基于自适应滤波的噪声抵消法

语音降噪就是从带噪语音信号中提取尽可能纯净的原始语音。文中介绍了一种基于自适应滤波的噪声抵消法，采用归一化最小均方误差算法，采集实际噪声环境下各种不同信噪比的带噪语音样本进行降噪处理，实验结果表明，处理后信号的信噪比得到了较大程度的提高，大大改善了听音效果，具有很高的可懂度，且语音自然度好，没有失真；并与谱减法进行了比较，自适应噪声抵消法的降噪幅度比谱减法有一定提高，在听音效果上，用自适应噪声抵消法处理后的语音在清晰度、自然度方面优于谱减法。     

一种约束稳定性最小均方噪声对消算法

研究了最小均方误差(LMS)算法、归一化的最小均方(NLMS)算法及变步长NLMS算法在自适应噪声干扰抵消器中的应用,针对目前这些算法在噪声对消器应用中的缺点,将约束稳定性最小均方(CS-LMS)算法应用到噪声处理中,并进一步结合变步长的思想提出来一种新的变步长CS-LMS算法。通过MATLAB进行仿真分析,结果证实提出的算法与其他算法相比,能很好地滤除掉噪声从而得到期望信号,明显的降低了稳态误差,并拥有好的收敛速度。     

Analysis of LMS and NLMS algorithms with delayed coefficient updateunder the presence of spherically invariant processes

Certain conditions require a delay in the coefficient update of the least mean square (LMS) and normalized least mean square (NLMS) algorithms. This paper presents an in-depth analysis of these modificated versions for the important case of spherically invariant random processes (SIRPs), which are known as an excellent model for speech signals. Some derived bounds and the predicted dynamic behavior of the algorithms are found to correspond very well to simulation results and a real time implementation on a fixed-point signal processor. A modification of the algorithm is proposed to assure the well known properties of the LMS and NLMS algorithms     

采用归一化最小均方误差准则的LM-BP算法

传统神经网络通常以最小均方误差(LMS)或最小二乘（RLS）为收敛准则,而在自适应均衡等一些应用中,使用归一化最小均方误差（NLMS）准则可以使神经网络性能更加优越。本文在NLMS准则基础上,提出了一种以Levenberg-Marquardt（LM）训练的神经网络收敛算法。通过将神经网络的误差函数归一化,然后采用LM算法作为训练算法,实现了神经网络的快速收敛。理论分析和实验仿真表明,与采用最速下降法的NLMS准则和采用LM算法的LMS准则相比,本文算法收敛速度快,归一化均方误差更小,应用于神经网络水印系统中实现了水印信息的盲提取,能更好的抵抗噪声、低通滤波和重量化等攻击,性能平均提高了4%。      

Multiprocessor Implementation of Adaptive Digital Filters

Adaptive filters, employing the transversal filter structure and the least mean square (LMS) adaptation algorithm, or its variations, have found wide application in data transmission equalization, echo cancellation, prediction, spectral estimation, on-line system identification, and antenna arrays. Recently, in response to requirements of fast start-up, or fast tracking of temporal variations, fast recursive least squares (FRLS) adaptation algorithms for both transversal and lattice filter structures have been proposed. These algorithms offer faster convergence than is possible with the LMS/ transversal adaptive filters, at the price of a five-to-tenfold increase in the number of multiplications, divisions, and additions. Here we discuss architectures and implementations of the LMS/transversal, fast-converging FRLS filter, and lattice filter algorithms which minimize the required hardware speed. We show how each of these algorithms can be partitioned so as to be realizable with an architecture based on multiple parallel processors.     

外辐射源雷达抗直达波干扰技术研究

外辐射源雷达系统中,直达波干扰严重影响了雷达对目标的探测性能.文中针对直达波干扰问题,通过对LMS、NLMS、改进的NLMS算法的收敛速度、时变系统跟踪能力、失调量等的分析,将改进的归一化LMS(NLMS)自适应滤波算法应用于直达波干扰抑制,取得了较好的处理效果,其对消得益可达40 dB;分析了滤波器阶数、参数选择对对消性能和信噪比损失的影响,给出了典型参数值.最后,真实数据的处理结果验证了该方法的有效性.     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

Architectural Synthesis of Computational Engines for Subband Adaptive Filtering

Architectural synthesis of low-power computational engines (hardware accelerators) for a subband-based adaptive filtering algorithm is presented. The full-band least mean square (LMS) adaptive filtering algorithm, widely used in various applications, is confronted by two problems, viz., slow convergence when the input correlation matrix is ill-conditioned, and increased computational complexity for applications involving use of large adaptive filter orders. Both of these problems can be overcome by the use of a subband-based normalized LMS (NLMS) adaptive filtering algorithm. Since this algorithm is not amenable to pipelining, delayed coefficient adaptation in the NLMS updation is used, which provides the required delays for pipelining. However, the convergence speed of this subband-based delayed NLMS (DNLMS) algorithm degrades with increase in the adaptation delay. We first present a pipelined subband DNLMS adaptive filtering architecture with minimal adaptation delay for any given sampling rate. The architecture is synthesized by using a number of function preserving transformations on the signal flow graph (SFG) representation of the subband DNLMS algorithm. With the use of carry-save arithmetic, the pipelined architecture can support high sampling rates limited only by the delay of two full adders and a 2-to-1 multiplexer. We then extend this synthesis methodology to synthesize a pipelined subband DNLMS architecture whose power dissipation meets a specified budget. This low-power architecture exploits the parallelism in the subband DNLMS algorithm to meet the required computational throughput. The architecture exhibits a novel tradeoff between algorithmic performance (convergence speed) and power dissipation. Finally, we incorporate configurability for filter order, sample period, power reduction factor, number of subbands and decimation/interpolation factor in the low-power architecture, thus resulting in a low-power subband computational engine for adaptive filtering.     

High Speed FPGA-Based Implementations of Delayed-LMS Filters

A variation of the least means squares (LMS) algorithm, called the delayed LMS (DLMS) algorithm is ideally suited for highly pipelined, adaptive digital filter implementations. In this paper, we present an efficient method to determine the delays in the DLMS filter. Furthermore, in order to achieve fully pipelined circuit architectures for FPGA implementation, we transfer these delays using retiming. The method has been used to derive a series of retimed delayed LMS (RDLMS) architectures, which allow a 66.7% reduction in delays and 5 times faster convergence time thereby giving superior performance in terms of throughput rate when compared to previous work. Three circuit architectures and three hardware shared versions are presented which have been implemented using the Virtex-II FPGA technology resulting in a throughput rate of 182 Msample/s.     

A New Sequential Block Partial Update Normalized Least Mean M-Estimate Algorithm and its Convergence Performance Analysis

This paper proposes a new sequential block partial update normalized least mean square (SBP-NLMS) algorithm and its nonlinear extension, the SBP-normalized least mean M-estimate (SBP–NLMM) algorithm, for adaptive filtering. These algorithms both utilize the sequential partial update strategy as in the sequential least mean square (S–LMS) algorithm to reduce the computational complexity. Particularly, the SBP–NLMM algorithm minimizes the M-estimate function for improved robustness to impulsive outliers over the SBP–NLMS algorithm. The convergence behaviors of these two algorithms under Gaussian inputs and Gaussian and contaminated Gaussian (CG) noises are analyzed and new analytical expressions describing the mean and mean square convergence behaviors are derived. The robustness of the proposed SBP–NLMM algorithm to impulsive noise and the accuracy of the performance analysis are verified by computer simulations.     

Gabor expansion for adaptive echo cancellation

A good echo cancellation algorithm should have a fast convergence rate, small steady-state residual echo, and less implementation cost. The normalized least mean square (NLMS) adaptive filtering algorithm may not achieve this goal. We show that using the Gabor expansion is a way to achieve this goal. For direct digital signal processing compatibility the Gabor expansion introduced in this paper is for discrete-time signals, although the Gabor expansion also can be used for continuous-time signals. The Gabor expansion can be defined as a discrete-time signal representation in the joint time-frequency domain of a weighted sum of the collection of functions (known as the synthesis functions). There are several design issues in the echo canceller based on the Gabor expansion: the design of the analysis functions for the far-end speech, the design of the analysis functions for the near-end signal containing the echo plus the near-end speech, the design of the adaptive filters in the subsignal path, and the design of the synthesis functions. All the adaptive filters are designed using identical NLMS adaptive filtering algorithms     

一种改进的NLMS自适应滤波器的FPGA实现

针对当前广泛应用的自适应滤波器,提出了一种改进的变步长NLMS自适应算法,在不增加计算复杂度的条件下获得了更好的收敛速度。在硬件实现过程中,利用FPGA并行处理的特点,采用自上而下的设计方法和流水线设计技术,获得了较好的滤波效果和较快的处理速度,完全满足自适应信号处理领域中实时性的要求。     

A general class of nonlinear normalized adaptive filteringalgorithms

The normalized least mean square (NLMS) algorithm is an important variant of the classical LMS algorithm for adaptive linear filtering. It possesses many advantages over the LMS algorithm, including having a faster convergence and providing for an automatic time-varying choice of the LMS stepsize parameter that affects the stability, steady-state mean square error (MSE), and convergence speed of the algorithm. An auxiliary fixed step-size that is often introduced in the NLMS algorithm has the advantage that its stability region (step-size range for algorithm stability) is independent of the signal statistics. In this paper, we generalize the NLMS algorithm by deriving a class of nonlinear normalized LMS-type (NLMS-type) algorithms that are applicable to a wide variety of nonlinear filter structures. We obtain a general nonlinear NLMS-type algorithm by choosing an optimal time-varying step-size that minimizes the next-step MSE at each iteration of the general nonlinear LMS-type algorithm. As in the linear case, we introduce a dimensionless auxiliary step-size whose stability range is independent of the signal statistics. The stability region could therefore be determined empirically for any given nonlinear filter type. We present computer simulations of these algorithms for two specific nonlinear filter structures: Volterra filters and the previously proposed class of Myriad filters. These simulations indicate that the NLMS-type algorithms, in general, converge faster than their LMS-type counterparts     

Sparse LMS/F algorithms with application to adaptive system identification

Standard least mean square/fourth (LMS/F) is a classical adaptive algorithm that combined the advantages of both least mean square (LMS) and least mean fourth (LMF). The advantage of LMS is fast convergence speed while its shortcoming is suboptimal solution in low signal‐to‐noise ratio (SNR) environment. On the contrary, the advantage of LMF algorithm is robust in low SNR while its drawback is slow convergence speed in high SNR case. Many finite impulse response systems are modeled as sparse rather than traditionally dense. To take advantage of system sparsity, different sparse LMS algorithms with l_p‐LMS and l₀‐LMS have been proposed to improve adaptive identification performance. However, sparse LMS algorithms have the same drawback as standard LMS. Different from LMS filter, standard LMS/F filter can achieve better performance. Hence, the aim of this paper is to introduce sparse penalties to the LMS/F algorithm so that it can further improve identification performance. We propose two sparse LMS/F algorithms using two sparse constraints to improve adaptive identification performance. Two experiments are performed to show the effectiveness of the proposed algorithms by computer simulation. In the first experiment, the number of nonzero coefficients is changing, and the proposed algorithms can achieve better mean square deviation performance than sparse LMS algorithms. In the second experiment, the number of nonzero coefficient is fixed, and mean square deviation performance of sparse LMS/F algorithms is still better than that of sparse LMS algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

On the convergence behavior of the LMS and the normalized LMSalgorithms

It is shown that the normalized least mean square (NLMS) algorithm is a potentially faster converging algorithm compared to the LMS algorithm where the design of the adaptive filter is based on the usually quite limited knowledge of its input signal statistics. A very simple model for the input signal vectors that greatly simplifies analysis of the convergence behavior of the LMS and NLMS algorithms is proposed. Using this model, answers can be obtained to questions for which no answers are currently available using other (perhaps more realistic) models. Examples are given to illustrate that even quantitatively, the answers obtained can be good approximations. It is emphasized that the convergence of the NLMS algorithm can be speeded up significantly by employing a time-varying step size. The optimal step-size sequence can be specified a priori for the case of a white input signal with arbitrary distribution     

基于DFP的二阶Volterra模型及其对Rössler混沌序列的预测

为克服最小二乘法或归一化最小二乘法在二阶Volterra建模时参数选择不当引起的问题,在最小二乘法基础上,应用一种基于后验误差假设的可变收敛因子技术,构建了一种基于Davidon-Fletcher-Powell算法的二阶Volterra模型（DFPSOVF）.给出参数估计中自相关逆矩阵估计的递归更新公式,并对其正定性、有界性和τ（n）的作用进行了研究.将DFPSOVF模型应用于Rössler混沌序列的单步预测,仿真结果表明其能够保证算法的稳定性和收敛性,不存在最小二乘法和归一化最小二乘法的发散问题.     

Virtex FPGA implementation of a pipelined adaptive LMS predictor for electronic support measures receivers

High-speed field-programmable gate array (FPGA) implementations of an adaptive least mean square (LMS) filter with application in an electronic support measures (ESM) digital receiver, are presented. They employ "fine-grained" pipelining, i.e., pipelining within the processor and result in an increased output latency when used in the LMS recursive system. Therefore, the major challenge is to maintain a low latency output whilst increasing the pipeline stage in the filter for higher speeds. Using the delayed LMS (DLMS) algorithm, fine-grained pipelined FPGA implementations using both the direct form (DF) and the transposed form (TF) are considered and compared. It is shown that the direct form LMS filter utilizes the FPGA resources more efficiently thereby allowing a 120 MHz sampling rate.     

Performance of Smart Antenna Under Different Fading Conditions

Optimizing the current distribution of an evenly spaced antenna array has shown to be an efficient approach for reducing side lobe levels. In this article, the Tchebyscheff distribution-based antenna array synthesis approach is combined with an adaptive signal processing algorithm for beamforming and side lobe level reduction in smart antennas in various fading situations. The performance of smart antennas in uniformly spaced linear, planar, circular, and semi-circular arrays are evaluated. The presence of Rayleigh and Rician channels is examined in the network. The least mean square (LMS) and normalised least mean square (NLMS) algorithms are applied as adaptive algorithms. In fading environments, the NLMS algorithm with Tchebyscheff distribution outperforms than the LMS algorithm with Tchebyscheff distribution, with a side lobe level decrease of 11.23 dB. The lowest side lobe achieved with the NLMS algorithm with Tchebyscheff distribution is???45.59 dB for uniform planar array.

     

Sparse least mean fourth algorithm for adaptive channel estimation in low signal‐to‐noise ratio region

Both least mean square (LMS) and least mean fourth (LMF) are popular adaptive algorithms with application to adaptive channel estimation. Because the wireless channel vector is often sparse, sparse LMS‐based approaches have been proposed with different sparse penalties, for example, zero‐attracting LMS and L_p‐norm LMS. However, these proposed methods lead to suboptimal solutions in low signal‐to‐noise ratio (SNR) region, and the suboptimal solutions are caused by LMS‐based algorithms that are sensitive to the scaling of input signal and strong noise. Comparatively, LMF can achieve better solution in low SNR region. However, LMF cannot exploit the sparse information because the algorithm depends only on its adaptive updating error but neglects the inherent sparse channel structure. In this paper, we propose several sparse LMF algorithms with different sparse penalties to achieve better solution in low SNR region and take the advantage of channel sparsity at the same time. The contribution of this paper is briefly summarized as follows: (1) construct the cost functions of the LMF algorithm with different sparse penalties; (2) derive their lower bounds; and (3) provide experiment results to show the performance advantage of the propose method in low SNR region. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive sparse system identification using normalized least mean fourth algorithm

Normalized least mean square (NLMS) was considered as one of the classical adaptive system identification algorithms. Because most of systems are often modeled as sparse, sparse NLMS algorithm was also applied to improve identification performance by taking the advantage of system sparsity. However, identification performances of NLMS type algorithms cannot achieve high‐identification performance, especially in low signal‐to‐noise ratio regime. It was well known that least mean fourth (LMF) can achieve high‐identification performance by utilizing fourth‐order identification error updating rather than second‐order. However, the main drawback of LMF is its instability and it cannot be applied to adaptive sparse system identifications. In this paper, we propose a stable sparse normalized LMF algorithm to exploit the sparse structure information to improve identification performance. Its stability is shown to be equivalent to sparse NLMS type algorithm. Simulation results show that the proposed normalized LMF algorithm can achieve better identification performance than sparse NLMS one. Copyright © 2013 John Wiley & Sons, Ltd.