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OPTICS LETTERS / Vol. 40, No. 3 / February 1, 2015
12-mode OFDM transmission using reduced-complexity maximum likelihood detection Adriana Lobato,1,* Yingkan Chen,2 Yongmin Jung,3 Haoshuo Chen,4 Beril Inan,2 Maxim Kuschnerov,5 Nicolas K. Fontaine,6 Roland Ryf,6 Bernhard Spinnler,5 and Berthold Lankl1 1
University of Federal Armed Forces Munich, Werner-Heisenberg-Weg 39, 85579 Neubiberg, Germany
2
Lehrstuhl für Nachrichtentechnik, Technische Universität München, Arcisstraße 21, 80333 Munich, Germany 3 Optoelectronics Research Centre, University of Southampton, Highfield, Southampton, Hampshire SO17 1BJ, UK 4
COBRA Institute, Eindhoven University of Technology, Den Dolech 2, 5612AZ Eindhoven, The Netherlands 5
6
Coriant R&D GmbH, St. Martin-Str. 76, 81541 Munich, Germany Bell Laboratories, Alcatel-Lucent, Holmdel, New Jersey 07733, USA *Corresponding author: [email protected]
Received August 5, 2014; revised November 18, 2014; accepted November 26, 2014; posted December 1, 2014 (Doc. ID 220403); published January 22, 2015 We report the transmission of 163-Gb∕s MDM-QPSK-OFDM and 245-Gb∕s MDM-8QAM-OFDM transmission over 74 km of few-mode fiber supporting 12 spatial and polarization modes. A low-complexity maximum likelihood detector is employed to enhance the performance of a system impaired by mode-dependent loss. © 2015 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.1660) Coherent communications; (060.2840) Heterodyne; (060.4230) Multiplexing. http://dx.doi.org/10.1364/OL.40.000328
Recently reported experimental work confirms not only the viability of space-division multiplexed (SDM) systems, but a successful capacity increase over hundreds of kilometers and wavelength-division multiplexed channels [1,2]. In particular, transmission over few-mode fiber (FMF) can potentially reduce the cost per bit by integrating optical inline components, e.g., with fewmode erbium-doped fiber amplifiers (FM-EDFAs) [3] and wavelength selective switches [4]. However, mode equalization is necessary using digital signal processing (DSP), which leads to an increase in computational complexity in comparison to single-mode systems, and consequently, energy consumption [5,6]. As proposed in [6], the use of orthogonal frequency division multiplexing (OFDM) allows for a reduced equalizer complexity compared with other frequency- and timedomain-based equalization schemes. With OFDM’s cyclic prefix, equalization can be simplified to a one-tap equalizer for dispersion, differential mode delay (DMD), and mode coupling compensation. Moreover, SDM systems are impaired by modedependent loss (MDL) [7]. Amplifiers, splices, and all kinds of inline optical components introduce MDL, and in great proportions can cause system outage [7]. In this Letter, we increase further the number of modes to six spatial modes and apply maximum likelihood (ML) detection with a reduced computational effort to diminish the effect of MDL. Its performance is evaluated by transmitting 163-Gb∕s mode-division multiplexed quadrature phase-shift keying OFDM (MDM-QPSK-OFDM) and 245-Gb∕s MDM 8-level quadrature amplitude modulation OFDM (MDM-8QAM-OFDM) signals over 74 km. Figure 1 shows the block diagram of the experimental setup. At the transmitter, the OFDM I and Q signals are loaded into an arbitrary waveform generator (AWG) whose sampling rate is 10 GS∕s. From 256 subcarriers, 174 are used for data, three for quasi-pilot aided (QPA) [8], and three pilot-aided (PA) phase noise (PN) 0146-9592/15/030328-04$15.00/0
estimation and compensation [9]. The rest of the subcarriers are employed for zero-padding, isolating the spectrum from the aliasing products generated by the AWG, which are filtered out by a 3.3-GHz 3-dB bandwidth electrical low pass filter (LPF). The signal is converted to the optical domain by an IQ Mach–Zehnder modulator, followed by a polarization-multiplexing stage having a two OFDM-symbol delay. For multiplexing the modes into the FMF, delay lines are included to create time multiplexed training sequences (TSs) [6], here, with 4, 8, 12, 16, and 20 OFDM-symbol delay. Every polarizationmultiplexed TS consists of one pair of identical binary phase-shift keying OFDM (BPSK-OFDM) symbols for synchronization and carrier frequency offset (CFO) compensation purposes. For mode (de)multiplexing ((D)MUX), the photonic lanterns described in [10] were used. The insertion loss of the (D)MUX ranges from 3 to 7.5 dB per port. The link consists of five spools of graded-index FMF with depressed cladding [11] supporting the spatial modes LP01 , LP11A , LP11B , LP21A , LP21B , and LP02 . As shown in Table 1, the fibers have positive and negative DMD to achieve DMD compensation. In Table 1, DMDA–B is the modal delay between the modes LPA and LPB . Figure 2 depicts the time-of-flight measurements used to compute the values in Table 1. As Fig. 2 shows, the DMD01–02 and DMD01–21 cannot be individually identified, since the group velocity of both modes is very similar; therefore, they are registered in Table 1 in a single column. The total residual DMD is 1.95 ns. A cyclic prefix (CP) of 8 ns was chosen to completely compensate for the intersymbol interference caused by the modal delay and dispersion, the latter being approximately 0.08 ns for 74 km, with the maximum dispersion parameter of all spools, which is around 19 ps∕nm · km. An attenuation of 17.5 dB was measured after splicing all spools together. After the multimode signal is demultiplexed into six dual-polarization signals, it is down-converted by a © 2015 Optical Society of America
February 1, 2015 / Vol. 40, No. 3 / OPTICS LETTERS
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Fig. 1. Block diagram of the experimental mode-division multiplexed OFDM system (LW, linewidth; PBC, polarization beam combiner).
Table 1. Relative Mode Delay with Respect to LP01 Length [m] 4550 10450 23787 29980 5400 Σ length:74167 m
DMD01–11 [ns]
DMD01–02∕21 [ns]
0.3 ∼0 −2.75 3.45 0.95
0.95 −0.65 −5.95 5.2 1.95
Σ DMD01–11 :1.95 ns
Σ DMD01–02 :1.5 ns
bols as S k S −k , where is the complex conjugate operator. This condition allows using the information of 2N p symbols for the PN estimation and, thus, averages the noise of 2N p subcarriers [9]. As in Eq. (1), for the QPA PN estimation the phase of two symbols have to be added, but if j argRk R−k j > π, Eq. (1) results in phase ambiguity. For this reason the QPA scheme is combined with the PA scheme. As Eq. (2) shows, residual phase rotation due to PN and possible cyclic slips generated with the QPA technique is extracted by averaging the phase difference between N p -transmitted pilot symbols and the corresponding received symbols [8]: X Np argRk R−k: ∕2 (1) ΦQPA arg k1
ΦPA
Np X k1
0
Relative Amplitude [dB]
local oscillator (LO) to an intermediate frequency (IF, 6.6 GHz). Then, it can be received by using two outputs of a coherent heterodyne receiver. Thus, the required number of RF input in the scope is 12. Subsequently, the 12 signals are sampled at 40 and 50 GS∕s, and processed offline. The first stage of the receiver DSP is the coarse CFO compensation, which is performed by identifying a minimum around the central region of the OFDM spectrum (evident in the inset in Fig. 1). This is possible since the central subcarrier is not modulated. Then, sampling frequency offset (SFO) is compensated, and the signals are downsampled to the transmitter sampling rate, i.e., 10 GS∕s. The signals are synchronized, and a fine CFO compensation is applied via the Schmidl and Cox method [12]. After removing the CP, the signals are converted into the frequency domain, followed by the channel estimation. In order to reduce the noise in the channel estimation, a moving averaging filter is applied to TSs of consecutive frames. Then, minimummean square error (MMSE) equalization is performed. Afterward, PN estimation and compensation is performed. It is composed of two stages. First, a coarse common phase rotation is estimated per OFDM symbol via QPA [8] and PA techniques [9]. The different expression for QPA and PA phase noise estimation are shown in Eqs. (1) and (2), respectively, where ΦQPA , ΦPA , Rk , S k , N p , k, are the QPA and PA phase estimation, received symbols after equalization, transmitted symbols, number of pilot subcarriers, and kth subcarrier, respectively. In the case of QPA, the phase of N p received symbols Rk are compared with their mirror subcarrier, R−k . Instead of using pilot symbols, QPA codes the transmitted sym-
argRk − argS k ∕N p .
23787 m
LP11
4550 m
-4
LP01
LP02/21
LP01
(2)
LP11
LP02/21
-8 -12 -16 -20 -5 0
-4
-3
-2 -1
0
1
2
3
4
LP11
LP01/11
-4
LP02/21
LP01
-8
6
4
2
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-2
-4
-6
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LP02/21 -12 -16 -20 -4 0
-2
0
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4
6
8
10
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10
12
5400 m
-5
LP11 LP02/21
-10 -15 -20
-1
0
1
2
3
4
5
6
7
Time [ns]
Fig. 2.
Time of flight measurements for fiber spools in Table 1.
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The second stage of the PN compensation is the expectation maximization (EM) [13]. EM is an iterative machine learning process, which is used to estimate the mean and co-variance of clusters of information, which can be described by a 2D Gaussian distribution. In this case, each cluster of information corresponds to an agglomerate of constellation points (e.g., 8QAM has eight clusters). The EM algorithm is especially beneficial when the constellation has an imprinted pattern, as in the case of highly coherent nonlinear phase noise and laser phase noise [13]. EM is applied on every OFDM symbol, estimating the center of each cluster, comparing it with the corresponding ideal constellation point, and rotating back the symbols from all subcarriers. The beneficial effect of the EM algorithm on the compensation of residual phase noise is depicted in Fig. 3 for QPSK, 8QAM and, back-to-back transmission using the (D)MUX. We compare the performance of the linear equalizer MMSE and the improved reduced-search maximum likelihood (IRSML) detection [14,15]. The IRSML algorithm computes the ML detection, over a reduced set of candidates S instead of evaluating every possible transmitted vector. According to [14], ML detection is beneficial in MDL-impaired environments, since in contrast to linear equalization it does not lead to noise amplification. Equation (3) shows this principle, where r, H, s, sˆIRSML , -1
10
8QAM
-2
10
QPSK
-3
BER
10
-4
10
QPA + PA + EM QPA + PA
-5
10
-6
10
10
15
OSNR [dB]
20
25
Fig. 3. Bit error rate (BER) versus OSNR with and without EM.
FEC limit -2
10
ΦCPE are the detector input vector, estimated channel matrix, vector of hypothetical transmitted symbols, detector output vector, estimated common phase error from the QPA, PA, and EM methods, respectively: sˆ IRSML arg min‖r − HsejΦCPE ‖2 .
To determine the search set S, it is necessary to compute the Euclidean distance δi;q [Eq. (4)] between the MMSE equalizer output yi;MMSE and all possible constellation points sˆ q i , for the ith tributary and the qth constellation point [15]. The smallest Euclidian distances correspond to most likely symbol candidates sˆ q i to feed the set S. A maximum of N max hypersymbol candidates are fed to the ML algorithm, which is determined beforehand according to the allowed computational complexity. In this case, N max is chosen to be eight, since increasing further the size of S does not change significantly the performance as the inset in Fig. 4(a) shows for the transmission over 74 km and 8QAM: δi;q jyi;MMSE − sˆ q i j.
Req. OSNR at BER = 1e-3 74 km - QPSK
12.3
-1
10
MMSE wIRSML
= 0.85
IRSML ( = 1) wIRSML optimum FEC limit
-2
10
12.1
-3
10
(4)
Ideally, if the channel estimation and the PN estimation are accurate, the detection output corresponds to Eq. (3). In this case, perfect channel knowledge is not possible to obtain and there is residual inter-carrier interference from the residual PN. With the purpose of improving the detection criteria in Eq. (3) and make it robust against such inaccuracies, we have modified the output of the IRSML algorithm by assigning a weight to the metric corresponding to the MMSE equalizer output after detection sˆ MMSE as described in Eq. (5) by the ρ, where sˆ wIRSML ; A and, sˆ 0 are output of the proposed weighted IRSML (wIRSML) algorithm, the set of hypersymbol candidates and the candidates themselves excluding sˆ MMSE . The value of ρ was chosen as a global optimum for all the measurements, corresponding to 0.85. An alternative to further optimize ρ would be to optimize it blindly by observing the corrected errors of the forward error correction (FEC) stage at the receiver. Figure 4 compares the performance of the MMSE equalizer and the IRSML
12.4
12.2
(3)
s∈S
BER
12 11.9 2
4
8
16 N max
32
74 km
64
-4
-3
10
10
74 km
(D)MUX -5
(a)
(b)
10
B2B
10
Fig. 4.
12
14
(D)MUX
16 18 OSNR [dB]
B2B
-4
20
22
24
10
12
14
16
18 20 OSNR [dB]
22
24
26
Average BER over all tributaries versus OSNR for (a) MDM-QPSK-OFDM and (b) MDM-8QAM-OFDM.
February 1, 2015 / Vol. 40, No. 3 / OPTICS LETTERS 15
74km Average: 74km
shows an improvement proportional to the MDL in the system by using only eight hypersymbols candidates.
(D)MUX Average: (D)MUX
The support of Phoenix Photonics, the German Federal Ministry of Education and Research (01BP12300A, EUREKA-Project SASER), and the European Committee 7th Framework Program under grant agreement 258033 (MODE-GAP) is gratefully acknowledged.
MDL [dB]
10
5 B2B Average: B2B 0
-3
Fig. 5.
-2
-1 0 1 Frequency [GHz]
2
3
MDL as a function of the frequency.
approaches for a set of measurements using MDM-QPSKOFDM and MDM-8QAM-OFDM. The curves show the performance of back-to-back (B2B) with and without (D)MUX and, 74-km transmission. The FEC limit is also shown for 20% overhead [6]. As an example, Fig. 4 depicts the wIRSML detection upper (IRSML) and lower (wIRSML with optimum ρ) bound for 74-km transmission. Figure 4 shows that the wIRSML scheme allows for superior performance in comparison with the MMSE equalizer. Its improvement for QPSK is 0.5 and 1.1 dB for the (D)MUX and 74 km curves, respectively, at 1e − 3 BER with respect to the MMSE equalizer. For 8-QAM, the performance improves by 0.9 and 1.3 dB at 1e − 2 BER with respect to the MMSE equalization. As shown in [14], and the references therein, in the presence of MDL, ML detection enhances the system performance and its improvement depends on the amount of MDL in the system: sˆ wIRSML arg min
s0 ∈A∨ˆsMMSE
331
ρ‖r − HˆsMMSE ejΦCPE ‖2 ; ‖r − Hs0 ejΦCPE ‖2
(5)
A fsjs ∈ S; s ≠ sˆMMSE g. The MDL in this system was computed and is depicted in Fig. 5. Similar to [10], an MDL of approximately 8 dB is observed by using the photonic lanterns. An additional MDL of 2 dB is observed after the transmission over 74 km, which is attributed to splicing imperfections, slightly different fiber attenuation coefficients per mode, and noise levels added from the single-mode amplifiers after demultiplexing the signal. In conclusion, we have assessed the performance of the proposed weighted IRSML (wIRSML) detection algorithm with the transmission of 163-Gb∕s MDM-QPSKOFDM and 245-Gb∕s MDM-8QAM-OFDM over 74 km. Compared to MMSE equalizer, the wIRSML detection
References 1. R. Ryf, S. Randel, N. K. Fontaine, X. Palou, E. Burrows, S. Corteselli, S. Chandrasekhar, A. H. Gnauck, C. Xie, R.-J. Essiambre, P. J. Winzer, R. Delbue, and P. Pupalaikis, Proceedings of European Conference on Optical Communication (2013), paper We.2.D.1. 2. V. A. J. M. Sleiffer, H. Chen, Y. Jung, P. Leoni, M. Kuschnerov, A. Simperler, H. Fabian, H. Schuh, F. Kub, D. J. Richardson, S. U. Alam, L. Grüner-Nielsen, Y. Sun, A. M. J. Koonen, and H. de Waardt, Opt. Express 21, 31036 (2013). 3. Y. Jung, Q. Kang, J. Kumar Sahu, B. Corbett, J. O’Callagham, F. Poletti, S. U. Alam, and D. J. Richardson, IEEE Photon. Technol. Lett. 26, 1100 (2014). 4. N. K. Fontaine, R. Ryf, C. Liu, B. Ercan, J. R. Salazar Gil, S. G. Leon-Saval, J. Bland-Hawthorn, and D. T. Neilson, Proceedings of Optical Fiber Communication Conference (2014), paper Th4 A.7. 5. M. Kuschnerov, Proceedings of Optical Fiber Communication Conference (2014), paper Th3 E.7. 6. B. Inan, Y. Jung, V. A. J. M. Sleiffer, M. Kuschnerov, L. Grüner-Nielsen, S. Adhikari, S. L. Jansen, D. J. Richardson, S.-U. Alam, B. Spinnler, and N. Hanik, Proceedings of Optical Fiber Communication Conference (2013), paper OW4 F.4. 7. P. J. Winzer and G. J. Foshini, Opt. Express 19, 16680 (2011). 8. S. T. Le, T. Kanesan, M. McCarthy, E. Giacoumidis, I. Phillips, M. F. Stephens, M. Tan, N. J. Doran, A. D. Ellis, and S. K. Turitsyn, Proceedings of Optical Fiber Communication Conference (2014), paper Tu3 G.4.X. 9. X. Yi, W. Shieh, and Y. Tang, IEEE Photon. Technol. Lett. 19, 919 (2007). 10. H. Chen, N. K. Fontaine, R. Ryf, B. Guan, S. J. B. Yoo, and A. M. J. Koonen, Proceedings of European Conference on Optical Communication (2014), paper We.1.1.4. 11. L. Grüner-Nielsen, Y. Sun, R. V. Jensen, J. W. Nicholson, and R. Lingle, Jr., Proceedings of European Conference on Optical Communication (2014), paper P. 1.15. 12. A. Lobato, F. Ferreira, M. Kuschnerov, D. van den Borne, S. L. Jansen, A. Napoli, B. Spinnler, and B. Lankl, Opt. Express 20, 29776 (2012). 13. D. Zibar, O. Winther, N. Franceschi, R. Borkowski, A. Caballero, V. Arlunno, M. N. Schmidt, N. Guerrero Gonzales, B. Mao, Y. Ye, K. J. Larsen, and I. Tafur, Opt. Express 20, B181 (2012). 14. A. Lobato, F. Ferreira, J. Rabe, M. Kuschnerov, B. Spinnler, and B. Lankl, Proceedings of Optoelectronics and Communications Conference (2014), paper TU4B-3. 15. M. Chouayakh, A. Knopp, and B. Lankl, Proccedings of IEEE 19th International Symposium on Personal (IEEE, 2008).
OPTICS LETTERS / Vol. 40, No. 3 / February 1, 2015
12-mode OFDM transmission using reduced-complexity maximum likelihood detection Adriana Lobato,1,* Yingkan Chen,2 Yongmin Jung,3 Haoshuo Chen,4 Beril Inan,2 Maxim Kuschnerov,5 Nicolas K. Fontaine,6 Roland Ryf,6 Bernhard Spinnler,5 and Berthold Lankl1 1
University of Federal Armed Forces Munich, Werner-Heisenberg-Weg 39, 85579 Neubiberg, Germany
2
Lehrstuhl für Nachrichtentechnik, Technische Universität München, Arcisstraße 21, 80333 Munich, Germany 3 Optoelectronics Research Centre, University of Southampton, Highfield, Southampton, Hampshire SO17 1BJ, UK 4
COBRA Institute, Eindhoven University of Technology, Den Dolech 2, 5612AZ Eindhoven, The Netherlands 5
6
Coriant R&D GmbH, St. Martin-Str. 76, 81541 Munich, Germany Bell Laboratories, Alcatel-Lucent, Holmdel, New Jersey 07733, USA *Corresponding author: [email protected]
Received August 5, 2014; revised November 18, 2014; accepted November 26, 2014; posted December 1, 2014 (Doc. ID 220403); published January 22, 2015 We report the transmission of 163-Gb∕s MDM-QPSK-OFDM and 245-Gb∕s MDM-8QAM-OFDM transmission over 74 km of few-mode fiber supporting 12 spatial and polarization modes. A low-complexity maximum likelihood detector is employed to enhance the performance of a system impaired by mode-dependent loss. © 2015 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.1660) Coherent communications; (060.2840) Heterodyne; (060.4230) Multiplexing. http://dx.doi.org/10.1364/OL.40.000328
Recently reported experimental work confirms not only the viability of space-division multiplexed (SDM) systems, but a successful capacity increase over hundreds of kilometers and wavelength-division multiplexed channels [1,2]. In particular, transmission over few-mode fiber (FMF) can potentially reduce the cost per bit by integrating optical inline components, e.g., with fewmode erbium-doped fiber amplifiers (FM-EDFAs) [3] and wavelength selective switches [4]. However, mode equalization is necessary using digital signal processing (DSP), which leads to an increase in computational complexity in comparison to single-mode systems, and consequently, energy consumption [5,6]. As proposed in [6], the use of orthogonal frequency division multiplexing (OFDM) allows for a reduced equalizer complexity compared with other frequency- and timedomain-based equalization schemes. With OFDM’s cyclic prefix, equalization can be simplified to a one-tap equalizer for dispersion, differential mode delay (DMD), and mode coupling compensation. Moreover, SDM systems are impaired by modedependent loss (MDL) [7]. Amplifiers, splices, and all kinds of inline optical components introduce MDL, and in great proportions can cause system outage [7]. In this Letter, we increase further the number of modes to six spatial modes and apply maximum likelihood (ML) detection with a reduced computational effort to diminish the effect of MDL. Its performance is evaluated by transmitting 163-Gb∕s mode-division multiplexed quadrature phase-shift keying OFDM (MDM-QPSK-OFDM) and 245-Gb∕s MDM 8-level quadrature amplitude modulation OFDM (MDM-8QAM-OFDM) signals over 74 km. Figure 1 shows the block diagram of the experimental setup. At the transmitter, the OFDM I and Q signals are loaded into an arbitrary waveform generator (AWG) whose sampling rate is 10 GS∕s. From 256 subcarriers, 174 are used for data, three for quasi-pilot aided (QPA) [8], and three pilot-aided (PA) phase noise (PN) 0146-9592/15/030328-04$15.00/0
estimation and compensation [9]. The rest of the subcarriers are employed for zero-padding, isolating the spectrum from the aliasing products generated by the AWG, which are filtered out by a 3.3-GHz 3-dB bandwidth electrical low pass filter (LPF). The signal is converted to the optical domain by an IQ Mach–Zehnder modulator, followed by a polarization-multiplexing stage having a two OFDM-symbol delay. For multiplexing the modes into the FMF, delay lines are included to create time multiplexed training sequences (TSs) [6], here, with 4, 8, 12, 16, and 20 OFDM-symbol delay. Every polarizationmultiplexed TS consists of one pair of identical binary phase-shift keying OFDM (BPSK-OFDM) symbols for synchronization and carrier frequency offset (CFO) compensation purposes. For mode (de)multiplexing ((D)MUX), the photonic lanterns described in [10] were used. The insertion loss of the (D)MUX ranges from 3 to 7.5 dB per port. The link consists of five spools of graded-index FMF with depressed cladding [11] supporting the spatial modes LP01 , LP11A , LP11B , LP21A , LP21B , and LP02 . As shown in Table 1, the fibers have positive and negative DMD to achieve DMD compensation. In Table 1, DMDA–B is the modal delay between the modes LPA and LPB . Figure 2 depicts the time-of-flight measurements used to compute the values in Table 1. As Fig. 2 shows, the DMD01–02 and DMD01–21 cannot be individually identified, since the group velocity of both modes is very similar; therefore, they are registered in Table 1 in a single column. The total residual DMD is 1.95 ns. A cyclic prefix (CP) of 8 ns was chosen to completely compensate for the intersymbol interference caused by the modal delay and dispersion, the latter being approximately 0.08 ns for 74 km, with the maximum dispersion parameter of all spools, which is around 19 ps∕nm · km. An attenuation of 17.5 dB was measured after splicing all spools together. After the multimode signal is demultiplexed into six dual-polarization signals, it is down-converted by a © 2015 Optical Society of America
February 1, 2015 / Vol. 40, No. 3 / OPTICS LETTERS
329
Fig. 1. Block diagram of the experimental mode-division multiplexed OFDM system (LW, linewidth; PBC, polarization beam combiner).
Table 1. Relative Mode Delay with Respect to LP01 Length [m] 4550 10450 23787 29980 5400 Σ length:74167 m
DMD01–11 [ns]
DMD01–02∕21 [ns]
0.3 ∼0 −2.75 3.45 0.95
0.95 −0.65 −5.95 5.2 1.95
Σ DMD01–11 :1.95 ns
Σ DMD01–02 :1.5 ns
bols as S k S −k , where is the complex conjugate operator. This condition allows using the information of 2N p symbols for the PN estimation and, thus, averages the noise of 2N p subcarriers [9]. As in Eq. (1), for the QPA PN estimation the phase of two symbols have to be added, but if j argRk R−k j > π, Eq. (1) results in phase ambiguity. For this reason the QPA scheme is combined with the PA scheme. As Eq. (2) shows, residual phase rotation due to PN and possible cyclic slips generated with the QPA technique is extracted by averaging the phase difference between N p -transmitted pilot symbols and the corresponding received symbols [8]: X Np argRk R−k: ∕2 (1) ΦQPA arg k1
ΦPA
Np X k1
0
Relative Amplitude [dB]
local oscillator (LO) to an intermediate frequency (IF, 6.6 GHz). Then, it can be received by using two outputs of a coherent heterodyne receiver. Thus, the required number of RF input in the scope is 12. Subsequently, the 12 signals are sampled at 40 and 50 GS∕s, and processed offline. The first stage of the receiver DSP is the coarse CFO compensation, which is performed by identifying a minimum around the central region of the OFDM spectrum (evident in the inset in Fig. 1). This is possible since the central subcarrier is not modulated. Then, sampling frequency offset (SFO) is compensated, and the signals are downsampled to the transmitter sampling rate, i.e., 10 GS∕s. The signals are synchronized, and a fine CFO compensation is applied via the Schmidl and Cox method [12]. After removing the CP, the signals are converted into the frequency domain, followed by the channel estimation. In order to reduce the noise in the channel estimation, a moving averaging filter is applied to TSs of consecutive frames. Then, minimummean square error (MMSE) equalization is performed. Afterward, PN estimation and compensation is performed. It is composed of two stages. First, a coarse common phase rotation is estimated per OFDM symbol via QPA [8] and PA techniques [9]. The different expression for QPA and PA phase noise estimation are shown in Eqs. (1) and (2), respectively, where ΦQPA , ΦPA , Rk , S k , N p , k, are the QPA and PA phase estimation, received symbols after equalization, transmitted symbols, number of pilot subcarriers, and kth subcarrier, respectively. In the case of QPA, the phase of N p received symbols Rk are compared with their mirror subcarrier, R−k . Instead of using pilot symbols, QPA codes the transmitted sym-
argRk − argS k ∕N p .
23787 m
LP11
4550 m
-4
LP01
LP02/21
LP01
(2)
LP11
LP02/21
-8 -12 -16 -20 -5 0
-4
-3
-2 -1
0
1
2
3
4
LP11
LP01/11
-4
LP02/21
LP01
-8
6
4
2
0
-2
-4
-6
5 -10 -8
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LP02/21 -12 -16 -20 -4 0
-2
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4
LP01
6
8
10
12
5400 m
-5
LP11 LP02/21
-10 -15 -20
-1
0
1
2
3
4
5
6
7
Time [ns]
Fig. 2.
Time of flight measurements for fiber spools in Table 1.
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The second stage of the PN compensation is the expectation maximization (EM) [13]. EM is an iterative machine learning process, which is used to estimate the mean and co-variance of clusters of information, which can be described by a 2D Gaussian distribution. In this case, each cluster of information corresponds to an agglomerate of constellation points (e.g., 8QAM has eight clusters). The EM algorithm is especially beneficial when the constellation has an imprinted pattern, as in the case of highly coherent nonlinear phase noise and laser phase noise [13]. EM is applied on every OFDM symbol, estimating the center of each cluster, comparing it with the corresponding ideal constellation point, and rotating back the symbols from all subcarriers. The beneficial effect of the EM algorithm on the compensation of residual phase noise is depicted in Fig. 3 for QPSK, 8QAM and, back-to-back transmission using the (D)MUX. We compare the performance of the linear equalizer MMSE and the improved reduced-search maximum likelihood (IRSML) detection [14,15]. The IRSML algorithm computes the ML detection, over a reduced set of candidates S instead of evaluating every possible transmitted vector. According to [14], ML detection is beneficial in MDL-impaired environments, since in contrast to linear equalization it does not lead to noise amplification. Equation (3) shows this principle, where r, H, s, sˆIRSML , -1
10
8QAM
-2
10
QPSK
-3
BER
10
-4
10
QPA + PA + EM QPA + PA
-5
10
-6
10
10
15
OSNR [dB]
20
25
Fig. 3. Bit error rate (BER) versus OSNR with and without EM.
FEC limit -2
10
ΦCPE are the detector input vector, estimated channel matrix, vector of hypothetical transmitted symbols, detector output vector, estimated common phase error from the QPA, PA, and EM methods, respectively: sˆ IRSML arg min‖r − HsejΦCPE ‖2 .
To determine the search set S, it is necessary to compute the Euclidean distance δi;q [Eq. (4)] between the MMSE equalizer output yi;MMSE and all possible constellation points sˆ q i , for the ith tributary and the qth constellation point [15]. The smallest Euclidian distances correspond to most likely symbol candidates sˆ q i to feed the set S. A maximum of N max hypersymbol candidates are fed to the ML algorithm, which is determined beforehand according to the allowed computational complexity. In this case, N max is chosen to be eight, since increasing further the size of S does not change significantly the performance as the inset in Fig. 4(a) shows for the transmission over 74 km and 8QAM: δi;q jyi;MMSE − sˆ q i j.
Req. OSNR at BER = 1e-3 74 km - QPSK
12.3
-1
10
MMSE wIRSML
= 0.85
IRSML ( = 1) wIRSML optimum FEC limit
-2
10
12.1
-3
10
(4)
Ideally, if the channel estimation and the PN estimation are accurate, the detection output corresponds to Eq. (3). In this case, perfect channel knowledge is not possible to obtain and there is residual inter-carrier interference from the residual PN. With the purpose of improving the detection criteria in Eq. (3) and make it robust against such inaccuracies, we have modified the output of the IRSML algorithm by assigning a weight to the metric corresponding to the MMSE equalizer output after detection sˆ MMSE as described in Eq. (5) by the ρ, where sˆ wIRSML ; A and, sˆ 0 are output of the proposed weighted IRSML (wIRSML) algorithm, the set of hypersymbol candidates and the candidates themselves excluding sˆ MMSE . The value of ρ was chosen as a global optimum for all the measurements, corresponding to 0.85. An alternative to further optimize ρ would be to optimize it blindly by observing the corrected errors of the forward error correction (FEC) stage at the receiver. Figure 4 compares the performance of the MMSE equalizer and the IRSML
12.4
12.2
(3)
s∈S
BER
12 11.9 2
4
8
16 N max
32
74 km
64
-4
-3
10
10
74 km
(D)MUX -5
(a)
(b)
10
B2B
10
Fig. 4.
12
14
(D)MUX
16 18 OSNR [dB]
B2B
-4
20
22
24
10
12
14
16
18 20 OSNR [dB]
22
24
26
Average BER over all tributaries versus OSNR for (a) MDM-QPSK-OFDM and (b) MDM-8QAM-OFDM.
February 1, 2015 / Vol. 40, No. 3 / OPTICS LETTERS 15
74km Average: 74km
shows an improvement proportional to the MDL in the system by using only eight hypersymbols candidates.
(D)MUX Average: (D)MUX
The support of Phoenix Photonics, the German Federal Ministry of Education and Research (01BP12300A, EUREKA-Project SASER), and the European Committee 7th Framework Program under grant agreement 258033 (MODE-GAP) is gratefully acknowledged.
MDL [dB]
10
5 B2B Average: B2B 0
-3
Fig. 5.
-2
-1 0 1 Frequency [GHz]
2
3
MDL as a function of the frequency.
approaches for a set of measurements using MDM-QPSKOFDM and MDM-8QAM-OFDM. The curves show the performance of back-to-back (B2B) with and without (D)MUX and, 74-km transmission. The FEC limit is also shown for 20% overhead [6]. As an example, Fig. 4 depicts the wIRSML detection upper (IRSML) and lower (wIRSML with optimum ρ) bound for 74-km transmission. Figure 4 shows that the wIRSML scheme allows for superior performance in comparison with the MMSE equalizer. Its improvement for QPSK is 0.5 and 1.1 dB for the (D)MUX and 74 km curves, respectively, at 1e − 3 BER with respect to the MMSE equalizer. For 8-QAM, the performance improves by 0.9 and 1.3 dB at 1e − 2 BER with respect to the MMSE equalization. As shown in [14], and the references therein, in the presence of MDL, ML detection enhances the system performance and its improvement depends on the amount of MDL in the system: sˆ wIRSML arg min
s0 ∈A∨ˆsMMSE
331
ρ‖r − HˆsMMSE ejΦCPE ‖2 ; ‖r − Hs0 ejΦCPE ‖2
(5)
A fsjs ∈ S; s ≠ sˆMMSE g. The MDL in this system was computed and is depicted in Fig. 5. Similar to [10], an MDL of approximately 8 dB is observed by using the photonic lanterns. An additional MDL of 2 dB is observed after the transmission over 74 km, which is attributed to splicing imperfections, slightly different fiber attenuation coefficients per mode, and noise levels added from the single-mode amplifiers after demultiplexing the signal. In conclusion, we have assessed the performance of the proposed weighted IRSML (wIRSML) detection algorithm with the transmission of 163-Gb∕s MDM-QPSKOFDM and 245-Gb∕s MDM-8QAM-OFDM over 74 km. Compared to MMSE equalizer, the wIRSML detection
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