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Multi-Frequency Co-Prime Arrays for High-Resolution Direction-of-Arrival Estimation | IEEE Journals & Magazine | IEEE Xplore

Multi-Frequency Co-Prime Arrays for High-Resolution Direction-of-Arrival Estimation


Abstract:

This paper presents multi-frequency operation for increasing the number of resolvable sources in high-resolution direction-of-arrival (DOA) estimation using co-prime arra...Show More

Abstract:

This paper presents multi-frequency operation for increasing the number of resolvable sources in high-resolution direction-of-arrival (DOA) estimation using co-prime arrays. A single-frequency operation requires complicated and involved matrix completion to utilize the full extent of the degrees of freedom (DOFs) offered by the co-prime configuration. This processing complexity is attributed to the missing elements in the corresponding difference coarray. Alternate single-frequency schemes avoid such complexity by utilizing only the filled part of the coarray and, thus, cannot exploit all of the DOFs for DOA estimation. We utilize multiple frequencies to fill the missing coarray elements, thereby enabling the co-prime array to effectively utilize all of the offered DOFs. The sources are assumed to have a sufficient bandwidth to cover all the required operational frequencies. We consider both cases of sources with proportional and nonproportional power spectra at the employed frequencies. The former permits the use of multi-frequency measurements at the co-prime array to construct a virtual covariance matrix corresponding to a filled uniformly spaced coarray at a single frequency. This virtual covariance matrix can be employed for DOA estimation. The nonproportionality of the source spectra casts a more challenging situation, as it is not amenable to producing the same effect as that of an equivalent single-frequency filled coarray. Performance evaluation of the multi-frequency approach based on computer simulations is provided under both cases of proportional and nonproportional source spectra.
Published in: IEEE Transactions on Signal Processing ( Volume: 63, Issue: 14, July 2015)
Page(s): 3797 - 3808
Date of Publication: 13 May 2015

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I. Introduction

Nonuniform linear arrays provide the ability to estimate the direction-of-arrival (DOA) of more sources than the number of physical sensors [1]–[6]. Recently, a new structure of nonuniform linear arrays, known as co-prime arrays, has been proposed [7], [8]. A co-prime configuration comprises two undersampled uniformly spaced subarrays with co-prime spatial sampling rates. Co-prime configurations have many advantages over other popular nonuniform configurations, including minimum redundancy arrays (MRA) [9], minimum hole arrays (MHA) [10], and nested arrays [11]. For a given number of physical sensors, MRAs and MHAs require an exhaustive search through all possible combinations of the sensors to find the optimal design [12], [13]. On the other hand, the positions of the sensors constituting the co-prime configuration have closed-form expressions. Although the same is true of nested arrays, the elements of one of the subarrays constituting the nested structure are closely separated, which may lead to problems due to mutual coupling between the sensors. Co-prime arrays reduce the mutual coupling between most adjacent sensors by spacing them farther apart [7]. Because of all of the aforementioned characteristics, co-prime arrays are finding broad applications in the areas of communications, radar, and sonar [14]–[20].

References

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