Efficient adaptive algorithms for ARX identification

Two efficient adaptive algorithmic families are developed for multichannel combiners characterized by unequal memory lengths for each input channel. The prewindowed, the covariance, and the sliding window case are addressed. The difference between the proposed methods lies in the way the Kalman gain vector is order-updated in each case. The first algorithm operates on both inputs simultaneously and thus utilizes block multichannel structured order recursions. The resulting scheme is called the diagonal-update algorithm. The second approach updates the Kalman gain in a two-step procedure by first reducing the size of one input and then the other input. The resulting method is called stairwise-update algorithm. Both algorithms are applicable to adaptive ARX (autoregressive exogenous) system identification, to adaptive control, and to the design of decision-feedback equalizers. Simulations are included     

RLS-based adaptive algorithms for generalized eigen-decomposition

The aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen-decomposition problem which arises in a variety of modern signal processing applications. First, we reinterpret the generalized eigen-decomposition problem as an unconstrained minimization problem by constructing a novel cost function. Second, by applying projection approximation method and recursive least-square (RLS) technique to the cost function, a parallel adaptive algorithm for a basis for the r-dimensional (r>0) dominant generalized eigen-subspace and a sequential algorithm based on deflation technique for the first r-dominant generalized eigenvectors are derived. These algorithms can be viewed as counterparts of the extended projection approximation subspace tracking (PAST) and PASTd algorithms, respectively. Furthermore, we modify the parallel algorithm to explicitly estimate the first r-generalized eigenvectors in parallel, not the generalized eigen-subspace. More important, the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences, while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique. Third, following convergence analysis methods for PAST and PASTd, we prove the asymptotic convergence properties of the proposed algorithms. Finally, computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms.     

Line search algorithms for adaptive filtering

Line search algorithms for adaptive filtering that choose the convergence parameter so that the updated filter vector minimizes the sum of squared errors on a linear manifold are described. A shift invariant property of the sample covariance matrix is exploited to produce an adaptive filter stochastic line search algorithm for exponentially weighted adaptive equalization requiring 3N+5 multiplications and divisions per iteration. This algorithm is found to have better numerical stability than fast transversal filter algorithms for an application requiring steady-state tracking capability similar to that of least-mean square (LMS) algorithms. The algorithm is shown to have faster initial convergence than the LMS algorithm and a well-known variable step size algorithm having similar computational complexity in an adaptive equalization experiment     

Integrated control circuit for adaptive sampling

A fully integrated controller for non-uniform data sampling suitable for the pre-processing of signals in a power- and size-restricted sensor front-end is presented. The sample rate is dynamically varied based on signal activity determined by the 2nd derivative of the input voltage. The derivative is realized with high-pass filters having 647 Hz cut-off frequency. A digital circuit generates the time-stamps and the trigger for an external analog-to-digital converter. Measured results of a 0.35 μm CMOS implementation show a sample rate variation of 7:1 and a system power advantage compared to conventional front-ends. The circuit dissipates 48 μW from ±1.5 V supplies and consumes an active area of 0.068 mm².     

An adaptive Kalman filter for ECG signal enhancement

The ongoing trend of ECG monitoring techniques to become more ambulatory and less obtrusive generally comes at the expense of decreased signal quality. To enhance this quality, consecutive ECG complexes can be averaged triggered on the heartbeat, exploiting the quasi-periodicity of the ECG. However, this averaging constitutes a tradeoff between improvement of the SNR and loss of clinically relevant physiological signal dynamics. Using a bayesian framework, in this paper, a sequential averaging filter is developed that, in essence, adaptively varies the number of complexes included in the averaging based on the characteristics of the ECG signal. The filter has the form of an adaptive Kalman filter. The adaptive estimation of the process and measurement noise covariances is performed by maximizing the bayesian evidence function of the sequential ECG estimation and by exploiting the spatial correlation between several simultaneously recorded ECG signals, respectively. The noise covariance estimates thus obtained render the filter capable of ascribing more weight to newly arriving data when these data contain morphological variability, and of reducing this weight in cases of no morphological variability. The filter is evaluated by applying it to a variety of ECG signals. To gauge the relevance of the adaptive noise-covariance estimation, the performance of the filter is compared to that of a Kalman filter with fixed, (a posteriori) optimized noise covariance. This comparison demonstrates that, without using a priori knowledge on signal characteristics, the filter with adaptive noise estimation performs similar to the filter with optimized fixed noise covariance, favoring the adaptive filter in cases where no a priori information is available or where signal characteristics are expected to fluctuate.     

Intelligent learning algorithms for adaptive digital filters

It is wellknown that gradient search fails in adaptive IIR filters, since their mean-square error surfaces may be multi-modal. In the letter a new approach based on learning algorithms is shown to be capable of performing global optimisation. The new algorithms are suitable for both adaptive FIR and IIR filters.<>     

Robust adaptive quasi-Newton algorithms for eigensubspace estimation

A novel quasi-Newton algorithm for adaptively estimating the principal eigensubspace of a covariance matrix by making use of an approximation of its Hessian matrix is derived. A rigorous analysis of the convergence properties of the algorithm by using the stochastic approximation theory is presented. It is shown that the recursive least squares (RLS) technique can be used to implement the quasi-Newton algorithm, which significantly reduces the computational requirements from O( pN/sup 2/ ) to O( pN), where N is the data vector dimension and p is the number of desired eigenvectors. The algorithm is further generalised by introducing two adjustable parameters that efficiently accelerate the adaptation process. The proposed algorithm is applied to different applications such as eigenvector estimation and the Comon-Golub (1990) test in order to study the convergence behaviour of the algorithm when compared with others such as PASTd, NIC, and the Kang et al. (see IEEE Trans. Signal Process., vol. 48, p.3328-33, 2000) quasi-Newton algorithm. Simulation results show that the new algorithm is robust against changes of the input scenarios and is thus well suited to parallel implementation with online deflation     

Proportionate adaptive algorithms for network echo cancellation

By analyzing the coefficient adaptation process of the steepest descent algorithm, the condition under which the fastest overall convergence will be achieved is obtained and the way to calculate optimal step-size control factors to satisfy that condition is formulated. Motivated by the results and using the stochastic approximation paradigm, the /spl mu/-law PNLMS (MPNLMS) algorithm is proposed to keep, in contrast to the proportionate normalized least-mean-square (PNLMS) algorithm, the fast initial convergence during the whole adaptation process in the case of sparse echo path identification. Modifications of the MPNLMS algorithm are proposed to lower the computational complexity.     

GLRT-based adaptive detection algorithms for range-spread targets

We address adaptive detection of a range-spread target or targets embedded in Gaussian noise with unknown covariance matrix. To this end, we assume that cells (referred to in the following as secondary data) that are free of signal components are available. Those secondary data are supposed to possess either the same covariance matrix or the same structure of the covariance matrix of the cells under test. In this context, we design detectors relying on the generalized likelihood ratio test (GLRT) and on a two-step GLRT-based design procedure. Remarkably, both criteria lead to receivers ensuring the constant false alarm rate (CFAR) property with respect to the unknown quantities. A thorough performance assessment of the proposed detection strategies, together with the evaluation of their processing cost, highlights that the two-step design procedure is to be preferred with respect to the plain GLRT. In fact, the former leads to detectors that achieve satisfactory performance under several situations of practical interest and are simpler to implement than those designed resorting to the latter     

Two-dimensional random adaptive sampling for image scanning

An efficient sampling algorithm for image scanning is proposed, suitable to represent "interesting" objects, defined as a set of spatially close measured values that springs out from a background noise (as in applied geophysics in the process of anomaly detection). This method generates a map of pixels randomly distributed in the plane and able to cover all the image with a reduced number of points with respect to a regular scanning. Simulation results show that a saving factor of about 50% is obtained without information loss. This result can be proved also by using a simplified model of the sampling mechanism. The algorithm is able to detect the presence of an object emerging from a low energy background and to adapt the sampling interval to the shape of the detected object. In this way, all of the interesting objects are well represented and can be adequately reconstructed, while the roughly sampling in the background produces an imperfect reconstruction. Simulation results show that the method is feasible with good performances and moderate complexity.     

Improved approximate QR-LS algorithms for adaptive filtering

This paper studies a class of O(N) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It reduces to the QR-LMS algorithm proposed by Liu et al. in 1998, when all the normalization constants are chosen as the Euclidean norm of the input signal vector. An improved transform-domain approximate QR-LS (TA-QR-LS) algorithm, where the input signal vector is first approximately decorrelated by some unitary transformations before the normalization, is proposed to improve its convergence for highly correlated signals. The mean weight vectors of the algorithms are shown to converge to the optimal Wiener solution if the weighting factor w of the algorithm is chosen between 0 and 1. New Givens rotations-based algorithms for the A-QR-LS, TA-QR-LS, and the QR-LMS algorithms are proposed to reduce their arithmetic complexities. This reduces the arithmetic complexity by a factor of 2, and allows square root-free versions of the algorithms be developed. The performances of the various algorithms are evaluated through computer simulation of a system identification problem and an acoustic echo canceller.     

Probabilistic algorithms for blind adaptive multiuser detection

Two probabilistic adaptive algorithms for jointly detecting active users in a DS-CDMA system are reported. The first one, which is based on the theory of hidden Markov models (HMMs) and the Baum-Welch (1070) algorithm, is proposed within the CDMA scenario and compared with the second one, which is a previously developed Viterbi-based algorithm. Both techniques are completely blind in the sense that no knowledge of the signatures, channel state information, or training sequences is required for any user. Once convergence has been achieved, an estimate of the signature of each user convolved with its physical channel response (CR) and estimated data sequences are provided. This CR estimate can be used to switch to any decision-directed (DD) adaptation scheme. Performance of the algorithms is verified via simulations as well as on experimental data obtained in an underwater acoustics (UWA) environment. In both cases, performance is found to be highly satisfactory, showing the near-far resistance of the analyzed algorithms     

Robust perturbation algorithms for adaptive antenna arrays

The generation of a perturbation sequence for an adaptive beamformer is described. This perturbation sequence permits simultaneous adaption and reception by use of weight perturbations that do not obstruct the look direction constraint. It is shown that this sequence is generally shorter in length than previously described sequences and offers scope for computational savings through reduction of the number of projection operations required. Convergence in the mean of the resulting adaptive algorithm is demonstrated. Experiments conducted using a four-element linear array operating in the MW RF range have confirmed that the predicted results are achievable under the nonideal conditions of quantized array weights and finite word length arithmetic     

多功能心电信号数据采样的研究

目的:对多功能心电信号发生器产生出来的数据进行研究;方法:在研究过程中,先介绍用到工具Matlab进行了一定的介绍,再详细阐述了利用Matlab对其产生信号数据的采样,最后对各种波形信号采样数据一一列出来;结果:经过软件调试的结果完全达到要求;结论:为将来设计的多功能心电信号发生器程序部分有所使用。     

Downlink adaptive array algorithms for cellular mobile communications

The capacity of wireless downlink communication to mobile receivers in a dense urban environment is limited primarily by co-channel interference. Downlink adaptive arrays can be used to mitigate this limitation by maximizing the power transmitted to desired in-cell mobiles in the reference cell while minimizing power to co-channel mobiles in neighboring cells. This is accomplished by using uplink measurements to estimate downlink covariance matrices and then solving a generalized eigenvalue problem. Several algorithms are proposed to adaptively estimate the optimal solution and are evaluated using a simplified signal model that allows efficient deterministic performance calculations.     

Rapidly converging second-order tracking algorithms for adaptive equalization

This paper is concerned with the design of second-order algorithms for an equalizer in a training or a tracking mode. The algorithms govern the iterative adjustment of the equalizer parameters for the minimization of the mean-squared error. On the basis of estimated bounds for the eigenvalues of the signal plus noise correlation matrix, an optimal second-order algorithm is derived. The resultant convergence is considerably faster than the commonly used first-order fixed-size gradient-search procedure. The variance of the optimal algorithm is shown to have a slightly larger bound than the present first-order fixed-step algorithm. However, a computer simulation for an input signal-to-noise ratio of 30 dB shows that for large intersymbol interference the improvement in the convergence of the mean more than compensates for the small increase in variance. For moderate intersymbol interference the simulation shows no variance increase. Suboptimum second-order algorithms with smaller improvement in the convergence rate and smaller increase in the variance bound are also considered. The results indicate that, on the average, the new algorithms lead to faster tracking of changes in the channel characteristics and thereby result in a smaller error rate.     

Low-complexity adaptive step size constrained constant modulus SG algorithms for adaptive beamforming

In this paper, we propose two low-complexity adaptive step size mechanisms to enhance the performance of stochastic gradient (SG) algorithms for adaptive beamforming. The beamformer is designed according to the constrained constant modulus (CCM) criterion and the proposed mechanisms are employed in the SG algorithm for implementation. A complexity comparison is provided to show their advantages over existing methods, and a sufficient condition for the convergence of the mean weight vector is established. Theoretical expressions of the excess mean-squared error (EMSE), in both the steady-state and tracking cases, are derived based on the energy conservation approach. The effects of multiple access interference (MAI) and additive noise are considered. Simulation experiments are presented for both the stationary and non-stationary scenarios, illustrating that the proposed algorithms achieve superior performance compared with existing methods, and verifying the accuracy of the analyses.     

Fast adaptive algorithms for multichannel filtering and systemidentification

Fast transversal and lattice least squares algorithms for adaptive multichannel filtering and system identification are developed. Models with different orders for input and output channels are allowed. Four topics are considered: multichannel FIR filtering, rational IIR filtering, ARX multichannel system identification, and general linear system identification possessing a certain shift invariance structure. The resulting algorithms can be viewed as fast realizations of the recursive prediction error algorithm. Computational complexity is then reduced by an order of magnitude as compared to standard recursive least squares and stochastic Gauss-Newton methods. The proposed transversal and lattice algorithms rely on suitable order step-up-step-down updating procedures for the computation of the Kalman gain. Stabilizing feedback for the control of numerical errors together with long run simulations are included     

Blind adaptive algorithms for minimum variance CDMA receivers

Constrained optimization methods have received considerable attention as a means to derive blind multiuser receivers with low complexity. The receiver's output variance is minimized subject to appropriate constraints which depend on the multipath structure of the signal of interest. When multipath is present, the constraint equations can be written in parametric form, and the constraint parameters jointly optimized with the linear receiver's parameters. We develop adaptive solutions for this joint, constrained optimization problem. Both stochastic gradient and recursive least-square-type algorithms are developed. The performance of the proposed methods is compared with other blind and trained methods and turns out to be close to the trained minimum mean-square-error receiver