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Daniël W.E. Schobben, Tech. University Eindhoven (The Netherlands)
Gerard P.M. Egelmeers, Tech. University Eindhoven (The Netherlands)
Piet C.W. Sommen, Tech. University Eindhoven (The Netherlands)
In many frequency domain adaptive filters Fast Fourier Fourier Transforms (FFTs) are used to transform signals which are augmented with zeros. The overall computational complexity of these adaptive filters is mainly determined by these windowed FFTs, rather than by the filtering operation itself. This contribution presents a new way of calculating these windowed FFTs efficiently. In addition, a method is deduced for implementing non-windowed FFTs of overlapping input data using the previously mentioned efficient windowed FFTs. Also, a method is presented for implementing the windowed FFTs in the update part even more efficient.
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Woo-Jin Song, POSTECH (Korea)
Min-Soo Park, LGIC (Korea)
This paper presents a new algorithm that can solve the problem of selecting appropriate update step size in the LMS algorithm. The proposed algorithm, called a Complementary Pair LMS (CP-LMS) algorithm, consists of two adaptive filters with different update step sizes operating in parallel, one filter re-initializing the other with the better coefficient estimates whenever possible. This new algorithm provides the faster convergence speed and the smaller steady-state error than those of a single filter with a fixed or variable step size.
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Marc Moonen, ESAT - K.U.Leuven (Belgium)
Ian K. Proudler, DRA (U.K.)
In this paper we consider a recursive least squares (RLS) adaptive filtering problem where the input signal can be modelled as the output of a low order autoregressive (AR) process. We will show how a good estimate of the Kalman gain vector can be obtained using a small least squares lattice (LSL) filter. This estimate can then be used in the normal way to determine the optimum filter coefficients. The resulting adaptive filtering algorithm is similar in concept to the Fast Newton algorithm. The main difference is the use of the LSL instead of a low order covariance domain fast RLS algorithm. The potential advantage of this new algorithm is that, unlike a covariance domain algorithm, a LSL can be implemented in a numerically stable form.
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Joao B. Destro Filho, Laboratoire I3S (France)
Gerard Favier, Laboratoire I3S (France)
Joao M. Travassos Romano, UNICAMP (Brazil)
This paper analyses the relation between Bussgang-based blind algorithms [1-5] and their respective associated cost functions. After proposing a general mathematical expression for representing all these cost functions, the paper discuss carefully the above relation in the case of DD [1] and of Bellinis [3] algorithm. Then, two new blind algorithms are proposed and experimentally evaluated.
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Victor Shtrom, ARGOSystems, Inc. (U.S.A.)
Howard Fan, University of Cincinnati. (U.S.A.)
The use of gradient descent recursive algorithms in blind adaptive equalization requires a cost function with a unique minimum such that the FIR equalizer setup removes sufficient Intersymbol Interference (ISI). A cost function based on minimizing the difference between the second and the fo urth norms of the joint channel-equalizer impulse response, each raised to the fourth power i.e., ||.||_2^4-||.||_4^4 is proposed. An implementable recusive on-line a lgorithm using the above cost function is also derived for QAM inputs. A sizabl e array of examples shows that the above class is unimodal in equalizer weights. Extensive simulations show that the performance of the newly proposed algorit hms is comparable to the CMA algorithms' performance without the misconvergences .
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Majid Nayeri, Michigan State University (U.S.A.)
Tsung Ming Lin, Michigan State University (U.S.A.)
John R. Deller, Michigan State University (U.S.A.)
Set-membership algorithms, including the conventional optimal bounding ellipsoid (OBE) algorithm, require a priori knowledge of exact error bounds which is unknown in most applications. Conservative (over-estimated) error bounds used in practice lead to inconsistent parameter estimation. The novel OBE algorithm with automatic bound estimation (OBE-ABE) is shown to be consistently convergent without a priori knowledge of error bounds, even in correlated-error environments. Computationally efficient variants of this algorithm for both time-invariant and time-varying systems are presented.
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Pi Sheng Chang, UCLA (U.S.A.)
Alan N. Willson, UCLA (U.S.A.)
A method for the direction-of-arrival (DOA) estimation of coherent signals is proposed, based on the adaptive version of Pisarenko's harmonic retrieval method. It is known that for the DOA estimation of coherent signals, the computed covariance matrix of the sensor array must be spatially smoothed to preserve its full rank. Adaptive algorithms using the Conjugate Gradient (CG) methods can take advantage of this pre-processing by incorporating the available smoothed matrix into the algorithm. The proposed algorithm uses the CG algorithm presented in [3] in combination with spatial and temporal smoothing techniques. Our simulations show that the proposed algorithm has a fast convergence rate even when the input signals are coherent. Due to the use of an updated covariance matrix at each time instant, no internal iterations are used as in regular CG methods, resulting in a more efficient algorithm than previously proposed CG methods.
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Phillip M.S. Burt, EPUSP (Brazil)
Max Gerken, EPUSP (Brazil)
A local analysis of the convergence speed and a global analysis of the reduced error surface of constant gain algorithms for direct form IIR adaptive filters are initially presented, showing the adverse effects that result from the proximity of the poles of the modelled system to the unit circle and, for complex poles, to the real axis. A polyphase IIR adaptive filter is then proposed and its local and global convergence properties are investigated, showing it to be specially well suited for applications with underdamped low-frequency poles. The polyphase structure is tested with different constant gain algorithms in an echo-cancellation example, attaining a gain of 14 to 70 times in global convergence speed over the direct form, at the price of a relatively modest increase in computational complexity. A theorem concerning the existence of stationary points for the polyphase structure is also presented.
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J. William Whikehart, Ford (U.S.A.)
Soura Dasgupta, University of Iowa (U.S.A.)
We consider adaptive periodic IIR filtering and present an extension of the Hyperstable Adaptive Recursive Filter (HARF). We give conditions for convergence of the parameter estimate error, involving passivity of certain operators in the identification loop, identifiability of the system parameters, and persistent excitation (pe). A necessary and sufficient condition for identifiability is given and subject to its satisfaction, input-only conditions guaranteeing pe are given.
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Fernando Gil Vianna Resende Jr., TIT (Japan)
Akinori Nishihara, TIT (Japan)
Paulo Sergio Ramirez Diniz, COPPE/UFRJ (Brazil)
Mineo Kaneko, JAIST (Japan)
A new method for adaptive autoregressive spectral estimation based on the least-squares criterion with multi-band decomposition of the linear prediction error and analysis of each band through independent variable forgetting factors is presented. The proposed method localizes the forgetting factor adaptation scheme in the frequency domain and in the time domain, in the sense that variations on the statistics of the input signal are independently evaluated for each band along the time. In this paper, a new forgetting factor adaptation technique depending exclusively on the input signal is introduced and applied to the multi-window analysis of the linear prediction error structure to generate time-varying autoregressive spectral estimates. An improvement on the fidelity of estimates is shown in computer experiments which compare the proposed method with conventional and multi-band least-squares methods with fixed forgetting factors.
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François Capman, Matra Communication (France)
Jerome Boudy, Matra Communication (France)
Philip Lockwood, Matra Communication (France)
With the increasing use of hands-free audio terminals in communication systems, the realization of a high quality hands-free function still remains a challenging research topic. The use of Fast QR Least-Squares algorithms, combined with a multirate structure have been proposed in [CAPMAN-95] for good performances and reduced complexity. In this paper, we propose to modify QR Least-Squares adaptive algorithms in order to control the adaptation process in the context of acoustic echo cancellation. This modification is based on a similar idea developped for Fast Transversal Filters, [BENALLAL-89][SLOCK-91]. Simulation results demonstrate the efficiency of this modified adaptation process for QR-LS adaptive algorithms.
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François Capman, Matra Communication (France)
Jerome Boudy, Matra Communication (France)
Philip Lockwood, Matra Communication (France)
Tianruo Yang, Linköping University (Sweden)
Man Lin, Linköping University (Sweden)
In the robot navigation problem, noisy sensor data must be filtered to obtain the best estimate of the robot position. The discrete Kalman filter, which usually is used for prediction and detection of signal in communication and control problems has become a commonly used method to reduce the effect of uncertainty from the sensor data. However, due to the special domain of robot navigation, the Kalman approach is very limited. Here we propose the use of a Iterative Total Least Squares Filter which is solved by applying the Lanczos bidiagonalization process. This filter is very promising for very large data information and from our experiments we can obtain more precise accuracy than the Kalman filter.
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Shigenori Kinjo, University of Ryukyus (Japan)
Masafumi Oshiro, University of Ryukyus (Japan)
Hiroshi Ochi, University of Ryukyus (Japan)
Two-dimensional (2-D) adaptive digital filters (ADFs) for 2-D signal processing have become a fascinating area of the adaptive signal processing. However, conventional 2-D FIR ADF's require a lot of computations. For example, the TDLMS requires 2N*N multiplications per pixel. We propose a new 2-D adaptive filter using the FFTs. The proposed adaptive filter carries out the fast convolution using overlap-save method, and has parallel structure. Thus, we can reduce the computational complexity to $O(log_2 N)$ per pixel.
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Yoshito Higa, TRDC (Japan)
Hiroshi Ochi, University of Ryukyus (Japan)
Shigenori Kinjo, University of Ryukyus (Japan)
The over-sampling subband ADFs are highly demanded because of shortening the convergence of adaptation algorithms and being able to avoid aliasing. However, the conventional methods must use the complex coefficients filter banks, which require a lot of computation compared to the real filter banks. The aim of this correspondence is to develop a new over-sampling subband ADF which does not require complex coefficient filter banks but real filter banks. The filter banks are optimized such that the MSE can be minimized. This turns out that the proposed scheme can minimize the aliasing effect due to decimation.
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