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Signal parameter estimation using fourth order statistics: multiplicative and additive noise environment.

Chandrakant J Gaikwad¹, Hemant K Samdani¹, Pradip Sircar¹

¹Department of Electrical Engineering, Indian Institute of Technology Kanpur, Kanpur, UP 208016 India.

|June 30, 2015

Summary

This study introduces a novel fourth-order cumulant (FOC) method for estimating parameters in complex signals corrupted by noise. The new approach enhances accuracy for both stationary and non-stationary signals compared to existing methods.

Keywords:

Fourth-order cumulant Higher-order statistics Multiplicative noise Parameter estimation

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Area of Science:

Signal Processing
Statistical Signal Analysis
Parameter Estimation

Background:

Accurate parameter estimation is crucial for analyzing complex signals.
Traditional methods struggle with signals affected by multiplicative and additive noise, especially non-stationary ones.
Fourth-order statistics offer potential for improved estimation but require robust definitions.

Purpose of the Study:

To develop and validate a new definition of the fourth-order cumulant (FOC) and accumulated FOC (AFOC) for parameter estimation.
To assess the performance of the proposed method for stationary and non-stationary complex sinusoidal, frequency modulated (FM) sinusoidal, and linear chirp signals.
To compare the proposed method against existing techniques and the Cramer-Rao (CR) bound.

Main Methods:

Derivation of analytical expressions for the FOC/AFOC of target signals.
Introduction of the accumulated cumulant concept to address time-varying signal properties.
Simulation studies comparing the proposed FOC/AFOC method with existing fourth-order statistics methods and CR bounds.

Main Results:

The proposed FOC/AFOC method demonstrates superior performance in parameter estimation for complex sinusoidal signals compared to existing methods.
The method effectively estimates parameters for non-stationary signals, including complex FM sinusoidal and linear chirp signals.
Simulation results for non-stationary signals show close agreement with derived Cramer-Rao bounds, validating the method's accuracy.

Conclusions:

The novel fourth-order cumulant definition provides a robust and accurate approach for parameter estimation in noisy complex signals.
The proposed method is effective for both stationary and non-stationary signal types.
This technique offers a significant advancement for signal parameter estimation in challenging noise environments.