Wavelength-Time Coding for Ultra Dense Wavelength Multiplexing

Transcription

1 Wavelength-Time Coding for Ultra Dene Wavelength Multiplexing Frank Schaich and Joachim Speidel Intitut für Nachrichtenübertragung, Univerität Stuttgart Pfaffenwaldring 7, D-759 Stuttgart Abtract By reducing channel pacing in dene wavelength diviion multiplexing (U-DWDM), the total bitrate can be ignificantly increaed. To cope with the reulting trong interchannel interference (ICI), a novel coding cheme i preented, which encode and decode in both time and wavelength direction (wavelength-time coding, C). The cheme i decribed in quite ome detail. Performance i compared to conventional U-DWDM with trict optical filtering to prevent ICI, however to the expene of increaed interymbol interference (ISI). 1 Introduction Due to the riing demand for broadband internet acce, pectral efficiency in bit Hz of the optical network ha to be increaed. Several cheme to reach thi goal are under invetigation in today reearch. Multilevel modulation uch a DQPSK [1], ASK-DPSK [], ASK- DQPSK [3], -DPSK [] can be ued to tranmit more than one bit per ymbol. The lower ymbol rate lead to maller pectra, which can be placed more denely without increaing the pectral overlap. A way to double pectral efficiency i to ue orthogonal polarization for data tranmiion [5]. Alo of great interet in today reearch activitie are more ophiticated coding cheme uch a LDPC code [] and turbo cheme [7] to mitigate channel ditortion. Within thi paper we introduce a novel coding cheme, which reduce the impact of ICI by jointly encoding the data of adjacent wavelength carrier. A a conequence, the channel pacing can be reduced without loing ignificant robutne againt channel ditortion. Thi cheme encode both in time and wavelength direction and i therefore called wavelength-time coding (C). In ection we invetigate the ICI and motivate the ue of C, which i decribed in more detail in ection 3. The performance i preented in ection. Section 5 conclude the paper. Interchannel Interference (ICI) When reducing channel pacing for a given bitrate per channel to increae pectral efficiency in U-DWDM ytem, ICI become more and more ignificant. Fig.1 how the eye-diagram after photo detection, in cae of a ingle wavelength ytem (a) and U-DWDM with a channel pacing of 5 GHz (b) and GHz (c). The bit rate i R b = 1 T b =.7 Gbit and the 3 dbbandwidth of the demultiplexer filter i chooen to GHz. Obviouly, the neigbouring channel caue a trong widening of the ignal tranition and the eye tend to cloe. v (i) x t/t b (a) v (i) x 1 3 v (i) x t/t b. 1 (c)... t/t b. 1 (b) Fig. 1. Eye-diagram after the photo diode. Single wavelength ytem (a), U-DWDM ytem with channel pacing 5 GHz (b) and GHz (c). Bitrate i.7 Gbit per channel. (The number in (a) reflect the underlying bit pattern.) A detailed invetigation and modeling of ICI i given in appendix I. 3 Wavelength-Time Coding (C) A hown in Fig., the bit equence a (i) k of channel i with wavelength λ i i fed into the encoder (i = 1,..., K; k dicrete time). The output bit c (i) m are eparately

2 ( 1) ( ) ( K ) encoder ( 1) ( ) ( K ) TX 1 TX TX i TX K MUX fiber link DEMUX RX 1 RX RX i RX K ( 1) ν m ( ) ν m ν m ( K ) ν m decoder ( 1) ( ) ( K ) Fig.. WDM tranmiion ytem tranmitted uing intenity modulation before being multiplexed and fed into the fiber link. Amplified pontaneou emiion of the optical amplifier at the receiver i conidered a the dominant noie ource. The ignal are demultiplexed and O/E-converted for further proceing in the -decoder. 3.1 encoder A the name indicate, data i not only encoded along time axi k but alo in wavelength direction i. N conecutive bit of M adjacent channel build up an M N input matrix A, where M K. The encoder add Q parity bit per channel yielding an M (N + Q) output matrix C with element c (i) m ν (ν =,..., N + Q 1; i = 1,..., M; m Z). To how the principle, we aume in the following M = adjacent channel. Thu the encoder execute the mapping: ( (i) a k N+1 a(i) k ) ( (i) c m N Q+1 a k N+1 ) c(i) m a k c m N Q+1 }{{}. c m }{{} A C Let 1 T and 1 T be the bitrate of a (i) k and c(i) m, repectively. A input and output block duration are the ame, i.e. TN = T (N+Q), output bitrate increae to 1 T = 1 RT, where R = N N+Q i the coderate. A an example, for N = 1 and Q = 1 poible mapping are: ( ) ( ) ( ) ( ) 1 ; 1 ( ) ( ) ( ) ( ) ;. 1 1 (1) The cardinality (number of element) of the et A and C are a follow: card{a} = MN card{c} = ( M x) N+Q. () x i the number of uppreed bit pattern. Obviouly, the cardinality of A and conequently the complexity of the encoder and the decoder grow exponentially with the number of channel M. Thu, to keep complexity low not all K channel of a typical WDM ytem hould be encoded jointly. Intead, we recommend to divide the et of K channel into K M ub-et with M channel each and to ue K M wavelength-time encoder and decoder in parallel. Thi lead to ome channel beeing located ide by ide without beeing encoded together. The conequence will be addreed later in thi chapter. In the following we chooe M =. N, the number of bit per codeword in (1), ha alo an exponential impact on the complexity. Thu, N hould be chooen a mall a poible. In the following we chooe N = 3. Finally, the number Q of parity bit per codeword in (1) ha to be found. Of coure card{c} card{a} ha to hold. Thereof we conclude with (): Q N( Mlg() 1). lg( M x) (3) Fig. 3 how the reulting code rate R a a function of N, when the minimal Q N i chooen and M =. In thi cae x = 1. Obviouly, there i a R Fig N= N=.5 1 N Code rate R a a function of N for minimal Q code rate R max, which cannot be exceeded. With (3) and M = we get R max = lg(3) lg() =.795. For N = 3 and Q = 1 the code rate i R =.75 and a good compromie between performance, overhead and complexity i obtained. In principle, a variety of mapping (1) exit. They hould be elected uch, that the bit error ratio (BER) at

3 the receiver output i minimized. We have card{c} card{a} degree of freedom for the mapping. They can be ued for different optimization trategie: I Maximize the Hamming ditance. II Minimize the number of 1 (Hamming weight) in each column of C to further reduce ICI. III Chooe C with the lowet number of 1 or 1 pattern in each row. Thee pattern are diadvantageou, a they increae ISI within the channel. 3. decoder At the receiver in Fig. the original bit equence have to be recovered by finding etimate â (i) k of a (i) k. We propoe a maximum a poteriori (MAP) ymbol-byymbol detector. For the given example M = the et of probabilitie for all poible codeword have to be calculated: P[c (i) m N Q+1,..., c(i) m, c m N Q+1,...,c m v (i) m N Q+1,...,v(i) m, v m N Q+1,..., v m ] = n= N Q+1 n= N Q+1 p(v (i) m+n c(i) m+n,c m+n )P[c(i) m+n,c m+n ] p(v (i) m+n ) p(v m+n c(i) m+n,c m+n )P[c(i) m+n,c m+n ]. p(v m+n ) The lower index of the received ymbol v.. (..) now indicate dicrete time. The MAP detector elect the ymbol with the maximal probability a olution. In () tatitically independent noie i aumed and p(..) i the chi -ditribution of the noiy ignal after the photodiode, depending on the underlying bit pattern with the a priori probability P[c (i) m+n, c m+n ]. p(v(i) m+n ) and p(v m+n ) are the overall probability denity function (pdf) of the photo diode output ignal. Without going into detail, we can take ISI into account, which reult in an extended verion of (). 3.3 Sytem parameter () Several parameter have an impact on the performance of the ytem, e.g. channel pacing, 3 db-bandwidth of the optical filter and the outer encoder, which are dicued in the following. A already mentioned encoding of all K channel of a WDM ytem jointly would increae complexity of the encoder and decoder too much. Intead, we propoe to group the channel into pair a hown in Fig. and apply on each pair encoding Outer encoder A indicated in Fig. we propoe to enhance the cheme by an outer encoder, which i a Reed Solomon encoder RS(N I + N C, N I, N b ). N I i the number of information ymbol, N C the number code ymbol per RS frame, and N b bit are ued to form a ymbol. We tudy three cheme (A)-(C) a hown in Fig. 5 The framed element repreent the RS ymbol. In (C) the pattern of the RS ymbol match the pattern of the C ymbol after decoding. In the following the ymbol error ratio (SER) before the RS decoder i ued a a performance figure Channel pacing The maller the channel pacing i the higher the bitrate per unit bandwidth are. However, ICI i increaed. Fig. how the required OSNR to achieve SER =.5 for different bitrate per unit bandwidth. The net bit rate per channel i Gbit. C with mapping II in ection 3.1 i ued. The two cheme without C apply threhold detection and maximumlikelihood equence etimation (MLSE), repectively. Obviouly, C i uperior for any bitrate under conideration. The higher the bitrate i, the larger the improvement by C i. Remember, that ICI increae with bitrate. In the following our invetigation tick to. bit Hz. Thi correpond to a channel pacing of GHz. When uing the cheme propoed in Fig., a nonuniform channel grid a hown in Fig. 7 lead to the bet performance. To minimize ICI the ditance of f noc between adjacent pair of pectra ha to be ufficiently large, while f C, the pacing within the pair, can be mall. Beide the channel grid, the 3-dB bandwidth of the optical filter of the multiplexer and demultiplexer have an impact on ICI. In appendix II, we how how thee parameter can be optimized. The reult are given in Table 1. b l b l b l ( i + ) b l c v m m â TX RX k bˆ encoder encoder decoder decoder l RS encoder RS ( i + ) TX fiber link encoder MUX DEMUX TX ( i + ) TX RX RX RX v m v m ( i + ) v m decoder ( i + ) RS decoder RS bˆ l bˆ l ( i + ) bˆ l Fig.. Propoed tranmiion ytem (cut-out)

4 ff ff (A) RS (55, 39, ) eparate for both channel: ( i ) bk bk (B) RS (55, 39, ) jointly for both channel: ( i ) bk bk (C) RS (,, ) jointly for both channel: ( i ) bk bk Fig. 5. Alternative cheme for RS encoding of two adjacent wavelength channel req OSNR@SER= C + RS(,, ) RS(55, 39, ), MLSE RS(55, 39, ), threhold detector bitrate per unit bandwidth (bit/ec/hz) Fig.. Required OSNR@SER=.5 a a function of the bitrate per unit bandwidth magnitude of the pectra Table 1 Configuration ued for imulation f C f noc C 5 GHz 55 GHz 7 GHz GHz no C GHz GHz 7 GHz GHz employ the extended verion of (). Fig. how the SER before RS decoding when uing C compared to ytem without C. For the cheme without C two kind of detector are ued, namely threhold detector and MLSE. All three cheme of the RS encoder given in Fig. 5 are compared. (C) lead to the bet reult. Obviouly, the ytem with C and cheme C) for the RS encoding outperform all the other. channel: i 1 i i + 1 i SER Fig. 7. f noc f C Non-uniform channel grid f noc Performance of C Performance of C i invetigated by Monte-Carlo- Simulation. One pair of channel (M = ) with N = 3 and Q = 1 i conidered. The net bitrate i Gbit per channel. CD and PMD are aumed to be fully compenated. The received ignal are corrupted by optical uncorrelated Gauian noie with zero mean. Codeword mapping II of ection 3.1 i ued. The MAP f 1 C A) C B) C C) no C, threhold, A) no C, threhold, B) no C, MLSE, A) 1 3 no C, MLSE, B) OSNR (db) Fig.. SER before RS decoding a a function of OSNR for variou coding cheme In Fig. 9 we have compared the three different code deign I, II and III from ection 3.1. II perform bet followed by III, both being uperior to I. Epecially in WDM ytem a major reaon for ignal degradation i the non-linearity of the fiber due to high power loading at the input. In appendix III

5 SER I II III OSNR (db) Fig. 9. Simulation reult for the different codeword-deign I, II and III in ection 3.1 we how, that the mean and the maximal number of 1 and thu the power load at the input of the fibre are reduced, when uing C. Table how the parameter of the ditribution and the maximum, the mean and the variance of the random variable are lited (in the cae of C codword deign II i ued): Table Parameter of the ditribution P 1 P max[z] E[Z] σ Z C II no C Fig. 1 and 11 illutrate thee ditribution. Monte- Carlo imulation are ued to confirm the reult. Thu 5 Concluion We have preented a novel coding cheme for U-DWDM. It allow dene packing of wavelength channel to increae total bitrate. The reulting interchannel interference (ICI) i reduced by encoding along both the dicrete-time and wavelength index. Different cheme for the Reed-Solomon (RS) coding are ued. In all cae CD and PMD i aumed to be compenated and net bitrate i Gbit per channel. We how that the new wavelength-time coding (C) method can achieve lower SER at low OSNR. The C receiver operate with maximum a poteriori (MAP) ymbol-by-ymbol detection. We how, that C concatenated with an outer RS code perform uperior a it provide an OSNR gain of 3 db and db over the ytem without C with threhold detection and MLSE, repectively. We have alo hown, that ISI per channel can be incorporated into the detection trategy for C. It i pointed out that encoder and decoder hardware can be parallelized, thu reducing peed requirement, which i crucial in the multi Gbit range. A imultaneou 1 in adjacent channel are prohibited by encoding, intantaneou power i reduced and conequently the effect of fiber non-linearitie are lowered. Degree of freedom of the variety of code can be ued in uch a way, that the number of outgoing 1 and 1 bit pattern in time direction i reduced, which minimize ISI per channel. P[Z=z K/,P 1 ] analytical calculation Monte Carlo imulation E[Z]= z 5 3 P[Z=z K,P 1 ] analytial calculation Monte Carlo imulation E[Z]= z Fig. 1. Ditribution of the Fig. 11. Ditribution of the number of 1 to be tranmitted imultaneouly when C i ued number of 1 to be tranmitted imultaneouly when no C i ued APPENDIX I MODELING OF ICI To further invetigate the ICI we calculate the ignal after photo detection of a ingle channel within a WDM ytem. Fig. 1 how in principal the magnitude of the pectra of the equivalent baeband repreentation of a WDM ignal before demultiplexing. For implification the pectra are approximated by triangle. The tranfer function of the demultiplexer of channel i i aumed to be contant within the pa-band. Channel pacing i given by f. the maximum and mean power fed into the fibre i reduced, when uing C. Thi lead to a minor impact of the non-linearitie compared to a ytem without C. Another advantage over RS coding with MLSE i the fact that the decoder and encoder can be highly parallelized to lower hardware peed. Thi i poible, becaue encoding and decoding i ymbol-byymbol wie. The MLSE i baed on equence detection and can thu hardly be parallelized leading to higher hardware requirement. channel no.: i 1 magnitude of the pectra f i ICI demux filter Fig. 1. Magnitude of the equivalent baeband repreentation of the WDM ytem with repect to channel i i + 1 f f

6 The equivalent baeband field ignal after demultiplexing within the band of channel i are give by: ejarc{ē(i) Ē (i) (I) = Ē(i) (I),x } (I),x Ē (i) ejarc{ē(i) (I),y } (I),y with: I {i 1, i, i + 1}. = A(i) (I),x ejϕ(i) (I),x A (i) (I),y ejϕ(i) (I),y (5) The underline indicate complex number and j = 1. Let Ē (i) (i) be the ignal of channel i and Ē (i) (i 1) and Ē (i) the interference ignal coming from the adjacent channel i 1 and i + 1, repectively. If we aume, that the contribution of the remaining channel of the WDM ytem are neglectable, the photo current at the output of the photo diode i: v (i) Ē (i) (i 1) + Ē (i) (i) + Ē (i). () Inerting (5) in () and dropping the upercript (i) to implify notation, we obtain: v (i) A (i 1),x + A (i),x + A,x +A (i 1),y + A (i),y + A,y +A (i 1),x A (i),x co( ϕ (i 1,i),x ) +A (i),x A,x co( ϕ (i,i+1),x ) +A (i 1),x A,x co( ϕ (i 1,i+1),x ) +A (i 1),y A (i),y co( ϕ (i 1,i),y ) +A (i),y A,y co( ϕ (i,i+1),y ) +A (i 1),y A,y co( ϕ (i 1,i+1),y ) with the phae difference: ϕ (I1,I),x = ϕ (I1),x ϕ (I),x ϕ (I1,I),y = ϕ (I1),y ϕ (I),y I1, I {i 1, i, i + 1}. (7) Of coure v (i) i a function of time t. In the following we conider v (i) at a certain point in time t, which we call a ample value v (i). t i dropped to implify notation. With a cloer look at (7), we ee that the ignal after the photo diode depend on the amplitude and phae difference of the interfering field. The phae difference can be modeled a random variable equally ditributed between and π. Fig. 13 confirm thi aumption a a reult of computer imulation. Thu, v (i) become a random variable phae difference (a) phae difference (b) Fig. 13. Hitogram of the phae difference ( ϕ (i) (i 1,i+1),x (a), ϕ (i) (i,i+1),y (b)) If only WDM channel i i active and the ignal of the adjacent channel are zero, we get from (7): v (i) A (i),x + A (i),y. Thi ignal i plotted a a function of time in Fig. 1(a). We ee from thi eye diagramm, that v (i) can take on different value due to ISI for a fixed t. The value depend on the temporal bit equence c (i) m 1 c(i) m c (i) m+1 at the input of channel i (t = kt b, T b bit interval). Thee pattern, 1,..., 111 are indicated in the eye diagram v (i) in Fig. 1(a). Throughout thi paper we aume that thoe three conecutive bit are ufficient to approximate the eye diagram and thu the effect of ISI in channel i. An extenion i traightforward. In Fig. 1(b) and (c), the adjacent channel i 1 and i+1 are active in addition with imilar temporal bit pattern. Obviouly, the reulting ICI caue a vat of value v (i) at a given time intant t. If only the interference ignal from channel i 1 i active in channel i, the eye diagram at the output of the photo diode would look imilar to Fig. 1(a). A an approximation, we alo aume roughly different level depending on the temporal bit pattern. The ame conideration hold, if only the interference ignal from channel i + 1 i active. Mathematically in ummary, conidering the 3 adjacent channel each with level at time intant t, we can define 3 = 51 ignal value v (i) within channel i. A the phae difference in (7) are random, we end up with 51 random variable. The expected value can be calculated a E[v (i) ] = A (i 1),x + A (i),x + A,x +A (i 1),y + A (i),y + A,y and the variance i σ v (i) = V ar[v (i) ] = A (i 1),x A (i),x +A (i),x A,x +A (i 1),x A,x +A (i 1),y A (i),y +A (i),y A,y +A (i 1),y A,y. () (9) Obviouly, the larger σ v (i) the higher the ditortion of the received ignal and bit error ratio (BER) are. From (9) we ee that the product of the quared amplitude of the three channel determine σ v (i). The higher thee value are the higher the variance i. It i crucial to avoid the ituation where both factor in each of the product in (9) are large, a thi reult in a high ditortion. The amplitude directly depend on the ymbol to be tranmitted. A 1 correpond to a high amplitude, a to a mall one. Thu, the wort cae cenario i, when a 1 i at each input of the two neighbouring channel at the ame time. C can uppre uch bit pattern.

7 APPENDIX II OPTIMAL FREQUENCY PARAMETERS FOR C To determine the optimal value of the channel pacing and the 3-dB bandwidth of the multiplexer and demultiplexer we ue (1): = P(E[v(i) 1 ] E[v(i) ])+P1(E[v(i) 1 ] E[v(i) 1 ]) P σ (i) +P1σ(i) 1 +P1σ(i) 1 (1) The lower index of the received ymbol v.. (..) again reflect the underlying bit pattern. In (1) E[v (i) c (i) ] i the mean value, σ (i) (i) P (i) c the a priori probability of v (i) m i defined a follow: m the tandard deviation and (i). P c m P = P + P 1 P P +P 1 P 1 = P 1 + P 1 P 1 P +P 1 (11) Equation (1) can eailiy be expanded to take ISI into account. Fig. 1, 15 and 1 how for different channel pacing grid a a function of the 3-dB bandwidth of the multiplexer and the demultiplexer, when uing C. OSNR i chooen to 1 db to take the influence of the noie into account.the non-uniform grid perform better than the uniform one, a predicted earlier. When extending (1) in that way that the ISI i taken into account, the dicrepancie get clearer (Fig. 17, 1 and 19). The 3-dB bandwidth of the multiplexer mut not be chooen too narrow (below GHz), a the ISI introduced by the filter woren the ignal quality. Thi lead to the concluion, that, when uing uch narrow channel pacing, it i not neceary to bandlimit the ignal at the tranmitter. The demultiplexer ha to cut out the channel and reduce the impact of the optical noie. Bandwidth around.. GHz produce the bet reult. Obviouly the non-uniform grid reduce the enitivity againt the bandwidth of the demultiplexer. Additionally the optimal bandwidth of the demultiplexer drop, when ISI i taken into account. Thi i plauible a a more narrow demultiplexer reduce ICI while increaing ISI. APPENDIX III DISTRIBUTION OF THE POWER LOAD AT THE INPUT OF THE FIBER Without C the bit at the input of the WDM channel do not depend on each other. Thu, thee bit tream can be modeled a K independent random generator with output or 1 (K i the number of channel). The number z of 1 being imultaneouly at the channel input i then binomial ditributed (P 1 i the a priori probability of the 1, P that of the, P 1 + P = 1): ( ) K P noc [Z = z K, P 1 ] = P z 1 z (1 P 1 ) K z. When uing C pairwie a in Fig., the bit at the channel input within thee pair depend on each Fig. 1. a a function of the 3-dB bandwidth of the multiplexer and the demultiplexer, when uing C. ( f C = GHz, f noc = GHz) Fig. 15. a a function of the 3-dB bandwidth of the multiplexer and the demultiplexer, when uing C. ( f C = 5 GHz, f noc = 55 GHz) Fig. 1. a a function of the 3-dB bandwidth of the multiplexer and the demultiplexer, when uing C. ( f C = GHz, f noc = GHz) Fig. 17. including ISI a a function of the 3-dB bandwidth of the multiplexer and the demultiplexer, when uing C. ( f C = GHz, f noc = GHz) Fig. 1. including ISI a a function of the 3-dB bandwidth of the multiplexer and the demultiplexer, when uing C. ( f C = 5 GHz, f noc = 55 GHz) Fig. 19. including ISI a a function of the 3-dB bandwidth of the multiplexer and the demultiplexer, when uing C. ( f C = GHz, f noc = GHz)

8 other. Now the overall ytem can be modelled a K independent random generator with output no 1 i to be tranmitted correponding to (c (i) m, c m ) = (, ) and one 1 i to be tranmitted correponding to (c (i) m, c m ) = (, 1) and (c (i) m, c m ) = (1, ). Now the number z of 1 imultaneouly to be tranmitted i again binomial ditributed, but with different parameter (P 1 i now the a priori probability of the output one 1 i to be tranmitted, P that of no 1 i to be tranmitted, P + P 1 = 1): ( K ) P C [Z = z K, P 1] = P1 z z (1 P 1 ) K z. The number of 1 at the input of the fiber directly impact the power load. ACKNOWLEDGMENT Thi work wa funded by the German Minitry of Reearch within the joint MultiTeraNet project with Alcatel Stuttgart. REFERENCES [1] R. A. Griffin, A. C. Carter, Optical Differential Quadrature Phae-Shift Key (odqpsk) for High Capacity Optical Tranmiion, OFC, Anaheim, CA, March, paper WX. [] M. Ohm, J. Speidel, Quaternary Optical ASK-DPSK and Receiver With Direct Detection, IEEE Photon. Technol. Lett., vol. 15, no. 1, pp , Jan. 3. [3] S. Hayae, N. Kikuchi, K. Sekine, S. Saaki, Propoal of - tate per ymbol (binary ASK and QPSK) 3-Gbit/ optical modulation/demodulation cheme, ECOC 3, Rimini, Italy, Sept. 3, paper Th... [] M. Ohm, Optical -DPSK and Receiver with Direct Detection and Multilevel Electrical Signal, IEEE/LEOS Workhop on Advanced Modulation Format, San Francico, CA, July, paper FC. [5] R. Fritch, J. Speidel, OQ AM - Optical QAM cheme with orthogonal polarization, ITG-Fachtagung, Leipzig, Germany, May 3, pp [] B. Vaic, I. B. Djordjevic, Low-Denity Parity Check Code for Long-Haul Optical Communication Sytem, IEEE photon. Technol. Lett., vol. 1, no., pp. 1-11, Aug.. [7] M. Jäger, T. Rankl, J. Speidel, F. Buchali, H. Bülow, Performance of Turbo Equalizer for Optical PMD Channel, Journal of Lightwave Technologie,, accepted for publication.