Bases théoriques pour l’égalisation adaptative en mode autodidacte

Stability and convergence of adaptive algorithms are studied under a theoretical viewpoint, for the problem of discrete data transmission and their recovery by means of adaptive filtering (equalization). The relationships between adaptive equalization using a known training data sequence (training mode) and self-adaptive equalization using self-recovered data (self-learning mode) are pointed out. A comprehensive overview clarifies the satisfactory decaying behaviour of the transient error that is valid for both modes. Then stability of the self-learning mode is proved, under reasonable regularity conditions for the received signal at the channel output. Finally the self-learning equalizer, initiated with a short preamble in the training mode, is theoretically analyzed and its convergence towards optimality is proved, in agreement with practice.     

Equalization of a hard-limited slowly-fading multipath signal usinga phase equalizer with time-reversal structure

Describes a low-complexity equalization technique for improving the reliability of portable radio links in the presence of multipath time delay spread. A technique that operates on hard-limited received signals, with only the phase information available, is presented. Suboptimum receivers based on a maximum likelihood estimation criterion are discussed, including a sequence estimator and a decision feedback phase detector. A low-complexity adaptive phase equalizer structure using decision-directed phase tracking is proposed. The equalizer does not require the multiplication operations required in most conventional equalization algorithms. The author also proposes a receiver that includes a time-reversal structure and a joint estimator for optimum timing recovery and equalizer training. The time-reversal structure plays a crucial role in maximizing the compensation capability of the phase equalizer. The combined use of phase equalization and diversity reception is also considered     

Blind Equalization and Carrier Recovery Using a "Stop-and-Go" Decision-Directed Algorithm

We show that the standard decision-directed estimatedgradient adaptation algorithm for joint MSE equalization and carrier recovery, normally utilized in the open-eye condition, can be turned into an algorithm providing effective blind convergence in the MSE sense, usable in the closed-eye startup phase with no need of a known training sequence. This is obtained by means of a simple flag telling both the equalizer and the synchronizer whether the current output error with respect to the decided symbol is sufficiently reliable to be used. If not, adaptation is stopped for the current iteration. In the paper, this "stopand-go" decision-directed algorithm is presented for both linear and decision-feedback MSE complex equalizers with joint blind carrier recovery. Simulation results demonstrate the effectiveness of the proposed technique.     

Baseband Equalization and Carrier Recovery in Digital Radio Systems

The influence of adaptive baseband equalization on decision-feedback carrier recovery performance is investigated. First, it is shown that the delay introduced by the equalizer in the carrier recovery loop does not have basic consequences on system performance. Second, the interaction between the two adaptive circuits is studied for four different equalizer adaptation algorithms. It is found that algorithms based on the zero-forcing criterion are unstable unless they are used with an appropriate constraint. With gradient-type algorithms based on the minimum mean square error criterion, the interaction leads to an improved carrier acquisition performance at the expense of a larger phase jitter. It is therefore concluded that even with these latter algorithms it is generally worthwhile to avoid the interaction by forcing the imaginary part of the equalizer reference tap to zero. The theoretical analysis (carried out with a single complex tap equalizer) is supported by experimental results and computer simulation.     

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     

Interior point least squares estimation: transient convergenceanalysis and application to MMSE decision-feedback equalization

In many communication systems, training sequences are used to help the receiver identify and/or equalize the channel. The amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization. In this paper, we propose the use of a new adaptive filtering method called interior point least squares (IPLS) for adaptive equalization. First, we show that IPLS converges exponentially fast in the transient phase. Then, we use the IPLS algorithm to update the weight vector for a minimum-mean-square-error decision-feedback equalizer (MMSE-DFE) in a CDMA downlink scenario. Numerical simulations show that when training sequences are short IPLS consistently outperforms RLS in terms of system bit-error-rate and packet error rate. As the training sequence gets longer IPLS matches the performance of the RLS algorithm     

Channel estimation and equalization for M-QAM transmission with ahidden pilot sequence

Blind equalization techniques are useful to counteract multipath effects in radio local loop (RLL) and in general for wireless point to multipoint transmissions. One of the main drawbacks of blind equalization is the slow convergence time of the equalizer. Another major problem of blind equalization is the possible convergence toward wrong solutions. When these two main disadvantages cannot be tolerated it is necessary to adopt trained channel estimation and/or equalization techniques to counteract multipath. The training sequence is usually time division multiplexed with the informative sequence. This solution reduces the bandwidth efficiency and can be unusable when too frequent updating of the communications parameters need to be performed in the receiver. It is shown that bandwidth efficiency can be preserved at the expense of an increase in the transmitted power. The additional transmitted power is used to send a known pilot sequence hidden into the informative sequence. The hidden sequence is superimposed onto the symbols to be transmitted before waveform modulation. Thus each pilot symbol has the same period of the informative symbol so that no bandwidth spreading is necessary. High spectral efficiency M-QAM modulation is considered but the technique can be easily extended to any type of digital modulation format. We analyze the problems of channel estimation and of equalization based on the hidden pilot sequence. To prove the effectiveness of the proposed technique simulation results are provided. It is observed that in the case of equalization a pilot recovery subsystem should be used before using the pilot to train the equalizer     

Sign algorithms for blind equalization and their convergence analysis

In blind equalization a communication channel is adaptively equalized without resorting to the usual training sequence. In this paper we have introduced two new algorithms for blind equalization, which hard limit the equalizer input or the error at the output of the equalizer. These new algorithms are simple to implement and reduce the number of multiplications by approximately one-half. We show by way of simulations that the performance of the algorithm resulting from hardlimiting the error is comparable with the performance of the corresponding algorithm in which the error is not hardlimited. We formulate the new sign-error algorithm as a stochastic minimization of an error functional and demonstrate that the case of zero intersymbol interference corresponds to local minima of this error functional. We also present convergence analysis to predict the output mean square error in both these sign algorithms. Since the algorithms are highly nonlinear we incorporate several simplifying approximations and provide heuristic justifications for the validity of these approximations when the algorithms are operated in a typical practical environment. Computer simulations demonstrate the accuracy of the predicted convergence behavior.This research was supported in part by the Office of Naval Research under Contract N00014-89-J-1538.     

Use of blind equalization for teletext broadcast systems

A new application of blind equalization that appears to ameliorate the delays and improve the reliability of teletext systems is presented. The compatibility with the existing TV system and the cost-effectiveness of this application were considered for practical purposes. Equalizer adaptation does not require a knowledge of the transmitted data sequence or carrier phase recovery. Therefore, a reduction in the existing teletext circuitry has been achieved. In addition, the proposed quadrature phase shift keying (QPSK) modulation scheme doubles the teletext data transmission rate and uses the allocated TV bandwidth efficiently. The performance of the proposed blind equalizer has been evaluated in the presence of a multipath broadcast channel. Simulations have shown that substantial improvements are observed in the bit-error-rates for both two-phase PSK and QPSK modulation schemes     

Application of Least Squares Lattice Algorithms to Adaptive Equalization

In many applications of adaptive data equalization, rapid initial convergence of the adaptive equalizer is of paramount importance. Apparently, the fastest known equalizer adaptation algorithm is based on a recursive least squares estimation algorithm. In this paper we show how the least squares lattice algorithms, recently introduced by Morf and Lee, can be adapted to the equalizer adjustment algorithm. The resulting algorithm, although computationally more complex than certain other equalizer algorithms (including the fast Kalman algorithm), has a number of desirable features which should prove useful in many applications.     

Adaptive equalization of indoor radio channels for 156-Mb/s,QPSK data transmission

Indoor radio communication in the 20–60 GHz band using TDMA with differentially encoded QPSK is consideed. A burst-type transmission, based on a basic time slot consisting of a preamble for synchronization and equalizer training and of an information data section, is adopted. We employ fractionally spaced decision feedback equalization and give the relevant analytical and simulated performance results in terms of Doppler frequency. An upper limit is determined for the channel variations which can be tracked by the equalizer. Performance results are obtained for equalization with and without carrier phase recovery. Calculated and simulated probability of error show that error propagation degrades the performance by about 6 dB at a bit error rate of 10^–3 for a channel without any diversity. However, the effect of past decision errors is negligible for dual diversity. Numerical stability, required accuracy, and hardware complexity are also discussed.     

高速突发传输中的均衡算法

通过对几种常用均衡算法的比较,确定高速突发传输中使用收敛速度较快、运算量较小的VLMS均衡算法。为降低高速突发信号中的训练序列开销,提高传输效率,提出了一种新的混合结构均衡方案。新方案充分利用数据辅助均衡与盲均衡的各自特点,将均衡过程分成两个阶段,数据辅助均衡阶段为盲均衡阶段提供一个足够精确的初始值,引导盲均衡实现快速收敛。仿真结果表明,该混合结构均衡方案能利用短训练序列实现收敛,而且能达到较好的性能。     

Dual-mode type algorithms for blind equalization

Adaptive channel equalization accomplished without resorting to a training sequence is known as blind equalization. The Godard algorithm and the generalized Sato algorithm are two widely referenced algorithms for blind equalization of a QAM system. These algorithms exhibit very slow convergence rates when compared to algorithms employed in conventional data-aided equalization schemes. In order to speed up the convergence process, these algorithms may be switched over to a decision-directed equalization scheme once the error level is reasonably low. The authors present a scheme which is capable of operating in two modes: blind equalization mode and a mode similar to the decision-directed equalization mode. In this proposed scheme, the dominant mode of operation changes from the blind equalization mode at higher error levels to the mode similar to the decision-directed equalization mode at lower error levels. Manual switch-over to the decision-directed mode from the blind equalization mode, or vice-versa, is not necessary since transitions between the two modes take place smoothly and automatically     

Some blind FRESH equalization algorithms with anti-interference capabilities

Some novel blind FREquency-SHift （FRESH） equalizer algorithms are proposed for the equalization of Finite Impulse Response （FIR） single channel with anti-interference capabilities. These algorithms based on FRESH filter can work well without any training sequence. Simulation results show that the equalizer algorithms can effectively reject many types of interferences and the performances of these new equalizer algorithms are superior to the conventional equalizer algorithms.     

一种适用于稀疏多径信道的自适应均衡算法

针对传统的自适应均衡算法在稀疏多径信道下性能表现不佳的问题,提出了一种基于基追踪降噪的自适应均衡算法。该算法利用稀疏多径信道下均衡器权值的稀疏性,将自适应均衡器的训练过程看作压缩感知理论中稀疏信号对字典的加权求和,并利用重构算法直接对稀疏权值进行求解,解决了迭代参数设置和收敛慢的问题。采用基追踪降噪作为重构算法并选用变量分离近似稀疏重构对该最优化问题进行求解,既提高了权值的重构精度又降低了计算的复杂度。仿真结果表明,所提算法能够以较低的计算量和较少的训练序列达到更优性能,这对提升系统的通信性能具有参考价值。     

A Supervised Constant Modulus Algorithm for Blind Equalization

Blind equalization is a technique for adaptive equalization of a communication channel without the aid of the usual training sequence. Although the Constant Modulus Algorithm (CMA) is one of the most popular adaptive blind equalization algorithms, it suffers from slow convergence rate. A novel enhanced blind equalization technique based on a supervised CMA (S-CMA) is proposed in this paper. The technique is employed to initialize the coefficients of a linear transversal equalizer (LTE) filter in order to provide a fast startup for blind training. It also presents a computational study and simulation results of this newly proposed algorithm compared to other CMA techniques such as conventional CMA, Normalized CMA (N-CMA) and Modified CMA (M-CMA). The simulation results have demonstrated that the proposed algorithm has considerably better performance than others.     

改进的水声信道载波恢复盲均衡算法

为提高修正的常数模算法(MCMA)的收敛速度,进一步降低算法的剩余均方误差,提出了3种改进的盲均衡算法,既保留了MCMA算法载波恢复的功能,又不同程度地提高了MCMA算法的收敛速度。最后通过水声信道仿真,对这些算法的性能进行了验证和比较。     

多模盲均衡载波同步联合架构及分析

对于QAM体制信号,多模盲均衡算法(MMA)具有优于恒模算法 (CMA)的性能,同时具有矫正固定相位偏差及一定载波频率偏差(CFO)的能力。但在实际通信系统中,MMA对载波频偏的适应能力有限,当系统存在较大CFO时,MMA均衡算法稳态性能大幅下降。为保证MMA算法的稳态性能,同时适应较大载波频率偏差,文中提出了一种均衡载波同步联合结构。该结构将均衡器置于载波同步环路中,在消除载波频偏对均衡器性能影响的同时,提升了系统的载波频偏跟踪能力。文中对联合结构的载波环路跟踪性能进行了详细的理论分析,给出了环路性能指标的计算方法。数值仿真结果验证了理论分析的正确性,同时指出多模盲均衡载波同步联合算法能够在满足较大载波频偏跟踪性能的同时,实现接近无频偏时的均衡效果,很好的解决了大频偏下MMA算法性能损失严重的问题。      

A fast linear programming algorithm for blind equalization

A fast implementation of a special non-MSE cost function for blind equalization is presented here. This baud-rate equalization algorithm is based on a convex cost function coupled with a simple linear constraint on the equalizer parameters. For a generic class of channels with persistently exciting quadrature amplitude modulation input signals, this new algorithm allows the convergence of equalizer parameters to a unique global minimum achieving intersymbol interference suppression and carrier phase recovery     

基于恒模准则的盲均衡算法仿真

阐述了用于信道盲均衡的恒模算法的数学模型和基本原理。针对恒模算法存在收敛速度慢和相位旋转等不足,对近年来出现的一些性能优良的基于恒模准则的盲均衡算法——变步长恒模算法、修正恒模算法和多模算法进行了分析与仿真,并对各种改进算法在不同调制方式下的优缺点进行了说明。最后得到不同算法均衡后的星座图和均方误差曲线,表明具有较好的均衡效果。