Abstract
Parameter estimation of various multi-component stationary and non-stationary signals in multiplicative and additive noise is considered in this paper. It is demonstrated that the parameters of complex sinusoidal signal, complex frequency modulated (FM) sinusoidal signal and complex linear chirp signal in presence of additive and multiplicative noise can be estimated using a new definition of the fourth order cumulant (FOC), and the computed accumulated FOC (AFOC). Analytical expressions for the FOC/AFOC of the above signals are derived. The concept of accumulated cumulant is introduced to handle the case of a non-stationary signal, for which the fourth order cumulant may be a function of both time and lag. Simulation study is carried out for all the three signals. In case of complex sinusoidal signals, the resul ts of parameter estimation show that the proposed method based on the new definition of fourth order cumulant performs better than an existing method based on fourth order statistics. The proposed method can be employed for parameter estimation of non-stationary signals also as mentioned above. For comparison purpose, the Cramer-Rao (CR) bound expressions are derived for all the signals considered for parameter estimation. The simulation results for non-stationary signals are compared with the CR bounds.
Highlights
Signal parameter estimation in multiplicative and additive noise has been reported employing the non-linear least squares (NLLS) techniques (Besson and Stoica 1995; Besson and Stoica 1998; Ghogho et al 2001; Besson et al 1999), the cyclostationary approaches (Shamsunder et al 1995; Zhou and Giannakis 1995; Giannakis and Zhou 1995; Ghogho et al 1999a, 1999b), and the methods based on higher order statistics
In this paper, the parameter estimation approach based on the symmetric fourth-order cumulant (FOC) or accumulated fourth order cumulant (FOC) (AFOC) is proposed for some stationary or nonstationary signals in multiplicative and additive noise
In case of parameter estimation of complex sinusoidal signal, the proposed method performs better than the method presented in (Swami 1994) at all signal-to-noise ratio (SNR) levels, even though the latter is another method based on the fourth order statistics
Summary
In many applications, such as Doppler radar signal processing (Besson and Castanie 1993), synthetic aperture radar image processing (Frost et al 1982; Lee and Jurkevich 1994), optical imaging under speckle or scintillation condition (Frankot and Chellappa 1987; Jain 2002), transmission of signals over fading channels (Makrakis and Mathiopoulos 1990a, b; Proakis 2001), speech processing in signal-dependent noise (Kajita and Itakura 1995; Quatieri 2002), and more, we need to consider the noise component to be both multiplicative and additive to the signal component. In the methods based on higher order statistics, our concern is to develop a way to reduce the higher dimensionality of higher order moments and cumulants Another issue is to tackle the non-stationarity of the observed signal, which makes the moments and cumulants time-varying in nature. When the additive noise process is Gaussian and the signal process modulated by the multiplicative noise is non-Gaussian, one may use the methods based on third or fourth order cumulants of the signal for estimating signal parameters (Swami and Mendel 1991; Swami 1994). We use the same definition for computing the symmetric fourth order moments and cumulants of some stationary and non-stationary signals in multiplicative and additive noise. The Cramer-Rao (CR) bound expressions for the simulated examples are derived in Appendices A–C
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