Abstract
A new method is presented to effectively estimate the direction-of-arrival of a source signal and the phase error of a uniform linear array. Assuming that one sensor (except the reference one) has been calibrated, the proposed method appropriately reconstructs the data matrix and establishes a series of linear equations with respect to the unknown parameters through eigenvalue decomposition. The unknown parameters can be determined directly by the least squares method. Unlike the conventional methods, the proposed method only requires one calibrated sensor, which may not be consecutively spaced to the reference one. The computational complexity analysis is given and the effectiveness of the proposed method is validated by simulation results.
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Appendix
Appendix
The proof of (34).
(1)
where \(\begin{array}{*{20}{c}} r\\ {\widetilde{\quad \quad }} \end{array}\) and \(\begin{array}{*{20}{c}} c\\ {\widetilde{\quad \quad }} \end{array}\) denote elementary row operation and elementary column operation, respectively, and they does not change the rank of a matrix. From the analysis above, we conclude that
(2)
So, we have
(3)
We have
From the proof above, we can conclude that
This completes the proof.
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Zhang, X., He, Z., Liao, B. et al. DOA and phase error estimation using one calibrated sensor in ULA. Multidim Syst Sign Process 29, 523–535 (2018). https://doi.org/10.1007/s11045-017-0484-x
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DOI: https://doi.org/10.1007/s11045-017-0484-x