Error probabilities for QAM systems on partially coherent channelswith intersymbol interference and crosstalk

We describe an efficient procedure to calculate the probability of error P_e for a quadrature amplitude modulation (QAM) communications system operating over a channel that introduces distortion, interference, and noise. The method is an extension of the saddlepoint integration technique introduced by Helstrom (1986) to efficiently evaluate P_e for one-dimensional pulse-amplitude modulation (PAM) systems with intersymbol interference (ISI) and crosstalk. We consider the effects of noise, random carrier phase offset, ISI, and crosstalk between the I and Q channels. The error probability is written as a double Laplace inversion integral and can be easily applied to any rectangular constellation. This integral is calculated by extending the saddlepoint integration technique to two complex dimensions. Results are presented for QAM systems with 16, 64, and 256 symbols. The technique can be directly extended to environments with cochannel interference consisting of other QAM signals     

Cross-phase modulation in multispan WDM optical fiber systems

The spectral characteristics of cross-phase modulation (XPM) in multispan intensity-modulation direct-detection (IM-DD) optical systems are investigated, both experimentally and theoretically. XPM crosstalk levels and its spectral features are found to be strongly dependent on fiber dispersion and optical signal channel spacing. Interference between XPM-induced crosstalk effects created in different amplified fiber spans is also found to be important to determine the overall frequency response of XPM crosstalk effects. XPM crosstalk between channels with different data rates is evaluated. The crosstalk level between higher and lower bit rate channels is found to be similar to that between two lower bit rate channels. The effect of dispersion compensation on XPM crosstalk in multispan optical systems is discussed and per span dispersion compensation was found to be the most effective way to minimize the effect of XPM crosstalk     

Effect of group velocity dispersion on stimulated Raman crosstalkin multichannel transmission systems

We investigate the effect of group velocity dispersion on stimulated Raman crosstalk in intensity modulated multichannel transmission systems. A theoretical model for bit-error rates (BERs) and power penalty calculation is provided, where the effects of modulation statistics and group velocity dispersion are taken into account. It has been found that walkoff effects may reduce stimulated Raman scattering (SRS) crosstalk, and can not be neglected for systems with a large number of channels     

基于MIMO信道的DSL传输模式研究

DSL技术是当前主流的宽带接入技术,串音干扰是制约DSL系统传输性能的重要因素。提出一种利用MIMO技术降低DSL系统中串音干扰的方法。在分析串扰对线路影响的基础上,建立了基于离散多音调制下的MIMO信道模型,应用奇异值分解法消除串扰,采用注水算法解决了MIMO-DSL信道的功率分配问题。Matlab仿真结果表明,其速率可以达到non-MIMO信道的1.5倍,有效降低了DSL系统串音干扰的影响。     

Effects of cross-phase modulation in wavelength-multiplexed SCMvideo transmission systems

Channel crosstalk effects in wavelength-multiplexed subcarrier-multiplexing video transmission systems due to cross-phase modulation are investigated. The crosstalk level depends on the spacing of optical channels. For analogue CATV transmissions in the 1.5 μm window using normal singlemode fibre, it is shown that the number of achievable optical channels is severely limited by cross-phase modulation for typical system parameters     

Effects of polarization-mode dispersion on cross-phase modulation in dispersion-managed wavelength-division-multiplexed systems

This paper develops a vector theory of cross-phase modulation (XPM) in optical fibers and use it to investigate the impact of polarization-mode dispersion (PMD) on the crosstalk induced by XPM in wavelength-division multiplexed lightwave systems. Under certain reasonable approximations, the theory permits us to obtain an analytic expression for the amplitude of probe fluctuations induced by a copropagating pump channel through XPM. We use this expression to calculate the average level of XPM-induced crosstalk together with its variance for several dispersion maps. We show that PMD not only reduces the crosstalk on average, but also impacts the efficiency of a commonly used polarization-interleaving technique.     

Crosstalk in 1.5-μm InGaAsP optical amplifiers

A dynamical model for multichannel amplification by near-traveling-wave optical amplifiers is presented, and results on crosstalk induced by either amplitude modulation or frequency modulation are given. The mechanisms influencing the crosstalk most are the residual facet reflectivities and the detuning of the channels relative to the amplifier Fabry-Perot spectrum. Calculations of worst-case crosstalk levels are included. The model is verified experimentally for amplitude-modulated signals, and crosstalk levels up to -7 dB are reported. For frequency-modulated signals, estimated crosstalk is significantly lower and can be reduced by high quality facet coatings     

Nonlinear crosstalk and two countermeasures in SCM-WDM opticalcommunication systems

We investigate, theoretically and experimentally, crosstalk between wavelengths in subcarrier-multiplexed (SCM) wavelength-division multiplexed (WDM) optical communication systems. Crosstalk arises mainly from interactions between subcarriers on one wavelength and the optical carrier of another wavelength. In a dispersive fiber, crosstalk can be attributed to stimulated Raman scattering (SRS) and cross-phase modulation (XPM) combined with group velocity dispersion (GVD). We investigate the phase relationship between SRS-induced and XPM-induced crosstalks. Crosstalks induced by SRS and XPM add in the electrical domain and can interfere constructively or destructively. Experimental results show that the combined crosstalk level can be as high as 40 dBc after 25 km of SMF with two wavelengths and 18 dBm per wavelength of transmitted power. We propose two crosstalk countermeasures. The first countermeasure uses parallel fiber transmission. We show theoretically that both SRS-induced and XPM-induced crosstalks can be cancelled to the first order. We present an experimental demonstration of concept which has achieved 15 dB of crosstalk cancellation over 200 MHz. The second countermeasure uses optical carrier suppression. We show, theoretically and experimentally, that by suppressing the optical carrier, we can significantly reduce crosstalk while maintaining the same link budget and carrier-to-noise ratio (CNR) at the receiver, 20 dB of crosstalk reduction over 2 GHz has been demonstrated experimentally     

光纤色散对WDM系统中受激喇曼散射串扰的影响

本文研究了波分复用系统中光纤色散对受激喇曼散射串扰的影响,提出了在考虑信号调制几率特性和脉冲走离效应后,系统误码率和功率代价的理论计算方法,并对典型系统进行了数值模拟。研究结果表明,由光纤色散引起的信号脉冲走离可以降低受激喇曼散射串扰,尤其是在复用信道较多、信号传输速率较高的系统中,光纤色散的作用更加明显     

Mean-Square Crosstalk in Tamed Frequency Modulation

An analytical expression for evaluating the mean-square crosstalk between adjacent channels in coherent tamed frequency modulation (TFM) systems is presented. Numerical results are obtained and compared to previous crosstalk results for minimum shift keying (MSK); the substantial superiority of TFM is confirmed. An equivalent white Gaussian noise model for crosstalk is included and used to estimate performance degradation as a function of frequency separation between channels. The crosstalk results are also used to show that TFM is about 0.9 dB more sensitive to tone jamming than MSK.     

Asymmetry of Raman crosstalk in wavelength division multiplexing transmission systems

The Raman crosstalk in wavelength division multiplexing transmission systems is analysed in respect of modulation statistical property and dispersion walk-off effect. Both the mean nonlinear depletions/gains and crosstalk variances experienced by individual channels are found to be asymmetric for intensity-modulated systems. The asymmetry increases with the number of channels and input power.     

A generalized suboptimum unequally spaced channel allocationtechnique. I. In IM/DD WDM systems

Four-wave mixing (FWM) is the most serious fiber nonlinearity associated with low-input optical power levels in long-haul multichannel optical systems employing dispersion-shifted fiber. To reduce the crosstalk due to FWM, a generalized suboptimum unequally spaced channel allocation (S-USCA) technique is proposed and investigated. Even though the developed technique is useful in combating FWM crosstalk in wavelength division multiplexing (WDM) lightwave systems with up to 12 channels, its main virtue is in designing multichannel WDM lightwave systems with more than 12 channels. Comparisons of power penalty due to FWM between equal channel spacing (ECS) systems and the S-USCA systems are presented. It is shown that for an intensity modulation/direct detection (IM/DD) transmission system operating in an optical bandwidth of 16 nm with 0 dBm (1 mW) peak optical input power per channel, while a conventional ECS WDM system with 0.84-nm channel spacing cannot even achieve a bit-error rate (BER)=10^-9, the suboptimum technique developed in this paper, for the same minimum channel spacing, can achieve a BER=10^-9 with an FWM crosstalk power of less than 1 dB at the worst channel in a 20-channel WDM system     

The Operation of Dual Polarized QAM Systems in the Presence of Depolarization Crosstalk and Differential Fading

The performance of dual-polarizedM-QAM systems is studied. By assuming coherence between the crosstalk and the desired signal, results are obtained for systems up to the modulation level of 64 QAM in each channel. Both balanced systems, with equal modulation levels in each channel, and unbalanced systems, with different modulation levels in each channel, are considered. Graphs are presented which show possible design tradeoffs to improve performance and suggest methods of system optimization. Each system is found to have an optimum value of relative transmitter power in the two channels. Analyses include the application of empirically based channel models giving relations between depolarization crosstalk, coplanar path attenuation, and differential fading levels.     

Analytical Model for Cross-Gain Modulation and Crosstalk in Quantum-Well Semiconductor Optical Amplifiers

An analytical model of the dynamic characteristics of a quantum-well (QW) semiconductor optical amplifier (SOA) is developed. Closed-form expressions for the optical gain and cross-gain modulation (XGM) for arbitrary input pulses are derived. The model takes into account the carrier capture and escape transitions between the QW and the continuum states. This model is also used to derive a closed-from expression for interchannel XGM crosstalk in multichannel SOA systems. The model/analysis provides insight into the effect of the SOA parameters on the performance of a wavelength-division multiplexed system. We found that crosstalk in a multichannel SOA system can be reduced by reducing the escape lifetime.     

Cross-phase modulation in an L-band EDFA

We measure the cross talk in a wavelength-division-multiplexed (WDM) system arising from cross-phase modulation (XPM) in an L-band erbium-doped fiber amplifier (EDFA). This effect has the potential of becoming the dominant nonlinear crosstalk mechanism in L-band WDM systems using standard fiber. We discuss how appropriate amplifier design can reduce the XPM in the EDFA     

Realization of multigigabit channel equalization and crosstalk cancellation integrated circuits

In this paper, we present integrated circuit solutions that enable high-speed data transmission over legacy systems such as short reach optics and electrical backplanes. These circuits compensate for the most critical signal impairments, intersymbol interference and crosstalk. The finite impulse response (FIR) filter is the cornerstone of our architecture, and in this study we present 5- and 10-Gsym/s FIR filters in 2-/spl mu/m GaAs HBTs and 0.18-/spl mu/m CMOS, respectively. The GaAs FIR filter is used in conjunction with spectrally efficient four-level pulse-amplitude modulation to demonstrate 10-Gb/s data throughput over 150 m of 500 MHz/spl middot/km multimode fiber. The same filter is also used to demonstrate equalization and crosstalk cancellation at 5 Gb/s on legacy backplane. The crosstalk canceller improves the bit error rate by five orders of magnitude. Furthermore, our CMOS FIR filter is tested and demonstrates backplane channel equalization at 10 Gb/s. Finally, building blocks for crosstalk cancellation at 10 Gb/s are implemented in a 0.18-/spl mu/m CMOS process. These circuits will enable 10-Gb/s data rates on legacy systems.     

Compensation of Interchannel Crosstalk Induced by Optical Fiber Nonlinearity in Carrier Phase-Locked WDM System

A scheme that compensates the waveform distortion induced by nonlinear interchannel crosstalk such as four-wave mixing (FWM) and cross-phase modulation as well as self-phase modulation in phase-locked wavelength-division-multiplexing transmission systems is proposed. Reduction of FWM-induced waveform distortion by controlling the phase relationship between neighbouring channels and its cancellation by precompensation is successfully demonstrated     

Frequency response of cross-phase modulation in multispan WDMoptical fiber systems

The spectral characteristics of cross-phase modulation (XPM) in multispan intensity-modulation direct-detection optical systems were investigated both experimentally and theoretically. XPM crosstalk levels and its spectral features were found to be strongly dependent on fiber dispersion and optical signal channel spacing. Interference between XPM-induced crosstalk effects created in different amplified fiber spans is also found to be important to determine the overall frequency response of XPM crosstalk effects     

柔软光纤传像束的传像特性

研究了柔软光纤传像束的传像特性.界面交扰是柔软光纤传像束最重要的传像特性之一.迄今为止,有关这些方面的研究尚未完善.描述了一种采用光学视频系统定量测量柔软光纤传像束交扰率的新技术,并通过对柔软光纤传像束的静态MTF的测量和目视法观察,分析对比了交扰率对传像束传像特性的影响,比较了多种传像束样品的测量结果.     

RF crosstalk in multiple-wavelength vertical-cavitysurface-emitting laser arrays

We present the crosstalk measured in multiple-wavelength vertical-cavity surface-emitting laser (VCSEL) arrays under RF modulation. The array consists of eight bottom-emitting VCSEL's arranged with a “pie”-like configuration within a 60-μm-diameter circle with a 3-μm spacing for coupling into a multimode fiber. The crosstalk is investigated by measuring a cross-modulation response of two VCSEL's in the array using a monochromator in an optical spectrum analyzer as a receiver. Excess crosstalk is minimized by flip-chip mounting the array and introducing a proper bias condition. The crosstalk observed In the adjacent VCSEL's is less than -40 dB at the modulation frequency below 700 MHz and it Increases at 20 dB/decade above this frequency when both VCSEL's are biased at 5.0 mA