利用自适应均衡滤波器改善大气湍流信道OWC性能

光无线通信是近年来无线通信领域的研究热点之一。大气湍流是影响光无线通信的重要因素,特别是在高速数字通信中会产生严重的码间干扰。本文分析了大气湍流信道的特性,提出采用自适应LMS均衡技术改善大气湍流信道的性能,对采用OOK调制方式的OWC系统均衡前后的误码率性能进行了分析比较。仿真结果表明自适应LMS均衡技术可以将系统的性能提高约10dB。     

高速率通信系统中均衡技术的研究

文章将原先用于时域均衡中经典的最小均方（LMS）算法与单载波频域均衡技术相结合,提出了使用LMS算法来更新频域均衡器的均衡系数,从而使均衡器的均衡系数根据信道特性自适应地变化。通过仿真验证了LMS算法在频域土毛衡技术中的有效性,并取得了良好的均衡效果。     

An adaptive algorithm for differentially coherent detection in the presence of intersymbol interference

An adaptive equalization method is proposed for use with differentially coherent detection of M-ary differential phase-shift keying (DPSK) signals in the presence of unknown carrier frequency offset. A decision-feedback or a linear equalizer is employed, followed by the differentially coherent detector. The equalizer coefficients are adjusted to minimize the post-detection mean squared error. The error, which is a quadratic function of the equalizer vector, is used to design an adaptive algorithm of stochastic gradient type. The approach differs from those proposed previously, which linearize the post-detection error to enable the use of least mean squares (LMS) or recursive least squares (RLS) adaptive equalizers. The proposed quadratic-error (Q) algorithm has complexity comparable to that of LMS, and equal convergence speed. Simulation results demonstrate performance improvement over methods based on linearized-error (L) algorithm. The main advantages of the technique proposed are its simplicity of implementation and robustness to carrier frequency offset, which is maintained for varying modulation level.     

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     

Convergence analysis of finite length blind adaptive equalizers

The paper presents some new analytical results on the convergence of two finite length blind adaptive channel equalizers, namely, the Godard equalizer and the Shalvi-Weinstein equalizer. First, a one-to-one correspondence in local minima is shown to exist between the Godard and Shalvi-Weinstein equalizers, hence establishing the equivalent relationship between the two algorithms. Convergence behaviors of finite length Godard and Shalvi-Weinstein equalizers are analyzed, and the potential stable equilibrium points are identified. The existence of undesirable stable equilibria for the finite length Shalvi-Weinstein equalizer is demonstrated through a simple example. It is proven that the points of convergence for both finite length equalizers depend on an initial kurtosis condition. It is also proven that when the length of equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition, the equalizer will converge to a stable equilibrium near a desired global minimum. When the kurtosis condition is not satisfied, generally the equalizer will take longer to converge to a desired equilibrium given sufficiently many parameters and adequate initialization. The convergence analysis of the equalizers in PAM communication systems can be easily extended to the equalizers in QAM communication systems     

Application of Fast Kalman Estimation to Adaptive Equalization

Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.     

Timing Recovery for Equalized Partial-Response Systems

It is shown that the sensitivity of the performance of least mean-square error (LMS) equalizers to the sampler phase is a function of equalizer length for partial-response systems. An LMS algorithm for the adjustment of sampler phase is derived for partial-response systems. This algorithm does not require the transmission of any pilot tones and is relatively easily implementable by digital circuits. A method of selecting a "good" initial sampler phase is also proposed.     

Combined RLS-LMS initialization for per tone equalizers in DMT-receivers

In discrete multitone receivers, the classical equalizer structure consists of a (real) time domain equalizer (TEQ) combined with complex one-tap frequency domain equalizers. An alternative receiver is based on a per tone equalization (PTEQ), which optimizes the signal-to-noise ratio (SNR) on each tone separately and, hence, the total bitrate. In this paper, a new initialization scheme for the PTEQ is introduced, based on a combination of least mean squares (LMS) and recursive least squares (RLS) adaptive filtering. It is shown that the proposed method has only slightly slower convergence than full square-root RLS (SR-RLS) while complexity as well as memory cost are reduced considerably. Hence, in terms of complexity and convergence speed, the proposed algorithm is in between LMS and RLS.     

自适应均衡算法在信道均衡技术中的应用研究

文中描述了两种非线性均衡器分别为判决反馈均衡器(DFE)和最大似然序列估计(MLSE)均衡器.所用信道模型为加性白高斯噪声信道,在DFE和线性均衡器(LE)中都是使用递归最小二乘(RLS)算法和最小均方(LMS)算法对数据进行分块处理.MLSE均衡器中使用了维特比最佳译码算法.就误比特性能来做以比较,DFE远好于LE,MLSE均衡器又明显优于DFE,并且它能达到几乎最优的性能.     

Importance sampling methodologies for simulation of communicationsystems with time-varying channels and adaptive equalizers

Two importance sampling (IS) methodologies for Monte Carlo simulation of communication links characterized by time-varying channels and adaptive equalizers are presented. One methodology is denoted as the twin system (TS) method. A key feature of the TS method is that biased noise samples are input to the adaptive equalizer, but the equalizer is only allowed to adapt to these samples for a time interval equal to the memory of the system. In addition to the TS technique, the IA method, a statistically biased, but simpler, technique for using IS with adaptive equalizers that is based on the independence assumption between equalizer input and equalizer taps is presented. Experimental results show run-time speedup factors of two to seven orders of magnitude for a static linear channel with memory, and of two to almost five orders of magnitude for a slowly-varying random linear channel with memory for both the IA and TS methods     

Set-membership adaptive equalization and an updator-sharedimplementation for multiple channel communications systems

This paper considers the problems of channel estimation and adaptive equalization in the novel framework of set-membership parameter estimation. Channel estimation using a class of set-membership identification algorithms known as optimal bounding ellipsoid (OBE) algorithms and their extension to tracking time-varying channels are described. Simulation results show that the OBE channel estimators outperform the least-mean-square (LMS) algorithm and perform comparably with the RLS and the Kalman filter. The concept of set-membership equalization is introduced along with the notion of a feasible equalizer. Necessary and sufficient conditions are derived for the existence of feasible equalizers in the case of linear equalization for a linear FIR additive noise channel. An adaptive OBE algorithm is shown to provide a set of estimated feasible equalizers. The selective update feature of the OBE algorithms is exploited to devise an updator-shared scheme in a multiple channel environment, referred to as updator-shared parallel adaptive equalization (USHAPE). U-SHAPE is shown to reduce the hardware complexity significantly. Procedures to compute the minimum number of updating processors required for a specified quality of service are presented     

Linear prediction methods for blind fractionally spacedequalization

We describe adaptive methods for estimating FIR zero-forcing blind equalizers with arbitrary delay directly from the linear predictions of the observations. While most current methods require inversion or singular value decomposition (SVD) of the correlation matrix, our methods need only to solve two linear prediction problems. They can be implemented as RLS or LMS algorithms to recursively update the equalizer estimation. they are computationally efficient. The computational complexity in each recursion can be less than 15(LN)² in the RLS case, where LN equals the equalizer length, and 3L(LN) in the LMS case, where L is the number of subchannels. The performance of the proposed methods and comparisons with existing approaches are shown by simulation to demonstrate their effectiveness     

A channel estimation using sliding window approach and tuningalgorithm for MLSE

A simultaneous sliding window channel estimation and timing adjustment method is proposed for adaptive maximum-likelihood sequence equalizer (MLSE) in the global system for mobile communication (GSM) system, and also a tuning scheme based on least mean squared (LMS) algorithm is presented in order to improve the performance of equalizer. Simulation results show that the proposed channel estimation technique is effective for channel estimation of the adaptive equalizer     

A soft decision-directed LMS algorithm for blind equalization

An adaptation algorithm for equalizers operating on very distorted channels is presented. The algorithm is based on the idea of adjusting the equalizer tap gains to maximize the likelihood that the equalizer outputs would be generated by a mixture of two Gaussians with known means. The decision-directed least-mean-square algorithm is shown to be an approximation to maximizing the likelihood that the equalizer outputs come from such an independently and identically distributed source. The algorithm is developed in the context of a binary pulse-amplitude-modulation channel, and simulations demonstrate that the algorithm converges in channels for which the decision-directed LMS algorithms does not converge     

Adaptive bit rate maximizing time-domain equalizer design for DMT-based systems

The classical discrete multitone receiver as used in, e.g., digital subscriber line (DSL) modems, combines a channel shortening time-domain equalizer (TEQ) with one-tap frequency-domain equalizers (FEQs). In a previous paper, the authors proposed a nonlinear bit rate maximizing (BM) TEQ design criterion and they have shown that the resulting BM-TEQ and the closely related BM per-group equalizers (PGEQs) approach the performance of the so-called per-tone equalizer (PTEQ). The PTEQ is an attractive alternative that provides a separate complex-valued equalizer for each active tone. In this paper, the authors show that the BM-TEQ and BM-PGEQ, despite their nonlinear cost criterion, can be designed adaptively, based on a recursive Levenberg-Marquardt algorithm. This adaptive BM-TEQ/BM-PGEQ makes use of the same second-order statistics as the earlier presented recursive least-squares (RLS)-based adaptive PTEQ. A complete range of adaptive BM equalizers then opens up: the RLS-based adaptive PTEQ design is computationally efficient but involves a large number of equalizer taps; the adaptive BM-TEQ has a minimal number of equalizer taps at the expense of a larger design complexity; the adaptive BM-PGEQ has a similar design complexity as the BM-TEQ and an intermediate number of equalizer taps between the BM-TEQ and the PTEQ. These adaptive equalizers allow us to track variations of transmission channel and noise, which are typical of a DSL environment.     

An efficient block adaptive decision feedback equalizer implemented in the frequency domain

In this paper, a new block adaptive decision feedback equalizer (DFE) implemented in the frequency domain is derived. The new algorithm is suitable for applications requiring long adaptive equalizers, as is the case in several high-speed wireless communication systems. The inherent "causality" problem appearing in the block adaptive formulation of the DFE equations is overcome by using tentative decisions in place of the unknown ones within each block. These tentative decisions are subsequently improved by using an efficient iterative procedure, which finally converges to the optimum decisions in a few iterations. This procedure is properly initialized by applying a minimization criterion that utilizes all the available information. The whole algorithm, including the iterative procedure, is implemented in the frequency domain and exhibits a considerable reduction in computational complexity, as compared with the conventional DFE, offering, at the same time, a noticeable increase in convergence speed. Additionally, the level of the steady-state MSE, which is achieved by the new algorithm, is practically insensitive to the block length.     

A transversal equalizer with an increased adaptation speed andtracking capability

A modification to the well-known least-mean-square (LMS) algorithm for adaptive equalizers is presented. It allows a flexible tradeoff between throughput rate and adaptation speed by adjusting the arithmetic expense per output sample. If the arithmetic expense is increased to that of recursive least-squares (RLS)-based algorithms, a comparable adaptation speed is achieved. A full-custom implementation of a transversal equalizer using timesharing by a factor of two and Booth-coded coefficients proves the feasibility and efficiency of the modified LMS. It achieves data rates of up to 75 MBaud in a 0.8-μm CMOS technology under worst case conditions. The convergence rate of the gradient lattice algorithm can be achieved by reducing the symbol rate to 15 MBaud. The modification requires about 15% additional area in the basic cell of the filter, a few additional control signals, and a buffer to store 40 input symbols     

Trellis-based soft-output adaptive equalization techniques for TDMAcellular systems

The concatenation of an equalizer and a Viterbi (1967) decoder is a powerful means for improving receiver performance in wireless communication systems. A soft-output equalizer increases the impact of this combination by enabling the use of soft-decision Viterbi decoding. It is well known that the maximum a posteriori (MAP) algorithm provides optimal reliability information, but at the cost of substantial complexity. This paper contains the results of an investigation into the design and performance of soft-output adaptive equalization techniques based on suboptimum trellis-based soft-output decoding algorithms. It is shown that the performance improvement relative to hard output equalizers is substantial, while the cost in terms of complexity is modest. A time-division multiple-access (TDMA) cellular system is used as the basis for comparisons. Simulation results and a complexity analysis are presented     

Nonsingular Constant Modulus Equalizer for PDM-QPSK Coherent Optical Receivers

Adaptive electronic equalizers using the constant modulus algorithm (CMA) algorithm often converge to a singular coefficient matrix that produces the same signal at multiple outputs. We address this issue in the context of optical communications systems with polarization-division multiplexing and coherent receivers. We study, by computer simulation, the performance of multiuser CMA equalizer, an enhanced CMA equalizer initially proposed for use in wireless multiuser and later multiple-input/multiple-output communications systems. We show that the proposed adaptive electronic equalizer does not exhibit singularities and, therefore, is superior to the commonly used CMA equalizer.     

MLSE Equalizers for Frequency Discrimination Receiver of MSK Optical Transmission System

We propose maximum-likelihood sequence estimator (MLSE) equalizers based on either Viterbi algorithm or template matching temple matching (TM) for the equalization of impairments imposed on the minimum shift keying (MSK) modulation formats in long haul transmission without optical dispersion compensation. The TM-MLSE equalizer is proposed as a simplified alternative for the Viterbi-MLSE equalizer. It is verified that the Viterbi-MLSE equalizer can operate optimally when noise approaches a Gaussian distribution. Simulation results of the performances of the two MLSE equalizers for optical frequency discrimination receiver-based optical MSK systems are described. The transmission performance is evaluated in terms of: (1) the chromatic dispersion (CD) tolerance for both Viterbi-MLSE and TM-MLSE equalizers; (2) transmission distance limits of Viterbi-MLSE equalizers with various number of states; (3)the robustness to fiber polarization mode dispersion (PMD) of Viterbi-MLSE equalizers; and (4) performance improvements for Viterbi-MLSE equalizers when utilizing sampling schemes with two and four samples per bit over the conventional single sample per bit. With a small number of states (64 states), the non-compensating optical link can equivalently reach up to approximately 928 km SSMF for 10 Gb/s transmission or 58 km SSMF for 40 Gb/s. The performance of 16-state Viterbi-MLSE equalizers for optical frequency discrimination receiver (OFDR)-based optical MSK transmission systems for PMD mitigation is also numerically investigated. The performance of Viterbi-MLSE equalizers can be further improved by using the sampling schemes with multiple samples per bit compared to the conventional single sample bit. The equalizer also offers high robustness to fiber PMD impairment.