Adaptive Tap Research Articles

Block-Sparsity Log-Sum-Induced Adaptive Filter for Cluster Sparse System Identification

In this work, an effective adaptive block-sparsity log-sum least mean square (BSLS-LMS) algorithm is proposed to improve the convergence performance of cluster sparse system identification. The main idea of the proposed scheme is to add a new block-sparsity induced term into the cost function of the LMS algorithm. We utilize the ${l}_{{1}}$ norm of adaptive tap weights and log-sum as a mixed constraint, via optimizing the cost function through the gradient descent method, the proposed adaptive filtering method can iteratively move the identified signals towards the optimal solutions, and finally identify the unknown system accurately. The cluster-sparse system response, with block length and arbitrary average sparsity, is generated by a Markov-Gaussian (M-G) model. For the white Gaussian input data, the theoretical formulas of the steady-state mis-adjustment and convergence behaviors of the BSLS-LMS are derived in a general sparse system and a block sparse system, respectively. Numerical experiments demonstrate that the proposed adaptive BSLS-LMS algorithm achieves much better convergence behavior than conventional sparse signal recovery solutions. The experimental study also verifies the consistency between the simulation results and the theoretical analysis.

High-temperature expansions and message passing algorithms

Improved mean-field techniques are a central theme of statistical physics methods applied to inference and learning. We revisit here some of these methods using high-temperature expansions for disordered systems initiated by Plefka, Georges and Yedidia. We derive the Gibbs free entropy and the subsequent self-consistent equations for a generic class of statistical models with correlated matrices and show in particular that many classical approximation schemes, such as adaptive TAP, expectation-consistency, or the approximations behind the vector approximate message passing algorithm all rely on the same assumptions, that are also at the heart of high-temperature expansions. We focus on the case of rotationally invariant random coupling matrices in the ‘high-dimensional’ limit in which the number of samples and the dimension are both large, but with a fixed ratio. This encapsulates many widely studied models, such as restricted Boltzmann machines or generalized linear models with correlated data matrices. In this general setting, we show that all the approximation schemes described before are equivalent, and we conjecture that they are exact in the thermodynamic limit in the replica symmetric phases. We achieve this conclusion by resummation of the infinite perturbation series, which generalises a seminal result of Parisi and Potters. A rigorous derivation of this conjecture is an interesting mathematical challenge. On the way to these conclusions, we uncover several diagrammatical results in connection with free probability and random matrix theory, that are interesting independently of the rest of our work.

Ising distribution as a latent variable model.

During the past decades, the Ising distribution has attracted interest in many applied disciplines, as the maximum entropy distribution associated to any set of correlated binary ("spin") variables with observed means and covariances. However, numerically speaking, the Ising distribution is unpractical, so alternative models are often preferred to handle correlated binary data. One popular alternative, especially in life sciences, is the Cox distribution (or the closely related dichotomized Gaussian distribution and log-normal Cox point process), where the spins are generated independently conditioned on the drawing of a latent variable with a multivariate normal distribution. This article explores the conditions for a principled replacement of the Ising distribution by a Cox distribution. It shows that the Ising distribution itself can be treated as a latent variable model, and it explores when this latent variable has a quasi-normal distribution. A variational approach to this question reveals a formal link with classic mean-field methods, especially Opper and Winther's adaptive TAP approximation. This link is confirmed by weak coupling (Plefka) expansions of the different approximations and then by numerical tests. Overall, this study suggests that an Ising distribution can be replaced by a Cox distribution in practical applications, precisely when its parameters lie in the "mean-field domain."

Block sparse reweighted zero‐attracting normalised least mean square algorithm for system identification

To improve the performance for identifying the block sparse system, a block sparse reweighted zero-attracting normalised least mean square algorithm (NLMS) (BS-RZA-NLMS) is proposed in this Letter. The proposed algorithm is derived by applying block sparsity constraint on the cost function of the NLMS, which is a log-sum penalty of adaptive tap weights with equal block partition sizes. The convergence behaviour of the BS-RZA-NLMS is analysed in terms of the zero attraction and block partition. Simulation results demonstrate the performance advantage of the proposed algorithm in the context of block sparse system identification.

A New Variable Step Size LMS Adaptive Filtering Algorithm and its Simulations

. Aiming at the disadvantage of the variable step size LMS adaptive filtering algorithms' convergence speed contradicting its steady-state error, a novel non-liner functional relationship between μ (n) and error signal e (n) was established. On the basis of the functional relationship, a new algorithm of variable step size LMS adaptive filtering was presented. The step size factor of the new algorithm is adjusted by the absolute value of the product of the current and former errors. It also uses the absolute estimation error compensation terms disturbance to speed up the convergence of adaptive filter tap weight vector. At the same time, the algorithm considers the relationship between step length of the last iteration and the former M error signal. As a result the algorithm has higher convergence characteristic and small steady state error. The theoretical analysis and simulation results show that the new algorithm has faster convergence speed, lower steady state error and better performance of noise suppression, also show the overall performance of this algorithm exceeds some others condition.

A New Echo Cancellation Algorithm without Double-Talk Detection Based on Correlation Function

In an adaptive echo canceller, the detection algorithm able to distinguish echo path change (EPC) from double-talk (DT) is vital to ensure that adaptive filter tap coefficients are updated in case of EPC and frozen during the DT period. The paper presents a new echo cancel algorithm, which can protect the adaptive filter performance during double-talk in acoustic echo cancellation of teleconference without setting a detector. A judgment value can be directly used in the iteration formula to control the iteration speed of the filter, which composed of the correlation of the far-end signal and near-end received signal, the pre-correlation of the error signal. The computer simulation results verify that the mentioned algorithm has the good double talk protection performance, and it is very useful and efficient in distinguishing EPC from DT but with less computational complexity contrast to the congener algorithm.

Mathematical structures of loopy belief propagation and cluster variation method

The mathematical structures of loopy belief propagation are reviewed for graphical models in probabilistic information processing in the stand point of cluster variation method. An extension of adaptive TAP approaches is given by introducing a generalized scheme of the cluster variation method. Moreover the practical message update rules in loopy belief propagation are summarized also for quantum systems. It is suggested that the loopy belief propagation can be reformulated for quantum electron systems by using density matrices of ideal quantum lattice gas system.

Adaptive sparse equalizer robust to fast fading and long delay spread for ATSC DTV

An equalization algorithm is proposed to guarantee a stable performance in fast fading channels for the advanced television system committee (ATSC) digital television (DTV) systems, in channels with high Doppler shifts, the conventional equalizer shows severe performance degradation. The conventional equalizer with long filter taps to overcome long delay profiles is not suitable for fast fading channels. The proposed sparse equalization algorithm is robust to the multipaths with long delay profiles as well as fast fading by utilizing channel estimation and an equalizer initialization. Fast fading channels with high Doppler shifts can be compensated with an adaptive tap selection technique as well as variable step-sizes. Under the ATSC test channels, the proposed algorithm is analyzed and compared with the conventional equalizer.

Adaptive equalisation for broadband predistortion linearisation of optical transmitters

Polynomial predistortion is known to have limited signal bandwidth and modulation-depth range above which the improvement gained by linearisation quickly diminishes. This problem has been studied for RF power amplifiers in the context of wireless communications but less so for analogue fibre optic links which could greatly benefit from a broadband, large dynamic range predistortion lineariser. Behavioural models are presented for static and dynamic nonlinearities based on the Volterra series. It is shown that for modulation frequencies much lower than the relaxation oscillation frequency, a simple predistortion architecture that employs only postfiltering is adequate to compensate for memory effects that limit predistortion bandwidth. Design considerations for an analogue adaptive tap delay line filter are also presented along with the general frequency response needed to compensate for memory. The dependence of predistortion parameters on modulation depth is analysed, and it is shown that an adaptive predistorter using instantaneous digital adaptation (IDA) provides both a larger signal-to-noise and distortion ratio (SNDR) and modulation depth range at the transmitter for a given noise floor.

A 28.8 Mb/s 4 /spl times/ 4 MIMO 3G CDMA receiver for frequency selective channels

This paper describes a silicon receiver for a multiple-input multiple-output (MIMO) wireless channel that supports up to 28.8 Mb/s using a 4 /spl times/ 4 QPSK configuration over a 5-MHz frequency selective channel. The architecture has two key components: a space-time equalizer that mitigates both spatial and temporal effects of the channel, and a maximum likelihood detector with approximate a posterior probability (ML-APP) soft estimates of the transmit vectors over the MIMO configuration. The space-time equalizer uses an adaptive tap training process that includes a pilot correlator to reduce adaptation noise. The device is 685 k effective logic gates (11.6 mm/sup 2/) in 0.18-/spl mu/m 6LM CMOS.

Probabilistic data modelling with adaptive TAP mean-field theory

We demonstrate for the case of single-layer neural networks how an extension of the TAP mean-field approach of disorder physics can be applied to the computation of approximate averages in probabilistic models for real data.

Tap-selectable decision-feedback equalization

This paper presents an adaptive tap assignment technique for improving the performance of a previously reported reduced-complexity decision-feedback equalizer (DFE) for broadband band wireless systems. The spacings of individual feedforward taps of the DFE are made selectable so that, when the channel consists of a sparsely distributed multipath with a large delay spread (e.g. hilly terrain (HT) delay profiles), the equalizer span can be increased without increasing the total number of taps. We propose simple tap selection algorithms and show that they provide: (1) performance gains over a contiguous-tap approach in various outdoor delay profiles and (2) improved robustness against fast fading.

On statistical efficiency of the LMS algorithm in system modeling

The conventional least-mean-square (LMS) algorithm is compared with the ideal LMS/Newton (ILMSN) algorithm. It is shown that, although under certain conditions, for similar misadjustment, the output mean-square error (MSE) of the ILMSN algorithm may converge much faster than the MSE of the LMS algorithm, the difference between the two algorithms may not be that great if misalignments of the adaptive filter tap gains are compared. Analytical results are presented, with computer simulations that support their validity. >

Quantization effects in transform-domain normalized LMS algorithm

The quantization effects of the transform domain normalized least mean square (LMS) algorithm are studied. The discussion is limited to the systems that employ an orthonormal transform to convert the incoming samples to a set of partially uncorrelated components, to be used as actual inputs to an adaptive linear combiner. The quantization effects of the transformation coefficients and the normalized step-sizes are studied separately. The quantization effects of the system variables and its adaptive tap weights are ignored. A performance index is used to derive analytical relations for the performance losses that arise. It is shown that representations of both the normalized step-sizes and the transformation coefficients require fairly low precision. Numerical results that support the development theories are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the Required Tap-Weight Precision for Digitally Implemented, Adaptive, Mean-Squared Equalizers

An analysis is made of the degree of precision required in a digitally implemented adaptive equalizer to achieve a satisfactory level of performance. Considering both the conventional synchronously spaced equalizer and the newer fractionally spaced equalizer, insight is provided into the relationship between the tap-weight precision and the steady-state, mean-squared error. It is demonstrated why the number of adaptive tap weights should be kept to a minimum (consistent with acceptable steady-state performance), both from convergence and precision requirements. A simple formula is given that displays the tradeoff among the equalizer mean-squared error, the number of taps, the channel characteristics, and digital resolution. For typical basic-conditioned voiceband channels operating at 9.6 kb/s, and neglecting the effects that limited resolution might have on timing and carrier phase tracking, analysis and simulation both indicate that the required top-weight resolution is of the order of 11 or 12 bits. Moreover, the minimum precision is only weakly dependent on the quality of the channel.