Fractionally-spaced Equalizer Research Articles

New Dual-Mode FSE Suitable for High-Order QAM Signals

In the digital transmission system, constant modulus algorithm (CMA) is a famous blind equalization to overcome the inter-symbol interference without the aid of training sequences. But for the non-constant modulus signals such as higher-order QAM signals, the CMA just achieve moderate steady-state mean square error (MSE). So a new dual-mode fractionally-spaced equalization (FSE) suitable for high-order QAM signals is proposed, which makes full use of the character which is that the high-order QAM signals have the different modulus. This algorithm uses the FSE based on CMA as the basal mode and in the second mode it uses the FSE based on variable modulus algorithm. The simulation results show that compared with CMA the proposed algorithm has faster convergence rate and lower steady-state mean square error.

A Joint Timing and Fractionally-Space Blind Equalization Algorithm

In this paper, we proposed a joint timing and fractionally-spaced blind equalization algorithm. It adopts Gardner algorithm instead of simple down-sampling in conventional fractionally-spaced equalization in order to overcome the problem of that the filter can’t compensate timing error. The simulations show that the performance of the proposed fractionally-spaced equalization algorithm is better than CMA in different SNR and in different number of channel taps.

Blind equalization based on T/4 fractionally spaced decision feedback equalizer with RLS algorithm

To further improve the performance of blind equalization based on T/4 fractionally spaced decision feedback equalizer, RLS algorithm is adopted to update the weights of equalizer according to simplified constant modulus algorithm (CMA) cost function. CMA cost function is simplified to meet second norm form in this work, and then the forward filter of equalizer with T/4 fractionally-spaced updates by RLS algorithm and the feedback filter of equalizer with symbol-spaced updates by gradient descent algorithm. Computer simulation results show that the algorithm proposed in this work has faster convergence rate and lower mean square error compare with blind equalization based on symbol-spaced and T/4 fractionally-spaced decision feedback equalizer based on gradient descend algorithm. DOI: http://dx.doi.org/10.11591/telkomnika.v11i6.2156 Full Text: PDF

High-order statistical equalizer for nonlinearity compensation in dispersion-managed coherent optical communications

Fiber nonlinearity has become a major limiting factor to realize ultra-high-speed optical communications. We propose a fractionally-spaced equalizer which exploits a trained high-order statistics to deal with data-pattern dependent nonlinear impairments in fiber-optic communications. The computer simulation reveals that the proposed 3-tap equalizer improves Q-factor by more than 2 dB for long-haul transmissions of 5,230 km distance and 40 Gbps data rate. We also demonstrate that the joint use of a digital backpropagation (DBP) and the proposed equalizer offers an additional 1-2 dB performance improvement due to the channel shortening gain. A performance in high-speed transmissions of 100 Gbps and beyond is evaluated as well.

Adaptive MMSE Equalizer for Blind Fractional Spaced CMA Channel Equalization through LMS Algorithm

Adaptive MMSE Equalizer for Blind Fractional Spaced CMA Channel Equalization through LMS Algorithm

室内可见光通信中的分数间隔均衡技术

The Fractionally Spaced Equalization(FSE) technology is investigated to mitigate the effects of Inter-symbol Interference(ISI) on the indoor Visible Light Communication(VLC) systems.Based on the propagation properties and signal modulation characteristics of indoor VLC systems,a link model for the indoor VLC communications is described,then the FSE method is proposed by using the link model.Furthermore,based on the minimum Mean Square Error(MSE) criterion,the FSE is optimized.Finally,the performance of the proposed FSE theory is evaluated by computer simulation.Experimental results indicate that the performance of T/2-fractionally spaced equalizer has improved 1-2 dB than that of the symbol interval equalizer in the same Bit Error Ratio(BER).It can eliminate the effects of the ISI induced by the multipath effectively,and can improve the reliability of signal transmission.

A Nuclear Norm Heuristic Approach to Fractionally Spaced Blind Channel Equalization

This letter proposes an algorithm for the blind fractionally spaced equalization (FSE). We show that the rank minimization approach leads to the reduction of degrees of freedom in the blind FSE problem and improves the quality of equalization. By introducing the nuclear norm heuristic, the design problem of blind channel equalization is formulated as the nuclear norm minimization problem. We also show that the effect of noise is reduced by minimizing the nuclear norm. Numerical examples demonstrate the effectiveness of the proposed algorithm.

New Concurrent Fractionally-Spaced Blind Equalization

The paper proposes a concurrent constant modulus algorithm (CMA) and decision-directed (DD) scheme for fractionally-spaced blind equalization. The proposed algorithm makes full use of the advantages of CMA and DD algorithm. A novel rule to control the adjustment of DD’s tap weights vector is proposed which avoids the hard switch between CMA and DD in practice. Simulations with underwater acoustic channels are used to compare the proposed algorithm with the famous CMA. And the simulation results show that the proposed algorithm has faster convergence rate and lower steady state mean square error.

An Electronic Domain Chromatic Dispersion Monitoring Scheme Insensitive to OSNR Using Kurtosis

In this paper we present an electronic domain solution for chromatic dispersion (CD) monitoring algorithm based on the estimated time domain channel in electronic domain using channel estimation methods. The proposed scheme utilizes kurtosis as a CD measurement, directly computed from the estimated inter-symbol-interference (ISI) channel due to the CD distortion. Hence, the proposed scheme exhibits robust performance under OSNR variation, in contrast to the existing electronic domain approach based on minimum mean squared error (MMSE) fractionally-spaced equalizer taps [1]. The simulation results verify the CD monitoring ability of the proposed scheme.

A CMOS 1 Gb/s 5-Tap Fractionally-Spaced Equalizer

This paper presents the design of a 1 Gb/s 5-tap T/2 fractionally-spaced equalizer. The T/2 delay lines are based on third-order linear-phase double terminated sections that offer a tunable group delay of 500 ps with less than 10% ripple and a 3 dB bandwidth greater than 600 MHz. Furthermore, the equalizer architecture introduces a broadband summing circuit using a transimpedance I/V converter that increases the bandwidth by a factor of 3.6 over a conventional resistive loaded analog adder. The topology's performance is demonstrated in the equalization of 1 Gb/s binary data through CAT5e twisted-pair cables for up to 23 meters. The vertical eye-opening increases from 0% to 58%. Implemented in CMOS 0.35 mum, the transversal equalizer occupies an area of 26 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and consumes 32 mA.

Digital Equalization of Chromatic Dispersion and Polarization Mode Dispersion

In this paper, we consider a fractionally spaced equalizer (FSE) for electronic compensation of chromatic dispersion (CD) and polarization-mode dispersion (PMD) in a dually polarized (polarization-multiplexed) coherent optical communications system. Our results show that the FSE can compensate any arbitrary amount of CD and first-order PMD distortion, provided that the oversampling rate is at least 3/2 and that a sufficient number of equalizer taps are used. In contrast, the amount of CD and PMD that can be corrected by a symbol-rate equalizer only approaches an asymptotic limit, and increasing the number of taps has no effect on performance due to aliasing that causes signal cancellation and noise enhancement.

Convergence and performance analysis of Godard family and multimodulus algorithms for blind equalization

We obtain the convergence of the Godard family [including the Sato and constant modulus (CM) algorithms] and the multimodulus algorithms (MMA) in a unified way. Our analysis also works for CMA fractionally spaced equalizer (FSE). Our assumptions are quite realistic: The channel input can be asymptotically stationary and ergodic, the channel impulse response is finite and can be stationary and ergodic (this models fading channels), and the equalizer length is finite. The noise is independent and identically distributed (i.i.d.). The channel input can be discrete or continuous. Our approach allows us to approximate the whole trajectory of the equalizer coefficients. This provides estimates of the rate of convergence, and the system performance (symbol error rate) can be evaluated under transience and steady state.

Subspace-Based Interference Suppression Technique for Long-Code Downlink CDMA Adaptive Receiver

This paper presents a multiple constrained subspace based multiuser detector for synchronous long-code downlink multirate DS-CDMA systems. The novel receiver adapts its fractionally-spaced equaliser tap-weights based upon two modes, namely training and decision-directed modes. Switching between two modes is achieved by changing the code constraint in the associated subspace algorithm. Moreover, detection of the desired user requires the knowledge of the desired user's spreading code only. Simulation results show that the proposed receiver is capable of multiple access interference (MAI) suppression and multipath mitigation. Besides, the results reveal the improvement in terms of convergence speed and mean square error (MSE) of the proposed receiver over the existing receiver in both static and dynamic environments.

Performance analysis of cyclostationary interference suppression for multiuser wired communication systems

This paper discusses cyclostationary interference suppression for multiuser wired communication systems. Crosstalk interference from digital signals in multipair cables has been shown to be cyclostationary. Many crosstalk equalization or suppression techniques have been proposed which make implicit use of the cy-clostationarity of the crosstalk interferer. In this paper, the convergence and steady-state behaviors of a fractionally spaced equalizer (FSE) in the presence of multiple cyclostationary crosstalk interference are thoroughly analyzed by using the equalizer's eigenstructure. The eigenvalues with multiple cyclostationary interference depend upon the folded signal and interferer power spectra, the cross power spectrum between the signal and the interferer, and the cross power spectrum between the interferers, which results in significantly different initial convergence and steady-state behaviors as compared to the stationary noise case. The performance of the equalizer varies depending on the relative clock phase of the symbol clocks used by the signal and multiple interferers. Measured characteristics as well as analytical model of NEXT/FEXT channel are used to compute the optimum and worst relative clock phases among the signal and multiple interferers.

A fractionally spaced blind equalizer based on linear programming

We formulate the blind fractionally spaced equalization (FSE) problem as one that minimizes a piecewise linear convex function subject to some linear constraints on the equalizer parameters. We show that this formulation achieves both the interference removal and the carrier phase recovery when the input signal possesses a certain quadrature amplitude modulation (QAM) type symmetry. A fast linear programming implementation is presented to solve the convex minimization problem. Computer simulation results indicate the new linear programming-based FSE is able to accurately equalize channels that are known to be not equalizable by T-spaced (or baud rate) blind equalizers and yields superior performance to other blind FSE methods.

Fast adaptation of fractionally spaced equalisers

Efficient subband structures that aim at fast adaptation of fractionally spaced equalisers (FSE), by exploiting the 'prewhitening' effect that a subband decomposition has on the spectral dynamics of the equaliser input are discussed. Two novel FSE structures are proposed, which differ in the extent to which the feed-forwars and feed-back sections of the FSE are implemented in the subband domain, with distinct impacts on the updating. Improved convergence is achieved at a reduced computational cost compared to a fullband benchmark.

Performance of Volterra and MLSD receivers for nonlinear band-limited satellite systems

This paper evaluates the performance of Volterra equalizers and maximum-likelihood sequence detection (MLSD) receivers for compensation of signal distortion in nonlinear band-limited satellite systems. In addition, the performance of a receiver with a fractionally-spaced equalizer followed by a Volterra equalizer is studied (FSE-Volterra equalizer). For the equalizers, adaptation of the equalizer weights is considered including a multiple-step LMS algorithm which improves the convergence characteristics. Two MLSD receiver structures are considered: the optimum receiver consisting of a matched-filter bank followed by a Viterbi (1967) detector and a suboptimum receiver consisting of a single receiver filter followed by a Viterbi detector. The performance of the MLSD receivers is then compared to that of the equalizers.

Timing-offset independent equalization techniques for robust indoor reception of ATSC DTV receivers

This paper presents a fractionally-spaced decision feedback equalizer with Stop-and-Go algorithm for robust indoor reception of ATSC DTV receivers. Many short delay echoes exist in an indoor environment and they can generate large symbol timing offsets. The conventional decision feedback equalizer performs poorly when large symbol timing offset occurs. But the proposed fractionally-spaced decision feedback equalizer with Stop-and-Go algorithm is independent of large symbol timing offsets. Therefore, the proposed equalizer outperforms the conventional decision feedback equalizer in the area of short delay echoes.

Robustness to fractionally-spaced equalizer length using the constant modulus criterion

This article studies robustness properties of the constant modulus (CM) criterion and the constant modulus algorithm (CMA) to the suboptimal but practical situation where the number of fractionally-spaced equalizer coefficients is less than what is needed to remove all intersymbol interference (ISI). Hence, there necessarily exists an error in the equalized signal. Relationships between CM and mean squared error cost functions are established.

Blind equalization using the constant modulus criterion: a review

This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical decisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.