# Subspace Complexity Reduction in Direction-of-Arrival Estimation via the RASA Algorithm

## TL;DR

This paper introduces a new algorithm called RASA to improve direction-of-arrival estimation by reducing computational complexity while maintaining accuracy.

## Contribution

A novel selective subspace refinement technique is proposed to enhance DoA estimation under challenging signal conditions.

## Key findings

- The RASA algorithm reduces computational complexity by up to 75% while maintaining high angular resolution.
- The method outperforms traditional approaches in accuracy and execution time for high-resolution DoA estimation.
- The correlation-aware subspace design improves robustness and numerical stability of the pseudo-spectrum.

## Abstract

The complexity and scale of contemporary datasets are increasing, making the need for reliable and effective subspace processing more pressing. In array signal processing, the quality of the projection matrix and the structure of the noise subspace have a significant impact on the Direction of Arrival (DoA) estimation accuracy. In this study, the limits of typical subspace sampling approaches are emphasized, especially when source coherence, restricted snapshots, or low Signal-to-Noise Ratio (SNR) are present. Traditional DoA estimate strategies are revisited. To overcome these problems, a selective subspace refinement-based enhanced dimensionality reduction technique is proposed. Using a correlation measure based on the ℓ2-norm, the suggested strategy minimizes the projection subspace by finding and keeping just the noise subspace’s least correlated columns. Adaptively choosing the first, last, and least dependent inner eigenvectors allows the method to maintain excellent angular resolution and estimation accuracy while drastically reducing computational complexity by up to 75%. This correlation-aware subspace design enhances the final pseudo-spectrum’s robustness, numerical stability, and orthogonality. The suggested method provides a scalable and effective solution for high-resolution DoA estimation in data-intensive signal environments, as demonstrated by experimental results that show it beats traditional methods in terms of accuracy and execution time.