Further Results on Adaptive Equalizer Improvements for 16 QAM and 64 QAM Digital Radio

Channel distortions due to multipath fading are a principal source of outage for high-capacity digital radio. Time domain equalization is increasingly becoming an effective means to compensate for fading induced ISI. This paper compares the performance of transversal and decision feedback equalizers used for 16 QAM and 64 QAM digital radio systems. The effect of tap spacing is examined by comparing the results of baud period spacing with fractionally spaced equalizers. The performance measure used is peak distortion. This measure is plotted against various fade parameters for the different equalizers studied, the two modulation schemes, forms of timing recovery, and the effects of joint operation of demodulation and symbol synchronization circuitry. Results clearly indicate, in terms of better signature curves, the superiority of fractionally spaced equalizers over synchronous equalizers. An additional advantage is the robustness of FSE's to timing phase errors. A decision feedback equalizer with fractional spacing on the feedforward part offers the best performance. It is shown that the performance of a DFE synchronized to the first precursor is significantly improved as compared to the conventional case of synchronizing with the main sample of the received pulse. With the new position of reference (first precursor), fractional DFE's benefit more than theirT-spaced counterpart.     

Multipath Outage Performance of Digital Radio Receivers Using Finite-Tap Adaptive Equalizers

Recent analysis/simulation studies have quantified the multipath outage statistics of digital radio systems using ideal adaptive equalization. In this paper, we consider the use of finite-tap delay line equalizers, with the aim of determining how many taps are needed to approximate ideal performance. To this end, we assume anM-level QAM system using cosine rolloff spectral shaping and an adaptive equalizer with either fractionally spaced or synchronously spaced taps. We invoke a widely used statistical model for the fading channel and computer-simulate thousands of responses from its ensemble. For each trial, we compute a detection signal-to-distortion measure, suitably maximized with respect to the tap gains. We can thereby obtain probability distributions of this measure for specified combinations of system parameters. These distributions, in turn, can be interpreted as outage probabilities (or outage seconds) versus the number of modulation levels. A major finding of this study is that, for the assumed multipath fading model, very few taps (the order of five) are needed to approximate the performance of an ideal infinite-tap equalizer. We also find that a simple, suboptimal form of timing recovery is generally quite adequate, and that fractionally spaced equalizers are more advantageous than synchronously spaced equalizers with the same number of taps. This advantage is minor for rolloff factors of 0.5 and larger but increases dramatically as the rolloff factor approaches zero.     

Blind estimation of direct sequence spread spectrum signals inmultipath

Self-recovering receivers for direct-sequence spread-spectrum signals with unknown spreading codes are discussed in this paper. Applications include signal interception, jamming, and low probability of intercept (LPI) communications. A multirate/multichannel, discrete-time model of the spread spectrum signal is introduced, which establishes links with array processing techniques. Borrowing blind channel estimation ideas, which were originally developed in the context of fractionally spaced equalizers or receivers with multiple antennas, linear solutions are obtained that are independent of the input distribution. The signal interception problem is further studied, and a zero-forcing (ZF) receiver/equalizer is proposed to recover the transmitted data. Its performance is analyzed, and some illustrative simulations are presented     

Performance of Volterra and MLSD receivers for nonlinearband-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     

Blind equalization for short burst wireless communications

In this paper, we propose a dual mode blind equalizer based on the constant modulus algorithm (CMA). The blind equalizer is devised for short burst transmission formats used in many current wireless TDMA systems as well as future wireless packet data systems. Blind equalization is useful for such short burst formats, since the overhead associated with training can be significant when only a small number of bits are transmitted at a time. The proposed equalizer overcomes the common problems associated with classic blind algorithms, i.e., slow convergence and ill-convergence, which are detrimental to applying blind equalization to short burst formats. Thus, it can eliminate the overhead associated with training sequences. Also, the blind equalizer is extended to a two branch diversity combining blind equalizer. A new initialization for fractionally spaced CMA equalizers is introduced. This greatly improves the symbol timing recovery performance of fractionally spaced CMA equalizers with or without diversity, when applied to short bursts. Through simulations with quasi-static or time-varying frequency selective wireless channels, the performance of the proposed equalizer is compared to selection diversity and conventional equalizers with training sequences. The results indicate that its performance is far superior to that of selection diversity alone and comparable to the performance of equalizers with short training sequences. Thus, training overhead can be removed with no performance degradation for fast time-varying channels, and with slight performance degradation for static channels     

Fractionally spaced equalizers

Modern digital transmission systems commonly use an adaptive equalizer as a key part of the receiver. The design of this equalizer is important since it determines the maximum quality attainable from the system, and represents a high fraction of the computation used to implement the demodulator. Analytical results offer a new way of looking at fractionally spaced equalizers and have some surprising practical implications. This article describes the data communications problem, the rationale for introducing fractionally spaced equalizers, new results, and their implications. We then apply those results to actual transmission channels     

Performance of trellis codes for a class of equalized ISI channels

The performance of trellis codes is examined for a class of intersymbol interference (ISI) channels that occur in high-frequency radio systems. The channels considered are characterized by in-band spectral nulls and by a rapid time variation. The baseline modulation technique is 4QAM (four-point quadrature amplitude modulation). When spectral nulls are absent, performance of fractionally spaced linear equalizers and trellis decoders is found to be near ideal and to be better than using symbol-spacing in the equalizer. However, error propagation in the feedback path, resulting from equalizer-based decisions, ruins the performance of the combination of decision-feedback equalizers and trellis decoders when spectral nulls are present. Their performance can be improved by using fractionally spaced feedforward equalizer sections and by designing the decoder to compensate for ISI. Rate 2/3 codes are found to outperform rate 1/2 codes in error performance     

l0-范数约束的稀疏多径信道分数间隔双模式盲均衡算法

针对深衰落稀疏多径信道下多进制相移键控（Multiple Phase Shift Keying,MPSK）信号的盲均衡问题,提出了一种l₀-范数约束的分数间隔稀疏自适应双模式盲均衡算法.该算法借鉴传统的分数间隔双模式盲均衡算法思想,结合稀疏自适应滤波理论,首先利用l₀-范数对均衡器抽头系数进行稀疏性约束,构造出一种l₀-范数约束的分数间隔双模式最小均方误差代价函数,然后依据梯度下降法推导出盲均衡器抽头系数更新公式,并对迭代步长进行归一化和比例系数化.理论分析和仿真实验表明,与基于门限稀疏化的盲均衡算法、基于分数阶范数的盲均衡算法及分数间隔双模式盲均衡算法相比,本文所提算法在保证较快收敛速度的前提下,能有效降低剩余符号间干扰.本文设计的盲均衡算法为水声通信系统中接收方恢复出发送信号,提供了一种快速有效的方法.     

Non-uniformly spaced tapped-delay-line equalizers

A systematic way to design nonuniformly spaced tapped-delay-line (TDL) equalizers is described, and the performance of such equalizers is compared to that of uniformly spaced TDL equalizers with the same number of tap coefficients. It is shown that the signal-to-mean-squared-error ratio at the output of a TDL equalizer can be improved by optimally choosing the positions of the tap weights. An algorithm to find both the tap positions and the corresponding tap weights for a given delay span and a given minimum tap spacing of the equalizer is presented. Typical results are illustrated by using, as an example, the magnetic recording channel. For two target waveforms at different densities of recording, it is shown that there is a potential for saving up to seven equalizer taps     

Cyclostationary crosstalk suppression by decision feedbackequalization on digital subscriber loops

Interference from digital signals in multipair cables has been shown to be cyclostationary under some conditions. This work evaluates the performance of a decision feedback equalizer (DFE) in the presence of cyclostationary interference (CI), intersymbol interference (ISI), and additive white noise (AWN). A comparison between a DFE with CI and one with stationary interference (SI) shows the ability of the DFE to substantially suppress CI. Fractionally spaced and symbol-rate DFE equalizers are also compared and the former is found to yield better performance, especially in the presence of CI. The use of a symbol-rate DFE using an adaptive timing technique that finds the receiver's best sampling phase is proposed for when the fractionally spaced DFE cannot be used because of its complexity. The results also demonstrate the potential benefits of synchronizing central office transmitter clocks, if a fractionally spaced DFE is used at the receiver     

Fractionally spaced linear and DF Mimo equalizers for multitone systems without guard time

WhenOFDM or multitone modulation is used, the dispersiveness of the channel is usually circumvented by means of the technique of guard time. As an alternative it is possible not to use a guard time but design receivers able to equalize theisi andici. In the present paper we show how to design fractionally spaced linear or decision-feedback Mimo equalizers for multitone systems without guard time. Full complexity and reduced complexity solutions are investigated. The design is made for anmmse criterion and the steady-state performance is analysed. It is shown that Mimo equalization outperforms the technique of guard time, that fractionally spaced devices are very effective and the complexity reduction produces a performance degradation which is negligible compared to full complexity fractionally spaced devices, especially when the processing rate is larger than the symbol rate.     

Polynomial perceptrons and their applications to fading channelequalization and co-channel interference suppression

This paper investigates the behaviors of polynomial perceptrons and introduces a fractionally spaced recursive polynomial perceptron with low complexity and fast convergence rate. The nonlinear mapping ability of the polynomial perceptron is analyzed. It is shown that a polynomial perceptron with degree L(⩾4) satisfies the Stone-Weierstrass theorem and can approximate any continuous function to within a specified accuracy. Moreover, the nonlinear mapping ability of a polynomial perceptron with degree L is similar to that of the three-layer perceptron with one hidden layer for time same number of neurons in the input layer. The nonlinear mapping ability of the fractionally spaced recursive polynomial perceptron is also presented. Applications of polynomial perceptrons for fading channel equalization and co-channel interference suppression in a 16-level quadrature amplitude modulation receiver system are considered. Computer simulations are used to evaluate and compare the performance of polynomial perceptron (PP) and fractionally spaced bilinear perceptron (FSBLP) with that of the synchronous decision feedback multilayer perceptron (SDFMLP), fractionally spaced decision feedback multilayer perceptron (FSDFMLP), and the conventional decision feedback equalizer (DFE). The results show that the performance of the fractionally spaced bilinear perceptron is clearly superior to that of the other structures     

基于线性预测的盲最小均方误差均衡器

盲过采样均衡器仅用二阶统计量便可减小码间干扰,该文采用线性预测方法,提出了一种盲最小均方误差(MMSE)均衡器。该方法不需要先估计信道,可直接利用过采样的接收信号均衡信道。此外,该均衡器可采用递推最小二乘算法自适应地实现,具有较高的计算效率。仿真结果表明,该均衡器比基于线性预测的盲置零均衡器有更小的符号估计均方误差。     

并行多信道判决引导CDL盲均衡算法

针对传统算法抽头系数较长和难以处理深衰落信道的问题,提出适用于通用数据链信号的并行多信道判决引导盲均衡算法。新算法借助判决反馈结构中前馈、反馈滤波器的独立优化特性,将加权后的判决值代入下一次的迭代过程,有利于消除拖尾效应;综合运用采样率高的分数间隔结构与稳态误差小的判决引导算法,对接收信号采用并行处理的方式,大大缩短了抽头系数长度。实验结果表明,针对CDL信号,新算法能够有效提升收敛速度、降低误码率。      

Advanced Time- and Frequency-Domain Adaptive Equalization in Multilevel QAM Digital Radio Systems

Digital radio systems employing multilevel QAM are at least optionally equipped with adaptive time- and/or frequency-domain equalizers. Their purpose is to reduce the vulnerability of these systems to linear distortion caused by multipath propagation. Linear transversal filters are prominent candidates for the realization of time-domain equalizers, especially for high-capacity applications. They are well known for their good performance and their relatively easy implementation at a high data rate. On the other hand, decision feedback equalizers are known to be very capable of eliminating linear distortion, especially of the so-called minimum-phase type. But realization problems are likely to occur in a high-speed application. A solution is proposed which merges the relative advantages of both the linear transversal and the decision feedback approaches. The goal of a frequency-domain equalizer, which is the restoration of the shape of the power density spectrum of the received signal without any recovered carrier and timing signals, can also be achieved with the aid of a transversal filter. The performance obtained with the joint utilization of the novel timeand frequency-domain equalizers is described.     

Fractionally Nyquist Sample Spaced ARMA Blind Equalizer for Direct Signal Recovery in Passive Bistatic Radar

This paper proposes a modified signal pro-cessing structure based on the fractionally Nyquist sample spaced structure for passive bistatic radar. To recover the direct signal from the multipath clutter, an equalizer of the Auto regressive moving average (ARMA) type is pro-posed based on the fractionally Nyquist sample spaced con-stant modulus algorithm. Compared with the conventional Nyquist sample spaced equalizer, the equalizer of the frac-tionally Nyquist sample spaced ARMA structure is more effective in dealing with deep fading multipath channels with zeros near the unit circle. Computer simulations and real data tests indicate that the proposed approach out-performs the conventional processing structure in terms of both clutter residual and mean square error.     

Fractionally Spaced Equalization Algorithms in 60GHz Communication System

Several fractionally spaced equalizers （FSE） which could be used in 60GHz systems are presented in this paper. For 60GHz systems, low-power equalization algorithms are favorable. We focus on FSE in both time domain （TD） and frequency domain （FD） in order to meet different complexity requirements of 60GHz systems. Compared with symbol spaced equalizer （SSE）, FSE can relax the requirement of sampling synchronization hardware significantly. Extensive simulation results show that our equalization algorithms not only eliminate ISI efficiently, but are also robust to timing synchronization errors.     

Channel equalization via channel identification: algorithms andsimulation results for rapidly fading HF channels

The problem of channel equalization via channel identification (CEQCID) that has previously been considered by a handful of researchers is explored further. An efficient algorithm for mapping the channel parameters to the equalizers coefficients is proposed. The proposed scheme is compared with a lattice least squares (LS) based receivers. For the particular application of the high frequency (HF) radio channels, we find that the CEQCID has lower computational complexity. In terms of the tracking performance, also, the CEQCID has been found to be superior to the LS based receivers. We emphasize on the implementation of a fractionally tap-spaced decision feedback equalizer (DFE) and compare that with the T-spaced DFE. We show that the former is a better choice for the multipath HF channels     

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.     

Adjustment of the Position of the Reference Tap of an Adaptive Equalizer

The present structure of adaptive least mean-square error (LMSE) equalizers for data transmission has an unnecessary constraint of a fixed position for the reference tap. This constraint limits their performance. In this paper a gradient-directed method of adjusting the position of the reference tap is developed to minimize the mean-square distortion (MSD). A scheme for implementing this modified equalizer is proposed. Results of computer simulation are shown that indicate that for channels with delay distortion some improvement in performance can be achieved.