Digital filters underpin the performance of coherent optical receivers which exploit digital signal processing (DSP) to mitigate transmission impairments. We outline the principles of such receivers and review our experimental investigations into compensation of polarization mode dispersion. We then consider the details of the digital filtering employed and present an analytical solution to the design of a chromatic dispersion compensating filter. Using the analytical solution an upper bound on the number of taps required to compensate chromatic dispersion is obtained, with simulation revealing an improved bound of 2.2 taps per 1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization tracking are outlined and through simulation, it is demonstrated that 100krad/s polarization rotations could be tracked using DSP with a clock frequency of less than 500MHz.

Digital filters for coherent optical receivers.

This paper presents a novel digital feedforward carrier recovery algorithm for arbitrary M-ary quadrature amplitude modulation (M-QAM) constellations in an intradyne coherent optical receiver. The approach does not contain any feedback loop and is therefore highly tolerant against laser phase noise. This is crucial, especially for higher order QAM constellations, which inherently have a smaller phase noise tolerance due to the lower spacing between adjacent constellation points. In addition to the mathematical description of the proposed carrier recovery algorithm also a possible hardware-efficient implementation in a parallelized system is presented and the performance of the algorithm is evaluated by Monte Carlo simulations for square 4-QAM (QPSK), 16-QAM, 64-QAM, and 256-QAM. For the simulations ASE noise and laser phase noise are considered as well as analog-to-digital converter (ADC) and internal resolution effects. For a 1 dB penalty at BER = 10-3, linewidth times symbol duration products of 4.1 x 10-4 (4-QAM), 1.4 x 10-4 (16-QAM), 4.0 x 10-5 (64-QAM) and 8.0 x 10-6 (256-QAM) are tolerable.

Hardware-Efficient Coherent Digital Receiver Concept With Feedforward Carrier Recovery for $M$ -QAM Constellations

The drive for higher performance in optical fiber systems has renewed interest in coherent detection. We review detection methods, including noncoherent, differentially coherent, and coherent detection, as well as a hybrid method. We compare modulation methods encoding information in various degrees of freedom (DOF). Polarization-multiplexed quadrature-amplitude modulation maximizes spectral efficiency and power efficiency, by utilizing all four available DOF, the two field quadratures in the two polarizations. Dual-polarization homodyne or heterodyne downconversion are linear processes that can fully recover the received signal field in these four DOF. When downconverted signals are sampled at the Nyquist rate, compensation of transmission impairments can be performed using digital signal processing (DSP). Linear impairments, including chromatic dispersion and polarization-mode dispersion, can be compensated quasi-exactly using finite impulse response filters. Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phase noise, can be compensated partially. Carrier phase recovery can be performed using feedforward methods, even when phase-locked loops may fail due to delay constraints. DSP-based compensation enables a receiver to adapt to time-varying impairments, and facilitates use of advanced forward-error-correction codes. We discuss both single- and multi-carrier system implementations. For a given modulation format, using coherent detection, they offer fundamentally the same spectral efficiency and power efficiency, but may differ in practice, because of different impairments and implementation details. With anticipated advances in analog-to-digital converters and integrated circuit technology, DSP-based coherent receivers at bit rates up to 100 Gbit/s should become practical within the next few years.

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Coherent detection in optical fiber systems

Digital coherent receivers have caused a revolution in the design of optical transmission systems, due to the subsystems and algorithms embedded within such a receiver. After giving a high-level overview of the subsystems, the optical front end, the analog-to-digital converter (ADC) and the digital signal processing (DSP) algorithms, which relax the tolerances on these subsystems are discussed. Attention is then turned to the compensation of transmission impairments, both static and dynamic. The discussion of dynamic-channel equalization, which forms a significant part of the paper, includes a theoretical analysis of the dual-polarization constant modulus algorithm, where the control surfaces several different equalizer algorithms are derived, including the constant modulus, decision-directed, trained, and the radially directed equalizer for both polarization division multiplexed quadriphase shift keyed (PDM-QPSK) and 16 level quadrature amplitude modulation (PDM-16-QAM). Synchronization algorithms employed to recover the timing and carrier phase information are then examined, after which the data may be recovered. The paper concludes with a discussion of the challenges for future coherent optical transmission systems.

Digital Coherent Optical Receivers: Algorithms and Subsystems

Celebrating the 20th anniversary of Optics Express, this paper reviews the evolution of optical fiber communication systems, and through a look at the previous 20 years attempts to extrapolate fiber-optic technology needs and potential solution paths over the coming 20 years. Well aware that 20-year extrapolations are inherently associated with great uncertainties, we still hope that taking a significantly longer-term view than most texts in this field will provide the reader with a broader perspective and will encourage the much needed out-of-the-box thinking to solve the very significant technology scaling problems ahead of us. Focusing on the optical transport and switching layer, we cover aspects of large-scale spatial multiplexing, massive opto-electronic arrays and holistic optics-electronics-DSP integration, as well as optical node architectures for switching and multiplexing of spatial and spectral superchannels.

Fiber-optic transmission and networking: the previous 20 and the next 20 years [Invited]

We report on an optical intradyne receiver experiment with frequency estimation. Frequency estimation allows, if performed prior to block phase estimation or other phase recovery techniques, for a much higher frequency difference between transmit laser and local oscillator laser. We demonstrate the feasibility of our approach in a 20-Gb/s quadrature phase-shift keying experiment

Frequency Estimation in Intradyne Reception

A 5-b flash A/D converter (ADC) is developed in an 0.18-/spl mu/m SiGe BiCMOS that supports sampling rates of 10 Gsample/s. The ADC is optimized to operate in digital equalizers for 10-Gb/s optical receivers, where the ADC has to deliver over three effective number of bits (ENOBs) at Nyquist. A fully differential flash ADC incorporating a wide-band track-and-hold amplifier (THA), a differential resistive ladder, an interpolation technique, and a high-speed comparator design is derived to resolve the aperture jitter and metastability error. The ADC achieves better than 4.1 effective bits for lower input frequencies and three effective bits for Nyquist input at 10 GS/s. The ADC dissipates about 3.6 W at the maximum clock rate of 10 GS/s while operating from dual -3.7/-3V supplies and occupies 3/spl times/3mm/sup 2/ of chip area.

A 5-b 10-GSample/s a/D converter for 10-gb/s optical receivers

We propose novel discrete cosine transform (DCT) pseudophase techniques to estimate shift/delay between two one-dimensional(1-D) signals directly from their DCT coefficients by computing the pseudophase shift hidden in DCT and then employing the sinusoidal orthogonal principles, applicable to signal delay estimation remote sensing. Under the two-dimensional (2-D) translational motion model, we further extend the pseudophase techniques to the DCT-based motion estimation (DXT-ME) algorithm for 2-D signals/images. The DXT-ME algorithm has certain advantages over the commonly used full search block-matching approach (BKM-ME) for application to video coding despite certain limitations. In addition to its robustness in a noisy environment and low computational complexity, O(M/sup 2/) for an M/spl times/M search range in comparison to the O(N/sup 2//spl middot/M/sup 2/) complexity of BKM-ME for an N/spl times/N block, its ability to estimate motion completely in DCT domain makes possible the fully DCT-based motion-compensated video coder structure, which has only one major component in the feedback loop instead of three as in the conventional hybrid video coder design, and thus results in a higher system throughput. Furthermore, combination of the DCT and motion estimation units can provide space for further optimization of the overall coder. In addition, the DXT-ME algorithm has solely highly parallel local operations and this property makes feasible parallel implementation suitable for very large scale integration (VLSI) design. Simulation on a number of video sequences is presented with comparison to BKM-ME and other fast block search algorithms for video coding applications even though DXT-ME is completely different from any block search algorithms.

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DCT-based motion estimation

A receiver for coherent detection of a PSK modulated optical carrier includes an optical detector, digital-to-analog converters, and a digital module. The optical detector is configured to mix the modulated optical carrier with two phase components of a reference optical carrier and to produce analog output signals representative of optical signals produced by said mixing. The digital-to-analog converters are connected to receive the analog output signals and to produce digital signals from the received analog output signals. The digital module is connected to receive the digital signals and to perform one of compensating the received digital signals for a conjugate phase misalignment between the mixed components, extracting phase of the received digital signals, and estimating a frequency offset between the two carriers from the received digital signals.

Coherent phase-shift-keying

A method and apparatus are provided for performing electronic equalization in optical communication systems. Coefficient values in equalizers, such as feed forward equalizers or decision feedback equalizers, are updated using higher-order algorithms in the Least-Mean-2Nth-Order family. An optical receiver includes a photo-detector for converting a received optical signal to an electrical signal; and an equalizer for removing intersymbol interference from the electrical signal, wherein coefficients of the equalizer are updated based upon a least-mean 2Nth-order (LMN) algorithm (N is greater than one). Feed forward equalizer and decision feedback equalizer implementations are disclosed. The non-symmetric nature of optical noise is addressed by varying A slicer threshold based on an incoming signal distribution to reduce bit errors.

Ut-Va Koc

Papers

Frequency Estimation in Intradyne Reception

A 5-b 10-GSample/s a/D converter for 10-gb/s optical receivers

DCT-based motion estimation

Coherent phase-shift-keying

Method and apparatus for electronic equalization in optical communication systems