Applications of Data-Selective Adaptive Filters

In this article we discuss the capabilities and importance of data selection mechanisms in real-world tasks. We show how data-selective adaptive filters can be explored in order to improve the performance of communication systems and acoustic echo cancellers. For communications systems we propose a dataselective algorithm for semi-blind equalization in OFDM-based systems employing a QPSK digital modulation scheme that increases in18% the system throughput, provided a minimum signalto-noise ratio is guaranteed. For the acoustic echo cancellation we propose data-selective algorithms that operate in the frequenc y domain and allow a significant reduction of the computational burden. The simulation results show that after convergence, the se algorithms update only 10% of the filter coefficients. Keywords— Data-selective adaptive filters, Semi-blind equalization, OFDM, acoustic echo cancellation. I. I NTRODUCTION In recent years, mainly due to the decreasing prices of sensors and storage devices, we have been witnessing an enormous increase in the amount of data to be processed and/or stored. For instance, multiple antennas are being us ed in communications systems to increase system capacity, multi ple microphones are being used in multimedia applications like audio enhancement and localization of a sound source, as wel l as databases are getting bigger. In this complex scenario, data-selective filters can be rega rded as tools for automatic evaluation/selection of data. Th ese tools have the potential to discard undesired data, such as outliers and redundancy, and to peep a reduced amount of data (filtered data) that is most relevant to the given applicatio n. Data-selective adaptive(DSA) filters are self-adjustable mechanisms whose learning process is based only on filtered Markus V. S. Lima, Breno N. Esp ı́ndola, F́abio P. Freeland e Paulo S. R. Diniz, Electrical Engineering Program/COPPE, Fe deral University of Rio de Janeiro, Rio de Janeiro, Brazil, E-ma ils: {markus,breno,ffreeland,diniz }@lps.ufrj. br. This work was supported by CNPq, CAPES and FAPERJ. data. Among the benefits of discarding data before performin g the adaptation of the filter are: 1) Saving computational resources, and thus energy, by not adapting all the time, 2) Better learning performance since undesired artifacts and d ta with no innovation are removed [1]. This paper presents results of ongoing research on DSA filters applied to the equalization of orthogonal frequencydivision multiplexing (OFDM) systems and acoustic echo cancellation. For the OFDM system we propose a semiblind equalization(SBE) scheme that has potential to increase system throughput allowing the receiver to track time-vary ing channels. For the acoustic echo cancellation we propose a frequency-domain data-selective algorithm that yields t he same perceived result as the state-of-the-art solutions, b ut requiring much lower computational power. This paper is organized as follows. In section II we present the set-membership filtering(SMF) paradigm which leads to DSA filters. In sections III and IV we show some applications of DSA filters to communications systems and echo cancellation. In both sections we follow a similar approach: first we explain the application in which a DSA filter has potential to enhance the performance, then we describe the proposed algorithm, and finally we show some simulation results. The conclusions are drawn in section V. Notation: We denote scalars by lowercase letters, vectors by lowercase boldface letters, and matrices by uppercase boldface letters. All vectors are column vectors. We use R and C to denote the real and complex fields respectively, R+ to denote the set of non-negative real numbers, and the set of natural numbers is represented by N. The point-wise multiplication and division between two vectors of the same size is represented by a ◦ b anda÷ b. In addition,diag{x} is a diagonal matrix havingx on its main diagonal. II. DATA -SELECTIVE ADAPTIVE FILTERING In general terms, data-selective adaptive(DSA) filters are special kinds of adaptive filters that evaluate the amount of information (innovation) present in the input data before u sing it to self-adjust its coefficients according to an algorithm . The DSA filters bring about robustness against noise and reduced overall computational burden [1]. In the following we prese nt the set-membership filtering(SMF) paradigm which has been successfully used to derive powerful data-selective algor ithms [2], [3], [4]. The SMF concept appeared in [2] and is applicable to adaptive filtering problems that are linear-in-parameters , i.e., whose input-output signals are related by y = wx , in which x ∈ R is the input vector,w ∈ R represents the filter coefficients, and the output of the filter is given by y. According to the SMF criterion, we want to estimate the parameterw that leads to an error signal e = d − y whose XXIX SIMPÓSIO BRASILEIRO DE TELECOMUNICAÇ̃OES SBrT’11, 02-05 DE OUTUBRO DE 2011, CURITIBA, PR magnitude is upper bounded by a constant γ ∈ R+, for all possible pairs(x, d), whered ∈ R is the desired-output signal. Denoting byS the set comprised of all possible pairs (x, d), and defining thefeasibility setΘ as