Multiaccess Interference Suppression in Orthogonal Space–Time Block Coded MIMO Systems by Adaptive Projected Subgradient Method

This paper introduces adaptive filters that are effective to suppress multiple access interference (MAI) in orthogonal space-time block coded/ multiple-input multiple-output (OSTBC-MIMO) systems. We define an optimal linear filter that minimizes the mean-square error between the filter output and a scaled version of the desired output under a constraint defined by the available channel state information (CSI). The adaptive filters refine a given estimate of the optimal filter by suppressing a sequence of closed convex functions with the adaptive projected subgradient method (APSM) at each iteration. To provide robustness against imperfect CSI, the adaptive filters use not only the available CSI but also estimates of previously transmitted symbols, which usually belong to a small finite set in digital communication systems. The resulting algorithms employ computationally efficient projections onto hyperplanes or hyperslabs and do not require any matrix inversion. An efficient recursive scheme based on such an algorithm is also presented. Convergence analysis and simulation results show the excellent performance of the proposed schemes.     

Stochastic analysis of an error power ratio scheme applied to the affine combination of two LMS adaptive filters

The affine combination of two adaptive filters that simultaneously adapt on the same inputs has been actively investigated. In these structures, the filter outputs are linearly combined to yield a performance that is better than that of either filter. Various decision rules can be used to determine the time-varying parameter for combining the filter outputs. A recently proposed scheme based on the ratio of error powers of the two filters has been shown by simulation to achieve nearly optimum performance. The purpose of this paper is to present a first analysis of the statistical behavior of this error power scheme for white Gaussian inputs. Expressions are derived for the mean behavior of the combination parameter and for the adaptive weight mean-square deviation. Monte Carlo simulations show good to excellent agreement with the theoretical predictions.     

A study of two adaptive filters in tandem

The tandem of adaptive filters is common in practice. An example is the tandem of echo cancellers in telecommunication networks. This paper analyzes the convergence characteristics and tracking behavior of two adaptive filters in tandem, together with a comparison of its performance with a single adaptive filter. The adaptive algorithm considered is the LMS and the analysis is on mean-square. The coefficient errors correspond to noise, lag bias and lag variance are examined separately The theoretical results are corroborated with simulations. The study shows that the tandem of two adaptive filters decreases the convergence speed compared to a single adaptive filter. In addition, in steady state and when the step-size is small tandeming increases the coefficient variance due to noise by a factor of 2.5, the coefficient variance due to tracking lag by a factor of 1.5, but decreases the mean-square coefficient bias due to lag by a factor of 2     

LMS adaptive filters using distributed arithmetic for high throughput

We present a new hardware adaptive filter architecture for very high throughput LMS adaptive filters using distributed arithmetic (DA). DA uses bit-serial operations and look-up tables (LUTs) to implement high throughput filters that use only about one cycle per bit of resolution regardless of filter length. However, building adaptive DA filters requires recalculating the LUTs for each adaptation which can negate any performance advantages of DA filtering. By using an auxiliary LUT with special addressing, the efficiency and throughput of DA adaptive filters can be of the same order as fixed DA filters. In this paper, we discuss a new hardware adaptive filter structure for very high throughput LMS adaptive filters. We describe the development of DA adaptive filters and show that practical implementations of DA adaptive filters have very high throughput relative to multiply and accumulate architectures. We also show that DA adaptive filters have a potential area and power consumption advantage over digital signal processing microprocessor architectures.     

Exact expectation analysis of the LMS adaptive filter

In almost all analyses of the least mean square (LMS) adaptive filter, it is assumed that the filter coefficients are statistically independent of the input data currently in filter memory, an assumption that is incorrect for shift-input data. We present a method for deriving a set of linear update equations that can be used to predict the exact statistical behavior of a finite-impulse-response (FIR) LMS adaptive filter operating upon finite-time correlated input data. Using our method, we can derive exact bounds upon the LMS step size to guarantee mean and mean-square convergence. Our equation-deriving procedure is recursive and algorithmic, and we describe a program written in the MAPLE symbolic-manipulation software package that automates the derivation for arbitrarily-long adaptive filters operating on input data with stationary statistics. Using our analysis, we present a search algorithm that determines the exact step size mean-square stability bound for a given filter length and input correlation statistics. Extensive computer simulations indicate that the exact analysis is more accurate than previous analyses in predicting adaptation behavior. Our results also indicate that the exact step size bound is much more stringent than the bound predicted by the independence assumption analysis for correlated input data     

The generalized multidelay adaptive filter: structure andconvergence analysis

Frequency-domain adaptive filters have long been recognized as an attractive alternative to time-domain algorithms when dealing with systems with large impulse response and/or correlated input. New frequency-domain LMS adaptive schemes have been proposed. These algorithms essentially retain the attractive features of frequency-domain implementations, while requiring a processing delay considerably smaller than the length of the impulse response. The authors show that these algorithms can be seen as particular implementations of a more general scheme, the generalized multidelay filter (GMDF). Within this general class of algorithms, we focus on implementations based on the weighted overlap and add reconstruction algorithms; these variants, overlooked in previous contributions, provide an independent control of the overall processing delay and of the rate of update of the filter coefficients, allowing a trade-off between the computational complexity and the rate of convergence. We present a comprehensive analysis of the performance of this new scheme and to provide insight into the influence of impulse response segmentation on the behavior of the adaptive algorithm. Exact analytical expressions for the steady-state mean-square error are first derived. Necessary and sufficient conditions for the convergence of the algorithm to the optimal solution within finite variance are then obtained, and are translated into bounds for the stepsize parameter. Simulations are presented to support our analysis and to demonstrate the practical usefulness of the GMDF algorithm in applications where large impulse response has to be processed     

Efficient computation of time-varying and adaptive filters

Two techniques for efficient computation of filters that support time-varying coefficients are developed. These methods are forms of distributed arithmetic that encode the data, rather than the filter coefficients. The first approach efficiently computes scalar-vector products, with which a digital filter is easily implemented in a transpose-form structure. This method, based on digital coding, supports time-varying coefficients with no additional overhead. Alternatively, distributed-arithmetic schemes that encode the data stream in sliding blocks support efficient direct-form filter computation with time-varying coefficients. A combination of both of these techniques greatly reduces the computation required to implement LMS adaptive filters     

On training fractionally spaced equalizers using intersymbolinterpolation

The use of an intersymbol interpolation method in training fractionally spaced equalizers (FSEs) is investigated. It is shown that the optimal interpolation filter depends on the amplitude frequency response of the transmitter filter and the channel. Using a nonoptimal interpolation filter increases the stead-state mean-square error of the FSE. An interpolated complex FSE (CFSE) using a stochastic gradient, or LMS, adaptive algorithm has very little advantage over an LMS CFSE with symbol-rate updating. However, an interpolated LMS phase-splitting FSE (PS-FSE) has a convergence speed that is twice as fast as a conventional PS-FSE. Special precautions for evaluating the performance of interpolated FSEs are discussed, and a novel evaluation scheme is proposed     

Mean-square performance of a convex combination of two adaptive filters

Combination approaches provide an interesting way to improve adaptive filter performance. In this paper, we study the mean-square performance of a convex combination of two transversal filters. The individual filters are independently adapted using their own error signals, while the combination is adapted by means of a stochastic gradient algorithm in order to minimize the error of the overall structure. General expressions are derived that show that the method is universal with respect to the component filters, i.e., in steady-state, it performs at least as well as the best component filter. Furthermore, when the correlation between the a priori errors of the components is low enough, their combination is able to outperform both of them. Using energy conservation relations, we specialize the results to a combination of least mean-square filters operating both in stationary and in nonstationary scenarios. We also show how the universality of the scheme can be exploited to design filters with improved tracking performance.     

A Modular Design of LMS Adaptive Filter Based on FPGA

针对LMS自适应滤波器在FPGA上实现结构灵活性的问题,提出了一种模块化设计方法。根据LMS算法结构特点,结合FPGA硬件语言特点进行模块化设计,分别阐述了各模块设计结构,对模块进行并行调用与综合。对模块化设计的自适应滤波器与纯串行及纯并行设计的自适应滤波器所占用的资源以及处理速率进行比较,8个并行模块结构比全串行结构处理速率快了近7.6倍,硬件资源占用比全并行结构减少了近50%;结果说明模块化LMS自适应滤波器设计具有更加灵活的结构特点。     

Performance comparison of two implementations of the leaky LMSadaptive filter

The leaky LMS adaptive filter can be implemented either directly or by adding random white noise to the input signal of the LMS adaptive filter. In this correspondence, we analyze and compare the mean-square performances of these two adaptive filter implementations for system identification tasks with zero mean i.i.d. input signals. Our results indicate that the performance of the direct implementation is superior to that of the random noise implementation in all respects. However, for small leakage factors, these performance differences are negligible     

Efficient subspace-based algorithm for adaptive bearing estimation and tracking

In some practical applications of array processing, the directions of the incident signals should be estimated adaptively, and/or the time-varying directions should be tracked promptly. In this paper, an adaptive bearing estimation and tracking (ABEST) algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow-band signals impinging on a uniform linear array (ULA) based on the subspace-based method without eigendecomposition (SUMWE), where a linear operator is obtained from the array data to form a basis for the space by exploiting the array geometry and its shift invariance property. Specifically, the space is estimated using the least-mean-square (LMS) or normalized LMS (NLMS) algorithm, and the directions are updated using the approximate Newton method. The transient analyses of the LMS and NLMS algorithms are studied, where the "weight" (i.e., the linear operator) is in the form of a matrix and there is a correlation between the "additive noise" and "input data" that involve the instantaneous correlations of the received array data in the updating equation, and the step-size stability conditions are derived explicitly. In addition, the analytical expressions for the mean-square error (MSE) and mean-square deviation (MSD) learning curves of the LMS algorithm are clarified. The effectiveness of the ABEST algorithm is verified, and the theoretical analyses are corroborated through numerical examples. Simulation results show that the ABEST algorithm is computationally simple and has good adaptation and tracking abilities.     

Analysis of Convergence of a Frequency-Domain LMS Adaptive Filter Implemented as a Multi-Stage Adaptive Filter

We present an analysis of the convergence of the frequency-domain LMS adaptive filter when the DFT is computed using the LMS steepest descent algorithm. In this case, the frequency-domain adaptive filter is implemented with a cascade of two sections, each updated using the LMS algorithm. The structure requires less computations compared to using the FFT and is modular suitable for VLSI implementations. Since the structure contains two adaptive algorithms updating in parallel, an analysis of the overall system convergence needs to consider the effect of the two adaptive algorithms on each other, in addition to their individual convergence. Analysis was based on the expected mean-square coefficient error for each of the two LMS adaptive algorithms, with some simplifying approximations for the second algorithm, to describe the convergence behavior of the overall system. Simulations were used to verify the results.     

Generalized sliding FFT and its application to implementation ofblock LMS adaptive filters

This paper has two contributions. First, the concept of the generalized sliding fast Fourier transform (GSFFT) as an efficient implementation of the hopping FFT is introduced. Application of the GSFFT is broad and not limited to what has been considered in this paper. The frequency domain block LMS (FBLMS) adaptive filters are then revised, and their implementations for block lengths less than the length of the adaptive filter are studied. The GSFFT and the available pruned FFTs are used to give an efficient implementation of these filters. In the particular case of the block length equal to one, where the FBLMS algorithm reduces to the frequency domain LMS (FLMS) algorithm, it is shown that the latter can be implemented with the order of M complexity, where M is the length of the adaptive filter     

Fast coupled adaptation for sparse impulse responses using a partial haar transform

This work presents a novel scheme for identifying the impulse response of a sparse channel. The scheme consists of two adaptive filters operating sequentially. The first adaptive filter adapts using a partial Haar transform of the input and yields an estimate of the location of the peak of the sparse impulse response. The second adaptive filter is then centered about this estimate. Both filters are short in comparison to the delay uncertainty of the unknown channel. The principle advantage of this scheme is that two short adaptive filters can be used instead of one long adaptive filter, resulting in faster overall convergence and reduced computational complexity and storage. The scheme is analyzed in detail for a least mean squares (LMS) LMS-LMS type of structure, although it can be implemented using any combination of adaptive algorithms. Monte Carlo simulations are shown to be in good agreement with the theoretical model for the behavior of the peak estimating filter as well as for the mean square error (MSE) behavior of the second filter.     

图像边缘提取的自适应Volterra滤波器设计

Ｖｏｌｔｅｒｒａ滤波是研究信号高阶统计冗余性的一种有效途径。我们提出了一种用于提取图像边缘的自适应二次Ｖｏｌｔｅｒｒａ滤波器设计方法。这种滤波器是推广型Ｔｅａｇｅｒ基滤子的线性组合，其系数用基于极小化最小均方能量函数的共轭梯度法研究；它兼有局域平均和高通特性，因而可均衡去除噪声和增强图像边缘。文章还给出了计算实例。     

Fast LMS/Newton algorithms based on autoregressive modeling andtheir application to acoustic echo cancellation

We propose two new implementations of the LMS/Newton algorithm for efficient realization of long adaptive filters. We assume that the input sequence to the adaptive filter can be modeled as an autoregressive (AR) process whose order may be kept much lower than the adaptive filter length. The two algorithms differ in their structural complexity. The first algorithm, which will be an exact implementation of the LMS/Newton algorithm if the AR modeling assumption is accurate, is structurally complicated and fits best into a digital signal processing (DSP)-based implementation. On the other hand, the second algorithm is structurally simple and is tailored more toward very large-scale integrated (VLSI) custom chip design. Analyses of the proposed algorithms are given. It is found that for long filters, both algorithms perform about the same. However for short filters, a noticeable difference between the two may be observed. Simulation results that confirm our theoretical findings are given. Moreover, experiments with speech signals for modeling the acoustics of an office room show the superior convergence of the proposed algorithms when compared with the normalized LMS algorithm     

改进子带自适应滤波算法及其在回波抵消中的应用

本文提出了两种基于多带结构的仿射投影符号子带自适应滤波器(Affine Projection Sign Subband Adaptive Filter, AP SSAF)的改进方法。针对稀疏系统的系统识别,设计了两种子带自适应滤波器。首先给出了AP SSAF的变正则化参数更新方程,文中采用随机梯度下降法来更新正则化参数,来使系统的均方偏差最小化,该方法能同时兼顾快速收敛及低稳态失调。其次将权重分布矩阵引入AP SSAF得到系数比例AP SSAF,该方法能够利用系统的稀疏性提高AP SSAF的收敛性能。仿真中将本文所提算法用于一般系统识别以及回波抵消,实验结果验证了本文的算法对脉冲噪声具有稳健性,具有较好的跟踪性能,并具有较快的收敛速度及低稳态失调。      

Subband adaptive filtering with real-valued subband signals foracoustic echo cancellation

Adaptive filtering in subbands was originally proposed to overcome the limitations of conventional least-mean-square (LMS) algorithms. In general, subband adaptive filters offer computational savings, as well as faster convergence over the conventional LMS algorithm. However, improvements to current subband adaptive filters could be further enhanced by a more elegant choice of their design/structure. Classical subband adaptive filters employ DFT-based analysis and synthesis filter banks which results in subband signals that are complex-valued. The authors modify the structure of subband adaptive filters by using single-sideband (SSB) modulated analysis and synthesis filter banks, which result in subband signals that are real-valued. This simplifies the realisation of subband adaptive filters