Energy constrained frequency-domain normalized LMS algorithm for blind channel identification

This paper deals with the blind adaptive identification of single-input multi-output (SIMO) finite impulse response acoustic channels from noise-corrupted observations. The normalized multichannel frequency-domain least-mean-squares (NMCFLMS) algorithm [1] is known to be a very effective and efficient technique for identification of such channels when noise effects can be ignored. It, however, misconverges in presence of noise [2]. In this paper, we present an analysis of noise effects on the NMCFLMS algorithm and propose a novel technique for ameliorating such misconvergence characteristics of the NMCFLMS algorithm for blind channel identification (BCI) with noise by attaching a spectral constraint in the adaptation rule. Experimental results demonstrate that the robustness of the NMCFLMS algorithm for BCI can be significantly improved using such a constraint.     

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.     

New Variable Step-Sizes Minimizing Mean-Square Deviation for the LMS-Type Algorithms

The least-mean-square-type (LMS-type) algorithms are known as simple and effective adaptation algorithms. However, the LMS-type algorithms have a trade-off between the convergence rate and steady-state performance. In this paper, we investigate a new variable step-size approach to achieve fast convergence rate and low steady-state misadjustment. By approximating the optimal step-size that minimizes the mean-square deviation, we derive variable step-sizes for both the time-domain normalized LMS (NLMS) algorithm and the transform-domain LMS (TDLMS) algorithm. The proposed variable step-sizes are simple quotient forms of the filtered versions of the quadratic error and very effective for the NLMS and TDLMS algorithms. The computer simulations are demonstrated in the framework of adaptive system modeling. Superior performance is obtained compared to the existing popular variable step-size approaches of the NLMS and TDLMS algorithms.     

Time-frequency 2-D LMS based long-range channel prediction for wireless OFDM systems

Adaptive modulation can optimize the spectrum efficiency and system performance with the channel state information achieved by the long-range channel prediction.To avoid re-estimating channel correlation function as the channel statioharity varies and to track the channel adaptively, LMS (Least-Mean-Square) based long-range channel prediction is discussed in the existing literature, but it needs long observation interval to reach the convergence.Given that all OFDM (Orthogonal Frequency Division Multiplexing) subcarriers have the identical time-domain correlation and sta- tionarity during the same time interval,this paper proposed a 2-D LMS based predictor which updates the filter weights in both time and frequency domain.The proposed scheme can effectively decrease the observation intervals and significantly speed up the convergence than the conventional LMS and Parallel LMS (PLMS).Complexity analysis and simulation results prove that the proposed scheme can improve the BER (Bit Error Rate) performance and spectrum efficiency with negligible complexity increase.     

基于小波变换变步长LMS自适应信道均衡的新方法

结合变换域最小均方(LMS)和变步长LMS算法的优势,提出了一种基于小波变换的变步长LMS自适应均衡方法。该方法中步长调整函数采用了改进的Sigmoid函数,该函数具有简单且误差信号接近零时变化缓慢的特点。并且,在训练模式、判决引导模式以及混合模式下,将提出方法和传统均衡方法进行了仿真比较。结果表明,所提出的方法比传统的线性LMS算法、变步长LMS以及小波变换LMS收敛更快、性能更优。     

Coherent LMS algorithms

Pilot symbol-assisted adaptive algorithms provide coherent detection for communication systems when the filtering coefficients, such as beamforming weights or equalizer coefficients, are converged. This property can be exploited to speed up the convergence of adaptive algorithms used. In this letter, two new adaptive algorithms, coherent least mean square (C-LMS) and coherent normalized LMS (CN-LMS), are proposed by constraining the desired signal component of the filtering output to be always coherent in phase with the reference signal at each iteration. For same adaption step size, these new algorithms provide faster convergence, while yield same steady-state excess mean-square error as compared with their standard LMS counterparts     

Noncoherent adaptive channel identification algorithms fornoncoherent sequence estimation

In this letter, two novel noncoherent adaptive algorithms for channel identification are introduced. The proposed noncoherent least-mean-square (LMS) and noncoherent recursive least squares (RLS) algorithms can be combined easily with noncoherent sequence estimation (NSE) for M-ary differential phase-shift keying signals transmitted over intersymbol interference (ISI) channels. It is shown that the resulting adaptive noncoherent receivers are very robust against carrier phase variations. For zero frequency offset, the convergence speed and the steady-state error of the noncoherent adaptive algorithms are similar to those of conventional LMS and RLS algorithms. However, the conventional algorithms diverge even for relatively small frequency offsets, whereas the proposed noncoherent algorithms converge for relatively large frequency offsets. Simulations confirm the good performance of NSE combined with noncoherent adaptive channel estimation in time-variant (fading) ISI channels     

特征参数自适应盲估计方法

 基于无线移动通信OFDM系统信道估计,提出了三种时域自适应特征参数估计最小均方盲方法——时变步长最小均方法(tvcpblms)、时变步长软判决最小均方法(tvcpsdwlms)、时变步长理想判决最小均方法(tvcpidwlms).这些方法通过对常规LMS算法步长进行自适应的科学设计以便跟踪特征参数变化,从而解决了常规LMS盲方法收敛速度慢、估计性能不高等缺点.仿真证明:对于不同的时延扩展、时间以及多普勒频移,这些方法均表现出了比常规方法更优的估计性能.同时,这些方法不仅可以估计无线移动通信系统信道特征参数,而且还可用于雷达、航天等多种领域估计其他特征参数.     

结构性稀疏阵列多信道联合估计

多信道估计时,如果利用信道的稀疏性和多信道的相关性,可以提高信道估计性能。本文利用阵列信道的结构性稀疏特性,提出了一种多路分组稀疏LMS算法(Group Sparse LMS,GS-LMS)。该算法将多路信道作为一个整体同时进行自适应信道估计,通过引入Ι_2,1范数,将结构性稀疏先验引入到稀疏LMS算法的代价函数中,导出新的滤波器权系数更新公式。仿真结果表明了在不同信道条件下,本文算法的稳态误差性能明显优于若干现有的稀疏LMS算法。      

Improved Soft Iterative Channel Estimation for Turbo Equalization of Time Varying Frequency Selective Channels

In this paper, we present computationally efficient iterative channel estimation algorithms for Turbo equalizer-based communication receiver. Least Mean Square (LMS) and Recursive least Square (RLS) algorithms have been widely used for updating of various filters used in communication systems. However, LMS algorithm, though very simple, suffers from a relatively slow and data dependent convergence behaviour; while RLS algorithm, with its fast convergence rate, finds little application in practical systems due to its computational complexity. Variants of LMS algorithm, Variable Step Size Normalized LMS (VSSNLMS) and Multiple Variable Step Size Normalized LMS algorithms, are employed through simulation for updating of channel estimates for turbo equalization in this paper. Results based on the combination of turbo equalizer with convolutional code as well as with turbo codes alongside with iterative channel estimation algorithms are presented. The simulation results for different normalized fade rates show how the proposed channel estimation based-algorithms outperformed the LMS algorithm and performed closely to the well known Recursive least square (RLS)-based channel estimation algorithm.     

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     

基于通道均衡的频域除法研究

在频域通道均衡中,一个关键技术是求解均衡滤波器的响应.文中利用循环卷积和离散傅里叶变换乘积之间的关系,研究了通道均衡中频域除法的两类求解法:一类是时域算法,包括循环矩阵伪逆求解法和循环卷积求循环反卷积算法;另一类是基于最小范数的矩阵形式的频域算法.借助于仿真数据,根据求得的均衡滤波器和待校滤波器的卷积对参考滤波器的逼近误差,验证了上述算法的有效性.实验结果表明,基于最小范数的矩阵形式的频域算法在逼近性能、实时性方面均优于上面两种时域算法.     

A computationally efficient frequency-domain LMS algorithm withconstraints on the adaptive filter

The frequency domain implementation of the LMS algorithm is attractive due to both the reduced computational complexity and the potential of faster convergence compared with the time domain implementation. Another advantage is the potential of using frequency-domain constraints on the adaptive filter, such as limiting its magnitude response or limiting the power of its output signal. This paper presents a computationally efficient algorithm that allows the incorporation of various frequency domain constraints into the LMS algorithm. A penalty function formulation is used with a steepest descent search to adapt the filter so that it converges to the new constrained minimum. The formulation of the algorithm is derived first, after which the use of some practical constraints with this algorithm and a simulation example for adaptive blind equalization are described     

A Modular Analog NLMS Structure for Adaptive Filtering

This paper proposes a modular Analog Adaptive filter (AAF) algorithm, in which the coefficient adaptation is carried out by using a time varying step size analog normalized LMS (NLMS) algorithm, which is implemented as an external analog structure. The proposed time varying step size is estimated by using the first element of the crosscorrelation vector between the output error and reference signal, and the first element of the crosscorrelation vector between the output error and the adaptive filter output signal, respectively. Proposed algorithm reduces distortion when additive noise power increases or DC offsets are present, without significatively decreasing the convergence rate nor increasing the complexity of the conventional NLMS algorithms. Simulation results show that proposed algorithm improves the performance of AAF when DC offsets are present. The proposed VLSI structure for the time varying step size normalized NLMS algorithm has, potentially, a very small size and faster convergence rates than its digital counterparts. It is suitable for general purpose applications or oriented filtering solution such as echo cancellation and equalization in cellular telephony in which high performance, low power consumption, fast convergence rates and small size adaptive digital filters (ADF) are required. The convergence performance of analog adaptive filters using integrators like first order low pass filter is analyzed.     

Adaptive filtering using the fast Walsh-Hadamard transformation

A fast implementation of the least-mean-square error (LMS) adaptive transversal filter is proposed. The fast Walsh-Hadamard transform technique is adopted in this implementation. This filter is shown to promise a significant reduction in computation over both the conventional time-domain and the frequency-domain LMS adaptive filters     

Performance of a class of adaptive data-driven echo cancellers

A study is made of the performance of a class of adaptive data-driven echo cancellers (DDECs). The authors first investigate the interrelationship in a unified framework among the system equations of various data-driven echo cancellers. As a result, they obtain a new DDEC algorithm that consists of only one real-valued adaptive structure. The authors analyze and compare the convergence behavior of DDECs. They analyze their complexities when the least-mean-square (LMS) algorithm and the frequency-domain block LMS algorithm are used for adjusting the canceller weights. The results show that the echo canceller structure realized in the frequency domain has advantages in convergence rate and in implementation complexity as compared to existing DDEC structures     

Set-membership binormalized data-reusing LMS algorithms

This paper presents and analyzes novel data selective normalized adaptive filtering algorithms with two data reuses. The algorithms [the set-membership binormalized LMS (SM-BN-DRLMS) algorithms] are derived using the concept of set-membership filtering (SMF). These algorithms can be regarded as generalizations of the previously proposed set-membership NLMS (SM-NLMS) algorithm. They include two constraint sets in order to construct a space of feasible solutions for the coefficient updates. The algorithms include data-dependent step sizes that provide fast convergence and low-excess mean-squared error (MSE). Convergence analyzes in the mean squared sense are presented, and closed-form expressions are given for both white and colored input signals. Simulation results show good performance of the algorithms in terms of convergence speed, final misadjustment, and reduced computational complexity.     

一种新的变步长LMS自适应滤波算法

在对传统LMS算法、变步长SVSLMS算法及归一化LMS算法分析的基础上,提出了一种改进的归一化变步长LMS算法即N-SVSLMS（Normalized-SVSLMS）算法。该算法结合了参考文献中两种算法的思想,得到了改进的归一化LMS自适应算法。该算法在信道环境多变的情况下,收敛速度和稳定性能有了进一步的提高。理论分析及计算机仿真结果表明,N-SVSLMS算法明显优于传统LMS算法、变步长SVSLMS算法及归一化的LMS算法。     

Enhanced-Convergence Normalized LMS Algorithm

Least mean square (LMS) algorithms have found great utility in many adaptive filtering applications. This article shows how the traditional constraints placed on the update gain of normalized LMS algorithms are overly restrictive. We present relaxed update gain constraints that significantly improve normalized LMS algorithm convergence speed.     

Transform domain adaptive linear phase filter

Describes a new adaptive linear-phase filter whose weights are updated by the normalized least-mean-square (LMS) algorithm in the transform domain. This algorithm provides a faster convergence rate compared with the time domain linear phase LMS algorithm. Various real-valued orthogonal transforms are investigated such as the discrete cosine transform (DCT), discrete Hartley transform (DHT), and power of two (PO2) transform, etc. By using the symmetry property of the transform matrix, an efficient implementation structure is proposed. A system identification example is presented to demonstrate its performance