一种变步长自适应算法在GPS空时抗干扰中的应用

GPS空时二维联合抗干扰处理算法能将强干扰以及多径干扰的强度抑制到接近噪底,并且不会对原信号产生严重的损失或者扭曲。研究发现它的干扰抑制性能优于纯空域滤波。但是此算法比纯空域算法的复杂度高,因为需要处理的采样数据协方差矩阵的维数很大,很难做到实时处理。为了解决这一问题,目前工程中普遍采用的是最小均方误差算法(LMS)。通过分析功率倒置(PI)算法,给出了一种变步长的最小均方误差算法(NLMS)。此算法的干扰抑制性能优于最小均方误差算法,能达到多级维纳滤波算法(MSWF)的抑制效果,满足工程需要,并且运算量低,运算时间短,具有更好的可行性和实用性。并将此算法与LMS和MSWF算法进行了仿真对比,验证了其有效性。     

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.

     

Comments on `Convergence and performance analysis of the normalizedLMS algorithm with uncorrelated Gaussian data'

Noting that a fine analysis is presented for the convergence and misadjustment of the normalized least-mean-square (NLMS) algorithm in the paper by Tarrab and Feuer (see ibid., vol.3, no.4, p.468091, July 1988), the commenter claims that the results and comparisons with the LMS algorithm are not in a form that readily enables the reader to draw practical conclusions. He points out that plotting mean-square error on a linear, instead of logarithmic (dB), scale hides the important detail of the error as it converges to its minimum value, which is exactly the region where the practical engineer requires detailed knowledge to assess performance. Moreover, in the comparison of the NLMS and LMS algorithm convergence rate and misadjustment, the practitioner wants to know how fast the algorithm will converge when the misadjustment is constrained to a specified value     

Normalized data nonlinearities for LMS adaptation

Properly designed nonlinearly-modified LMS algorithms, in which various quantities in the stochastic gradient estimate are operated upon by memoryless nonlinearities, have been shown to perform better than the LMS algorithm in system identification-type problems. The authors investigate one such algorithm given by W_k+l=W_k+μ(d_k-W_k^t X_k)X_kf(X_k) in which the function f(X_k) is a scalar function of the sum of the squares of the N elements of the input data vector X_k. This form of algorithm generalizes the so-called normalized LMS (NLMS) algorithm. They evaluate the expected behavior of this nonlinear algorithm for both independent input vectors and correlated Gaussian input vectors assuming the system identification model. By comparing the nonlinear algorithm's behavior with that of the LMS algorithm, they then provide a method of optimizing the form of the nonlinearity for the given input statistics. In the independent input case, they show that the optimum nonlinearity is a single-parameter version of the NLMS algorithm with an additional constant in the denominator and show that this algorithm achieves a lower excess mean-square error (MSE) than the LMS algorithm with an equivalent convergence rate. Additionally, they examine the optimum step size sequence for the optimum nonlinear algorithm and show that the resulting algorithm performs better and is less complex to implement than the optimum step size algorithm derived for another form of the NLMS algorithm. Simulations verify the theory and the predicted performance improvements of the optimum normalized data nonlinearity algorithm     

Adaptive antenna systems

A system consisting of an antenna array and an adaptive processor can perform filtering in both the space and the frequency domains, thus reducing the sensitivity of the signal-receiving system to interfering directional noise sources. Variable weights of a signal processor can be automatically adjusted by a simple adaptive technique based on the least-mean-squares (LMS) algorithm. During the adaptive process an injected pilot signal simulates a received signal from a desired "look" direction. This allows the array to be "trained" so that its directivity pattern has a main lobe in the previously specified look direction. At the same time, the array processing system can reject any incident noises, whose directions of propagation are different from the desired look direction, by forming appropriate nulls in the antenna directivity pattern. The array adapts itself to form a main lobe, with its direction and bandwidth determined by the pilot signal, and to reject signals or noises occurring outside the main lobe as well as possible in the minimum mean-square error sense. Several examples illustrate the convergence of the LMS adaptation procedure toward the corresponding Wiener optimum solutions. Rates of adaptation and misadjustments of the solutions are predicted theoretically and checked experimentally. Substantial reductions in noise reception are demonstrated in computer-simulated experiments. The techniques described are applicable to signal-receiving arrays for use over a wide range of frequencies.     

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.     

The behavior of LMS and NLMS algorithms in the presence ofspherically invariant processes

The behavior of least-mean-square (LMS) and normalized least-mean-square (NLMS) algorithms with spherically invariant random processes (SIRPs) as excitations is shown. Many random processes fall into this category, and SIRPs closely resemble speech signals. The most pertinent properties of these random processes are summarized. The LMS algorithm is introduced, and the first- and second-order moments of the weight-error vector between the Wiener solution and the estimated solution are shown. The behavior of the NLMS algorithm is obtained, and the first- and second-order moments of the weight-error vector are calculated. The results are verified by comparison with known results when a white noise process and a colored Gaussian process are used as input sequences. Some simulation results for a K₀-process are then shown     

Algorithm for multichannel LMS adaptive filtering

A modification of the LMS algorithm is presented in which the coefficients of an array of FIR filters, whose outputs are linearly coupled to an array of sensors, are adapted to minimise the mean-square sum of the error signals from these sensors. The application of the algorithm to the control of distributed parameter systems is discussed.     

Second-order H∞ optimal LMS and NLMS algorithmsbased on a second-order Markov model

It is shown that two algorithms obtained by simplifying a Kalman filter considered for a second-order Markov model are H^∞ suboptimal. Similar to least mean squares (LMS) and normalised LMS (NLMS) algorithms, these second order algorithms can be thought of as approximate solutions to stochastic or deterministic least squares minimisation. It is proved that second-order LMS and NLMS are exact solutions causing the maximum energy gain from the disturbances to the predicted and filtered errors to be less than one, respectively. These algorithms are implemented in two steps. Operation of the first step is like conventional LMS/NLMS algorithms and the second step consists of the estimation of the weight increment vector and prediction of weights for the next iteration. This step applies simple smoothing on the increment of the estimated weights to estimate the speed of the weights. Also they are cost-effective, robust and attractive for improving the tracking performance of smoothly time-varying models     

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。     

基于LMS算法的自适应滤波及在回声消除中的应用

介绍NLMS和NVLMS两种算法控制步长的思想。在此基础上，提出了新的变步长算法，同时使用误差积累和误差控制步长变化，并构建了基于自适应滤波算法的回声消除系统，将三种算法分别在此系统中应用，仿真验证了提出的算法具有更快的收敛速度和更小的稳态误差。并且在发生系统跳变时也能快速收敛。     

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     

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     

Convergence and performance analysis of the normalized LMSalgorithm with uncorrelated Gaussian data

It is demonstrated that the normalized least mean square (NLMS) algorithm can be viewed as a modification of the widely used LMS algorithm. The NLMS is shown to have an important advantage over the LMS, which is that its convergence is independent of environmental changes. In addition, the authors present a comprehensive study of the first and second-order behavior in the NLMS algorithm. They show that the NLMS algorithm exhibits significant improvement over the LMS algorithm in convergence rate, while its steady-state performance is considerably worse     

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     

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     

基于MUSIC和LMS算法的智能天线设计

基于来渡方向估计和自适应波束成形的智能天线系统,用多重信号分类(MUSIC)算法实现来波方向估计,辨识天线阵列上接收信号的各个方向,使用最小均方误差(LUS)的自适应算法控制天线的主辩方向,实现对期望信号的跟踪,同时实现对干扰信号的零陷处理.文中使用Matlab编程进行计算机仿真,通过仿真结果,MUSIC算法可以识别天线接收端的信号的入射方向,LMS算法可以实现对干扰信号的抑制.     

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.     

依据迭代系数状态因子分段的变步长NLMS算法

针对固定步长的归一化LMS算法（NLMS）存在不能同时兼顾收敛速度与稳态误差的问题,本文提出一种依据迭代系数状态因子进行分段的变步长NLMS算法。该变步长NLMS算法采用迭代系数状态因子作为表征迭代系数与实际系数的逼近状态的指标。当迭代系数状态因子值大于1,则说明迭代系数有偏离真实系数的趋势,此时采用步长因子较大的变步长方案;反之,说明迭代系数有逼近真实系数的趋势,应该采样步长因子较小的变步长方案。这样的自适应选择措施使得算法具有较强的收敛能力。理论分析和实验表明:在同样实验条件下,本文算法能够获得比其他文献更快的收敛速度和更小的稳态误差。      

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.