Algorithms for Blind Components Separation and Extraction from the Time-Frequency Distribution of Their Mixture
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Algorithms for Blind Components Separation and Extraction from the Time-Frequency Distribution of Their Mixture B. Barkat School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, 639798 Singapore Email: [email protected]
K. Abed-Meraim ´ Signal and Image Processing Department, Ecole National Sup´erieure des T´el´ecommunications, Telecom Paris, 75013 Paris, France Email: [email protected] Received 20 February 2003; Revised 29 November 2003; Recommended for Publication by Petar Djuri´c We propose novel algorithms to select and extract separately all the components, using the time-frequency distribution (TFD), of a given multicomponent frequency-modulated (FM) signal. These algorithms do not use any a priori information about the various components. However, their performances highly depend on the cross-terms suppression ability and high time-frequency resolution of the considered TFD. To illustrate the usefulness of the proposed algorithms, we applied them for the estimation of the instantaneous frequency coefficients of a multicomponent signal and the results are compared with those of the higher-order ambiguity function (HAF) algorithm. Monte Carlo simulation results show the superiority of the proposed algorithms over the HAF. Keywords and phrases: time-frequency signal analysis, components separation, polynomial phase signals, instantaneous frequency estimation.
1. INTRODUCTION The joint time-frequency analysis has proved to be a powerful tool in the analysis of nonstationary signals, that is, signals whose spectral contents vary with time [1]. Such signals may be found in many engineering applications such as radar, sonar, telecommunications, and biomedical engineering. These signals can be classified in two groups: monocomponent and multicomponent. In this paper, we focus our analysis on multicomponent signals. By a multicomponent signal, we mean a signal whose time-frequency representation presents multiple ridges in the time-frequency plane. Analytically, it may be defined as s(t) =
M
si (t),
(1)
i=1
where each component si (t), of the form si (t) = ai (t)e jφi (t) ,
(2)
is assumed to have only one ridge, or one continuous curve, in the time-frequency plane. An example of a multicomponent signal, consisting of three components, is displayed in Figure 1.
Recovery of a particular component from a given multicomponent signal has always been a challenge for the timefrequency community. The objective of this paper is to address this particular problem. Specifically, we present two different algorithms in order to retrieve and extract separately the components from the time-frequency distribution (TFD) of their mixture signal. The motivation behind this can be found in situations where the user may be interested in the instantaneous frequency (IF) law of one of the components only. For instance, in telecommunications the received signal may be a mixture of several source signals (multiple access interference) but the user may wish to recover only one source signal (
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