Direction of Arrival Estimation Using Co-prime Arrays: A Super Resolution Viewpoint (1312.7793v1)

Abstract: We consider the problem of direction of arrival (DOA) estimation using a newly proposed structure of non-uniform linear arrays, referred to as co-prime arrays, in this paper. By exploiting the second order statistical information of the received signals, co-prime arrays exhibit O(MN) degrees of freedom with only M + N sensors. A sparsity based recovery method is proposed to fully utilize these degrees of freedom. Unlike traditional sparse recovery methods, the proposed method is based on the developing theory of super resolution, which considers a continuous range of possible sources instead of discretizing this range into a discrete grid. With this approach, off-grid effects inherited in traditional sparse recovery can be neglected, thus improving the accuracy of DOA estimation. In this paper we show that in the noiseless case one can theoretically detect up to M N sources with only 2M + N sensors. The noise 2 statistics of co-prime arrays are also analyzed to demonstrate the robustness of the proposed optimization scheme. A source number detection method is presented based on the spectrum reconstructed from the sparse method. By extensive numerical examples, we show the superiority of the proposed method in terms of DOA estimation accuracy, degrees of freedom, and resolution ability compared with previous methods, such as MUSIC with spatial smoothing and the discrete sparse recovery method.

• The paper demonstrates that co-prime arrays can detect up to M² sources using only 2M+N sensors in noiseless settings.
• It leverages a super resolution framework that overcomes limitations of subspace and sparse recovery methods by employing second-order statistics.
• Extensive simulations validate the approach, showing enhanced estimation accuracy, increased degrees of freedom, and improved resolution for applications like radar and sonar.

A Super Resolution Perspective on Direction of Arrival Estimation Using Co-Prime Arrays

The paper "Direction of Arrival Estimation Using Co-prime Arrays: A Super Resolution Viewpoint" addresses the inherently complex problem of Direction of Arrival (DOA) estimation by proposing the use of co-prime arrays. Co-prime arrays, introduced initially to overcome limitations due to mutual coupling in nested sensor arrays, promise O(MN) degrees of freedom using O(M + N) sensors, thus significantly enhancing resolution and estimation capabilities. This paper articulates novel methodologies leveraging second-order statistical insights and super resolution principles for accurate DOA estimation, highlighting its advantages over traditional sparse recovery approaches.

The research underscores two key methodologies in using co-prime arrays for DOA estimation: the subspace methods, epitomized by the MUSIC algorithm, and sparsity-based recovery techniques. Subspace methods, while typically effective, are found to be constrained by reduced aperture owing to spatial smoothing, whereas sparsity-based methods suffer from grid mismatch issues, potentially impairing accuracy when off-grid sources are present. Through the paper, super resolution is proposed as an alternative that addresses these issues by considering a continuum of potential sources instead of discretizing them ontologically into grid points. This innovative approach ensures improved accuracy by avoiding model mismatch and providing a robust estimation framework, even under Gaussian noise conditions.

A cornerstone of this work is the demonstration of the theoretical capability of co-prime arrays to detect up to M² sources utilizing only 2M + N sensors in a noiseless context. This capability underscores a significant increase from traditional methods, thereby showcasing a leap in source estimation potential. Further, the noise inherent in co-prime arrays is rigorously analyzed, revealing a complex noise structure conducive to the developed optimization method's robustness.

Through extensive numerical simulations, the authors illustrate the superiority of their proposed method in terms of DOA estimation accuracy, degrees of freedom, and resolution capability over traditional methods, such as MUSIC and discrete sparse recovery approaches. Particularly noteworthy is the capability of super resolution to resolve sources closely located in parameter space, a long-standing challenge in signal processing.

Implications of this research are profound, enhancing both the theoretical framework for array processing and the practical applications in fields such as radar, sonar, and wireless communications. The proposed methodology pushes the boundaries of source number detection, allowing for the detection of a higher number of sources as manifested through advancements like CSORTE, a continuous sparse recovery based on the SORTE algorithm.

Future research directions may consider the development of computationally efficient algorithms for large-scale implementations and the integration of source correlation effects, which remain largely unexplored within the scope of co-prime array processing. Moreover, systematic approaches for parameter selection in optimization problems are necessary to further fine-tune and enhance real-world applications of these techniques. Overall, this research sets a paradigm for leveraging theoretical advancements in super resolution to achieve practical DOA estimation enhancements, offering a compelling avenue for continued exploration and development in array signal processing.