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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.


Related in: MedlinePlus

Root mean square error (RMSE) of the DOA estimates versus input SNR.
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f4-sensors-13-04272: Root mean square error (RMSE) of the DOA estimates versus input SNR.

Mentions: Second, we consider the same scenario as in the first one. Define the root mean square error (RMSE) of the DOA estimates as:RMSE=11000K∑k=1K∑n=11000[(θ^k(n)−θk)2+(ϕ^k(n)−ϕk)2]where and are the estimates of θk and ϕk for the nth trial,respectively. K is the number of signals. The comparison of Cramer-Rao lower bound (CRB), computed according to formulas provided in [19] and the RMSE of DOA estimates of 2-D UESPRIT-like method, 2-D ESPRIT-like method and 2-D SS are plotted in Figure 4. The SNR changes from −10 dB to 20 dB. Simulation result shows that the estimation errors of all the methods decrease obviously as the SNR increase. Moreover, our proposed method is observed to have a superior performance over the others and to be close to the CRB most. When the SNR is lower than 0 dB, the 2-D SS method fails to distinguish the two closely located sources, while our algorithm can still accomplish it very well. The same phenomenon appears for the 2-D ESPRIT-like method when the SNR is lower than −7 dB.


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)

Root mean square error (RMSE) of the DOA estimates versus input SNR.
© Copyright Policy
Related In: Results  -  Collection

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

f4-sensors-13-04272: Root mean square error (RMSE) of the DOA estimates versus input SNR.
Mentions: Second, we consider the same scenario as in the first one. Define the root mean square error (RMSE) of the DOA estimates as:RMSE=11000K∑k=1K∑n=11000[(θ^k(n)−θk)2+(ϕ^k(n)−ϕk)2]where and are the estimates of θk and ϕk for the nth trial,respectively. K is the number of signals. The comparison of Cramer-Rao lower bound (CRB), computed according to formulas provided in [19] and the RMSE of DOA estimates of 2-D UESPRIT-like method, 2-D ESPRIT-like method and 2-D SS are plotted in Figure 4. The SNR changes from −10 dB to 20 dB. Simulation result shows that the estimation errors of all the methods decrease obviously as the SNR increase. Moreover, our proposed method is observed to have a superior performance over the others and to be close to the CRB most. When the SNR is lower than 0 dB, the 2-D SS method fails to distinguish the two closely located sources, while our algorithm can still accomplish it very well. The same phenomenon appears for the 2-D ESPRIT-like method when the SNR is lower than −7 dB.

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