Spatial power spectral density estimation using a Welch coprime sensor array processor.

Area of Science:

• Signal processing
• Array signal processing
• Underwater acoustics

Background:

• Coprime sensor arrays (CSAs) offer reduced sensor count but increased variance in spatial power spectral density (PSD) estimation.
• Nonstationary sonar environments limit increasing snapshots for variance reduction.
• Existing methods like Bartlett and Welch improve variance at the cost of resolution.

Purpose of the Study:

• To propose the Welch overlapping segment averaging product (WOSA-product) processor for CSAs.
• To achieve unambiguous PSD estimates with improved variance for passive direction of arrival (DOA) estimation.
• To analyze the statistical properties of the proposed WOSA-product processor.

Main Methods:

• Development of the WOSA-product processor for coprime arrays.
• Derivation of the first two moments of the spatial PSD estimate in closed-form for Gaussian processes.
• Monte Carlo simulations to validate analytical results.

Main Results:

• The WOSA-product processor provides unambiguous PSD estimates with reduced variance.
• Analytical derivations for the first two moments are presented for white Gaussian processes.
• Simulations confirm variance reduction and analyze trade-offs between segment length, resolution, and sidelobe levels.

Conclusions:

• The WOSA-product processor effectively reduces variance in PSD estimation for CSAs.
• This method is suitable for passive DOA estimation in challenging sonar environments.
• The study provides a theoretical framework and simulation-based validation for the proposed technique.