Electrical Mitigation of Penalties Caused by Group Delay Ripples for Different Modulation Formats

Electrical equalizers are proposed to mitigate the distortions caused by group delay ripples (GDRs) of cascaded optical filters (e.g., fiber Bragg gratings for chromatic dispersion (CD) compensation). Different electrical equalizers including feedforward equalizer (FFE), decision-feedback equalizer (DFE), nonlinear FFE-DFE, and maximum-likelihood sequence estimator are investigated and compared comprehensively for four different modulation formats: ON-OFF keying, optical duobinary, optical single sideband, and differential phase-shift keying. Especially, we find that the relationship of electrical equalization performance on the modulation format is very similar for the mitigation of GDR and CD.     

Nonlinear Electrical Equalization for Different Modulation Formats With Optical Filtering

Based on bit-error-ratio simulations, we investigate electrical-dispersion-compensation performance by using a nonlinear electrical equalizer based on nonlinear Volterra theory for different modulation formats. This nonlinear equalizer is compared to conventional decision-feedback equalizer as well as to maximum-likelihood sequence estimation. Especially, we show that nonlinear equalizers, in conjunction with narrowband optical filtering of the light signal, result in improved performance. First of all, the system can benefit from the noise reduction due to narrowband filtering. Second, interacting with chromatic dispersion, nonlinear equalizers benefit from the improved dispersion tolerance through spectrum reshaping by narrowband optical filtering. Finally, nonlinear equalizers can efficiently mitigate the distortion resulting from strong optical filtering     

应用于10 Gbit/s光通信及背板传输的自适应均衡器设计

描述了一种既可用于背板传输也可用于光纤通信的高速串行收发器前端均衡器的设计。为适应光信号在传播中的色散效应,使用前馈均衡器(FFE)加判决反馈均衡器(DFE)的组合,取代了背板通信中常用的连续时间线性均衡器(CTLE)和DFE的组合。设计使用3 pre-tap、3 post-tap和1个main tap的抽头组合方式,兼顾pre-cursor和post-cursor的信号失真,有效补偿范围为15 dB。补偿系数采用完全自适应算法调整,对FFE采用模拟MSE算法调整,DFE引擎采用1/16速率数字sign-sign最小均方差(LMS)算法实现。芯片使用UMC 28 nm工艺流片,输入信号频率为10 Gbit/s。     

MLSE Equalizers for Frequency Discrimination Receiver of MSK Optical Transmission System

We propose maximum-likelihood sequence estimator (MLSE) equalizers based on either Viterbi algorithm or template matching temple matching (TM) for the equalization of impairments imposed on the minimum shift keying (MSK) modulation formats in long haul transmission without optical dispersion compensation. The TM-MLSE equalizer is proposed as a simplified alternative for the Viterbi-MLSE equalizer. It is verified that the Viterbi-MLSE equalizer can operate optimally when noise approaches a Gaussian distribution. Simulation results of the performances of the two MLSE equalizers for optical frequency discrimination receiver-based optical MSK systems are described. The transmission performance is evaluated in terms of: (1) the chromatic dispersion (CD) tolerance for both Viterbi-MLSE and TM-MLSE equalizers; (2) transmission distance limits of Viterbi-MLSE equalizers with various number of states; (3)the robustness to fiber polarization mode dispersion (PMD) of Viterbi-MLSE equalizers; and (4) performance improvements for Viterbi-MLSE equalizers when utilizing sampling schemes with two and four samples per bit over the conventional single sample per bit. With a small number of states (64 states), the non-compensating optical link can equivalently reach up to approximately 928 km SSMF for 10 Gb/s transmission or 58 km SSMF for 40 Gb/s. The performance of 16-state Viterbi-MLSE equalizers for optical frequency discrimination receiver (OFDR)-based optical MSK transmission systems for PMD mitigation is also numerically investigated. The performance of Viterbi-MLSE equalizers can be further improved by using the sampling schemes with multiple samples per bit compared to the conventional single sample bit. The equalizer also offers high robustness to fiber PMD impairment.     

A nonlinear electrical equalizer with decision feedback for OOK optical communication systems

In this paper we introduce a nonlinear equalizer using the Radial Basis Function (RBF) network with decision feedback equalizer (DFE) for electronic dispersion compensation in optical communication systems with on-off-keying and a direct detection receiver. The RBF method introduces a non-linear equalization technique suitable for optical communication direct detection systems that include nonlinear transformation at the photodetector. A bit error rate performance comparison shows that the RBF with DFE out performs the RBF without DFE and achieves similar results provided by maximum likelihood sequence estimator.     

A class of block-iterative equalizers for intersymbol interferencechannels: fixed channel results

A new and efficient class of nonlinear equalizers is developed for intersymbol interference (ISI) channels. These -"iterated-decision equalizers” use an optimized multipass algorithm to successively cancel ISI from a block of received data and generate symbol decisions whose reliability increases monotonically with each iteration. These equalizers have an effective complexity comparable to the decision-feedback equalizer (DFE), yet asymptotically achieve the performance of maximum-likelihood sequence detection (MLSD). We show that, because their structure allows cancellation of both precursor and postcursor ISI, iterated-decision equalizers outperform the minimum mean-square error DFE by 2.507 dB on severe ISI channels even with uncoded systems. Moreover, unlike the DFE, iterated-decision equalizers can be readily used in conjunction with error-control coding, making them attractive for a wealth of applications     

On the Decision-Feedback Equalizer in Optically Amplified Direct-Detection Systems

This paper investigates the combined feed-forward and decision-feedback equalizer (DFE) in a lightwave system with optical amplifiers and a direct-detection receiver. Based on a nonlinear channel model, the paper provides a modification of the classical minimum mean square error theory of the DFE. Furthermore, an analytical method that is capable of accurate bit error rate (BER) evaluation is used to optimize the DFE for minimum BER. The paper evaluates the DFE performance for both optical ON-OFF keying and duobinary modulation formats in the presence of chromatic dispersion as well as the DFE performance for the mitigation of higher order polarization mode dispersion in first-order compensated systems. The paper shows that the DFE can compensate for the BER degradation due to narrow-band receiver-side optical filtering and can significantly improve the spectral efficiency of dense wavelength-division multiplexed systems.     

Electrical Dispersion Compensation for 40-Gb/s DQPSK Signal Utilizing MIMO DFEs

We investigate electrical dispersion compensation for 40-Gb/s differential quadrature phase-shift keying modulation signals utilizing multi-input–multi-output (MIMO) decision-feedback equalizers (DFEs). In our scheme, all branch signals after balanced-photodiode detection or single-photodiode detection are analogous to antennae in a MIMO wireless transmission systems. Chromatic dispersion and polarization-mode dispersion tolerances for various MIMO DFE configurations are compared. The flexible scheme can be easily extended to ${m}$ -ary PSK modulation formats.      

Electrical Dispersion Compensation Equalizers in Optical Direct- and Coherent-Detection Systems

We study the performances of several electrical dispersion compensation (EDC) equalizers in the presence of chromatic dispersion (CD) and polarization mode dispersion (PMD) for optical coherent and direct detection on-off keying systems. The EDCs that are analyzed include the decision-feedback equalizer, linear equalizer, and maximum-likelihood sequence estimator (MLSE). We present an inclusive quantitative analysis of the performance difference between the various techniques. The MLSE gives a good indication of the best possible performance     

A Hammerstein-type equalizer for concatenated fiber-wireless uplink

In optical fiber-based wireless access schemes, the radio signal is transmitted through fiber without frequency conversion radio-over-fiber (ROF). Although the fiber has adequate bandwidth, nonlinear distortion due to electrical to optical (E/O) conversion is a concern. In the uplink, the dynamic multipath wireless channel is followed by this static memoryless ROF link; this forms a Wiener system. In this paper, we propose a Hammerstein type decision feedback equalizer (HDFE) for the fiber-wireless uplink to combat the nonlinear distortion and the wireless channel dispersion. The proposed equalizer is less complex because it handles static and dynamic distortions separately. The nonlinear distortion is compensated first, reducing the power of cross modulation products significantly. Analytical results show that the lower bound of the mean squared error depends on the optical and wireless channel noise. The bit error rate (BER) performance of the HDFE for the nonlinear channel approaches the performance of a decision feedback equalizer (DFE) in a linear channel when the nonlinearity is adequately compensated.     

On the performance of the electrical equalization technique in MMF links for 10-gigabit ethernet

In this paper, the electrical equalization technique utilized in multimode fiber (MMF) links for 10-Gigabit Ethernet is reported. This paper presents and compares three kinds of equalizers: linear equalizer, decision feedback equalizer (DFE), and a nonlinear finite-impulse-response DFE (NL-FIR-DFE) based on the analysis of nonlinear operations of direct modulation and detection in MMF links. Computer simulations reveal that NL-FIR-DFE exhibits superior performance in comparison with normal DFE. The equalization performance for an MMF channel with bandwidth 500 MHz-km as well as 160 MHz-km is demonstrated. It is demonstrated that with direct modulation of cost-effective vertical-cavity surface-emitting laser (VCSEL) or Fabry-Perot laser, the transmission distance for installed MMF with a bandwidth of 500 MHz-km at 10 Gb/s can be extended to 300 m with an appropriate offset restricted mode launch condition by utilizing normal DFE and to more than 650 m for NL-FIR-DFE. Moreover, it is shown that the transmission distance for an MMF with a bandwidth of 160 MHz-km can reach 300 m with more than seven times bandwidth improvement by using NL-FIR-DFE.     

A New Class of Efficient Block-Iterative Interference Cancellation Techniques for Digital Communication Receivers

A new and efficient class of nonlinear receivers is introduced for digital communication systems. These iterated-decision receivers use optimized multipass algorithms to successively cancel interference from a block of received data and generate symbol decisions whose reliability increases monotonically with each iteration. Two variants of such receivers are discussed: the iterated-decision equalizer and the iterated-decision multiuser detector. Iterated-decision equalizers, designed to equalize intersymbol interference (ISI) channels, asymptotically achieve the performance of maximum-likelihood sequence detection (MLSD), but only have a computational complexity on the order of a linear equalizer (LE). Even more importantly, unlike the decision-feedback equalizer (DFE), iterated-decision equalizers can be readily used in conjunction with error-control coding. Similarly, iterated-decision multiuser detectors, designed to cancel multiple-access interference (MAI) in typical wireless environments, approach the performance of the optimum multiuser detector in uncoded systems with a computational complexity comparable to a decorrelating detector or a linear minimum mean-square error (MMSE) multiuser detector.     

基于DFE均衡器的线性化拆分算法的研究和应用

利用DFE非线性均衡器,通过数学处理对其进行线性化拆分,拆分后的两个线性均衡器分别置于信道的接收和发送端,使其能用于强多径干扰的信号传输环境(如存在强多径干扰的隧道中的高速信号传输).该方法降低了实现的复杂度,同时保持了高抗干扰性,且这种相互对称的均衡器结构有利于系统双向传输的实现.计算机仿真结果验证了该方法的有效性.     

A Flexible,High-Performance FPGA Implementation of a Feed-Forward Equalizer for Optical Interconnects up to 112 Gb/s

Commodity optoelectronic components and multi-level modulation formats are combined nowadays in optical networks to increase their throughput while decreasing their cost. To overcome the inherent limitations of such interconnects, research focuses on digital equalizers that compensate for the effects of the developed channels. The current paper proposes the use of FPGAs to enhance the speed, power and flexibility of digital equalization for the next generation 100 Gb/s rack-to-rack optical links in datacenters. We present the high-performance hardware architecture of a flexible feed-forward equalizer (FFE) with multiple reconfigurations. We describe parallelization techniques to accelerate FFE, accuracy analysis for various FFE scenarios, as well as a design space exploration leading to a fine-tuned and platform-dependent FFE customization. Our final implementation on a single Xilinx XC7VH580T FPGA device with GTZ transceivers can support a single link of up to 112 Gbps (56 GSa/s with PAM-4 modulation) and 2.26?10^?6 Bit-Error-Rate.     

自适应均衡算法在信道均衡技术中的应用研究

文中描述了两种非线性均衡器分别为判决反馈均衡器(DFE)和最大似然序列估计(MLSE)均衡器.所用信道模型为加性白高斯噪声信道,在DFE和线性均衡器(LE)中都是使用递归最小二乘(RLS)算法和最小均方(LMS)算法对数据进行分块处理.MLSE均衡器中使用了维特比最佳译码算法.就误比特性能来做以比较,DFE远好于LE,MLSE均衡器又明显优于DFE,并且它能达到几乎最优的性能.     

Performance of an MLSE-EDC Receiver With SOA-Induced Nonlinear Impairments

We experimentally investigate the performance of maximum-likelihood sequence estimation (MLSE) electronic dispersion compensation for signals impaired by nonlinear optical effects induced in a semiconductor optical amplifier (SOA). Single- and multichannel effects are investigated. We study 10.7-Gb/s nonreturn-to-zero, low-pass filter duobinary, and differential phase-shift-keying signals detected as optical duobinary, each with different amounts of uncompensated dispersion before amplification by the SOA and detection. The results show performance variability by the MLSE receiver with increasing nonlinearity, from small penalties back-to-back compared to a standard receiver for most formats to advantages of several decibels with uncompensated dispersion.     

On the performance of electrical equalization in optical fiber transmission systems

A variety of equalizers have been proposed to improve the bit-error rate (BER) of optical fiber communications by reducing the effects of chromatic dispersion (CD), polarization-mode dispersion (PMD), and other fiber impairments. Therefore, it is of interest to establish the ultimate performance of electrical equalizers under different conditions. The results presented here are based on the fact that maximum-likelihood sequence detection (MLSD) obtains the lowest BER of all possible detectors, under mild conditions. Thus, the MLSD performance is a lower bound on the BER of any electrical equalizer. We consider linear channels with PMD (all orders), CD, and the nonlinear effect of the photodetector.     

Analysis of predistortion, equalization, and ISI cancellationtechniques in digital radio systems with nonlinear transmit amplifiers

An analysis made of the performance of predistortion, equalization, and intersymbol interference (ISI) cancellation techniques in compensating for the transmit amplifier nonlinearity in digital microwave radio systems. The study is carried out using the 64 QAM and 256 QAM signal formats and two values of the roll-off factor in the Nyquist pulse shaping. The simulated compensation techniques include three types of predistortion, two ISI cancellers, and several nonlinear equalizers with or without decision feedback. A basic result is that decision-feedback equalizers do not offer any significant advantage over nonrecursive equalizers. It is also shown that ISI cancelers with a memoryless equalizer as first-stage decision device do not perform any better than nonlinear equalizers of similar complexity. Another contribution an improved fifth-order analog signal predistortion technique is analyzed. The gain that can be achieved using a modified 256 QAM signal constellation that is more robust to nonlinear distortion is quantified     

Functional link neural network cascaded with Chebyshev orthogonal polynomial for nonlinear channel equalization

Nonlinear intersymbol interference (ISI) leads to significant error rate in nonlinear communication and digital storage channel. In this paper, therefore, a novel computationally efficient functional link neural network cascaded with Chebyshev orthogonal polynomial is proposed to combat nonlinear ISI. The equalizer has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomial and Chebyshev orthogonal polynomial. Due to the input pattern and nonlinear approximation enhancement, the proposed structure can approximate arbitrarily nonlinear decision boundaries. It has been utilized for nonlinear channel equalization. The performance of the proposed adaptive nonlinear equalizer is compared with functional link neural network (FLNN) equalizer, multilayer perceptron (MLP) network and radial basis function (RBF) along with conventional normalized least-mean-square algorithms (NLMS) for different linear and nonlinear channel models. The comparison of convergence rate, bit error rate (BER) and steady state error performance, and computational complexity involved for neural network equalizers is provided.     

基于光纤差分相移键控的色散补偿方案的研究

为了研究光差分相移键控(DPSK)调制格式在光纤高速传输系统中的色散补偿, 利用色散补偿光纤(DCF)的色散补偿原理, 对40Gbit/s光纤传输系统进行色散补偿, 分析了40Gbit/s单通道光纤传输系统中3种DPSK调制格式信号的频谱特性; 仿真了3种码型的色散容忍度以及3种调制格式在考虑光纤的非线性下的色散补偿方案。结果表明, 光非归零码差分相移键控(NRZ-DPSK)信号具有最好的色散容忍度, 但其受非线性的影响比较大; 33%归零码差分相移键控(33%RZ-DPSK)信号的色散容忍度差, 但其色散补偿后的效果优于NRZ-DPSK; 而载波抑制归零码差分相移键控信号对色散和非线性效应都有较好的抑制; 3种DPSK调制格式均在对称补偿2方案中色散补偿的效果最佳。此仿真研究对光DPSK信号在光纤中的色散补偿具有参考意义。