Direction-of-Arrival Estimation in Coprime Array Using the ESPRIT-Based Method.

Area of Science:

• Signal Processing
• Array Signal Processing
• Array Geometry

Background:

• Coprime arrays offer enhanced degrees-of-freedom for direction-of-arrival (DOA) estimation with fewer sensors.
• Existing methods like ESPRIT face challenges with rank-deficient covariance matrices in virtual uniform linear arrays.
• Traditional reconstruction methods can lead to performance degradation and computational burden.

Purpose of the Study:

• To propose a novel DOA estimation algorithm for coprime arrays based on ESPRIT.
• To address the rank deficiency issue in the virtual uniform linear array's covariance matrix.
• To achieve a closed-form solution for DOA estimation without peak searching.

Main Methods:

• Derivation of the observation vector for the virtual uniform linear array.
• Development of a modified Toeplitz matrix reconstruction method using non-zero covariance matrix rows.
• Application of an improved ESPRIT technique to the reconstructed full-rank Toeplitz covariance matrix.

Main Results:

• A theoretically proven full-rank reconstructed Toeplitz covariance matrix.
• A closed-form solution for DOA estimation in coprime arrays.
• Avoidance of spatial smoothing techniques, mitigating performance degradation and computational load.

Conclusions:

• The proposed modified ESPRIT algorithm effectively estimates DOAs in coprime arrays.
• The method provides a computationally efficient and accurate alternative to traditional techniques like MUSIC.
• Numerical examples validate the effectiveness and advantages of the proposed DOA estimation approach.