Paulo S. R. Diniz

Set-membership binormalized data-reusing LMS algorithms

This paper presents and analyzes novel data selective normalized adaptive filtering algorithms with two data reuses. The algorithms [the set-membership binormalized LMS (SM-BN-DRLMS) algorithms] are derived using the concept of set-membership filtering (SMF). These algorithms can be regarded as generalizations of the previously proposed set-membership NLMS (SM-NLMS) algorithm. They include two constraint sets in order to construct a space of feasible solutions for the coefficient updates. The algorithms include data-dependent step sizes that provide fast convergence and low-excess mean-squared error (MSE). Convergence analyzes in the mean squared sense are presented, and closed-form expressions are given for both white and colored input signals. Simulation results show good performance of the algorithms in terms of convergence speed, final misadjustment, and reduced computational complexity.

New structures for adaptive filtering in subbands with critical sampling

Some properties of an adaptive filtering structure that employs an analysis filterbank to decompose the input signal and sparse adaptive filters in the subbands are investigated in this paper. The necessary conditions on the filterbank and on the structure parameters for exact modeling of an arbitrary linear system with finite impulse response (FIR) are derived. Then, based on the results obtained for the sparse subfilter structure, a new family of adaptive structures with critical sampling of the subband signals, which can also yield exact modeling, is obtained. Two adaptation algorithms based on the normalized LMS algorithm are derived for the new subband structures with critical sampling. A convergence analysis, as well as a computational complexity analysis, of the proposed adaptive structures are presented. The convergence behavior of the proposed adaptive structures is verified by computer simulations and compared with the behavior of previously proposed algorithms.

Convergence analysis of the binormalized data-reusing LMS algorithm

Normalized least mean squares algorithms for FIR adaptive filtering with or without the reuse of past information are known to converge often faster than the conventional least mean squares (LMS) algorithm. This correspondence analyzes an LMS-like algorithm: the binormalized data-reusing least mean squares (BNDR-LMS) algorithm. This algorithm, which corresponds to the affine projection algorithm for the case of two projections, compares favorably with other normalized LMS-like algorithms when the input signal is correlated. Convergence analyses in the mean and in the mean-squared are presented, and a closed-form formula for the mean squared error is provided for white input signals as well as its extension to the case of a colored input signal. A simple model for the input-signal vector that imparts simplicity and tractability to the analysis of second-order statistics is fully described. The methodology is readily applicable to other adaptation algorithms of difficult analysis. Simulation results validate the analysis and ensuing assumptions.

Adaptive IIR filtering algorithms for system identification: a general framework

Adaptive IIR (infinite impulse response) filters are particularly beneficial in modeling real systems because they require lower computational complexity and can model sharp resonances more efficiently as compared to the FIR (finite impulse response) counterparts. Unfortunately, a number of drawbacks are associated with adaptive IIR filtering algorithms that have prevented their widespread use, such as: convergence to biased or local minimum solutions; requirement of stability monitoring; and slow convergence. Most of the recent research effort on this field is aimed at overcoming some of the above mentioned drawbacks. In this paper, a number of known adaptive IIR filtering algorithms are presented using a unifying framework that is useful to interrelate the algorithms and to derive their properties. Special attention is given to issues such as the motivation to derive each algorithm and the properties of the solution after convergence. Several computer simulations are included in order to verify the predicted performance of the algorithms. >

The Compression of Electric Signal Waveforms for Smart Grids: State of the Art and Future Trends

In this paper, we discuss the compression of waveforms obtained from measurements of power system quantities and analyze the reasons why its importance is growing with the advent of smart grid systems. While generation and transmission networks already use a considerable number of automation and measurement devices, a large number of smart monitors and meters are to be deployed in the distribution network to allow broad observability and real-time monitoring. This situation creates new requirements concerning the communication interface, computational intelligence and the ability to process data or signals and also to share information. Therefore, a considerable increase in data exchange and in storage is likely to occur. In this context, one must achieve an efficient use of channel communication bandwidth and a reduced need of storage space for power system data. Here, we review the main compression techniques devised for electric signal waveforms providing an overview of the achievements obtained in the past decades. Additionally, we envision some smart grid scenarios emphasizing open research issues regarding compression of electric signal waveforms. We expect that this paper will contribute to motivate joint research efforts between electrical power system and signal processing communities in the area of signal waveform compression.

Set-Membership Proportionate Affine Projection Algorithms

Proportionate adaptive filters can improve the convergence speed for the identification of sparse systems as compared to their conventional counterparts. In this paper, the idea of proportionate adaptation is combined with the framework of set-membership filtering (SMF) in an attempt to derive novel computationally efficient algorithms. The resulting algorithms attain an attractive faster converge for both situations of sparse and dispersive channels while decreasing the average computational complexity due to the data discerning feature of the SMF approach. In addition, we propose a rule that allows us to automatically adjust the number of past data pairs employed in the update. This leads to a set-membership proportionate affine projection algorithm (SM-PAPA) having a variable data-reuse factor allowing a significant reduction in the overall complexity when compared with a fixed data-reuse factor. Reduced-complexity implementations of the proposed algorithms are also considered that reduce the dimensions of the matrix inversions involved in the update. Simulations show good results in terms of reduced number of updates, speed of convergence, and final mean-squared error.

Energy Detection Technique for Adaptive Spectrum Sensing

The increasing scarcity in the available spectrum for wireless communication is one of the current bottlenecks impairing further deployment of services and coverage. The proper exploitation of white spaces in the radio spectrum requires fast, robust, and accurate methods for their detection. This paper proposes a new strategy to detect adaptively white spaces in the radio spectrum. Such strategy works in cognitive radio (CR) networks whose nodes perform spectrum sensing based on energy detection in a cooperative way or not. The main novelty of the proposal is the use of a cost-function that depends upon a single parameter which, by itself, contains the aggregate information about the presence or absence of primary users. The detection of white spaces based on this parameter is able to improve significantly the deflection coefficient associated with the detector, as compared to other state-of-the-art algorithms. In fact, simulation results show that the proposed algorithm outperforms by far other competing algorithms. For example, our proposal can yield a probability of miss-detection 20 times smaller than that of an optimal soft-combiner solution in a cooperative setup with a predefined probability of false alarm of 0.1.

On the design of high-complexity cosine-modulated transmultiplexers based on the frequency-response masking approach

Two efficient techniques exploiting the frequency-response masking (FRM) approach are proposed in order to make it feasible to design prototype filters for highly selective nearly perfect-reconstruction cosine-modulated transmultiplexers and filter banks (CMTs and CMFBs) having a very large number of channels. In these design schemes, the number of unknowns is drastically reduced when compared with the corresponding techniques for designing direct-form prototype filters. Furthermore, in the proposed techniques, the main figures of merits, that is, the intersymbol interference and the interchannel interference for CMTs and the overall and aliasing distortions for CMFBs are taken into account in a controlled manner. In order to speed up the convergence of these two optimization techniques, simplifications for computing the resulting nonlinear constraints and the corresponding gradient vectors are proposed. They differ from each other in the sense that the first and second ones utilize the frequency-domain and time-domain constraints for controlling the figures of merit, respectively. Combining these two techniques results in numerically efficient algorithms for designing optimized CMTs (or CMFBs) with a reduced computational complexity (number of arithmetic operations per output sample), particularly when both branches of the FRM structure are required. Design examples are included illustrating the efficiency of the design methods and the high performance of the resulting CMT structures.

Sparsity-Aware Data-Selective Adaptive Filters

We propose two adaptive filtering algorithms that combine sparsity-promoting schemes with data-selection mechanisms. Sparsity is promoted via some well-known nonconvex approximations to the l0 norm in order to increase convergence speed of the algorithms when dealing with sparse/compressible signals. These approximations circumvent some difficulties of working with the l0 norm, thus allowing the development of online data-selective algorithms. Data selection is implemented based on set-membership filtering, which yields robustness against noise and reduced computational burden. The proposed algorithms are analyzed in order to set properly their parameters to guarantee stability. In addition, we characterize their updating processes from a geometrical viewpoint. Simulation results show that the proposed algorithms outperform the state-of-the-art algorithms designed to exploit sparsity.

Affine projection algorithms for sparse system identification

We propose two versions of affine projection (AP) algorithms tailored for sparse system identification (SSI). Contrary to most adaptive filtering algorithms devised for SSI, which are based on the l1 norm, the proposed algorithms rely on homotopic l0 norm minimization, which has proven to yield better results in some practical contexts. The first proposal is obtained by direct minimization of the AP cost function with a penalty function based on the l0 norm of the coefficient vector, whereas the second algorithm is a simplified version of the first proposal. Simulation results are presented in order to evaluate the performance of the proposed algorithms considering three different homotopies to the l0 norm as well as competing algorithms.