Fuzzy stochastic gradient decision feedback equalizer for VSBterrestrial HDTV broadcasting

We present a fuzzy stochastic gradient (FSG) decision feedback equalizer (DFE) for VSB terrestrial HDTV broadcasting. This equalizer employs a well-designed fuzzy Takagi-Sugeno (1985) model to automatically regulate the step size of the descent gradient vector, combining a fast convergence rate and a low excess mean square error (MSE). The only penalty paid is a slight increase in the computational complexity compared with the LMS algorithm. Simulation results show that this equalizer provides 3.5 dB signal-to-noise ratio (SNR) improvement at a BER of 3.0×10^-6 with respect to the conventional LMS DFE recommended by the Grand Alliance     

Adaptive LMS filters for cellular CDMA overlay situations

This paper extends and complements previous research we have performed on the performance of nonadaptive narrowband suppression filters when used in cellular code-division multiple-access (CDMA) overlay situations. An adaptive least mean square (LMS) filter is applied to a cellular CDMA overlay in order to reject narrowband interference. An accurate expression for the steady-state tap-weight covariance matrix is derived for the real LMS algorithm for arbitrary statistics of the overlaid interference. Numerical results illustrate that when the ratio of the narrowband interference bandwidth to the spread spectrum bandwidth is small, the LMS filter is very effective in rejecting the narrowband interference. Furthermore, it is seen that the performance of the LMS filter in a CDMA overlay environment is not significantly worse than the performance of an ideal Wiener filter, assuming the LMS filter has had sufficient time to converge     

Adaptive decision feedback equalization: can you skip the trainingperiod?

This paper presents a novel unsupervised (blind) adaptive decision feedback equalizer (DFE). It can be thought of as the cascade of four devices, whose main components are a purely recursive filter (ℛ) and a transversal filter (𝒯). Its major feature is the ability to deal with severe quickly time-varying channels, unlike the conventional adaptive DFE. This result is obtained by allowing the new equalizer to modify, in a reversible way, both its structure and its adaptation according to some measure of performance such as the mean-square error (MSE). In the starting mode, ℛ comes first and whitens its own output by means of a prediction principle, while 𝒯 removes the remaining intersymbol interference (ISI) thanks to the Godard (1980) (or Shalvi-Weinstein (1990)) algorithm. In the tracking mode the equalizer becomes the classical DFE controlled by the decision-directed (DD) least-mean-square (LMS) algorithm. With the same computational complexity, the new unsupervised equalizer exhibits the same convergence speed, steady-state MSE, and bit-error rate (BER) as the trained conventional DFE, but it requires no training. It has been implemented on a digital signal processor (DSP) and tested on underwater communications signals-its performances are really convincing     

DFT/LMS算法在DSSS中的应用及性能分析

本文分析了直接序列扩频(DSSS)系统中最小错误概率(MPE)意义下的最优滤波器,并依据矩阵求逆引理证明最小均方误差(MMSE)意义下的最优滤波——维纳滤波也是MPE意义下的最优滤波。在DSSS中应用自适应滤波,无须先验已知扩频码的码型和干扰的统计特性,就能一并完成解扩以及有效抑制干扰。离散傅立叶变换/最小均方(DFT/LMS)算法的收敛速度远快于LMS算法,而运算量、稳健性与LMS算法基本相同。基于DFT/LMS算法的自适应滤波大大简化DSSS系统接收机的设计,显著增强系统抗干扰能力,具有很强的实用性。     

Stochastic analysis of the LMS algorithm with a saturationnonlinearity following the adaptive filter output

This paper presents a statistical analysis of the least mean square (LMS) algorithm with a zero-memory scaled error function nonlinearity following the adaptive filter output. This structure models saturation effects in active noise and active vibration control systems when the acoustic transducers are driven by large amplitude signals. The problem is first defined as a nonlinear signal estimation problem and the mean-square error (MSE) performance surface is studied. Analytical expressions are obtained for the optimum weight vector and the minimum achievable MSE as functions of the saturation. These results are useful for adaptive algorithm design and evaluation. The LMS algorithm behavior with saturation is analyzed for Gaussian inputs and slow adaptation. Deterministic nonlinear recursions are obtained for the time-varying mean weight and MSE behavior. Simplified results are derived for white inputs and small step sizes. Monte Carlo simulations display excellent agreement with the theoretical predictions, even for relatively large step sizes. The new analytical results accurately predict the effect of saturation on the LMS adaptive filter behavior     

Modified leaky LMS algorithm for channel estimation in DS-CDMAsystems

A simple adaptive least mean square (LMS) type algorithm for channel estimation is developed based on certain modifications to finite-impulse response (FIR) Wiener filtering. The proposed algorithm is nearly blind since it does not require any training sequence or channel statistics, and it can be implemented using only noise variance knowledge. A condition guaranteeing the convergence of the algorithm and theoretical mean square error (MSE) values are also derived. Computer simulation results demonstrate that the proposed algorithm can yield a smaller MSE than existing techniques, and that its performance is close to that of optimal Wiener filtering     

A space-time-filtered Viterbi receiver for CCI/ISI reduction in TDMA systems

In this paper, we present a hybrid space-time-filtered Viterbi receiver using multiple antennas for co-channel interference (CCI) reduction and intersymbol interference (ISI) equalization in a slow Rayleigh fading channel. In this approach, a space-time filter is first applied at the antenna outputs to maximize the signal-to-interference-plus-noise ratio (SINR), and the scalar output is then sent to a Viterbi equalizer. We propose a closed-form solution to jointly determine the weight vector for the space-time filter and the channel vector for the Viterbi equalizer. We also examine the need for a whitening filter prior to the Viterbi equalizer and show that it only marginally improves the performance. Simulation results are provided to validate our approach and to compare the performance of our receiver with that of different existing receivers.     

Performance of Reduced-Rank Equalization

We evaluate the performance of reduced-rank equalizers for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) frequency-selective channels. Each equalizer filter is constrained to lie in a Krylov subspace, and can be implemented as a reduced-rank multistage Wiener filter (MSWF). Both reduced-rank linear and decision-feedback equalizers (DFEs) are considered. Our results are asymptotic as the filter length goes to infinity. For SISO channels, the output mean-squared error (MSE) is expressed in terms of the moments of the channel spectrum. For MIMO channels, both successive and parallel interference cancellation are considered. The asymptotic performance in that case requires the computation of moments, which depend on shifted versions of the channel impulse response for different users. Those are also expressed in terms of the MIMO channel frequency response. Numerical results are presented, which show that near full-rank performance can be achieved with relatively low-rank equalizers     

Error whitening criterion for adaptive filtering: theory and algorithms

Mean squared error (MSE) has been the dominant criterion in adaptive filter theory. A major drawback of the MSE criterion in linear filter adaptation is the parameter bias in the Wiener solution when the input data are contaminated with noise. We propose and analyze a new augmented MSE criterion called the Error Whitening Criterion (EWC). EWC is able to eliminate this bias when the noise is white. We will determine the analytical solution of the EWC, discuss some interesting properties, and develop stochastic gradient and other fast algorithms to calculate the EWC solution in an online fashion. The stochastic algorithms are locally computable and have structures and complexities similar to their MSE-based counterparts (LMS and NLMS). Convergence of the stochastic gradient algorithm is established with mild assumptions, and upper bounds on the step sizes are deduced for guaranteed convergence. We will briefly discuss an RLS-like Recursive Error Whitening (REW) algorithm and a minor components analysis (MCA) based EWC-total least squares (TLS) algorithm and further draw parallels between the REW algorithm and the Instrumental Variables (IV) method for system identification. Finally, we will demonstrate the noise-rejection capability of the EWC by comparing the performance with MSE criterion and TLS.     

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     

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。     

适用于紫外光通信的延迟判决均衡算法

为了消除紫外光通信过程中强烈散射所引起的码间干扰，采用一种带信道估计的最小均方误差-最大似然估计(LMS-MLE)延迟判决均衡算法进行了理论分析和仿真验证。通过选取合适的判决延迟深度来调整LMS自适应滤波器抽头系数进行信道跟踪，获取新的信道估计向量，最后利用MLE均衡算法得到最优序列输出。结果表明, 该算法可以明显提升紫外光通信系统的性能，在没有提高复杂度的情况下，性能接近最优MLE均衡算法，并且可以实现信道跟踪, 紫外光通信中算法的最佳延迟量取值为20。这一结果对紫外光通信性能提升以及MLE均衡器的工程实现是有帮助的。     

An adaptive correlator receiver for direct-sequence spread-spectrumcommunication

This paper presents a novel receiver for direct sequence spread-spectrum signals over channels containing interference and multipath. The receiver employs an adaptive correlator that jointly detects the transmitted data, removes interference, and compensates for multipath. The optimum correlation vector is derived by determining the Wiener vector that minimizes the mean squared error (MSE) between the transmitted data bit and the correlator output. For an additive white Gaussian noise (AWGN) channel, the optimal correlation vector is the spreading sequence used by the transmitter. For interference and multipath channels, the optimal correlation vector will suppress the interference and combine the multipath while optimizing the detection of the transmitted data bit. The paper presents analytical and simulation results which illustrate the bit-error rate (BER) performance of the receiver in multipath and narrowband interference. Additionally, simulation results are presented illustrating the convergence performance of the receiver when the tap weights are adjusted using either the least mean square (LMS) or recursive least squares (RLS) adaptive algorithms     

基于多小波双变换的非线性卫星信道盲均衡算法

针对非线性卫星信道Volterra盲均衡系统收敛缓慢、计算复杂高等不足,提出了基于多小波双变换的非线性卫星信道盲均衡算法.该算法用Wiener均衡器代替Volterra均衡器,减小了均衡器结构的复杂性;用平衡正交多小波对Wiener均衡器的输入信号进行变换,降低了输入信号的自相关性;在Wiener均衡器输出端增加一级判决反馈滤波器,同时对其输入信号作平衡多小波变换,又降低了判决反馈滤波器输出信号的自相关性.仿真结果验证了该算法的有效性.     

VLSI implementation of a new LMS-based algorithm for noise removal in ECG signal

Least mean square (LMS)-based adaptive filters are widely deployed for removing artefacts in electrocardiogram (ECG) due to less number of computations. But they posses high mean square error (MSE) under noisy environment. The transform domain variable step-size LMS algorithm reduces the MSE at the cost of computational complexity. In this paper, a variable step-size delayed LMS adaptive filter is used to remove the artefacts from the ECG signal for improved feature extraction. The dedicated digital Signal processors provide fast processing, but they are not flexible. By using field programmable gate arrays, the pipelined architectures can be used to enhance the system performance. The pipelined architecture can enhance the operation efficiency of the adaptive filter and save the power consumption. This technique provides high signal-to-noise ratio and low MSE with reduced computational complexity; hence, it is a useful method for monitoring patients with heart-related problem.     

一种用于QAM解调信号的LMS自适应均衡器

设计了一种用于QAM(Quadrature Amplitude Modulation)解调信号的LMS自适应均衡器。此均衡器采用线性自适应算法中的最小均方算法(LMS)．其结构由线性横向滤波器和需要训练序列的滤波器抽头系数更新模块组成．它可实现16／64／256点的QAM解调。利用MATLAB／Simulink对LMS自适应均衡器的收敛速度、误码率等指标进行仿真模拟,仿真结果表明,此LMS自适应均衡器对通过非理想信道的QAM传输信号具有较好的均衡性能。     

Modified LMS algorithm for unbiased impulse response estimation innonstationary noise

In the presence of input interference, the Wiener solution for impulse response estimation is biased. It is proved that bias removal can be achieved by proper scaling of the optimal filter coefficients and a modified least mean squares (LMS) algorithm is then developed for accurate system identification in noise. Simulation results show that the proposed method outperforms two total least squares (TLS) based adaptive algorithms under nonstationary interference conditions     

On statistical efficiency of the LMS algorithm in system modeling

The conventional least-mean-square (LMS) algorithm is compared with the ideal LMS/Newton (ILMSN) algorithm. It is shown that, although under certain conditions, for similar misadjustment, the output mean-square error (MSE) of the ILMSN algorithm may converge much faster than the MSE of the LMS algorithm, the difference between the two algorithms may not be that great if misalignments of the adaptive filter tap gains are compared. Analytical results are presented, with computer simulations that support their validity     

Adaptive AR modeling in white Gaussian noise

Autoregressive (AR) modeling is widely used in signal processing. The coefficients of an AR model can be easily obtained with a least mean square (LMS) prediction error filter. However, it is known that this filter gives a biased solution when the input signal is corrupted by white Gaussian noise. Treichler (1979) suggested the γ-LMS algorithm to remedy this problem and proved that the mean weight vector can converge to the Wiener solution. In this paper, we develop a new algorithm that extends works of Vijayan et al. (1990), for adaptive AR modeling in the presence of white Gaussian noise. By theoretical analysis, we show that the performance of the new algorithm is superior to the γ-LMS filter. Simulations are also provided to support our theoretical results     

Gaussian Noise Filtering from ECG by Wiener Filter and Ensemble Empirical Mode Decomposition

Empirical mode decomposition (EMD) is a powerful algorithm that decomposes signals as a set of intrinsic mode function (IMF) based on the signal complexity. In this study, partial reconstruction of IMF acting as a filter was used for noise reduction in ECG. An improved algorithm, ensemble EMD (EEMD), was used for the first time to improve the noise-filtering performance, based on the mode-mixing reduction between near IMF scales. Both standard ECG templates derived from simulator and Arrhythmia ECG database were used as ECG signal, while Gaussian white noise was used as noise source. Mean square error (MSE) between the reconstructed ECG and original ECG was used as the filter performance indicator. FIR Wiener filter was also used to compare the filtering performance with EEMD. Experimental result showed that EEMD had better noise-filtering performance than EMD and FIR Wiener filter. The average MSE ratios of EEMD to EMD and FIR Wiener filter were 0.71 and 0.61, respectively. Thus, this study investigated an ECG noise-filtering procedure based on EEMD. Also, the optimal added noise power and trial number for EEMD was also examined.