S S S uξ S S uξ ξ=tt µ= j= b g ν, ξ kt b dξ g ν, ξ kt b dξ c µ,aµ,k,jc ν,,j c ν,,j g ξ j kt b dξ S S is the photo sensitivity of the avalanche photo diode APD see later The signal at the output of the sampler at discrete time t = k + T b is d ν,k = P S S µ= j= c µ,aµ,k,jc ν,,j c ν,,j } {{ } = c T µ,a c µ,k ν, c ν, g t dt } {{ } = 5 For optical CDMA, the coder is often implemented as an FIR filter ith the coefficient vector c ν,i, eg by optical delay lines This also holds for the correlation at the receiver hich is often implemented ith optical matched FIR filter ith coefficients, hich are arranged in visa versa order [5] Aim of this ork is to investigate the bit error probability as a function of the signal-to-noise ratio for OTDMA and OCDMA using different codes Both, optical and electrical decoders are compared II CODES In this paper e consider three codes listed in Table I: The TDM Code TDMC, as a special case of a CDMA code, the ut g ν, tkt b g ν, tkt b tt b tt b O O d ν t + + Fig 3 Model of receiver ν TABLE I t=k+t b CODES FOR SYNCHRONOUS OCDMA d ν,k TDM Code Walsh Hadamard Code Perf Diff Code n ν c ν, n ν c ν, c ν, n ν c ν, â ν, k Walsh Hadamard Code WHC [6] and the Perfect Difference Code PDC [7] The length n of the codeords and the number n of transmitters per code is equal For simplicity e assume that all users send bit and bit ith the same a priori probability A TDM Code TDMC Synchronous CDMA includes TDMA as a special case In this case e call the signature sequence c ν,i TDM Code As the coder in Fig operates in the optical domain, this multiplexing technique can also be refered to as Optical TDM OTDM TDMC has the property, that only the chip c ν,,ν in the codeord c ν, is equal to and all other chips are In terms of OTDM, the position of the chip defines the time slot of the transmitter Thus, the received signal d ν,k contains no multi user interference MUI, because bit is encoded ith c ν, =, ν =,,, n and c ν, c µ, c T ν, c µ, =, ν µ, ν, µ =,,, n For TDMC = and e get from 5 d ν,k = P S S B Walsh Hadamard Code WHC c T ν,a ν,k c ν, = P S S a ν,k 6 WHC in Tab I shos the property, that c ν, is the inverse of c ν, With = n e obtain from 5 d ν,k = P { S S n n + a,k n ν= n n + a ν,k n ν=,3,,n

3 = P S S a ν,k P { S S n + P S S ν= ν=,,n 7 TABLE II PARAMETERS OF O/E CONVERTER AT RECEIVER Obviously, d ν,k does not contain bits a µ,k of other users µ ν, so it is free of MUI, just a constant level is added This is surprising on the first glance, because ith some exceptions the c ν,i are not orthogonal The reason hy no MUI is present lies in the differential structure of the receiver, hich e propose in Fig 3 As a consequence, the resulting c ν, c ν,, ν =, 3,, n are bipolar versions of Walsh Hadamard codeords hich are orthogonal to c µ,i, i =, ; µ =,,, n; µ ν Only c, c, = c, remains unipolar But this does not matter, because c T µ,i c, = n = const, µ =, 3,, n, independent of i Thus, only the decision threshold has to be adjusted properly at the rx in Fig 3 The eye opening PSS is the same as for the system ith TDMC C Perfect Difference Code PDC PDC are discussed in detail in [7] Hoever, in [7] the poer at the input of each of the n receivers in Fig is kept constant Recall, that in our consideration, the input poer at the head end is kept constant, So, e take the poer splitters of the head end into account, to provide a fair comparison of the different proposals Thus, the results differ in this respect Furthermore, is given by 4n 3 + = 8 4 Without details of the calculation, e obtain ith = and d ν,k = P S S 4n 3 3 4n = + a ν,k 9 r 4n is an additional attenuation of the upper path and r is a parameter of the loer path of the receiver, [7] III BIT ERROR PROBABILITY WITH OPTICAL RECEIVER For O/E conversion an electronic receiver ith Avalanche Photodiode APD shall be used Transmitted bits and have equal a priori probabilities The output d ν,k of the receiver in Fig 3 is no considered to be corrupted by additive noise of the APD and thermal noise of the load resistor R L The total noise is assumed to be hite gaussian ith zero mean As the target of our investigation is the impact of noise on the bit error probability, fiber optic transmission is considered to be linear and ith no intersymbol interference The poer density spectrum PDS of the noise is assumed to be S o f = e I D + ηλe hc p ν,k M F M from APD + k BT r R L from R L The parameters are listed in Table II p ν,k is the received optical poer We model the optical receiver as an ideal lo pass filter Name Symbol Value Wavelength of the light source λ 3 nm APD quantum efficiency η 6 APD gain M APD leakage current I D na chip duration ns Receiver noise temperature T r 35 K Receiver load resistor R L Ω Planck s constant h Js Boltzmann s constant k B J K Electron charge e As speed of light c m s Excess noise factor F M M 3 photo sensitivity S S M ηλe hc ith the cut-off frequency f c = and gain Then e get the variance of the additive gaussian noise σ = f c f c S o f df = A TDM Codes e I D + ηλe hc p ν,km F M + 4k BT r R L The loer path of the receiver in Fig 3 can be dropped for TDMC, because c µ, =, µ =,,, n From 6 the poer signal at the input of the APD in the upper path is p ν,k = P a ν,k 3 Thus, if e replace p ν,k in by 3 e get the noise variance σ a ν,k = e I D + ηλe hc P a ν,k M F M + 4k BT r 4 R L hich depends on the bits a ν,k A straightforard calculation yields the mean bit error probability of each user P b = [ Q PS S σ E ] E + Q 5 σ ith the optimal decision threshold E for minimum P b E = and σ σ the Q-function [ PS S ] + σ σ σ ln σ σ σ P S S σ 6 Q = e u du 7 π

4 B Walsh-Hadamard Codes Both paths of the receiver in Fig 3 are in use Thus, there are to statistically independent noise sources As is ell knon, their poer density spectra are added by the summing node in Fig 3 First, e have to calculate the input poer signals of the to APDs and then the PDS For the upper u branch in Fig 3 e get p u ν,k = P n n n }{{ } from user µ=,,n from user µ=,,n µ ν + na,k from user n n + n }{{ 4 } a,k from user S o u f = e I D + ηλe hc pu ν,k For the loer l branch e obtain p l ν,k = P n + n a ν,k from user ν ν= ν n 8 M F M 9 ν= n n + n }{{ 4 } a,k from user from µ=,,n user µ ν S o l f = e I D + ηλe hc pl ν,k + n a ν,k from userν ν n M F M Summing up the poer density spectra of the noise currents of the to APDs, e obtain S APDs o f=e I D+ ηλe hc P n +a,k M F M p u ν,k +pl ν,k As can be seen, depends only on the bits a,k of user We no assume, that e have only one amplifier for both O/Econverters in Fig 3, hich also implements the summation and hich is modelled as ideal lo pass filter ith gain, cut-off frequency f c = and ith resistor load R L Hence S RL o = k BT r R L 3 is the poer density spectrum of the third noise source We get the total noise variance of each receiver ν =,,, n σ a,k = f c f c [ S APDs o ] f + S o RL f df = e [ ηλe I D +P hc a,k+ n ] M F M + 4k BT r R L 4 Thus, the mean bit error probability of each receiver of an OCDMA system ith WHC is [ P b = PS S E ] E Q + Q 5 σ σ ith the optimal decision threshold E for minimum P b according to 6 ith σ and σ given in 4 C Perfect Difference Codes Similar to the calculation of P b for WHC e obtain ithout details the poer density spectrum S o APDs f = em F M I D + ηλe hc here P I k = 8I k + 4n 3 + 6a ν,k r + 4n a µ,k 7 µ= µ ν is the number of other users µ ν sending bit This leads to the noise variance σa ν,k I k = 4k BT r + e [ M F M I D + ηλe R L hc P 8I k + 4n 3 + 6a ν,k r + 4n 3 + ] 8 The bit error probability of each receiver of an OCDMA system ith PDC ith n users is n n P S S 4n3 n P b = Q E 3 4n3+ i σ i= i ] E +Q 9 σ i IV BIT ERROR PROBABILITY WITH ELECTRICAL RECEIVER If the head end converts the optical signal at the input into an electrical signal, no optical splitters are necessary If an A/D converter follos the O/E converter and the remaining functions are done digitally, the attenuation = = Thus for TDMC and WHC the results above can be used ith = Only in case of PDC e assume a different receiver ith the principal structure depicted in Fig 4 As c ν, is equal to the inverted codeord c ν,, g ν, is given ith 3 by g ν, t = c ν,,j g t j 3 j= As can be seen from Tab I, each codeord c ν, of a PDC consists of -chips and c T µ, c ν, = ith µ ν holds is given in 8 Thus, the -chip positions of the considered receiver ν are disturbed by I k and the -chip positions by

5 S Sut g ν,tkt b g ν,tkt b tt b tt b d ν t + + t=k+t b Fig 4 principal structure of receiver ν for PDC d ν,k â ν, k I k Hence the signal at the output of the sampler at discrete time t = k + T b in Fig 4 is d ν,k = P S S a ν,k + I k upper path I k loer path = P S S a ν,k The eye opening is PSS and is the same as for the system ith TDMC With the noise variance σa ν,k I k = 4k BT r R L P + e [ M F M a ν,k + I k I D + ηλe hc ] the formulas 8, 7 and 9 of the optical case can be used V COMPARISON 3 P is the average poer at the input of the head end For comparison, optical receivers ith reduced attenuation are used In Fig 5 the head end of a synchronous OCDMA system ith WHC for 4 users is shon It can be seen, this head end has got the attenuation = = 8 In the folloing e assume the attenuations listed in Tab III of the head end The values of for TDMC are theoretical, because a TDMA system TABLE III ASSUMED ATTENUATIONS OF THE HEAD END TDM Code Walsh Hadamard Code Perfect Difference Code n = n n n normally ill be implemented ith an electrial receiver ith = For PDC a combination of optical and electrical head end ith 4n3+ APDs is also possible, because there are only 4n3+ different receiver filters The other filters are only delayed versions In all diagrams the duration of one chip is the same Thus, the bit rate of each user n decreases for increasing n The overall bitrate n n of all n users together keeps constant All curves are calculated ith the optimum decision thresholds eg in 6 In case of PDC the parameter r is chosen such, that the bit error probability P b is minimized In Fig 6 the optimum values of r versus the poer P at the input of the head end are plotted The optimum r increases ith increasing n Fig 7 shos the bit error probability versus the poer P at the input of the head end for TDMC and WHC The curve for TDMC moves to the right by 3 if n is doubled This is because of the attenuation of the head end Tab III With WHC P b increases much more for increasing n Thus, optical receivers ith attenuations listed in Tab III are not feasible for ut O + O + O + O + O + + O O + O + + gt gt gt gt â,k â 3,k â 4,k â,k r n = 83 n = 33 n = 9 n = 73 n = 57 n = 3 n = n = 3 n = 7 n = P Fig 5 Head end ith reduced attenuation for synchronous OCDMA ith Walsh Hadamard Code for 4 users Fig 6 Optimum parameter r versus poer P at head end input for various numbers n of transmitter

6 P b TDMC WHC P n= n= n=4 n= n=4 n=8 n=56 n=8 n=64 Fig 7 Bit Error Probability P b of TDM Codes and Walsh Hadamard Codes WHC versus poer P at head end input for various numbers n of transmitter and optical decoding systems ith more than n = 8 subscribers Fig 8 shos P b versus the poer P at the input of the head end for TDMC and PDC Note, that n differs in principle for PDC and WHC, as can be seen from Tab I Obviously, to achieve P b, PDC requires more than about input poer P compared to TDMC for n < 3 Hoever, for n 3, PDC outperforms WHC As can be seen from Tab III, the major reason is, that the attenuation in the head end increases sloer for PDC than for WHC ith increasing n Hoever, as can be seen from Figs 7 and 8 the performance of both, PDC and WHC ith optical receivers having attenuations listed in Tab III, is much orse compared to TDMC The attenuation of the head end given in Tab III turns out to be the crucial impact on the performance Thus, in the folloing a head end ith a single APD at the input, folloed by an A/D conversion of the total electrical signal at chip rate and a subsequent digital processing is investigated Of course, due to the high bandidth of the electrical signal, this is a technological challenge Fig 9 shos the bit error probability P b versus the poer P at the input of the head end for TDMC, WHC and PDC With such a receiver, P b for TDMC is independent of the number n of transmitters The curve is identical ith the optical receiver in Fig 7 and Fig 8 for n = TDMC again outperforms the other synchronous OCDMA codes As can be seen, WHC is still superior to PDC for a small number of transmitters n 4 With the electrical receiver a reasonable P b is reached ith a much smaller input poer P VI CONCLUSIONS We have investigated the performance of three synchronous multiplexing schemes hich can make access to a Passive Optical Netork PON: Optical TDMA OTDMA and optical CDMA OCDMA ith Walsh Hadamard Codes and Perfect Difference Codes In optical CDMA e are faced ith the fact, that optical poer signals are alays positive, and thus the orthogonality relation cannot be fulfilled precisely To mitigate n=3 n=6 P b TDMC PDC P n= n=3 n=7 n=3 n=3 n=7 n=3 n=83 n=33 Fig 8 Bit Error Probability P b of TDM Codes and Perfect Difference Codes PDC versus poer P at head end input for various numbers n of transmitter and optical decoding P b n=3 n=7 n=3 n= TDMC WHC PDC n=3 n=57 n=73 n=9 n=33 n= P n= n= n=4 Fig 9 Bit Error Probability P b of TDMC, WHC and PDC versus poer P at head end input for various numbers n of transmitter and electrical decoding this effect, e propose special codes for bit and bit hich allo for differential decoding at the optical receiver As a result, multi user interference MUI is reduced to zero The different codes have been compared ith respect to bit error probability and the number of transmitters alloed, in the presence of additive hite Gaussian noise Both, electrical and optical decoders have been studied We have shon, that TDMA, either optical or electrical, performs best This also holds, if electrical decoders are used by the other schemes Our proposed Walsh Hadamard Code outperforms the Perfect Difference Code in case of a small number of transmitters up to about 8 The significant performance gap beteen electrical and optical decoding results from the fact, that passive poer splitters are used for optical decoders, hich reduce the available poer at each decoder Thus, the signal to noise ratio is loered and consequently the bit error probability is increased This ill change, if the poer loss due to the splitters is compensated by an optical amplifier at the n= n=9 n=73 n=57 n=3

7 expense of an increased noise level We have considered exclusively synchronous access schemes Hoever, it should be noted finally, that asynchronous OCDMA shos advantages, if additional transmitters have to be added to a given access netork ithout the execution of complicated ranging procedures VII ACKNOWLEDGEMENT Parts of this study ere carried out ithin the FMS-Project Forschungsverbund Medientechnik Südest The financing by the ministeries of Baden-Württemberg and Rheinland-Pfalz is greatfully acknoledged REFERENCES [] Fan R K, Chung, Jaad A Salehi, Victor K Wei, Optical Orthogonal Codes: Design Analysis, and Applications, IEEE Transactions on Information Theory, vol 35, no 3, May 989 [] Jaad A Salehi, Code Division Multiple-Access Techniques in Optical Fiber Netorks - Part I: Fundamental Principles, IEEE Transactions on Communications, vol 37, pp , August 989 [3] Jaad A Salehi, Charles A Brackett, Code Division Multiple-Access Techniques in Optical Fiber Netorks - Part II: Systems Performance Analysis, IEEE Transactions on Communications, vol 37, pp , August 989 [4] AF Mohammed, Near-far problem in direct-sequence code-division multiple-access systems, Seventh IEEE European Conference on Mobile and Personal Communications, pp 5-54, Dec 993 [5] Roman Dischler, FMS Projekt III3: Digitale Übertragungsverfahren in hybriden Teilnehmerzugangsnetzen; Arbeitsbereich: Optisches CDMA als Mehrfachzugriffsverfahren für Rückkanäle in optischen Verteilnetzen im Teilnehmerzugangsbereich, Berichte/Projekt III3/fms33-pdf; 3 März 998 [6] John G Proakis, Digital Communications, 4th ed, pp [7] Chi-Shun Weng, Jingshon Wu, Perfect Difference Codes for Synchronous Fiber-Optic CDMA Communication Systems, Journal of Lightave Technology, vol 9, no, pp 86-94, February