[Paper Review] Non-Coherent Direction of Arrival Estimation via Frequency Estimation

Hadi Zayyani, Mehdi Korki|arXiv (Cornell University)|Jun 21, 2016

Direction-of-Arrival Estimation Techniques14 references3 citations

TL;DR

This paper proposes a non-coherent direction of arrival (DOA) estimation method using frequency estimation of the magnitude-squared array output, leveraging harmonic components to derive nonlinear equations in DOA. By introducing a high-amplitude reference target at low angles, ambiguities are resolved, and virtual array extension or multi-snapshot integration enhances accuracy. The method achieves two orders of magnitude faster computation than non-coherent GESPAR and outperforms it in low SNR regimes.

ABSTRACT

This letter investigates the non-coherent Direction of Arrival (DOA) estimation problem dealing with the DOA estimation from magnitude only measurements of the array output. The magnitude squared of the array output is expanded as a superposition of some harmonics. Hence, a frequency estimation approach is used to find some nonlinear relations between DOAs, which results in inherent ambiguities. To solve the nonlinear equations and resolve the ambiguities, we assume a high amplitude reference target at low angles to estimate the true DOA's with no ambiguities. However, the proposed algorithm requires a large number of antenna array elements to accurately estimate the DOA's. To overcome this drawback, and to enhance the estimation accuracy, we suggest two variants of the algorithm. One is to add virtual elements in the array and the second is to integrate multiple snapshots. Simulation results show that the proposed frequency estimation-based algorithm outperforms the non-coherent GESPAR algorithm in the low signal to noise ratio (SNR) regime and it is two orders of magnitude faster than the non-coherent GESPAR algorithm.

Motivation & Objective

• To address the challenge of DOA estimation from magnitude-only measurements, avoiding reliance on phase synchronization.
• To resolve inherent ambiguities in non-coherent DOA estimation using a high-amplitude reference target at low angles.
• To improve estimation accuracy and reduce computational complexity compared to existing methods like non-coherent GESPAR.
• To enable robust DOA estimation under phase errors and low SNR conditions.

Proposed method

• Model the magnitude-squared array output as a superposition of harmonics in element index, treating array elements as time samples.
• Use FFT-based frequency estimation to extract harmonic frequencies, which are nonlinearly related to DOA pairs.
• Introduce a strong reference target at low angle (e.g., 0°) to reduce the number of nonlinear equations to K and resolve ambiguities.
• Apply virtual array synthesis to effectively increase the number of array elements and improve resolution.
• Use coherent integration of multiple snapshots to enhance estimation accuracy.
• Solve the resulting nonlinear system using the reference target's known DOA to disambiguate solutions.

Experimental results

Research questions

• RQ1 Can frequency estimation of the magnitude-squared array output provide a robust alternative to phase-based DOA estimation in the absence of phase synchronization?
• RQ2 How can ambiguities in the nonlinear equations derived from harmonic components be resolved without relying on multiple reference targets?
• RQ3 To what extent does virtual array synthesis or multi-snapshot integration improve estimation accuracy in non-coherent DOA estimation?
• RQ4 How does the proposed method compare in performance and speed to non-coherent GESPAR under low SNR and phase error conditions?

Key findings

• The proposed method outperforms non-coherent GESPAR in the low SNR regime (SNR < 10 dB), particularly in terms of estimation accuracy.
• For SNR ≥ 10 dB, non-coherent GESPAR slightly outperforms the proposed method, indicating performance saturation due to array size limitations.
• The proposed algorithm is approximately two orders of magnitude faster than non-coherent GESPAR, making it highly efficient for real-time applications.
• Phase errors larger than 13 degrees cause coherent DOA estimation to degrade significantly, while the non-coherent method remains robust, outperforming coherent methods under high phase error conditions.
• The use of a single high-amplitude reference target at low angles effectively resolves ambiguities, simplifying the solution process compared to multiple reference targets.
• Virtual array synthesis and multi-snapshot integration significantly improve estimation accuracy, especially in low SNR and limited element scenarios.