Maria D. Miranda

Tracking issues of some blind equalization algorithms

Due to the growing demand for mobile communications, blind adaptive algorithms have an important role in improving data transmission efficiency. In this context, the convergence and tracking analysis of such algorithms is a problem of interest. Recently, a tracking analysis of the Constant Modulus Algorithm was presented based on an energy conservation relation. In this letter we extend that analysis to blind quasi-Newton algorithms that minimize the Constant Modulus cost function. Under certain conditions, the considered algorithms can reach the same steady-state mean-square error. Close agreement between analytical and simulation results is shown.

A hybrid least squares QR-lattice algorithm using a priori errors

This paper presents a new minimal and backward stable QR-LSL algorithm obtained through the proper interpretation of the system matrix that describes the adaptation and filtering operations of QR-RLS algorithms. The new algorithm is based on a priori prediction errors normalized by the a posteriori prediction error energy-as suggested by the interpretation of the system matrix-and uses the fact that the latter quantities can be computed via a lattice structure. Backward consistency and backward stability become guaranteed under simple numerical conventions. In contrast with the known a posteriori QR-LSL algorithm, the new algorithm present; fewer numerical complexity, and backward consistency is guaranteed without the constraint of passive rotations in the recursive lattice section. Furthermore, reordering of some operations results in a version with identical numerical behavior and inherent parallelism that can be exploited for fast implementations. Both a priori and a posteriori QR-LSL algorithms are compared by means of simulations. For small mantissa wordlengths and forgetting factors /spl lambda/ not too close to 1, the proposed algorithm performs better due to dispensing with passive rotations. For forgetting factors very close to one and small wordlengths, both algorithms are sensitive to the accuracy of some well-identified computations.

A regional multimodulus algorithm for blind equalization of QAM signals: Introduction and steady-state analysis

It is well known that constant-modulus-based algorithms present a large mean-square error for high-order quadrature amplitude modulation (QAM) signals, which may damage the switching to decision-directed-based algorithms. In this paper, we introduce a regional multimodulus algorithm for blind equalization of QAM signals that performs similar to the supervised normalized least-mean-squares (NLMS) algorithm, independently of the QAM order. We find a theoretical relation between the coefficient vector of the proposed algorithm and the Wiener solution and also provide theoretical models for the steady-state excess mean-square error in a nonstationary environment. The proposed algorithm in conjunction with strategies to speed up its convergence and to avoid divergence can bypass the switching mechanism between the blind mode and the decision-directed mode.

Avoiding Divergence in the Shalvi–Weinstein Algorithm

The most popular algorithms for blind equalization are the constant-modulus algorithm (CMA) and the Shalvi-Weinstein algorithm (SWA). It is well-known that SWA presents a higher convergence rate than CMA, at the expense of higher computational complexity. If the forgetting factor is not sufficiently close to one, if the initialization is distant from the optimal solution, or if the signal-to-noise ratio is low, SWA can converge to undesirable local minima or even diverge. In this paper, we show that divergence can be caused by an inconsistency in the nonlinear estimate of the transmitted signal, or (when the algorithm is implemented in finite precision) by the loss of positiveness of the estimate of the autocorrelation matrix, or by a combination of both. In order to avoid the first cause of divergence, we propose a dual-mode SWA. In the first mode of operation, the new algorithm works as SWA; in the second mode, it rejects inconsistent estimates of the transmitted signal. Assuming the persistence of excitation condition, we present a deterministic stability analysis of the new algorithm. To avoid the second cause of divergence, we propose a dual-mode lattice SWA, which is stable even in finite-precision arithmetic, and has a computational complexity that increases linearly with the number of adjustable equalizer coefficients. The good performance of the proposed algorithms is confirmed through numerical simulations.

A family of algorithms for blind equalization of QAM signals

We propose blind equalization algorithms that perform similarly to supervised ones, independently of the QAM order. They converge approximately to the Wiener solution, which generally provides a relatively low misadjustment. Besides presenting strategies to speed up their convergences, we provide sufficient conditions for the stability of the symbol-based decision algorithm, which is an extension of the decision-directed algorithm. Their behaviors are illustrated through simulation results.

A hybrid QR-lattice least squares algorithm using a priori errors

A fast algorithm for RLS filtering is presented which is a hybrid between QR and lattice algorithms. Its prediction section is based upon normalized a priori prediction errors. It is of minimal complexity and, using simple numerical conventions, is backward stable under persistent excitation.

Thermolysin as a catalyst in enzymatic synthesis of asparagine-containing peptides

Thermolysin was used as a catalyst to obtain the following protected di- and tripeptide esters: Z-Asn-Leu-OEt, Z-Asn-Phe-OEt, Moz-Asn-Leu-Gly-OEt, Boc-Asn-Leu-Gly-OEt, Z-Asn-Leu-Gly-OEt, Moz-Asn-Leu-Gly-OBzl, Moz-Asn-Leu-Gly-OtBu, Moz-Gln-Leu-Gly-OEt, Moz-Asn-Ile-Gly-OEt, and Moz-Asn-Leu-Ala-OEt. These compounds were obtained in pure form and the yields exceeded 50%, except for Moz-Asn-Leu-Gly-OtBu and Boc-Asn-Leu-Gly-OEt. H-Cys(Bzl)-OtBu and H-Cys(Bzl)-Pro-Leu-Gly-NH2 were both inadequate as amino components for obtaining Moz-Asn-Cys(Bzl)-OtBu, Z-Asn-Cys(Bzl)-OtBu and Moz-Asn-Cys(Bzl)-Pro-Leu-Gly-NH2 in the thermolysin-catalyzed reactions. In the attempted synthesis of the protected pentapeptide amide, this protease cleaved the Pro-Leu bond of the amino component H-Cys(Bzl)-Pro-Leu-Gly-NH2 and catalyzed the coupling between the resulting dipeptide amide and Moz-Asn-OH, thus yielding Moz-Asn-Leu-Gly-NH2 as the main product.

Avoiding divergence in the constant modulus algorithm

One of the most popular algorithms for blind equalization is the constant modulus algorithm (CMA), due to its simplicity and low computational cost. However, if the step-size is not properly chosen or if the initialization is distant from the optimal solution, CMA can diverge or converge to undesirable local minima. In order to avoid divergence, we propose a dual-mode algorithm, which works as CMA with a time-variant step-size, but rejects non-consistent estimates of the transmitted signal. We present a deterministic analysis of the stability of the new algorithm for scalar filters. In the vector case, the good performance of the new algorithm is confirmed through numerical simulations.

A stable and efficient DSP implementation of a LSL algorithm for acoustic echo cancelling

We present an optimized DSP implementation of a modified error-feedback lattice least-square (EF-LSL) adaptive filtering algorithm. Simple measures that provide numerical stability for poor persistent excitation are also proposed. As a result of the optimization and the stability measures, an efficient and stable implementation of a fast algorithm of the RLS family was attained. We present the results of an acoustic echo cancelling experiment performed with the implemented algorithm. With a 40 MIPS SHARC DSP, up to 290 adaptive filter coefficients can be used. This represents an effective alternative to algorithms of the LMS family, while still retaining the good convergence properties of the RLS family.

Conventional and Inverse QRD-RLS Algorithms

This chapter deals with the basic concepts used in the recursive least-squares (RLS) algorithms employing conventional and inverse QR decomposition. The methods of triangularizing the input data matrix and the meaning of the internal variables of these algorithms are emphasized in order to provide details of their most important relations. The notation and variables used herein will be exactly the same used in the previous introductory chapter. For clarity, all derivations will be carried out using real variables and the final presentation of the algorithms (tables and pseudo-codes) will correspond to their complex-valued versions.