Daniel J. F. Barros

Coherent detection in optical fiber systems

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.

Comparison of Orthogonal Frequency-Division Multiplexing and Pulse-Amplitude Modulation in Indoor Optical Wireless Links

We evaluate the performance of three direct-detection orthogonal frequency-division multiplexing (OFDM) schemes in combating multipath distortion in indoor optical wireless links, comparing them to unipolar M-ary pulse-amplitude modulation (M-PAM) with minimum mean-square error decision-feedback equalization (MMSE-DFE). The three OFDM techniques are DC-clipped OFDM and asymmetrically clipped optical OFDM (ACO-OFDM) and PAM-modulated discrete multitone (PAM-DMT). We describe an iterative procedure to achieve optimal power allocation for DC-OFDM. For each modulation method, we quantify the received electrical SNR required at a given bit rate on a given channel, considering an ensemble of 170 indoor wireless channels. When using the same symbol rate for all modulation methods, M-PAM with MMSE-DFE has better performance than any OFDM format over a range of spectral efficiencies, with the advantage of (M-PAM) increasing at high spectral efficiency. ACO-OFDM and PAM-DMT have practically identical performance at any spectral efficiency. They are the best OFDM formats at low spectral efficiency, whereas DC-OFDM is best at high spectral efficiency. When ACO-OFDM or PAM-DMT are allowed to use twice the symbol rate of M-PAM, these OFDM formats have better performance than M-PAM. When channel state information is unavailable at the transmitter, however, M-PAM significantly outperforms all OFDM formats. When using the same symbol rate for all modulation methods, M-PAM requires approximately three times more computational complexity per processor than all OFDM formats and 63% faster analog-to-digital converters, assuming oversampling ratios of 1.23 and 2 for ACO-OFDM and M-PAM, respectively. When OFDM uses twice the symbol rate of M-PAM, OFDM requires 23% faster analog-to-digital converters than M-PAM but OFDM requires approximately 40% less computational complexity than M-PAM per processor.

Optimized Dispersion Compensation Using Orthogonal Frequency-Division Multiplexing

Orthogonal frequency-division multiplexing (OFDM) can compensate for linear distortions, such as group-velocity dispersion (GVD) and polarization-mode dispersion (PMD), provided the cyclic prefix is sufficiently long. Typically, GVD is dominant, as it requires a longer cyclic prefix. Assuming coherent detection, we show how to analytically compute the minimum number of subcarriers and cyclic prefix length required to achieve a specified power penalty, trading off power penalties from the cyclic prefix and from residual inter-symbol interference (ISI) and inter-carrier interference (ICI). We derive an analytical expression for the power penalty from residual ISI and ICI.

Optical Modulator Optimization for Orthogonal Frequency-Division Multiplexing

Orthogonal frequency-division multiplexing (OFDM) has a high peak-to-average ratio (PAR), which can result in low optical power efficiency when modulated through a Mach-Zehnder (MZ) modulator. In addition, the nonlinear characteristic of the MZ can cause significant distortion on the OFDM signal, leading to in-band intermodulation products between subcarriers. We show that a quadrature MZ with digital predistortion and hard clipping is able to overcome the previous impairments. We consider quantization noise and compute the minimum number of bits required in the digital-to-analog converter (D/A). Finally, we discuss a dual-drive MZ as a simpler alternative for the OFDM modulator, but our results show that it requires a higher oversampling ratio to achieve the same performance as the quadrature MZ.

Comparison of Orthogonal Frequency-Division Multiplexing and On-Off Keying in Amplified Direct-Detection Single-Mode Fiber Systems

We discuss the use of orthogonal frequency-division multiplexing (OFDM) for combating group-velocity dispersion (GVD) effects in amplified direct-detection (DD) systems using single-mode fiber. We review known OFDM techniques, including asymmetrically clipped optical OFDM (ACO-OFDM), DC-clipped OFDM (DC-OFDM) and single-sideband OFDM (SSB-OFDM), and derive a linearized channel model for each technique. We present an iterative procedure to achieve optimum power allocation for each OFDM technique, since there is no closed-form solution for amplified DD systems. For each technique, we minimize the optical power required to transmit at a given bit rate and normalized GVD by iteratively adjusting the bias and optimizing the power allocation among the subcarriers. We verify that SSB-OFDM has the best optical power efficiency among the different OFDM techniques. We compare these OFDM techniques to on-off keying (OOK) with maximum-likelihood sequence detection (MLSD) and show that SSB-OFDM can achieve the same optical power efficiency as OOK with MLSD, but at the cost of requiring twice the electrical bandwidth and also a complex quadrature modulator. We compare the computational complexity of the different techniques and show that SSB-OFDM requires fewer operations per bit than OOK with MLSD.

Coherent detection in optical fiber systems: erratum

We correct a table showing the signal-to-noise ratio obtained in coherent detection. We also clarify a table showing the bandwidth requirements for homodyne and heterodyne downconverters. Otherwise, our previous results and conclusions are unchanged.

Comparison of Orthogonal Frequency-Division Multiplexing and ON–OFF Keying in Direct-Detection Multimode Fiber Links

We compare the performance of several direct-detection orthogonal frequency-division multiplexing (OFDM) schemes to that of ON-OFF keying (OOK) in combating modal dispersion in multimode fiber links. We review known OFDM techniques, including dc-clipped OFDM (DC-OFDM), asymmetrically clipped optical OFDM (ACO-OFDM) and pulse-amplitude modulated discrete multitone (PAM-DMT). We describe an iterative procedure to achieve optimal power allocation for DC-OFDM and compare analytically the performance of ACO-OFDM and PAM-DMT. We also consider unipolar M -ary pulse-amplitude modulation ( M-PAM) with minimum mean-square error decision-feedback equalization (MMSE-DFE). For each technique, we quantify the optical power required to transmit at a given bit rate in a variety of multimode fibers. For a given symbol rate, we find that unipolar M-PAM with MMSE-DFE has a better power performance than all OFDM formats. Furthermore, we observe that the difference in performance between M-PAM and OFDM increases as the spectral efficiency increases. We also find that at a spectral efficiency of 1 bit/s/Hz, OOK performs better than ACO-OFDM using a symbol rate twice that of OOK. At higher spectral efficiencies, M -PAM performs only slightly better than ACO-OFDM using twice the symbol rate, but requires less electrical bandwidth and can employ analog-to-digital converters at a speed only 81% of that required for ACO-OFDM.

Compensation of dispersion and nonlinearity in WDM transmission using simplified digital backpropagation

We study digital backpropagation for compensating linear and nonlinear impairments for wavelength-division-multiplexed transmission in single-mode fiber using a simplified numerical algorithm based on a non-iterative asymmetric split-step Fourier method.

Bandwidth-Scalable Long-Haul Transmission Using Synchronized Colorless Transceivers and Efficient Wavelength-Selective Switches

We propose a modular scalable long-haul architecture supporting variable-bandwidth channels with bit rates from 100 Gbit/s to beyond 1 Tbit/s. Colorless transceivers have two operating modes. One transceiver can transmit/receive a conventional narrow-band channel occupying a 30-GHz bandwidth and conveying 100 Gbit/s, or a set of M transceivers can cooperate to transmit/receive a wideband channel occupying an M 50-GHz bandwidth and conveying roughly 160 Gbit/s per 50 GHz (assuming polarization-multiplexed quaternary phase-shift keying). A colorless wavelength-selective switch supports two modes of add/drop (or (de)multiplexing) operation. It can add/drop narrow-band channels (each from/to one port) with minimal loss, or can add/drop wideband channels (each from/to M ports) without spectral gaps, with an additional loss not exceeding 1/3 (-4.8 dB), independent of M. Transceivers can use either single-carrier modulation or orthogonal frequency-division multiplexing (OFDM). We analyze and simulate OFDM-based systems to determine key design requirements, especially for synchronization of cooperating transceivers. A representative design achieves 1520-km reach with 1.4-dB margin in a dispersion-managed network using only erbium-doped fiber amplifiers, improving average spectral efficiency from about 2 to nearly 3 bits/s/Hz.

Analysis of continuous diaphragm electromyographic signal: results from a patient with amyotrophic lateral sclerosis.

Introduction: Analysis of continuous diaphragm electromyography (dEMG) has not been well studied. We describe a system of analyzing continuous dEMG using implanted electrodes. Methods: dEMG signal was acquired via two pairs of electrodes near the diaphragm motor points. Raw bursts of dEMG signal were compared to externally captured electrocardiogram (ECG) using adaptive filtering in order to remove cardiac contamination. Differential energy levels were used to identify each dEMG burst, and average amplitude and area values from both hemidiaphragms were aggregated and averaged for the duration of the recording. Results: A 64‐year‐old patient with amyotrophic lateral sclerosis underwent three serial dEMG studies every 6 months. An average of three tracings were collected per visit, and all had excellent intertest reliability (κ > 0.8). Average dEMG area correlated with forced vital capacity and mean inspiratory pressure (r2 > 0.9). Conclusions: The approach described represents a comprehensive method for capturing and analyzing continuous diaphragm EMG signal. Muscle Nerve, 2011