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     

Performance analysis of a split-path LMS adaptive filter for ARmodeling

A split-path adaptive filter is proposed for extracting the model parameters of an autoregressive process. The structure is composed of two linear phase filters connected in parallel, one antisymmetric and the other symmetric. The two filters are adapted independently on a sample-by-sample basis using the least-mean-square (LMS) algorithm. The performance of the system in terms of convergence speed and excess mean square error is analyzed in detail, and comparisons with the conventional transversal structure are made. Theoretical analysis and experimental results show that the model can provide a much faster rate of convergence at the expense of only a moderate increase in computation. Two methods for choosing control parameters for the split-path adaptive filter are also suggested to improve further the convergence behavior     

An adaptive wavelength tunable optical filter employing anangle-tuned interference filter and an intelligent digital controller

This paper describes an adaptive wavelength tunable optical filter, which is composed of an angle-tuned interference optical filter and an intelligent digital controller. The new angle-tuned interference filter consists of a dielectric interference optical filter and a piezoelectric angle-tuning mechanism. It achieves quick wavelength switching within 2.5 ms in a 30 nm tuning range and a sufficiently low crosstalk less than -30 dB. The intelligent digital controller has two functions: wavelength tracking and wavelength channel selection. Combining these technologies, we have developed a practical low-cost tunable filter suitable for a post-optical-amplifier filter in a high-sensitivity detection system and a channel selector in a WDM system that requires 10-100 ms channel selection time. With a wavelength tracking operation, we have confirmed -35 dBm high-sensitivity detection in 20 nm wavelength range in a 10 Gb/s system. We have also confirmed a wavelength channel selection operation within 18 ms in a three-channel wavelength division multiplexed (WDM) system whose channel spacing is 4.4 nm     

Lifting-based wavelet domain adaptive Wiener filter for image enhancement

A method of applying lifting-based wavelet domain Wiener filter (LBWDMF) in image enhancement is proposed. Lifting schemes have emerged as a powerful method for implementing biorthogonal wavelet filters. They exploit the similarity of the filter coefficients between the low-pass and high-pass filters to provide a higher speed of execution, compared to classical wavelet transforms. LBWDMF not only helps in reducing the number of computations but also achieves lossy to lossless performance with finite precision. The proposed method utilises the multi-scale characteristics of the wavelet transform and the local statistics of each subband. The proposed method transforms an image into the wavelet domain using lifting-based wavelet filters and then applies a Wiener filter in the wavelet domain and finally transforms the result into the spatial domain. When the peak signal-to-noise ratio (PSNR) is low, transforming an image to the lifting-based wavelet domain and applying the Wiener filter in the wavelet domain produces better results than directly applying Wiener filter in spatial domain. In other words each subband is processed independently in the wavelet domain by a Wiener filter. Moreover, in order to validate the effectiveness of the proposed method the result obtained using the proposed method is compared to those using the spatial domain Wiener filter (SDWF) and classical wavelet domain Wiener filter (CWDWF). Experimental results show that the proposed method has better performance over SDWF and CWDWF both visually and in terms of PSNR.     

Alternative and effective adaptive IIR filter structure

An adaptive IIR filter with a full-feedback structure is presented and a suitable LMS algorithm is derived. Using this algorithm, some examples are demonstrated where this structure has a distinct performance advantage over the conventional adaptive IIR filter structure     

Performance analysis for an adaptive filter code-tracking techniquein direct-sequence spread-spectrum systems

This paper investigates tracking of direct-sequence spread-spectrum (DS/SS) signals based on an adaptive filtering technique. It is shown that a previously proposed hardware for code acquisition is also capable of code-tracking, and, hence, by performing both acquisition and tracking with the same circuitry, a significant simplification in the overall DS/SS receiver structure is gained. Analytical results show that the proposed scheme has a good tracking performance, as measured by the hold-in time and the false alarm penalty time, and is less sensitive to variations in the signal-to-noise ratio (SNR) compared to conventional delay-locked loops (DLLs). Moreover, simulation results show that the proposed adaptive filter tracking scheme has a smaller residual tracking error than that produced by a conventional maximum-likelihood estimator (MLE)     

The wavelet transform-domain LMS adaptive filter with partial subband-coefficient updating

In this paper, we propose and analyze the wavelet transform-domain LMS (WTDLMS) algorithm where only a subset of the adaptive filter coefficients are updated at each iteration. The use of wavelets or subband filterbanks can lead to several novel schemes whose combinations can lead to other sub-schemes as well. In the proposed scheme, the coefficients can be selected altogether as a block and not just individually as done earlier in the literature. This algorithm is then tested in the context of system identification and equalization.     

A stable adaptive Hammerstein filter employing partial orthogonalization of the input signals

This paper presents an algorithm that adapts the parameters of a Hammerstein system model. Hammerstein systems are nonlinear systems that contain a static nonlinearity cascaded with a linear system. In this paper, the static nonlinearity is modeled using a polynomial system, and the linear filter that follows the nonlinearity is an infinite-impulse response (IIR) system. The adaptation of the nonlinear components is improved by orthogonalizing the inputs to the coefficients of the polynomial system. The step sizes associated with the recursive components are constrained in such a way as to guarantee bounded-input bounded-output (BIBO) stability of the overall system. This paper also presents experimental results that show that the algorithm performs well in a variety of operating environments, exhibiting stability and global convergence of the algorithm.     

Compact and low-loss interleave filter employing lattice-form structure and silica-based waveguide

This paper describes a compact and practical interleave filter with uniform multi/demultiplexing properties and a wide operational wavelength range realized by using a lattice-form structure and a silica-based waveguide. In the design, we optimized the bandwidth by controlling the lattice stage number and the loss ripple in the spectrum. Moreover, we propose a novel coupler with a large fabrication tolerance, a new tandem configuration that provides uniform characteristics and low dispersion, a polarization dependence compensation method, and a folded configuration, which are effective in realizing a high-performance interleave filter. Based on the above techniques, we fabricated a 50-GHz channel spacing interleave filter by using planar-lightwave-circuit technologies and demonstrated that it performed well throughout the C-band, exhibiting a low insertion loss of about 2 dB, a low chromatic dispersion of within +/-20 ps/nm, a 1-dB passband width of over 34 GHz, and a 30-dB stopband width of over 25 GHz, which are sufficient for a 10-Gbps transmission system.     

C.C.D. adaptive filter employing parallel coefficient updating

A charge-coupled-device adaptive transversal filter is described which incorporates parallel tap-weight coefficient updating. The prototype filter was based on a clipped least-mean-squares algorithm with digital tap-weight storage. The design of an 8-tap prototype filter capable of being clocked between 1 and 100 kHz is reported and its performance assessed by testing its ability to separate two sinusoidal waveforms.     

自适应天线的两级分组信号处理结构性能分析

本文讨论了两级分组信号处理结构性能。从理论和仿真中可以看出,两组分组信号处理结构和传统一级信号处理结构具有类似的性能,但是,可以节省很大的计算量。通过这种方法,基本可以解决计算性能的限制,增加系统的性能。     

A new delayless subband adaptive filter structure

Adaptive subband techniques have been developed to reduce complexity and slow convergence problems of the traditional fullband high-order adaptive filters. Some of the disadvantages often encountered in most of the proposed architectures are the effect of aliasing associated with the multirate structure, which is a source of error in the modeling of the unknown system, and the delay introduced in the signal path. We present a new delayless maximally decimated structure where the optimal subband filters are related to the wideband system in a closed form. They make use of a special DFT analysis filterbank where the polyphase components of the prototype filter represent fractional delays so that there is no need for adaptive cross-filters, and the unknown system can modeled perfectly in a closed-loop scheme. We interpret the proposed structure as a special case of a block adaptive filter with lower computational complexity than the conventional fullband LMS algorithm. Some computer simulations are presented in order to verify the good features of the proposed structure     

Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation

In order to get an efficient image representation we introduce a new adaptive Haar wavelet transform, called Tetrolet Transform. Tetrolets are Haar-type wavelets whose supports are tetrominoes which are shapes made by connecting four equal-sized squares. The corresponding fast filter bank algorithm is simple but very effective. In every level of the filter bank algorithm we divide the low-pass image into 4 × 4 blocks. Then in each block we determine a local tetrolet basis which is adapted to the image geometry in this block. An analysis of the adaptivity costs leads to modified versions of our method. Numerical results show the strong efficiency of the tetrolet transform for image approximation.     

Performance analysis of the sign algorithm for a constrained adaptive IIR notch filter

Adaptive infinite impulse response (IIR) notch filters are very attractive in terms of their reasonable performances and low computational requirements. Generally, it is very difficult to assess their performances analytically due to their IIR nature. This paper analyzes in detail the steady-state performance of the sign algorithm (SA) for a well-known adaptive IIR notch filter with constrained poles and zeros. Slow adaptation and Gaussianity of the notch filter output are assumed for the sake of analysis. Two difference equations are first established for the convergences in the mean and mean square in the vicinity of the steady state of the algorithm. Steady-state estimation error or bias and mean square error (MSE) of the SA are then derived in closed forms. A coarse stability bound is also derived for the algorithm. Theory-based comparison between the algorithm and the plain gradient (PG) algorithm is done in some detail. Extensive simulations are conducted to demonstrate the validity of the analytical results for both slow and relatively fast adaptations.     

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     

Performance analysis of an adaptive receiver structure for digital mobile communications

In this paper we investigate the performance of a combined estimation/equalization technique for the mobile radio channel, assuming a GSM-recommended transmission format (narrowband TDMA with midamble, recommendation 5.04) and MSK modulation scheme. Channel estimation is performed via correlation of the received signal with a suitably modulated replica of the transmitted midamble. Equalization is then obtained by means of a maximum likelihood sequence estimation (MLSE) scheme in the form of a so-called Viterbi equalizer. Our analysis provides theoretical results concerning the bit error rate (BER) attained by the receiver for a given stationary multipath channel model. Simulation results are also presented in order to integrate and validate the theory.     

Performance analysis of MUSIC employing conjugate symmetricbeamformers

If one incorporates a beamformer composed of conjugate centro-symmetric weight vectors as a preprocessor to an eigenstructure direction finding algorithm, a real-valued decomposition can be employed to estimate the noise and signal subspaces from the sample covariance matrix. The effect of employing the real processing methodology on the angle estimation performance of beamspace MUSIC is explored. Specifically, the distribution of the real-valued signal subspace eigenvectors is derived and used in an asymptotic analysis of the bias and variance of the MUSIC estimator. The theoretical analysis shows that processing the real part of the beamspace sample covariance matrix offers significant performance gains, in addition to the obvious computational benefit, relative to the conventional complex-valued procedure, particularly in the case of correlated sources. Monte Carlo simulations are included to verify the theoretical expressions. A trade-off study of the estimation accuracy versus the desire to provide adequate rejection of unwanted signals in a sector-based interrogation scheme for various beamforming architectures is also presented     

Performance of adaptive matched filter receivers over fadingmultipath channels

A unified discrete channel model from the information source up to the sampler was developed for fading multipath channels. Different methods for adaptive channel measurement was studied. The performance of a discrete matched filter using different adaptation techniques and working over a troposcatter channel is predicted. It is shown that the effects of channel measurement noise are less damaging for the decision-directed adaptation technique as compared to any kind of reference-directed adaptation     

Further improved 2-D lattice filter structure employing missing reflection coefficients

A new lattice filter structure to model two-dimensional (2-D) autoregressive (AR) fields is proposed. The proposed structure utilizes and extracts the information contained in the backward prediction error fields and their delayed versions. The main idea is to use two sets of reflection coefficients corresponding to two quadrant filters and to increase the number of reflection coefficients with the order of the lattice filter. Increasing the number of reflection coefficients at each stage produces a sufficient number of independent parameters to model AR fields up to order three, which is an improvement over the existing 2-D lattice filter structures. The improvement is confirmed by computer simulations. In addition, a relationship between the reflection coefficients and the AR coefficients is derived. It is also shown that the entropy contained in the backward prediction error field vector of the proposed structure is closer to the input entropy when compared to those contained in existing 2-D lattice filters.     

RECURSIVE STRUCTURE AND QUASI-RECURSIVE STRUCTURE OF ADAPTIVE VOLTERRA FILTER AND THEIR ALGORITHMS AND APPLICATIONS

The recursive structure and quasi-recursive structure of Adaptive Volterra Fil-ter(AVF) are put forward, their algorithms are given, and their characteristics and applications are discussed. The introduction of recursive structure can remarkably reduce the parameters and computational cost of AVF.