A Novel Parameter Estimation Method Based on a Tuneable Sigmoid in Alpha-Stable Distribution Noise Environments

Area of Science:

• Signal Processing
• Radar Systems Engineering
• Statistical Signal Processing

Background:

• Wideband echoes from linear frequency modulation (LFM) pulse radar are susceptible to noise interference, particularly impulsive noise found in alpha-stable distribution environments.
• Accurate estimation of Doppler stretch and time delay is crucial for radar applications, but challenging in non-Gaussian noise conditions.
• Existing methods often struggle with impulsive noise or require prior knowledge of noise characteristics.

Purpose of the Study:

• To propose a novel method for estimating Doppler stretch and time delay of wideband echoes from LFM pulse radar.
• To address the challenge of operating in alpha-stable distribution noise environments, characterized by impulsive interference.
• To develop a robust algorithm that does not require a priori knowledge of the noise characteristics.

Main Methods:

• Employs a combination of fractional Fourier transform and a tuneable Sigmoid transform.
• Introduces two novel functions: a tuneable Sigmoid fractional correlation function (TS-FC) and a tuneable Sigmoid fractional power spectrum density (TS-FPSD).
• Develops a novel algorithm based on the TS-FPSD for estimating Doppler stretch and time delay, with derivations for unbiasedness and consistency.

Main Results:

• The proposed TS-FPSD method demonstrates boundness to symmetric alpha-stable (SαS) noise.
• Derivation and closed-form computation of the Cramér-Rao bound indicate superior performance.
• Simulation results and theoretical analysis confirm the method's applicability and effectiveness.

Conclusions:

• The novel method effectively suppresses impulsive noise interference in alpha-stable distribution environments.
• The proposed algorithm achieves higher estimation accuracy for Doppler stretch and time delay without needing prior noise knowledge.
• The technique offers a significant advancement in radar signal processing for challenging noise conditions.