An Affine Projection Sign Algorithm Robust Against Impulsive Interferences

A new affine projection sign algorithm (APSA) is proposed, which is robust against non-Gaussian impulsive interferences and has fast convergence. The conventional affine projection algorithm (APA) converges fast at a high cost in terms of computational complexity and it also suffers performance degradation in the presence of impulsive interferences. The family of sign algorithms (SAs) stands out due to its low complexity and robustness against impulsive noise. The proposed APSA combines the benefits of the APA and SA by updating its weight vector according to the $L_{1}$-norm optimization criterion while using multiple projections. The features of the APA and the $L_{1}$-norm minimization guarantee the APSA an excellent candidate for combatting impulsive interference and speeding up the convergence rate for colored inputs at a low computational complexity. Simulations in a system identification context show that the proposed APSA outperforms the normalized least-mean-square (NLMS) algorithm, APA, and normalized sign algorithm (NSA) in terms of convergence rate and steady-state error. The robustness of the APSA against impulsive interference is also demonstrated.      

Real-Time Implementation of Parallel Architecture Based Noise Minimization from Speech Signals on FPGA

In recent years, the real time hardware implementation of LMS based adaptive noise cancellation on FPGA is becoming popular. There are several works reported in this area in the literature. However, NLMS based implementation of adaptive noise cancellation on FPGA using Xilinx System Generator (XSG) is not reported. This paper explores the various forms of parallel architecture based on NLMS algorithm and its hardware implementation on FPGA using XSG for noise minimization from speech signals. In total, the direct form, binary tree direct form and transposed form of parallel architecture of normalized least mean square (NLMS), delayed normalized least mean square and retimed delayed normalized least mean square algorithms are implemented on FPGA using hardware co-simulation model. The performance parameters (SNR and MSE) of these algorithms are analyzed for the adaptive noise cancellation system and the comparison is made with parallel architectures of least mean square (LMS), delayed least mean square, and retimed delayed least mean square algorithms respectively. The hardware utilization of all the said algorithms are also analyzed and compared. The result shows that NLMS based implementations outperform than that of LMS for all forms of parallel architecture for the given parameters with negligence increase in device utility. The binary tree direct form of retimed delayed NLMS achieves the maximum SNR improvement (39.83 dB) in comparison to other NLMS variants at the cost of optimum resource utilization.     

一种改进的NLMS算法在声回波抵消中的应用

收敛速度和残余均方误差是衡量最小均方算法性能的重要指标。在声回波抵消算法中,为了寻求收敛速度快和计算量小的自适应算法,在归一化最小均方误差算法基础上,把当前时刻以前的误差引入归一化收敛因子中得到一种新算法,可以减小信号样本波动对权重带来的影响。该算法比传统的归一化最小均方算法收敛性能更好,稳态失调也比其小。计算机仿真结果表明,新算法在自适应回波抵消中的综合性能要优于传统的归一化最小均方误差算法。     

$$L_{0}$$-norm constraint normalized logarithmic subband adaptive filter algorithm

With the purpose of identifying sparse unknown system better, a novel sparsity-aware normalized logarithmic subband adaptive filter algorithm is developed by introducing the \(L_{0}\)-norm constraint of the estimated coefficient vector into the normalized logarithmic cost function. The gradient descent technique is utilized in the derivation of the weight vector updating formula. The proposed algorithm not only acquires a lower steady-state error, but also possesses good robustness against impulsive noise for sparse system. Besides, the reason why its performance is improved is interpreted by rigorous mathematical analysis. Simulation results in the context of sparse system identification have revealed the advantage of the proposed algorithms over other existing algorithms in impulsive noise environments.     

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.     

A Novel Normalized Sign Algorithm for System Identification Under Impulsive Noise Interference

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies.     

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.     

Performance of NLMS-based Parallel Interference Cancellation (PIC) For Up-Link CDMA Systems

Parallel interference cancellation (PIC) is a promising detection technique to suppress multiple access interference (MAI) for up-link direct-sequence CDMA (DS-CDMA) systems. Adaptive PICs are attractive due to its low implementation complexities and good performance. In this paper, we propose a general framework for analyzing the bit error rate (BER) and convergence performance of the normalized LMS (NLMS) based PIC. To further improve the convergence speed of the PIC system, a novel switch-mode noise-constrained NLMS (SNC-NLMS) algorithm for the adaptive multistage PIC (AMPIC) is also proposed. Simulation results show that the analytical results are reasonably accurate and the SNC-NLMS AMPIC outperforms the NLMS-based one, if the algorithm parameters are properly chosen.     

水声通信系统中基于迭代自适应的脉冲噪声抑制方法

针对水声通信系统中脉冲噪声抑制问题,提出了一种迭代自适应的脉冲噪声抑制方法。基于 OFDM子载波之间的正交性,该方法首先利用空子载波矩阵从接收信号中提取出背景噪声和脉冲噪声。然后,利用空子载波矩阵构造导频矩阵,得到脉冲噪声的干扰协方差矩阵,并在加权最小二乘准则下通过对代价函数的求解得到脉冲噪声的闭式解。最后,在接收信号中减去脉冲噪声的估计值,完成对脉冲噪声的抑制。仿真结果表明,本文方法有效降低了水声通信系统的误码率,且在高信干噪比下性能提升更加明显。     

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。     

基于NLMS的CDMA盲自适应多用户检测算法研究

多用户检测是抑制DS-CDMA系统多址干扰最有效的技术之一。由于所需的先验知识仪有期望用户的地址码,盲多用户检测技术的研究尤受重视。最小输出能量(MOE)准则被广泛用于盲线性多用户检测。目前已提出的该类检测器多采用LMS或RLS算法。本文则研究基于NLMS算法的盲自适应检测技术,并进一步提出盲自适应变步长NLMS检测器和参数可变的盲自适应变步长NLMS检测器。它们具备很好的收敛速度和跟踪能力,以及较高的输出信干比,同时计算复杂度仅为O(3N)或O(4N),非常适合硬件实现。     

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.     

抗冲激干扰的稀疏惩罚约束遗漏最小均方算法

当被识别系统是稀疏系统时,传统的遗漏最小均方( LLMS )自适应算法收敛性能较差,特别在非高斯噪声环境中,该算法性能进一步恶化甚至算法不平稳收敛。为了解决因信道的稀疏性使算法收敛变慢的问题,对LLMS算法的代价函数分别利用加权詛1-norm和加权零吸引两种稀疏惩罚项进行改进;为了优化算法的抗冲激干扰的性能,利用符号函数对已改进的算法迭代式作进一步改进。同时,将提出的两个算法运用于非高斯噪声环境下的稀疏系统识别,仿真结果显示提出的算法性能优于现存的同类稀疏算法。     

基于自适应系统辨识的收发隔离技术研究

收发隔离是机载干扰机不可避免的难题。如果收发隔离问题解决不好,轻则削弱干扰机效率,重则造成自发自收,形成自激励。固定步长的归一化最小均方误差(NLMS)算法在解决基于自适应系统辨识的收发隔离的问题时,由于精度不够,隔离效果很不理想。针对此问题提出一种基于先验误差的变步长NLMS算法,该算法依据相邻时刻先验误差的相关系数改变步长因子,改变后的步长因子能够在算法收敛过程中削弱噪声的影响,提高算法精度。理论分析和仿真结果证明:基于文中的变步长NLMS算法的收发隔离方案与基于其他最小均方误差算法的隔离方案相比,隔离性能有较大的改善。     

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     

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     

Robust M-estimate adaptive filtering

An M-estimate adaptive filter for robust adaptive filtering in impulse noise is proposed. Instead of using the conventional least-square cost function, a new cost function based on an M-estimator is used to suppress the effect of impulse noise on the filter weights. The resulting optimal weight vector is governed by an M-estimate normal equation. A recursive least M-estimate (RLM) adaptive algorithm and a robust threshold estimation method are derived for solving this equation. The mean convergence performance of the proposed algorithm is also analysed using the modified Huber (1981) function (a simple but good approximation to the Hampel's three-parts-redescending M-estimate function) and the contaminated Gaussian noise model. Simulation results show that the proposed RLM algorithm has better performance than other recursive least squares (RLS) like algorithms under either a contaminated Gaussian or alpha-stable noise environment. The initial convergence, steady-state error, robustness to system change and computational complexity are also found to be comparable to the conventional RLS algorithm under Gaussian noise alone     

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     

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%。      

一种新的GPS接收机宽带干扰抑制方法

该文针对GPS扩频接收机空时自适应处理结构,提出了一种新的极大抑制干扰的波束形成算法。通过估计空时二维功率谱得到各干扰信号的导向矢量矩阵,并求解出该矩阵的一组最接近期望信号导向矢量的正交基,作为空时二维最优权值。仿真结果表明,该算法增强了空时自适应结构方向图的零陷深度,比传统宽带多线性约束LCMV算法更有效地进行干扰抑制,明显提高了信号干扰噪声比。