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An Ambiguity-Solving Method for DOA Estimation with Unfolded Co-prime Arrays

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Academic year: 2021

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HAL Id: hal-02167974

https://hal.archives-ouvertes.fr/hal-02167974

Submitted on 3 Jul 2019

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

An Ambiguity-Solving Method for DOA Estimation

with Unfolded Co-prime Arrays

Xiao Yang, Yide Wang, Pascal Chargé

To cite this version:

Xiao Yang, Yide Wang, Pascal Chargé. An Ambiguity-Solving Method for DOA Estimation with Unfolded Co-prime Arrays. Fifth Sino-French Workshop on Information and Communication Tech-nologies (SIFWICT 2019), Jun 2019, Nantes, France. �hal-02167974�

(2)

General Co-prime Linear Array

Unfolded Co-prime Linear Array

Ambiguity Problem for Unfolded Co-prime Linear Arrays

Consider there are four signals coming from 𝜃

1

, 𝜃

2

,

𝜃

3

and 𝜃

4

, satisfying

The directional vector of each one of the four

angles can be represented as a linear combination

of the directional vectors of the other three, lying

in the signal subspace and being orthogonal to the

noise subspace, resulting in an ambiguity in the

MUSIC spectrum.

Ambiguity-Solving Method

candidate angles:

𝜃

1

𝜃

2

𝜃

3

𝜃

4

directional vectors: 𝐚(𝜃

1

) 𝐚(𝜃

2

) 𝐚(𝜃

3

) 𝐚(𝜃

4

)

Classical

Beamforming

powers:

𝑃

𝐶𝐵𝐹,𝑞

=

𝐚

𝐻

𝜃

𝑞

𝐑𝐚(𝜃

𝑞

)

𝑁

2

𝜃

𝑞

𝜃

1

𝜃

2

𝜃

3

𝜃

4

𝑃

𝐶𝐵𝐹,𝑞

big

big

big

small

True or

Ambiguous

true

true

true

ambiguous

An Ambiguity-Solving Method for DOA Estimation

with Unfolded Co-prime Arrays

Xiao Yang

University of Nantes

[email protected]

Yide Wang

University of Nantes

[email protected]

Pascal Chargé

University of Nantes

[email protected]

sin𝜃

1

= sin𝜃

2

+

2𝑎

𝑀

1

sin𝜃

1

= sin𝜃

3

+

2𝑏

𝑀

2

sin𝜃

4

= sin𝜃

2

+

2𝑐

𝑀

2

sin𝜃

4

= sin𝜃

3

+

2𝑑

𝑀

1

𝐚

1

𝜃

1

= 𝐚

1

𝜃

3

𝐚

2

𝜃

1

= 𝐚

2

𝜃

2

𝐚

1

𝜃

4

= 𝐚

1

𝜃

2

𝐚

2

𝜃

4

= 𝐚

2

𝜃

3

𝐚 𝜃

1

− 𝐚 𝜃

2

− 𝐚 𝜃

3

+ 𝐚 𝜃

4

= 𝟎

1. Zheng, W., Zhang, X., Gong, P., & Zhai, H. (2017). DOA estimation for coprime linear arrays: An ambiguity-free method involving full DOFs.

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