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2-D unitary ESPRIT-like direction-of-arrival (DOA) estimation for coherent signals with a uniform rectangular array.

Ren S, Ma X, Yan S, Hao C - Sensors (Basel) (2013)

Bottom Line: By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly.Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry.The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signalsmore thoroughly.

View Article: PubMed Central - PubMed

Affiliation: The State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Science, Beijing 100190, China. renshiwei@mail.ioa.ac.cn

ABSTRACT
A unitary transformation-based algorithm is proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signalsmore thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.

No MeSH data available.


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RMSE of the DOA estimates versus correlation factor.
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f6-sensors-13-04272: RMSE of the DOA estimates versus correlation factor.

Mentions: In the last simulation, we investigate the ability of four algorithms to decorrelate coherent signals. Assume there are two narrowband signals with (ϕ, θ) = (10°, 0°), (5°, −5°) and SNR = 5dB. Their correlation factor varies in the range (0,1). For each value of γs, 1,000 independent estimates are carried out to examine the RMSE of DOA estimates. First, we compare the 2-D ESPRIT method with the other three decorrelation algorithms. As Figure 6 has shown, when the signals are uncorrelated or partly correlated with low correlation factor, the conventional 2-D ESPRIT is the best choice for DOA estimation. The reason is the use of decorrelation in the other methods results in a small effective aperture, which can reduce the resolution significantly. However, as γs increases, the performance of the 2-D ESPRIT degrades slowly. Until γs = 0.9, it totally fails to identify DOA, because of the serious rank loss of Rx. Besides, Figure 6 also demonstrates that the 2-D SS method provides a much better performance than the 2-D ESPRIT-like method, as well as our proposed method, when rs ≤ 0.32. This is due to the fact that in such a low correlation, it is sufficient for 2-D SS to decorrelate signals, and it can restrain noise to some extent. When the signals become nearly coherent, that is γs ≥ 0.95, the superiority of our proposed scheme and the 2-D ESPRIT-like method appears to be remarkable for the excellent decorrelation ability, while in terms of the veracity of DOA estimates, it is obvious that the new method outperforms 2-D ESPRIT-like method all the time.


2-D unitary ESPRIT-like direction-of-arrival (DOA) estimation for coherent signals with a uniform rectangular array.

Ren S, Ma X, Yan S, Hao C - Sensors (Basel) (2013)

RMSE of the DOA estimates versus correlation factor.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3673083&req=5

f6-sensors-13-04272: RMSE of the DOA estimates versus correlation factor.
Mentions: In the last simulation, we investigate the ability of four algorithms to decorrelate coherent signals. Assume there are two narrowband signals with (ϕ, θ) = (10°, 0°), (5°, −5°) and SNR = 5dB. Their correlation factor varies in the range (0,1). For each value of γs, 1,000 independent estimates are carried out to examine the RMSE of DOA estimates. First, we compare the 2-D ESPRIT method with the other three decorrelation algorithms. As Figure 6 has shown, when the signals are uncorrelated or partly correlated with low correlation factor, the conventional 2-D ESPRIT is the best choice for DOA estimation. The reason is the use of decorrelation in the other methods results in a small effective aperture, which can reduce the resolution significantly. However, as γs increases, the performance of the 2-D ESPRIT degrades slowly. Until γs = 0.9, it totally fails to identify DOA, because of the serious rank loss of Rx. Besides, Figure 6 also demonstrates that the 2-D SS method provides a much better performance than the 2-D ESPRIT-like method, as well as our proposed method, when rs ≤ 0.32. This is due to the fact that in such a low correlation, it is sufficient for 2-D SS to decorrelate signals, and it can restrain noise to some extent. When the signals become nearly coherent, that is γs ≥ 0.95, the superiority of our proposed scheme and the 2-D ESPRIT-like method appears to be remarkable for the excellent decorrelation ability, while in terms of the veracity of DOA estimates, it is obvious that the new method outperforms 2-D ESPRIT-like method all the time.

Bottom Line: By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly.Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry.The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signalsmore thoroughly.

View Article: PubMed Central - PubMed

Affiliation: The State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Science, Beijing 100190, China. renshiwei@mail.ioa.ac.cn

ABSTRACT
A unitary transformation-based algorithm is proposed for two-dimensional (2-D) direction-of-arrival (DOA) estimation of coherent signals. The problem is solved by reorganizing the covariance matrix into a block Hankel one for decorrelation first and then reconstructing a new matrix to facilitate the unitary transformation. By multiplying unitary matrices, eigenvalue decomposition and singular value decomposition are both transformed into real-valued, so that the computational complexity can be reduced significantly. In addition, a fast and computationally attractive realization of the 2-D unitary transformation is given by making a Kronecker product of the 1-D matrices. Compared with the existing 2-D algorithms, our scheme is more efficient in computation and less restrictive on the array geometry. The processing of the received data matrix before unitary transformation combines the estimation of signal parameters via rotational invariance techniques (ESPRIT)-Like method and the forward-backward averaging, which can decorrelate the impinging signalsmore thoroughly. Simulation results and computational order analysis are presented to verify the validity and effectiveness of the proposed algorithm.

No MeSH data available.


Related in: MedlinePlus