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.     

Performance analysis of LMS adaptive prediction filters

The conditions required to implement real-time adaptive prediction filters that provide nearly optimal performance in realistic input conditions are delineated. The effects of signal bandwidth, input signal-to-noise ratio (SNR), noise correlation, and noise nonstationarity are explicitly considered. Analytical modeling, Monte Carlo simulations and experimental results obtained using a hardware implementation are utilized to provide performance bounds for specified input conditions. It is shown that there is a nonlinear degradation in the signal processing gain as a function of the input SNR that results from the statistical properties of the adaptive filter weights. The stochastic properties of the filter weights ensure that the performance of the adaptive filter is bounded by that of the optimal matched filter for known stationary input conditions     

Bit-serial VLSI implementation of delayed LMS adaptive FIR filters

The delayed least-mean-square (DLMS) algorithm is useful for adaptive finite impulse response (FIR) filtering applications where high throughput rates are required. In the paper, a bit-serial bit-level systolic array based on new schemes for multiplication and inner-product computation is presented to implement DLMS adaptive N-tap FIR filters. The architecture is highly regular, modular, and thus well-suited to VLSI implementation. It has an efficiency of 100% and a throughput rate of one filter output per 2B cycles, where B is the word length of input data. In addition, the proposed array uses a small delay of [(4B+N/2+4)/2B] in the filter coefficient adaptation, where [x] is the smallest integer greater than or equal to x. This ensures that the DLMS algorithm can have good performance under proper selection of the step size. Based on a conservative design technique of static complementary metal oxide semiconductor (CMOS) logic, it is shown that the proposed system can be realized in a single chip for most practical applications     

基于LMS的自适应去噪滤波器设计

讨论了自适应滤波去噪原理，采用LMS算法设计了自适应去噪滤波器，分析了MAT-LAB／SIMULINK中DSP Builder模块库在FPGA中的设计优点，最后应用DSP Builder模块库对自适应滤波器进行仿真。为自适应滤波器硬件实现提供了实验依据。     

基于FPGA的横向LMS算法的实现

横向LMS算法是实现自适应数字波束形成的基本方法之一.提出了一种用Matab/Simulink中DSP Builder模块库设计算法模型,然后应用FPGA设计软件Modelsim、QuartusⅡ分析自适应滤波器时钟速度和消耗逻辑单元数的设计方法.实验表明:该方法易于实现、简单可靠.     

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     

Design of linear phase FIR filters using the LMS algorithm

The application of the stochastic gradient (least mean square) algorithm, the design of linear phase finite impulse response (FIR) filters, is discussed. Analytical results are presented and supported by simulation experiments to demonstrate the superior performance of the LMS algorithm equipped with the linear phase constraint as compared to the standard LMS algorithm     

The use of the modified escalator algorithm to improve theperformance of transform-domain LMS adaptive filters

This paper describes a new algorithm that improves the convergence performance of the transform-domain least mean-square (TRLMS) algorithm. The algorithm exploits the sparse structure of the correlation matrix of the transformed input process to derive a data dependent Gram-Schmidt orthogonalization type transform of the process. We show its faster convergence compared with the time-domain least mean-square (LMS) algorithm and the DCT or the DWT-based TRLMS algorithm. The Gram-Schmidt orthogonalization is realized using a modified adaptive escalator algorithm. The modification significantly reduces the computational complexity of the adaptive escalator algorithm and determines the computational complexity of the proposed algorithm     

Steady-state MSE convergence of LMS adaptive filters withdeterministic reference inputs with applications to biomedical signals

We analyze the steady-state mean square error (MSE) convergence of the LMS algorithm when deterministic functions are used as reference inputs. A particular adaptive linear combiner is presented where the reference inputs are any set of orthogonal basis functions-the adaptive orthogonal linear combiner (AOLC). Several authors have applied this structure always considering in the analysis a time-average behavior over one signal occurrence. We make a more precise analysis using the deterministic nature of the reference inputs and their time-variant correlation matrix. Two different situations are considered in the analysis: orthogonal complete expansions and incomplete expansions. The steady-state misadjustment is calculated using two different procedures with equivalent results: the classical one (analyzing the transient behavior of the MSE) and as the residual noise at the output of the equivalent time-variant transfer function of the system. The latter procedure allows a very simple formalism being valid for colored noise as well. The derived expressions for steady-state misadjustment are contrasted with experimental results in electrocardiographic (ECG) signals, giving exact concordance for any value of the step size     

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.     

Digital compensation in IQ modulators using adaptive FIR filters

This paper discusses digital compensation for frequency-dependent transfer characteristics and implementation errors in digital PAM/continuous-phase frequency-shift keying (CPFSK) quadrature modulators. Recently, several methods have been proposed to digitally compensate for the shortcomings of the analog reconstruction filters in IQ modulators. While these methods have shown to be effective, they result in filters with long coefficients that are computationally demanding to implement on the DSP. Furthermore, the modulator needs to be taken offline while the precompensation filters are updated to reflect the changes in the I and Q channel characteristics. In this paper, a digital compensation method is proposed here using two adaptive finite-impulse response filters to compensate for the magnitude and phase characteristics of the analog reconstruction filters in the IQ modulator. The experimental results show that this technique is effective and lead to substantial improvement of the output envelope ripples.     

Performance of adaptive filters using combined lattice and transform techniques

A composite scheme combining lattice and transform techniques for implementation of adaptive filters is discussed. Results of the eigenvalue spreads and convergence time for simple correlation cancelers in combination with Walsh-Hadamard Transform (WHT) are reported.     

Analysis of adaptive filters using normalized signed regressor LMSalgorithm

In this paper, adaptive filters using the normalized signed regressor LMS algorithm (NSRA) with Gaussian reference inputs are proposed and analyzed to yield difference equations for theoretically calculating expected convergence of the filters. A simple difference equation for mean squared error (MSE) is derived when the filter input is a white and Gaussian process, whereas approximate difference equations for colored Gaussian inputs are proposed and tested. Stability conditions and residual MSE after convergence are also obtained. Agreement of theoretical results with those of simulation in the experiment with some examples of filter convergence shows sufficient accuracy of the theory and assures the usefulness of the difference equations in estimating filter performances, thus facilitating the design of adaptive filters using the NSRA     

Steady-state analysis of the long LMS adaptive filter

For the well-known LMS adaptive algorithm no general analytic solutions are available for the steady-state weight-error statistics under stationary stochastic excitation. Only approximate tools have been developed using certain assumptions (like the “independence assumption”) and producing more or less reliable results in practical situations. It is only for the case of a vanishingly small stepsize that such assumptions are not required. There a closed-form solution can be determined for any colouring of the input signal and the additive noise.Here another particular problem is analyzed: the long filter, i.e. a tapped-delay line structure with a large number of taps. For the limiting case of an infinitely long filter, exact closed-form solutions are derived for the steady-state weight-error correlations and the associated “misadjustment”, again valid for any colouring of the input signal and the additive noise, and now also for any stepsize guaranteeing stability.The analysis is based upon a feedback approach, with a forward branch generating the above-mentioned solution for vanishing stepsize and a peculiar feedback branch responsible for higher-order corrections. As in any feedback structure, instability can occur beyond a critical value of the feedback parameter. In our case an experimentally supported maximum stepsize is found, beyond which spontaneous oscillations might occur.     

Quantization and other nonlinear effects in the LMS adaptive algorithm

Quantization effects in the complex_lms adaptive algorithm are studied for two cases. For frequency domain adaptation, the complex scalarlms algorithm is analyzed by modeling the accumulator input quantizer as a memoryless nonlinearity. For time domainlms adaptation, weight vector adaptation is studied by adding of dither. The dither linearizes the rounding quantizer at each accumulator input. The effects of both the dither and quantization noise on algorithm performance are studied. Results are also presented for an arbitrary nonlinear operation on the data input to the weight update for the real lms algorithm with a gaussian data model. Difference equations are derived and solved for the weight first and second moments. The solutions are used to minimize the mean square error over the choice of nonlinearity for a fixed transient behaviour.     

Performance characteristics of the median LMS adaptive filter

The median least-mean-square (MLMS) adaptive filter alleviates the problem of degradation of performance when inputs are corrupted by impulsive noise by protecting the filter coefficients from the impact of the impulses. MLMS is obtained from the least mean square (LMS) by applying a median operation to the raw gradient estimates of the mean-squared-error performance surface. The algorithm is analyzed for the class of independent and identically distributed inputs, establishing exponential convergence. The rate of convergence is shown to depend on order statistics of the input but shows little dependence on characteristics of the impulsive interference. Analysis of the steady-state performance indicates a significantly improved performance for MLMS compared to LMS. Analytic predictions for both convergence and steady-state behavior are supported by simulations     

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     

Sequential tuning of microwave filters using adaptive models and parameter extraction

This paper describes a sequential procedure for computer-aided tuning and diagnosis of multiple-coupled resonator filters. The method is based on a sequential parameter estimation and a systematic tuning procedure and employs three different filter models. A detuned model represents the initial status of the filter after a well-defined detuning procedure. The target filter is described by an ideal model, whereas the actual state of the filter at each tuning step is represented by a coarse adaptive model. The goal of the procedure is the convergence of the coarse model to the ideal model and will be obtained by systematically centering resonant frequencies and coupling coefficients. Practical examples comprising low- and high-degree filters confirm the effectiveness of the proposed approach in both tuning and fault diagnosis.     

Stationary and nonstationary learning characteristics of the LMS adaptive filter

This paper describes the performance characteristics of the LMS adaptive filter, a digital filter composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive algorithm. For stationary stochastic inputs, the mean-square error, the difference between the filter output and an externally supplied input called the "desired response," is a quadratic function of the weights, a paraboloid with a single fixed minimum point that can be sought by gradient techniques. The gradient estimation process is shown to introduce noise into the weight vector that is proportional to the speed of adaptation and number of weights. The effect of this noise is expressed in terms of a dimensionless quantity "misadjustment" that is a measure of the deviation from optimal Wiener performance. Analysis of a simple nonstationary case, in which the minimum point of the error surface is moving according to an assumed first-order Markov process, shows that an additional contribution to misadjustment arises from "lag" of the adaptive process in tracking the moving minimum point. This contribution, which is additive, is proportional to the number of weights but inversely proportional to the speed of adaptation. The sum of the misadjustments can be minimized by choosing the speed of adaptation to make equal the two contributions. It is further shown, in Appendix A, that for stationary inputs the LMS adaptive algorithm, based on the method of steepest descent, approaches the theoretical limit of efficiency in terms of misadjustment and speed of adaptation when the eigenvalues of the input correlation matrix are equal or close in value. When the eigenvalues are highly disparate (λmax/λmin> 10), an algorithm similar to LMS but based on Newton's method would approach this theoretical limit very closely.     

Tracking of time-varying channels using two-step LMS-type adaptive algorithm

This paper presents a modified version of the two-step least-mean-square (LMS)-type adaptive algorithm motivated by the work of Gazor. We describe the nonstationary adaptation characteristics of this modified two-step LMS (MG-LMS) algorithm for the system identification problem. It ensures stable behavior during convergence as well as improved tracking performance in the smoothly time-varying environments. The estimated weight increment vector is used for the prediction of weight vector for the next iteration. The proposed modification includes the use of a control parameter to scale the estimated weight increment vector in addition to a smoothing parameter used in the two-step LMS (G-LMS) algorithm, which controls the initial oscillatory behavior of the algorithm. The analysis focuses on the effects of these parameters on the lag-misadjustment in the tracking process. The mathematical analysis for a nonstationary case, where the plant coefficients are assumed to follow a first-order Markov process, shows that the MG-LMS algorithm contributes less lag-misadjustment than the conventional LMS and G-LMS algorithms. Further, the stability criterion imposes upper bound on the value of the control parameter. These derived analytical results are verified and demonstrated with simulation examples, which clearly show that the lag-misadjustment reduces with increasing values of the smoothing and control parameters under permissible limits.