[from the Guest Editors]
Ivan B. Djordjevic, William Shieh, Xiang Liu, and Moshe Nazarathy
Advanced Digital Signal Processing and Coding for Multi-Tb/s Optical Transport
T
he exponential Internet traffic growth places an enormous transmission capacity demand on the underlying information infrastructure at all levels, ranging from core to access networks. In response to the capacity demand, the IEEE ratified a 40/100 Gb/s Ethernet (GbE) standard (IEEE 802.3ba) in June 2010. The deployment of 100GbE has been underway at an accelerated pace. To meet the ever-increasing capacity demands, 1Tb/s Ethernet (TbE) rates and beyond (e.g., 4 TbE and 10 TbE) are expected to be standardized in the near future. There are several emerging technologies, such as Nyquist wavelength- division multiplexing (WDM), orthogonal frequency-division multiplexing (OFDM), polarization-division multiplexing (PDM), and high-level modulation formats, potentially usable in concert to deliver multiTbE services. However, many challenges still exist with respect to practical and cost-effective implementations of these new technologies. The reality is that TbE or multi-TbE connectivity requires massive parallel processing in both the optical and electronic domains. The envisioned capacity growth in Internet traffic is about to place enormous demand not only on transmission speed at every level but also on the energy consumption required for information creation, distribution, and reception. Recent studies indicate that the power consumed by the information and communication technology (ICT), currently about 2–4% of total carbon emissions, is going to be doubled by the end of this decade, provided the current trend continues. Therefore, the Internet is becoming constrained not only by Digital Object Identifier 10.1109/MSP.2013.2288652 Date of publication: 12 February 2014
achievable speed and capacity but also by tolerable energy consumption. It is a wellknown fact that large data centers are built closer to power plants to provide ample and cost-effective energy supply. It can be concluded that it is imperative for the research and development community to address, sooner rather than later, both bandwidth and energy constraints; any technological advances on this subject, even seemingly incremental, would be meaningful and beneficial. This issue of IEEE Signal Processing Magazine aims to highlight diverse recent advances in digital signal processing (DSP) and coding, enabling TbE and multi-TbE optical transport while addressing bandwidth and energy constraints. The addressed topics range from sophisticated modulation and coding schemes to advanced detection schemes. The multiTb/s optical transports over either singlemode fibers or few-mode/few-core fibers are also topics covered in this special issue. The main technologies covered by this special issue comprise multiple-input, multiple-output (MIMO) signal processing, advanced multilevel and multidimensional modulation schemes, advanced multiplexing schemes, signal processing for superchannel transmission, advanced DSP for signal detection and equalization, and advanced coding, all aiming at achieving multi-Tb/s optical transports. Liu et al. introduce the concept of superchannel and review recent advances in the generation, transmission, and detection of optical superchannels at channel data rates of the order of Tb/s. The authors describe the multi-Tb/s enabling DSP techniques including Nyquist-WDM, multiband OFDM, software-defined modulation and detection, advanced coding, and joint DSP among the superchannel constituents.
IEEE SIGNAL PROCESSING MAGAZINE [15] march 2014
Arık et al. present the fundamentals of MIMO signal processing for mode-division multiplexing (MDM) in multimode fiber (MMF). They further compare the performance and complexity of MIMO signal processing architectural candidates, establishing that programmable frequencydomain equalization (FDE) of chromatic dispersion and adaptive FDE of modal dispersion (MD) provide an attractive combination. The authors also review two major algorithms for adaptive FDE of MD, mainly least mean squares and recursive least squares, analyzing their complexity, throughput and adaptation speed. Zhou provides a systematic review of the challenges and recent progress in timing and carrier synchronization techniques for high-speed optical transmission systems using single-carrier-based coherent optical modulation formats. Du et al. review different approaches to the mitigation of fiber nonlinearity impairments, including methods directly compensating fiber nonlinearity, such as digital back-propagation, as well as the technique of optimizing the modulation format to reduce the transmission impairments resulting from fiber nonlinearities. Yoshida et al. describe a critical technique for cycle slip (CS) compensation in nondifferential coded coherent optical transmission systems. They describe how CS can be estimated from a shorter block of symbols by monitoring sparse and asymmetric polarization block coded symbols. Nazarathy and Tolmachev describe the use of underdecimated filter banks to digitally slice the optical channel bandwidth into multiple spectrally disjoint subbands to be processed in parallel. This is an alternative approach to the parallelization of (continued on page 142)
[lecture notes]
continued
verifying the so-called double Levinson recursion [7] a NM (i) = a NM- 1 (i) + C N, M c NM- 1 (N - i) (30) N N-1 N-1 c M (i) = c M (i) + K N, M a M (N - i) (31) with i = 0, 1, f, N. These recursions reproduce twice (8), because both polynomials are forward. We can define also two backward polynomials verifying two recursions identical to (9). When M = 0 these polynomials are equal and the recursion recovers the one stated in (15). The sets of a NM (i), c NM (i) i = 0, 1, f, N are the solutions of the normal equations, (17) and (18), respectively. It can be shown that A NM (z) and N C M + 1 (z) are aside a constant reverse polynomials, which leads to
C N, M K N, M + 1 = 1, (32)
an important relation that is useful in the determination of the orders. From these polynomials we can ■■ construct a recursive algorithm for obtaining the MA parameters
[from the Guest Editors]
CONCLUSIONS There is an alternative solution for the normal equations that lead to different use of the predictor coefficients when defining the forward and backward prediction error filters. A simple algorithm for the computation of the predictor coefficients was presented. Its generalization for the computation of the AR parameters of an ARMA model was also described.
References
[1] T. A. Baran and A. V. Oppenheim, “A derivation of the recursive solution to the autocorrelation normal equations,” IEEE Signal Processing Mag., vol. 30, no. 1, pp. 142–144, Jan. 2013. [2] J. P. Burg, “Maximum entropy spectral analysis,” Ph.D. dissertation, Dept. Geophys., Stanford Univ., Stanford, CA, May 1975. [3] J. Le Roux and Y. Grenier, “An iterative procedure for moving average models estimation,” in Proc. IEEE ICASSP, 1980. [4] M. D. Ortigueira, “Methodology, implementation and evaluation in spectral analysis (in Portuguese),” Ph.D. dissertation, Instituto Superior Tecnico, Lisbon, 1984. [5] M. D. Ortigueira, “ARMA realization from the reflection coefficient sequence,” Signal Processing, vol. 32, no. 3, June 1993. [6] M. D. Ortigueira and J. M. Tribolet, “Global versus local minimization in least-squares AR spectral estimation,” Signal Processing, vol. 7, pp. 267–281, 1984.
Acknowledgment This work was partially funded by national funds through the Foundation for Science and Technology of Portugal.
[7] M. D. Ortigueira and J. M. Tribolet, “On the double Levinson recursion formulation of ARMA spectral estimation,” in Proc. Int. Conf. Acoustics, Speech, and Signal Processing, Boston, MA, 1983.
AUTHOR Manuel D. Ortigueira (
[email protected]) is an associate professor of the Department of Electrical Engineering of Faculty of Sciences and Technology of Universidade Nova de Lisboa and senior investigator in the signal processing group of UNINOVA.
[9],J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications. Englewood Cliffs, NJ: Prentice Hall, 2007.
[8] M. D. Ortigueira and A. J. Serralheiro, “Pseudofractional ARMA modelling using a double Levinson recursion,” IET Control Theory Applicat., vol. 1, no. 1, pp. 173–178, Jan. 2007.
[10] E. A. Robinson and S. Treitel, “Maximum entropy and the relationship of the partial autocorrelation to the reflection coefficients of a layered system,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. ASSP-28, no. 2, Apr. 1980.
[SP]
(continued from page 15)
the receiver signal processing task to multiple slower processors, performed in the frequency domain (FD) rather than in the time domain. They show that subbandbased FD parallelization is especially suited to long-haul optical fiber communication systems. Lau et al. describe the advances in DSP techniques that enable Tb/s transmission as well as software-defined flexible transponders supporting adaptive modulation formats and elastic optical networks. Among the covered DSP topics are carrier phase estimation for high spectral efficiency and adaptive signal processing techniques. Progress towards a universal DSP platform for arbitrary QAM transmission is also covered. Beygi et al. review the joint design of forward error correction and modulation for fiber-optic communications. The authors use an information-theoretic design framework to investigate coded modulation (CM) techniques for
■■ obtain an ARMA Burg-like algorithm, but this goes beyond the objectives of this column [5], [8].
fiber-optic channels. The authors further discuss two- and four-dimensional CM schemes. They also address the computational complexity and hardware constraints of CM schemes. Finally, the authors treat signal shaping and rateadaptation capabilities to accommodate different signal qualities. Djordjevic et al. describe how to jointly address the limited bandwidth of the transport infrastructure, high energy consumption, and network heterogeneity issues. They present an adaptive software-defined low-density parity check-coded multiband approach involving spatial-MIMO and alloptical-OFDM, enabling energy-efficient high-bandwidth delivery with fine granularity and elastic bandwidth utilization. The modulation is based on multidimensional signaling to improve the tolerance to fiber nonlinearities and imperfect compensation of channel impairments, based on a hybrid nature employing both electrical and optical degrees of freedom.
IEEE SIGNAL PROCESSING MAGAZINE [142] march 2014
The guest editors would like to express their gratitude to colleagues and individuals who directly or indirectly contributed to this special issue. In particular, we would like to acknowledge all the authors who have submitted their manuscripts as well as all the reviewers whose review comments have greatly improved the overall quality of the issue. Special thanks are extended to Editor-in-Chief Abdelhak Zoubir and Special Issues Area Editor Fulvio Gini for their tremendous support during the solicitation and review processes, as well as to Rebecca Wollman for her professional administrative assistance in the logistics of the special issue and its promotion. All the aforementioned supports that we received are indispensable for making this special issue happen. We hope that this issue will provide the readers with insights into a broad scope of advanced DSP and coding technologies for future multi-Tb/s optical transport. [SP]
