Milos Doroslovacki

Improving convergence of the PNLMS algorithm for sparse impulse response identification

A proportionate normalized least mean square (PNLMS) algorithm has been proposed for sparse impulse response identification. It provides fast initial convergence, but it begins to slow down dramatically after the initial period. In this letter, we analyze the coefficient adaptation process of the steepest descent algorithm and derive how to calculate the optimal proportionate step size in order to achieve the fastest convergence. The results bring forward a novel view of the concept of proportion. We propose a /spl mu/-law PNLMS (MPNLMS) algorithm using an approximation of the optimal proportionate step size. Line segment approximation and partial update techniques are discussed to bring down the computational complexity.

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.

Wavelet-based linear system modeling and adaptive filtering

It is shown how linear time-varying systems can be modeled in several different ways by discrete-time wavelets or, more generally, by some set of functions. Interpretation of physical meanings, possible efficiency, and other characteristics of the modeling are considered. System identification minimizing the mean square output error is studied. Optimal coefficients and the corresponding minimum mean square error are found, and they are, in general, time varying. Least-mean-square adaptive filtering algorithms are derived for on-line filtering and system Identification. Theoretically and by simulations, the advantages of using wavelet-based filtering are shown: separation of adaptation effects from unknown time-varying system behavior and fast convergence. Adaptive coefficients estimated by a recursive-least-square algorithm can tend toward constants, even in the case of time-varying systems. Time-invariant system identification and adaptive filtering is given as a special case of the general time-varying setting.

Cascade lattice IIR adaptive filters

The feedback lattice filter forms, including the two-multiplier form and the normalized form, are examined with respect to their relationships to the feedback direct form filter. Specifically, the transformation matrix between the lattice forms and the direct form is derived; parameter and state relationships between the lattice forms and the direct form are therefore obtained. An IIR filter structure-the cascade lattice IIR structure-is constructed. Based on this structure, three IIR adaptive filtering algorithms in the two-multiplier form can then be developed following the gradient approach, the Steiglitz-McBride approach and the hyperstability approach. Convergence of these algorithms is theoretically analyzed using either the ODE approach or the hyperstability theorem. These algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms. Relationships of the simplified algorithms to the direct form algorithms are also studied, which disclose a consistency in algorithm structure regardless of the filter form. Three normalized lattice algorithms can also be derived from the two-multiplier lattice algorithms. Experimental results show much improved performance of the normalized lattice algorithms over the two-multiplier lattice algorithms and the direct form algorithms. >

Product of second moments in time and frequency for discrete-time signals and the uncertainty limit

Abstract The product of ordinary second moments in time and frequency for discrete-time signals has a unique global minimum for the unit sample sequence. When the ordinary-second-moment product is used as the measure of localization in the continuous-time case, Gaussian signals are the best localized simultaneously in time and frequency. But sampling of the Gaussian signals provides discrete-time signals which are far from being the best localized. In general, it turns out that the product of ordinary second moments in time and frequency is not a most reasonable measure of simultaneous time–frequency localization for discrete-time signals. Motivated by this discrepancy, in this paper an uncertainty relation for the product of generalized second signal moments in time and frequency is derived, and optimal signals that reach the uncertainty limit are found. The requirement for convolution invariance between the optimal signals offers a new uncertainty relation for the discrete-time case. The set of optimal discrete-time signals, beside the unit sample sequence, binomial sequences, the sampled band-limited minimum-effective-duration signal, contains also, as a limit case, the Gaussian signals. The second moments involved in the uncertainty relation are described in more details.

Wavelet-based adaptive filtering

Theoretical and experimental analysis and description of wavelet-based filtering are given in the case of a stationary desired signal. The impulse responses of the adaptive filter and the unknown system producing the desired signal are represented by discrete-time wavelet series. The authors have found the coefficients that minimize the mean square error and pointed out the time-frequency localized structure of the modeling error. An LMS (least mean square) adaptive filtering algorithm is derived. Its transform domain interpretation is shown, as are possibilities for faster convergence and better numerical properties. The authors have observed better modeling of desired signals in the time-frequency plane, faster convergence, and smaller error than in the case of FIR (finite impulse response) filters.<<ETX>>

New sparse adaptive algorithms using partial update

In this paper, we propose two new sparse adaptive filtering algorithms using partial update. By taking advantage of both impulse response sparseness and partial update, we design different criteria to determine which coefficients to be updated in order to improve the performance of typical partial update algorithms. Compared with the normalized least mean square (NLMS), selective partial update NLMS (SPUNLMS) and proportionate NLMS (PNLMS++) algorithm, the proposed partial update sparse NLMS (PSNLMS) algorithms achieve faster convergence speed with even less computational complexity. Simulation results show that they perform well in applications where identification of long sparse impulse responses is needed. Network echo cancellation is a typical example.

Digital modulation recognition using support vector machine classifier

We propose four features to classify amplitude shift keying with two levels and four levels, binary phase shift keying, quadrature phase keying, frequency shift keying with two carriers and four carriers. After that we present a new method of classification based on support vector machine (SVM) that uses the four proposed features. We study the performance of SVM classifier and compare it to the previous work done in the literature on the digital modulation classification problem.

On-line identification of echo-path impulse responses by Haar-wavelet-based adaptive filter

Long-distance telephone communications of good quality require absence of echoes. The physical characteristics of an echo path are time varying and the impulse responses measured at different times can differ from each other. This means that an echo canceller must track the changes. Using a small number of coefficients in Haar-wavelet-based models we can efficiently identify echo paths which have certain typical impulse response shapes. The modeling error energy obtained is low (less than 2%). A simple wavelet-based LMS adaptive filter can be used for on-line estimation of the coefficients. A low number of time-consuming computations is obtained per input sample due to the usage of Haar wavelets. This number is less than the ones obtained by the FIR of DFT domain based modeling.

Gain allocation in proportionate-type NLMS algorithms for fast decay of output error at all times

In this paper, we propose three new proportionate-type NLMS algorithms: the water filling algorithm, the feasible water filling algorithm, and the adaptive μ-law proportionate NLMS (MPNLMS) algorithm. The water filling algorithm attempts to choose the optimal gains at each time step. The optimal gains are found by minimizing the mean square error (MSE) at each time with respect to the gains, given the previous mean square weight deviations. While this algorithm offers superior convergence times, it is not feasible. The second algorithm is a feasible version of the water filling algorithm. The adaptive MPNLMS (AMPNLMS) algorithm is a modification of the MPNLMS algorithm. In the MPNLMS algorithm, the parameter μ of the μ-law compression is constant. In the AMPNLMS algorithm the parameter μ is allowed to vary with time. This modification allows the algorithm more flexibility when attempting to minimize the MSE. Compared with several feasible algorithms, the AMPNLMS algorithm has the fastest MSE decay for almost all times.