Chromatic dispersion mitigation in long-haul fiber-optic communication networks by sub-band partitioning

We propose and experimentally demonstrate a novel sub-band multiplexed data architecture for chromatic dispersion (CD) mitigation. We have demonstrated 32 GBaud multi-sub-band (MSB) dual-polarization (DP) 16QAM transmission over 2400 km. Using this approach, the transmitted signal bandwidth is divided into multiple narrow-bandwidth sub-bands, each operating at a lower baud rate. Within each sub-band bandwidth, the CD frequency response can be approximated as a linear-phase band-pass filter, which can be considered as an analog delay that does not require compensation. Therefore, the resulting receiver digital signal processing (DSP) is simplified due to the removal of the CD compensation equalizer. In addition, this leads to efficient parallelization of DSP tasks by deploying multiple independent sub-band processors running at a lower clock rate. The proposed system reduces receiver computational complexity and offers 1 dB higher Kerr-nonlinearity tolerance and 2% extended transmission reach in comparison to the conventional single carrier systems. ©2015 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.4230) Multiplexing; (060.1660) Coherent communications. References and links 1. M. Kuschnerov, T. Bex and P. Kainzmaier, “Energy efficient digital signal processing,” in Optical Fiber Communications Conference and Exhibition (Optical Society of America, 2014), paper Th3E.7. 2. B. S. G. Pillai, B. Sedighi, K. Guan, N. P. Anthapadmanabhan, W. Shieh, K. J. Hinton, and R. S. Tucker, “Endto-end energy modeling and analysis of long-haul coherent transmission systems,” J. Lightwave Technol. 32(18), 3093–3111 (2014). 3. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). 4. A. Tolmachev and M. Nazarathy, “Filter-bank based efficient transmission of reduced-guard-interval OFDM,” Opt. Express 19(26), B370–B384 (2011). 5. M. Nazarathy and A. Tolmachev, “Subbanded DSP architectures based on underdecimated filter banks for coherent OFDM receivers: Overview and recent advances,” IEEE Signal Process. Mag. 31(2), 70–81 (2014). 6. M. Malekiha, I. Tselniker, M. Nazarathy, A. Tolmachev, and D. V. Plant, “Experimental demonstration of lowcomplexity fiber chromatic dispersion mitigation for reduced guard-interval OFDM coherent optical communication systems based on digital spectrum sub-band multiplexing,” Opt. Express 23(20), 25608–25619 (2015). 7. K. P. Ho, “Subband equaliser for chromatic dispersion of optical fibre,” Electron. Lett. 45(24), 1224–1226 (2009). 8. C. Li, Q. Yang, T. Jiang, Z. He, M. Luo, C. Li, X. Xiao, D. Xue, X. Yi, and S. Yu, “Investigation of Coherent Optical Multiband DFT-S OFDM in Long Haul Transmission,” IEEE Photonics Technol. Lett. 24(19), 1704– 1707 (2012). 9. X. Liu, S. Chandrasekhar, B. Zhu, P. Winzer, A. Gnauck, and D. Peckham, “448-Gb/s Reduced-Guard-Interval CO-OFDM Transmission Over 2000 km of Ultra-Large-Area Fiber and Five 80-GHz-Grid ROADMs,” J. Lightwave Technol. 29(4), 483–490 (2011). 10. X. Liu, P. Winzer, C. Sethumadhavan, S. Randel, and S. Corteselli, “Multiband DFT-Spread-OFDM Equalizer with Overlap-and-Add Dispersion Compensation for Low-Overhead and Low-Complexity Channel Equalization,” in Optical Fiber Communication Conference, (Optical Society of America, 2013), paper OW3B.2. 11. J. Munir, A. Mezghani, H. Khawar, I. Slim, and J. A. Nossek, “Chromatic dispersion compensation using filter bank based complex-valued all-pass filter,” in 10th International ITG Conference on Systems, Communications and Coding (2015), paper 1403.1732. #251041 Received 28 Sep 2015; revised 6 Dec 2015; accepted 7 Dec 2015; published 10 Dec 2015 (C) 2015 OSA 14 Dec 2015 | Vol. 23, No. 25 | DOI:10.1364/OE.23.032654 | OPTICS EXPRESS 32654 12. M. Nazarathy, A. Tolmachev, and S. Ben-Ezra, “Sub-banding DSP for flexible optical transceivers,” in 14th International Conference on Transparent Optical Networks (2012), paper 6253734. 13. C. Liu, J. Pan, T. Detwiler, A. Stark, Y. T. Hsueh, G. K. Chang, and S. E. Ralph, “Super receiver design for superchannel coherent optical systems,” Proc. SPIE 8284, 828405 (2012). 14. F. J. Harris, C. Dick, and M. Rice, “Digital receivers and transmitters using polyphase filter banks for wireless communications,” IEEE Trans. Microw. Theory Tech. 51(4), 1395–1412 (2003). 15. J. G. Proakis, Digital Communications (McGraw Hill, 2001). 16. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1164–1179 (2010). 17. G. P. Agrawal, Fiber-Optic Communication Systems (John Wiley & Sons 2012). 18. M. Qiu, Q. Zhuge, M. Chagnon, Y. Gao, X. Xu, M. Morsy-Osman, and D. V. Plant, “Digital subcarrier multiplexing for fiber nonlinearity mitigation in coherent optical communication systems,” Opt. Express 22(15), 18770–18777 (2014).


Introduction
To satisfy the ever-increasing capacity demand in optical fiber communications, both the spectral efficiency and the data rate carried by individual wavelength division multiplexed channels have to be increased.Currently, CD equalizer's high power and area requirements in long-haul and metro line-card application-specific integrated circuitries (ASICs) [1,2] is one of the major obstacles for implementing advanced DSP techniques such as nonlinearity compensation.Coherent optical OFDM is an attractive 100 Gb/s modulation format [3], and it is well suited for multi-sub-band (MSB) filter-bank (FB)-based detection [4].It enables compensation of all linear channel impairments, including CD, via one-tap equalizers [3].OFDM however is not spectrally efficient due to the large required overhead.The main overhead arises from the long cyclic prefix (CP) length required to accommodate the accumulated CD.Dispersion-induced delay spread scales quadretically with the signal bandwidth [4].A subbanded OFDM receiver architecture has been proposed to significantly reduce CP-overhead (i.e.guard interval between OFDM frames) [4,5].Using this approach, the transmitted signal bandwidth is divided into multiple narrow bandwidth OFDM subbands.This bandwidth partitioning allows for CD compensation on a per sub-band basis and achieves higher DSP efficiency as well as a simplified parallelization.Recently, we experimentally demonstrated a reduced-guard-interval (RGI) multi-sub-band (MSB) OFDM DSP architecture [6].We observed that transmission reach is reduced in comparison to conventional single carrier systems.This is due to the higher sensitivity of OFDM systems to local oscillator frequency offset and phase noise.Furthermore, because of optical modulator DC leakage center subcarriers were not used for data transmission and the data sub-carrier allocation was modified.This complicates the filter-bank polyphase implementation and reduces the spectral efficiency.In order to improve DSP efficiency, a subbanded CD equalizer has been proposed for single carrier systems where each subband is individually dispersion compensated [7].Multi-band DFTS (MB-DFTS) OFDM equalization was introduced to realize sub-band CD equalization by allocating a sufficiently large guard interval to reduce the CD equalizer complexity [8].MB-DFTS OFDM is essentially a single carrier frequency multiplexing (SC-FDM) technique with frequency domain equalization (FDE).Moreover, CD compensation can be applied prior to OFDM signal processing in order to reduce CP overhead and improve spectral efficiency [9].X. Liu et.al. proposed a novel MB-DFTS OFDM equalizer that combines CD pre-compensation with OFDM equalization and sub-band demultiplexing in order to significantly reduced DSP complexity [10].
In this work, we further investigate the multi-sub-band processing architecture.We replace the DFTS-OFDM multiplexing/demultiplexing with an array of low rate single carrier (SC) sub-bands combined with polyphase channelizer.This improves the system tolerance to phase noise and local oscillator frequency offset.In addition, we used a conventional timedomain SC equalizer applied to each sub-band individually rather than using the frequencydomain DFTS-OFDM channel equalization technique.This approach allowed us to eliminate the CP overhead and improve the spectral efficiency.Using this approach, the transmitted signal bandwidth is divided into multiple sub-bands, each operating at a lower baud rate.For a 32 GHz channel, we have find the number of sub-bands at different transmission distance required to fully mitigate the effects of CD and to remove the CD compensation equalizer at the receiver.This method allows for a significant reduction of the receiver DSP computational complexity and it offers a simplified implementation for flexible optical transceivers.Finally, we compared the performance and transmission reach of the proposed method against conventional single carrier systems.
In conventional single carrier systems, fiber CD is modeled as a quadratic-phase all-pass filter.In our proposed transmission scheme, we can approximate CD frequency response as a bank of M narrow-bandwidth linear-phase band-pass filters, each having different, yet constant group delay.As a result, the bandwidth partitioning technique transforms CD into different analog delays for each sub-band.Moreover, it achieves higher DSP efficiency as well as simplified parallelization [4,5,11].In addition, flexible optical transceivers (with reconfigurable rates and modulation formats) may be efficiently realized using this filter-bank based digital sub-banding approach [12].For example, it allows flexible spectral occupancy by turning on and off certain sub-bands.Also, when operating with a fixed spectral occupancy, this allows changing the constellation size of all or a sub-set of the sub-bands in order to engineer the desired data throughput.Moreover, all sub-bands share the same optical transmission path therefore they experience common channel properties.This fact allows for the utilization of more accurate and efficient impairment compensation techniques by jointly processing multiple sub-bands and taking advantage of information from other sub-bands [13].Additionally, each sub-band is considerably flatter in its frequency response due to its narrow bandwidth, which implies smaller channel eigenvalue spread.Therefore, they maintain faster and more accurate convergence for their adaptive filter coefficients in comparison to full-band conventional single carrier systems.This convergence speed-up will be manifested in every adaptive DSP algorithms.Consequently, rapid and accurate adaptive algorithms convergence means low data-aided overhead [5].
The partitioning and assembly of the sub-bands can be performed efficiently in the digital domain [14,15].In this work, we utilized an underdecimated uniform discrete Fourier transform (DFT) based filter-banks (FBs) transmitter and receiver with non-trivial prototype filter (i.e.overlapping sub-bands) [15].The remainder of the paper is organized as follows: Section 2 describes the motivation and principles for multi-sub-band signaling.Section 3 summarizes filter-bank base implementation of multi-sub-band communication systems.Section 4 explains the transmitter and receiver DSP architecture.In Section 5, we introduce the experimental setup.In Section 6, the performance of the multi-sub-band system is presented and discussed.The final Section 7 summarizes the multiple features of the proposed system.

Motivation and principles of multi-sub-band signaling
Digital signal processing (DSP) has played an important role in supporting the recent capacity expansion of optical networks.Modern coherent optical communications has benefited from many powerful DSP techniques because of the access to the full optical field information (phase and amplitude) at both transmitter and receiver.In the absence of Kerr nonlinearity, fiber can be regarded as a linear system.In principle, all the linear impairments can be fully compensated by digital filters [15].Fiber CD is a time-invariant distortion and accumulated CD may exceed several thousands of ps/nm at the receiver.Therefore, it is desirable to use a non-adaptive filter with fixed taps for CD compensation [16].On the other hand, the polarization-mode dispersion (PMD) may be modelled by the Jones matrix, and varies rapidly due to the fiber birefringence [17].As a result, the compensation of PMD should be adaptive to continuously adjust the filter taps coefficients.Consequently, channel equalization can be efficiently realized by separately addressing slowly time-varying transmission effects such as CD (by a long fixed-tap frequency-domain filter), from rapidly varying effects such as PMD, inter-symbol interference and other time-varying fiber impairments (by a short time-domain adaptive butterfly filter) [16].
Fiber CD results in temporal optical pulse broadening [17].Therefore, transmitted data is received with a delay spread (normalized in units of discrete-time sampling intervals, T s , at the receiver), which is given by [5]: 2 2 .
Where 2 β , BW and L are fiber group velocity dispersion parameter, signal bandwidth and transmission distance, respectively.At the receiver, the sampling rate is also proportional to the signal bandwidth as , where η is a factor related to the spectral efficiency and the oversampling ratio.Therefore, the delay spread caused by CD is given by: 2 2
(2) It is evident that the delay-spread (i.e.temporal pulse broadening) is quadratic in the bandwidth.This implies that it would be advantageous to decrease the bandwidth of the transmitted signal in order to significantly reduce the CD-induced delay spread.The complexity cost, C , for a finite impulse response time domain implementation of the CD compensation equalizer is ( ) When the CD equalizer is implemented in frequency domain, utilizing the fast Fourier transform (FFT) algorithm, the complexity cost can be as low as (log( )) . Therefore, dividing the total channel bandwidth into M subbands allows for per-sub-band compensation of CD while the delay spread in each sub-band is dramatically reduced by a factor of 2 M .For example, for a 32 GHz channel transmitted over a 2, 000 km link of standard single mode fiber, CD compensation of the un-partitioned BW transmission requires 250 taps per symbol, while dividing the BW into 8 M = subbands reduces this number to  In this section we pursue the computationally efficient digital implementation of the filterbank based communications.set of filters with common input) comprising filters.Notice that at this point each filterbank output still runs at the high sampling rate of the analog-to-digital converter (ADC), which is M times faster than a rate commensurate with sub-bands reduced BW M bandwidth.Therefore, we may place down-samplers (as described by arrow-down-K blocks) after the band pass filter outputs, retaining every K-th sample and discarding the samples in between, in effect reducing the sampling rate by a factor of K .The multiple outputs of the filter-bank are taken at the decimator outputs [15].

Filter-bank based communication systems
In practice, filter-bank systems are almost never directly implemented as shown in Fig. 1 (as band pass filters).The reason being that, in this configuration, filters must operate at a rate that is K times faster than the symbol rate 1 T .If the band-pass frequency responses are appropriately selected, it is possible to achieve quite efficient realizations.For example in the critically sampled case (i.e.K M = ), if the M receiver filters are selected as frequencyshifted versions of a single baseband filter (f)  G , the so-called prototype filter, the system of Fig. 1 becomes equivalent to that shown in Fig. 2. The next step is to realize the discrete-time modulations with the complex exponentials, by means of an inverse discrete Fourier transform (IDFT) applying linear time-invariant (LTI) filtering operations on the M branches (Fig. 3), inserting M filters corresponding to the so-called polyphase components of the prototype filter [15].The complexity of the resulting DFT + polyphase filters structure is very low [14].

Transmitter and receiver DSP structure
Figure 4 illustrates the block diagram of the transmitter-side DSP.The multi-sub-band signal was efficiently generated by utilizing a DFT-based synthesis filter-bank architecture [12].We adopted root-raised cosine (RRC) filter as a prototyping filter and calculated its polyphase  Figure 5 shows the top-level block diagram of multi-sub-band receiver.The DSP code starts with front-end compensation, including the DC removal, IQ imbalance compensation and optical hybrid IQ orthogonalization [16].Next, local oscillator (LO) laser frequency offset is compensated based on the DFT of the signal [16].For sub-band demultiplexing, the key element is a bank of M parallel digital band-pass filters, each handling 1 M of the channel bandwidth.This is implemented by a twice-underdecimated DFT-based filter-bank structure.The receiver prototype filter was selected to be matched to the pulse-shaping filter [5].According to Fig. 5, each of the M filter-bank outputs feeds a corresponding sub-band receiver processor.As a result, we have an array of M low-speed sub-band receivers working simultaneously and in parallel.The rationale for this approach is that while we have invested some computational overhead in partitioning the spectrum into M sub-bands at the transmitter, this allows operating each sub-band receiver at an M-times slower rate (compared to unpartitioned twice-oversampled single-carrier detection).In addition, this facilitates the realization of the receiver since each sub-band DSP processor does not require a conventional full-band CD compensation equalizer.Each sub-band DSP code starts with synchronization and timing recovery in order to facilitate data aided modulation transparent equalization.For synchronization, the integer part of each sub-band delay (measured in units of sub-band sample rate) may be readily corrected by conventional correlate and delay algorithms such as Schmidl-Cox [16] and using a simple digital buffer without any CD pre-equalization.Next, fractional part of the delay, as well as any additional channel linear impairments are corrected blindly by the low complexity multi-tap butterfly equalizer.This adaptive equalizer is implemented in the time domain, operating at 2 samples per symbol [16].The carrier phase is recovered using the superscalar parallelization based phase locked loop (PLL) [18].Finally, the symbols were mapped to bits and the bit error rate (BER) was counted over 100,000 bits and a soft-decision forward error correction (20% overhead) BER threshold of 2 2 10 − × was considered.We compared our results with a conventional single carrier transmission system.For this purpose, we removed the FFT-based filter-bank multi-sub-band encoder at the transmitter.At the receiver, we replaced the poly-phase filter-bank array with the overlap-and-save frequency domain CD equalizer, followed by matched filtering (as shown in Fig. 5.b).The remaining DSP blocks and other parameters are identical for both transmission schemes.

Experimental (simulation) setup
Figure 6 shows the schematic diagram of the experimental/simulation setup.On the transmitter side offline DSP, four 2-tuple independent pseudo-random bit sequences (PRBS) with length of 2 17 are mapped to 16QAM symbols, followed by multi-sub-band multiplexing (outlined in Fig. 4.a) for each polarization.A Ciena WaveLogic 3 (WL3) line card was employed, which contains four 39.5 GSa/s 6 bit digital-to-analog converter (DACs), a tunable frequency laser source, and a dual-polarization (DP) IQ modulator.The transmitter laser was operating at 1554.94 nm.The transmitter analog frequency response is compensated using the on-board built-in DSP of the WL3.The output optical signal is then boosted to 23 dBm using an erbium-doped fiber amplifier (EDFA), and subsequently attenuated using a conventional variable optical attenuator (VOA) in order to get a desired optical launch power.The optical signal is then launched into a recirculating loop.This loop consists of four spans of 80 km of single mode fiber (SMF-28e + LL) and four inline EDFAs.Each inline EDFA has a noise figure of 5.5 dB.A tunable bandwidth and tunable center wavelength band-pass filter (T-T BPF) is inserted after the 4th span in order to reject out-of-band amplified spontaneous emission (ASE) noise accumulated during transmission.The gain of the last EDFA is adjusted (increased by 10 dB compared to the other EDFAs) in order to compensate for losses occurring inside the recirculating loop, including switches, couplers and the band-pass filter.At the receiver side, an optical spectrum analyzer (OSA) was used in order to measure the optical signal-to-noise ratio (OSNR) at 0.5 nm resolution bandwidth and then it was converted to a 0.1 nm noise bandwidth.The gain of the pre-amplifier EDFA was adjusted to ensure that the signal power reaching the coherent receiver was held constant at 5 dBm.Finally, a 0.8 nm BPF was used to filter out the out-of-band amplified spontaneous emission (ASE) noise generated by the pre-amplifier.At the polarization-diversity 90° optical hybrid, the signal was mixed with 15.5 dBm local oscillator (LO) light from an external-cavity laser (ECL) with a linewidth of 100 kHz.The beating outputs were passed through four balanced photodetectors.
A 4-channel real-time oscilloscope sampled the signal at a sampling rate of 80 GSa/s digitized it with 8-bit resolution.
For the simulation model the DACs, optical modulator, fiber optic recirculating loop and coherent receiver were assumed ideal and implemented in OptiSystem v13.In addition, the LO frequency offset and fiber nonlinearity parameters were set to zero.

Discussion and results
In this section, we investigate the performance of multi-sub-band (MSB) architecture against conventional single carrier (SC) systems.Unlike conventional SC systems, the MSB technique does not require CD compensation equalizer, but other DSP blocks and parameters are identical for both schemes (also demonstrated in Fig. 5).For all measurements, a root raised cosine filter with a roll-off factor equal to 0.01 is chosen as a pulse-shaping filter for 32-GBaud DP-16QAM transmission.We used a nontrivial DFT filter-bank (i.e.overlapping sub-bands) structure for efficient implementation, therefore, a small roll-of factor reduces the linear cross-talk between overlapped neighbouring sub-bands and maximizes the spectral efficiency.Also, the butterfly filter has 15 adaptive taps at 2 Sa/symbol in both techniques.Figure 7 demonstrates the Q-factor penalty vs. number of sub-bands obtained at different transmission lengths, when the multi-sub-band signal architecture has been employed exclusively (i.e.no CD compensation).We observed that for 960, 1760, 2560 and 3360 km transmission 6, 8, 9 and 10 sub-bands is sufficient in order to reduce the Q-factor penalty below 0.5, 0.35, 0.2 and 0.1 dB, respectively.This residual penalty originates from the linear cross-talk between overlapped neighbouring sub-bands.It should be noted that this Q-factor penalty due to linear cross-talk decreases for smaller roll-of factors and longer transmission distances when the ASE noise becomes the dominant impairment.
Figure 8 shows minimum number of required sub-bands, in order to fully mitigate the effects CD for different distances (when no other impairments exist).According to Eq. ( 1), the CD-induced delay-spread decreases quadratically when decreasing the transmitted data bandwidth.Based on Fig. 5 and in accordance with Eq. ( 1), it is evident that the range from metro (typically less than 500 km) to long-haul (less than 5000 km) applications only requires a few sub-bands (less than 12) in order to mitigate CD.In addition, this can be efficiently implemented using a polyphase FFT-based filter-bank structures.This enables a highly efficient parallelization of DSP tasks by deploying multiple processors running at a lower clock rates.We want to point out that this multi-sub-band processing is essentially parallelization of the DSP in the frequency domain rather than the time domain.In experiment, the back-to-back performance is investigated first.Figure 9 summarizes the BER versus OSNR (at 0.1 nm noise bandwidth) curves for different numbers of sub-bands for 32 GBaud MSB-DP-16QAM.The OSNR is swept by using receiver-side noise loading and controlling the noise power using a VOA.As shown in both figures, small penalties are observed when we increase the number of subcarriers.It demonstrates that in the high OSNR regime the MSB architecture suffers from linear cross talk due to overlapping neighboring sub-bands.At low OSNRs both systems have similar performance.However, as the OSNR increases, MSB signal performance degrades due to the cross-talk between neighboring subbands.The penalty at the soft forward error correction (FEC) BER threshold of  Next, we investigate the BER under different launch powers.The investigated distance is 2240 km.shown in Fig. 10, if the power launched into the fiber is low both systems are mainly limited by linear impairments and the BER is approximately the same.However, as the launch power increases, fiber nonlinearities become more significant and MSB signaling enables a lower BER than the conventional single carrier signal.As demonstrated in Fig. 9 MSB signaling suffers from linear-crosstalk between neighboring sub-bands but after transmission the overall system performance improved due the higher nonlinearity tolerance of the MSB technique.The improvement is particularly significant when the launch power is larger than 1 dBm and it has been investigated and demonstrated previously in [18].In accordance with the results in Fig. 10, the achievable transmission distances of SC signals is slightly larger in comparison to MSB signals in the linear regime with low launch powers due to absence of crosstalk between neighboring sub-bands.However, if we investigate the maximum transmission distance of the two signals at their respective optimum launch powers, we can see that the achievable reach is extended for the multi-sub-band signals by 2% due to its higher nonlinearity tolerance while the complexity of receiver significantly decreases due to the elimination of the CD compensation equalizer and the reduced data rates of each subband receiver.

Conclusion
We numerically and experimentally demonstrated a novel DSP structure for the CD mitigation.The proposed concept is based on digitally partitioning the optical channel bandwidth into multiple sub-bands in order to process data in parallel and mitigate CD.It should be noted that this parallelization is performed in the frequency domain.Each narrowbandwidth sub-band is characterized by a flatter frequency response and a smaller CDinduced delay-spread, compared to the full-band SC signal.This enables per-sub-band compensation of CD by elementary timing recovery and minimal equalization.In terms of the DSP architecture, this approach allows for a highly efficient receiver implementation by deploying multiple processors running at a lower clock rate.Finally, we experimentally demonstrate that filter-bank based multi-sub-band signaling offers longer transmission reach, better nonlinearity tolerance, simplified realization of flexible optical transceivers in addition to evident lower computational complexity due to the elimination of CD compensation from the receiver DSP.This demonstrates the potential of multi-sub-banding for next generation flexible data-rate adaptive and spectral efficient high-speed communication systems.
for each sub-band[5].Therefore, the CD memory length decreased dramatically for each sub-band and it is comparable to other time-variant transmission effects such as PMD.As a result, a multi-sub-band processing architecture allows for compensation of all channel linear impairments including CD and PMD by a short time-domain adaptive butterfly equalizer.

Fig. 1 .
Fig. 1.A generic frequency-division-multiplexed communication link based on a synthesis filter-bank in the transmitter and an analysis filter-bank in the receiver (notice that the usual combination of filter-banks in DSP textbooks, for data compression purposes, has the opposite order of the analysis and synthesis filter-banks).
Figure 1 shows the block-diagram of a communication system employing filter-bank based multi-band modulation and demodulation concepts [14,15].A set of M modulated symbols is fed in parallel into a set of M discrete-time filters (with transfer functions (f), k 0,1, , M k H =  ).This set of filters with common additive output represents a synthesis filter-bank.At the receiver, demodulation is achieved by an analysis filter-bank (a #251041 Received 28 Sep 2015; revised 6 Dec 2015; accepted 7 Dec 2015; published 10 Dec 2015 (C) 2015 OSA

Fig. 2 .
Fig. 2. Equivalent filter-bank representation of the frequency-division-multiplexed communication link based on discrete-time up/down converters and baseband prototype filters.

Fig. 3 .
Fig. 3. Equivalent filter-bank representation of the frequency-division-multiplexed communication link based on M-points (I)DFT and M polyphase filters (corresponding to the uniform maximally decimated FBs).Notice that the receive filters were selected here to be matched filters relative to the transmit filters.
2015; revised 6 Dec 2015; accepted 7 Dec 2015; published 10 Dec 2015 (C) 2015 OSA coefficients required for the implementation.Next, we each sub-band power in order to have similar performance in back-to-back configuration.

Fig. 4 .
Fig. 4. a Transmitter-side DSP based on an M-point IDFT and M polyphase filters (corresponding to the M polyphases of the prototype pulse-shaping filter), 4.b optical spectra of transmitted multi-sub-band signal.

Fig. 5 .
Fig. 5. a Receiver-side DSP based on twice under-decimated M-points DFT and polyphase filters (The M receive polyphases were selected here to be matched filters relative to the transmit filters).5.b Conventional singe carrier receiver DSP.
4 dB for all cases of 4, 6 and 8 sub-bands partitioning.