Ricardo Merched

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.

An embedding approach to frequency-domain and subband adaptive filtering

Frequency-domain and subband implementations improve the computational efficiency and the convergence rate of adaptive schemes. The well-known multidelay adaptive filter (MDF) belongs to this class of block adaptive structures and is a DFT-based algorithm. We develop adaptive structures that are based on the trigonometric transforms, discrete cosine transform (DCT) and discrete sine transform (DST), and on the discrete Hartley transform (DHT). As a result, these structures involve only real arithmetic and are attractive alternatives in cases where the traditional DFT-based scheme exhibits poor performance. The filters are derived by first presenting a derivation for the classical DFT based filter that allows us to pursue these extensions immediately. The approach used in this paper also provides further insights into subband adaptive filtering.

Order-recursive RLS Laguerre adaptive filtering

This paper solves the problem of designing recursive-least-squares (RLS) lattice (or order-recursive) algorithms for adaptive filters that do not involve tapped-delay-line structures. In particular, an RLS-Laguerre lattice filter is obtained.

Extended fast fixed-order RLS adaptive filters

The existing derivations of conventional fast RLS adaptive filters are intrinsically dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. We show, unlike what original derivations may suggest, that fast fixed-order RLS adaptive algorithms are not limited to FIR filter structures. We show that fast recursions in both explicit and array forms exist for more general data structures, such as orthonormally based models. One of the benefits of working with orthonormal bases is that fewer parameters can be used to model long impulse responses.

Fast techniques for computing finite-length MIMO MMSE decision feedback equalizers

Multiple-input multiple-output (MIMO) digital communication systems have received great attention due to their potential of increasing the overall system throughput. In such systems, MIMO decision feedback equalization (DFE) schemes are often used to mitigate intersymbol interference (ISI) resulting from channel multipath propagation. In this context, the existing computationally efficient methods for exact estimation of the DFE filters under minimum mean-square-error criteria (MMSE-DFE) rely on fast Cholesky decomposition and backsubstitution or Levinson techniques. These methods may still present several difficulties in implementation as the demand on higher transmission rates increases, and thus a simple solution is necessary. In this paper, new procedures for fast computation of the MIMO-MMSE-DFE are presented. The new algorithms are obtained from a simple observation, namely, that the optimal feedforward filter (FFF) is related to the well-known Kalman gain matrix, commonly encountered in fast recursive least squares adaptive algorithms-for which fast recursions exist and are readily applicable. Moreover, the feedback filter can be easily computed via stable fast MIMO convolution techniques. As a result, the proposed method is less complex, more structured, and can be as reliable in finite precision as known approaches in the literature.

Extended RLS lattice adaptive filters

This paper solves the problem of developing exact fast weighted RLS lattice adaptive filters for input signals induced by general orthonormal filter models. The resulting algorithm can be viewed as a counterpart of the extended fast fixed-order RLS adaptive filters previously derived.

RLS-Laguerre lattice adaptive filtering: error-feedback, normalized, and array-based algorithms

This paper develops several lattice structures for RLS-Laguerre adaptive filtering including a posteriori and a priori based lattice filters with error-feedback, array-based lattice filters, and normalized lattice filters. All structures are efficient in that their computational cost is proportional to the number of taps, albeit some structures require more multiplications or divisions than others. The performance of all filters, however, can differ under practical considerations, such as finite-precision effects and regularization. Simulations are included to illustrate these facts.

Fast computation of finite-length MIMO MMSE decision feedback equalizers

We present a new fast algorithm for computing multi-input-multi-output (MIMO) minimum mean-square-error decision feedback equalizer (MMSE-DFE) taps. The new algorithm is obtained by identifying the feedforward equalizer solution as a well known expression encountered in fast recursive least squares (RLS) adaptive algorithms, and the feedback equalizer as a convolution of the feedforward equalizer with the channel. The proposed method is less complex, more structured, and more stable in finite precision than known algorithms in the literature, which rely on fast methods for Cholesky decomposition.

Fast techniques for computing finite-length MMSE decision feedback equalizers

Existing computationally efficient methods for computing the finite length minimum mean-square-error decision feedback equalizers (MMSE-DFE) rely on fast methods for Cholesky decomposition, which may face several implementation difficulties. As the demand for broadband communications increases, developing less complex methods is highly motivated. We propose new techniques for computing the MMSE-DFE coefficients. The new algorithms are obtained by identifying the relationship between the feedforward equalizer computation and well known fast recursive least squares (RLS) adaptive algorithms, and the feedback equalizer as a convolution of the feedforward equalizer with the channel. The proposed algorithms are less complex, more structured, and more stable in finite precision than known methods encountered in the literature.

Extended fast fixed order RLS adaptive filters

Conventional derivations of fast fixed-order RLS filters rely on the shift structure that is characteristic of regressors in a tapped-delay line implementation. In this paper, we study adaptive Laguerre networks, where shift structure no longer holds. We show that fast fixed-order updates are still possible.