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.     

Wiener solution of electrical equalizer coefficients in lightwave systems

Electrical dispersion compensation equalizer is a key and cost-effective element in optical communication on-off-keying systems in the presence of chromatic dispersion. Here, for the first time, to the best of the authors? knowledge, an analytical solution is established for the electrical equalizer coefficients in an optical communication system. The solution is based on minimum mean-square error criterion. The analytical results show a perfect match with computer simulation. In addition BER performance comparison with the adaptive least mean square (LMS) method reveals that the analytical solution performs better due to LMS excess mean-square error.     

Electrical equalization for advanced optical communication systems

We investigate equalizers for electronic dispersion compensation (EDC) of dispersion limited optical fibre communication links in combination with different modulation formats. We show that the performance of conventional equalizers including feedforward equalizer (FFE) and decision feedback equalizer (DFE) are fundamentally limited by the nonlinearity of square-law detection of the photodiode in direct detection systems. Advanced modulation formats such as differential phase shift keying (DPSK) and optical duobinary further enhance this kind of nonlinearity and degrade further FFE/DFE performance. However, nonlinear FFE–DFE and maximum likelihood sequence estimation (MLSE) take into account the mitigation of nonlinear inter symbol interference (ISI) and hence can achieve much better performance. We show that in contrast to other modulation formats, optical single sideband modulation results in approximately linear distortions after detection and thus a simple linear FFE equalizer can achieve good compensation.     

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.     

Spatial-temporal equalization for IS-136 TDMA systems with rapiddispersive fading and cochannel interference

In this paper, we investigate spatial-temporal equalization for IS-136 time-division multiple-access (TDMA) cellular/PCS systems to suppress intersymbol interference and cochannel interference and improve communication quality. This research emphasizes channels with large Doppler frequency (up to 184 Hz), delay dispersion under one symbol duration, and strong cochannel interference. We first present the structure of the optimum spatial-temporal decision-feedback equalizer (DFE) and linear equalizer and derive closed-form expressions for the equalizer parameters and mean-square error (MSE) for the case of known channel parameters. Since the channel can change within an IS-136 time slot, the spatial-temporal equalizer requires parameter tracking techniques. Therefore, we present three parameter tracking algorithms: the diagonal loading minimum MSE algorithm, which uses diagonal loading to improve tracking ability, the two-stage tracking algorithm, which uses diagonal loading in combination with a reduced complexity architecture, and the simplified two-stage tracking algorithm, which further reduces complexity to one M×M and one 3×3 matrix inversion for weight calculation with M antennas. For a four-antenna system, the simplified two-stage tracking algorithm can attain a 10^-2 bit error rate (BER) when the channel delay spread is half of the symbol duration and the signal-to-interference ratio (SIR) of the system is as low as 5 dB, making it a computationally feasible technique to enhance system performance for IS-136 TDMA systems     

Performance analysis of visible light communication using the STBC-OFDM technique for intelligent transportation systems

Visible light communication (VLC) applied in an intelligent transportation system (ITS) has attracted growing attentions, but it also faces challenges, for example deep path loss and optical multi-path dispersion. In this work, we modelled an actual outdoor optical channel as a Rician channel and further proposed space-time block coding (STBC) orthogonal frequency-division multiplexing (OFDM) technology to reduce the influence of severe optical multi-path dispersion associated with such a mock channel for achieving the effective BER of 10^?6 even at a low signal-to-noise ratio (SNR). In this case, the optical signals transmission distance can be extended as long as possible. Through the simulation results of STBC-OFDM and single-input-single-output (SISO) counterparts in bit error rate (BER) performance comparison, we can distinctly observe that the VLC–ITS system using STBC-OFDM technique can obtain a strongly improved BER performance due to multi-path dispersion alleviation.     

Iterative Equalization using Improved Block DFE for Synchronous CDMA Systems

Iterative equalization using optimal multiuser detector and optimal channel decoder in coded CDMA systems improves the bit error rate (BER) performance tremendously. However, given large number of users employed in the system over multipath channels causing significant multiple-access interference (MAI) and intersymbol interference (ISI), the optimal multiuser detector is thus prohibitively complex. Therefore, the sub-optimal detectors such as low-complexity linear and non-linear equalizers have to be considered. In this paper, a novel low-complexity block decision feedback equalizer (DFE) is proposed for the synchronous CDMA system. Based on the conventional block DFE, the new method is developed by computing the reliable extrinsic log-likelihood ratio (LLR) using two consecutive received samples rather than one received sample in the literature. At each iteration, the estimated symbols by the equalizer is then saved as a priori information for next iteration. Simulation results demonstrate that the proposed low-complexity block DFE algorithm offers good performance gain over the conventional block DFE.     

基于多用户反馈的判决反馈均衡器的研究

本文提出的一种新颖的基于多用户反馈的判决反馈均衡器,解决了在CDMA多用户检测中传统自适应判决反馈均衡器误码率高、系统容量小的缺点.它由具有误差反馈滤波器的判决反馈均衡器(Decision Feedback Equalizer with Error Feedback Filter,DFE-EFF)构成,并在判决后反馈多用户数据抵消多址干扰(多用户反馈干扰抵消).文中给出其结构图,分析各种判决反馈均衡算法.理论证明,具有误差反馈滤波器的多用户反馈干扰抵消判决反馈均衡器(多用户反馈干扰抵消DFE-EFF)较各种判决反馈均衡器为最优,它能同时有效处理ISI,MAI和噪声的干扰.仿真结果表明,在误码率性能和系统容量两方面,多用户反馈干扰抵消DFE-EFF比DFE、DFE-EFF均有较大改善.     

三阶色散效应对光码分多址系统误码率的影响

光码分多址(OCDMA)系统的误码率是评价系统性能的重要指标,由于色散和非线性效应会导致超短光脉冲在光纤传输过程中脉宽的展宽,进而影响OCDMA系统的误码率。在基于理想情况的OCDMA系统误码率定义的基础上,研究了三阶色散和三阶非线性效应对系统误码率的影响,进一步分析了有硬限幅器和二维OCDMA系统的误码率。结果表明,三阶色散和三阶非线性效应都会导致OCDMA系统误码率的增大,但三阶非线性效应对系统性能影响没有三阶色散效应明显;在系统参数相同基础上,接收端引入光硬限幅器和系统采用二维编码均可优化系统性能。     

Optimized decision-feedback equalization for convolutional coding with reduced delay

Error propagation is a significant problem with the decision-feedback equalizer (DFE) at low-to-moderate signal-to-noise ratios. In particular, when a DFE is concatenated with a convolutional code, the burst errors associated with error propagation can severely degrade performance, since the convolutional code is optimized for the additive white Gaussian noise channel. In this paper, we explore the compensation of error propagation in the DFE so as to break up error bursts and improve performance with convolutional codes, without incurring larger overall decoding delay. We propose certain stationary error models and derive a modified DFE (MDFE) based on these models which can compensate for the error propagation. The MDFE differs from the conventional DFE only in its tap values. The incorporation of the bias into the model and the removal of the bias during the design process is discussed. Simulations explore the performance of the MDFE for both uncoded and convolutionally coded systems. With coding, the MDFE can significantly improve on the conventional DFE in terms of bit-error rate, and the MDFE without interleaving can improve on the conventional DFE with interleaving in terms of decision delay.     

RLS Algorithm with Variable Fogetting Factor for Decision Feedback Equalizer over Time-Variant Fading Channels

In a high-rate indoor wireless personal communication system, the delay spread due to multipath propagation results in intersymbol interference (ISI) which can significantly increase the transmission bit error rate (BER). Decision feedback equalizer (DFE) is an efficient approach to combating the ISI. Recursive least squares (RLS) algorithm with a constant forgetting factor is often used to update the tap-coefficient vector of the DFE for ISI-free transmission. However, using a constant forgetting factor may not yield the optimal performance in a nonstationary environment. In this paper, an adaptive algorithm is developed to obtain a time-varying forgetting factor. The forgetting factor is used with the RLS algorithm in a DFE for calculating the tap-coefficient vector in order to minimize the squared equalization error due to input noise and due to channel dynamics. The algorithm is derived based on the argument that, for optimal filtering, the equalization errors should be uncorrelated. The adaptive forgetting factor can be obtained based on on-line equalization error measurements. Computer simulation results demonstrate that better transmission performance can be achieved by using the RLS algorithm with the adaptive forgetting factor than that with a constant forgetting factor previously proposed for optimal steady-state performance or a variable forgetting factor for a near deterministic system.     

Modeling and verification of FEC performance for optical transmission systems using a proposed uniformly quantized symbol error probability model

We investigate the estimation of the bit-error rate (BER) performance of optical transmission systems with forward error correction (FEC) coding using a proposed uniformly quantized symbol error probability model. This model has been verified by the measurement of BER characteristics of coded and uncoded 10 Gb/s optical signals transmitted over 100 km. The measured results are very similar to the calculated results from the proposed model as well as Monte Carlo (MC) simulations. Our results suggest that the proposed uniformly quantized symbol error probability model using more than 8-decision levels can be applied to estimate BER performance for coded systems without degrading accuracy.     

Phase precoding for frequency-selective Rayleigh and Rician slowlyfading channels

This paper presents a novel phase precoding (pre-equalization) technique to equalize frequency-selective Rayleigh and Rician slowly fading channels for personal communication systems using phase modulation. In order to achieve intersymbol interference (ISI)-free transmission, the precoding technique pre-distorts the signal transmitted from a base station to a portable unit. The novelty of the technique lies in using a spiral curve design: (1) to ensure the stability of the precoder even in equalizing a non-minimum-phase channel; (2) to obtain an ISI-free received signal; and (3) to keep a constant transmitted signal amplitude. Using the precoder can improve the bit-error-rate (BER) transmission performance without increasing the complexity of the portable unit receiver. The BER performance of coherent quadrature phase-shift-keying (QPSK) with the channel pre-equalization is analyzed theoretically for both Rayleigh and Rician fading channels. Analytical and simulation results demonstrate that coherent QPSK using the proposed channel precoder has a significantly lower BER than that using a conventional decision-feedback equalizer (DFE) because the precoder does not suffer from error propagation     

A wide-band radial basis function decision feedbackequalizer-assisted burst-by-burst adaptive modem

The performance of radial basis function-based decision feedback equalized (RBF DFE) burst-by-burst adaptive quadrature amplitude modulation (AQAM) is presented for transmissions over dispersive wide-band mobile channels. This scheme is shown to give a significant improvement in terms of the mean bit error rate (BER) and bits per symbol (BPS) performance compared to that of the individual fixed modulation modes. The structural equivalence of the RBF DFE to the optimal Bayesian equalizer enables it to potentially outperform the conventional Kalman-filtered AQAM DFE scheme     

Error-rate evaluation of linear equalization and decision feedbackequalization with error propagation

We propose applying an approximate Fourier series to evaluate efficiently the bit-error-rate (BER) performance of finite-length linear equalization (LE) and decision feedback equalization (DFE). By extending the Fourier series, we enable BER calculations for quadrature phase-shift keying (QPSK) transmission on complex channels with in-phase and crosstalk intersymbol interference (ISI). The BER calculation is based on determining the residual ISI samples and background Gaussian noise variance at the equalizer output for static channels or for realizations of quasi-static fading channels. A simple bound on the series error magnitude in terms of the Fourier series parameters ensures the required accuracy and precision. Improved state transition probability estimates are derived and verified by simulation for an approximate Markov model of the DFE error propagation for the case in which residual ISI exists even when the previous decisions stored in the feedback filter (FBF) are correct. We demonstrate the ease and widespread applicability of our approach by producing results which elucidate a variety of equalization tradeoffs. Our analysis includes symbol-spaced and fractionally spaced minimum mean-square error (MMSE)-LE, zero-forcing (ZF)-LE, and MMSE-DFE (with and without error propagation) on static ISI channels and multipath channels with quasi-static Rayleigh fading; a comparison between suboptimum and optimum receiver filtering in conjunction with equalization; and an assessment of the accuracy of some widely used equalization BER approximations and bounds     

The influence of cross-phase modulation on optical FDM PSK homodynetransmission systems

A combination of optical frequency division multiplexing (FDM) and phase-shift-keying (PSK) homodyne detection can increase transmission capacity. However, phase sensitive transmission systems, especially repeatered ones, suffer from data-dependent optical amplitude fluctuation that is converted to phase fluctuation by fiber nonlinearity. The authors discuss how this data-dependent amplitude fluctuation affects the error rate performance of optical FDM PSK homodyne detection systems. If only the optical amplitude fluctuation induced by phase modulators is taken into account, the allowable power fluctuation to keep the power penalty at 0.5 dB at a bit error rate (BER) of 10^-10 is below 0.17 mW for BPSK homodyne detection and 0.09 mW for QPSK homodyne detection. However, if only the amplitude fluctuation induced by the fiber chromatic dispersion is taken into account, the allowable number of repeaters to keep a 0.5-dB power penalty due to XPM at a BER of 10^-10 is 1 for BPSK homodyne detection and below 5 for QPSK homodyne detection     

Performance evaluation of various decision schemes for frequencydemodulation of narrow-band digital FM signals in land mobile radio

The decision feedback equalizer (DFE), three-level eye, and maximum-likelihood sequence estimator (MLSE) decision schemes for frequency demodulation of 16-kb/s GMSK signals are evaluated. Laboratory experimental results on bit error rate (BER) and block error rate (BKER) performances are presented. In additive white Gaussian noise channels, two-bit DFE achieves the best BER performance, whereas MLSE is the best for cochannel interference-limited channels. BKER performance was also examined. The three-level eye decision is a bit-by-bit decision, and thus has superior performance because there is no error propagation. In fading environments, however, this superiority tends to diminish because bursty errors due to deep fades predominate rather than error propagation effects. Some of the laboratory experimental results have been confirmed with field experiments at a 1.45-GHz carrier frequency     

Performance of a hybrid decision feedback equalizer structure forCAP-based DSL systems

We study the performance of a class of derision feedback equalizer (DFE) structures for high-speed digital transmission systems. We first present mathematical formulation of minimum mean-square error (MMSE) and the optimum tap coefficients for various finite-length phase-splitting equalizers over the loop in the presence of colored noise, such as near-end crosstalk (NEXT) and far-end crosstalk (FEXT). The performance of the equalizers is also analyzed in the presence of narrowband interference and the channel reflections introduced by bridged taps. The hybrid-type DFE (H-DFE) is presented as a practical equalizer structure for these applications. The results of analysis show that the H-DFE has advantages in the performance and/or in the implementation complexity as compared with the existing DFE structures. An additional advantage of the H-DFE is in the transmission systems that employ the precoding technique. The precoding for the H-DFE allows the system to track small changes in the channel     

Ultimate performance of optical DSB signal-based millimeter-wavefiber-radio system: effect of laser phase noise

It is theoretically shown that the phase noise of laser light source can be automatically eliminated by compensating the differential group delay due to the fiber dispersion between the two sidebands of the optical DSB signal. The bit error rate (BER) measurement of 60 GHz millimeter (mm)-wave subcarrier multiplexed optical double-sideband (DSB) signal transport in dispersion-compensated optical fiber link using fiber Bragg grating (FBG) mill show that the effect of the laser phase noise on the BER is as small as a few % relative to the other additive noise effect, thus realizing almost the ultimate performance     

Adaptive DFE for GMSK in indoor radio channels

We simulate the performance of an equalized Gaussian minimum shift keying (GMSK) signal in an indoor radio environment with fading, noise, imperfect carrier recovery, cochannel interference (CCI), and intersymbol interference (ISI). We show that data rates of 20 Mb/s at bit error rates (BER) ⩽10^-4 are possible with root mean square (RMS) delay spreads up to 25 ns using a simple limiter-discriminator-integrator (LDI) receiver and a (6, 4) decision feedback equalizer (DFE). In environments with larger RMS delay spreads, coherent detection is required for the same performance. We show that using a decision-directed second-order digital carrier synchronizer with time varying loop filters, frequency offsets up to 200 kHz can be corrected with negligible performance degradation. This paper utilizes a DFE structure which compensates for both modulator and channel ISI, and yet requires no power-intensive multiplication operations in the feedback section. A DFE (8, 8) with two-level switched (selection) diversity is shown to allow 20 Mb/s data transfer at a BER⩽10^-4 for RMS delay spreads under 150 ns, with CCI. A light BCH (26, 31) code allows error-free reception of over 90% of packets with RMS delay spreads under 150 ns, and up to 70% of packets with RMS delays of 150 ns