Cramér-Rao Bound for Wideband DOA Estimation with Uncorrelated Sources

In this paper, the closed-form Cramér-Rao bound (CRB) is derived for direction-of-arrival (DOA) estimation under the unconditional model assumption (UMA) for uncorrelated wideband sources. The existence of the CRB is proved based on the rank condition of the introduced augmented co-array manifold (ACM) matrix. The resolution capacity is then investigated and it is found that the number of resolvable sources for the wideband model can exceed the limitation in the narrowband case without requirement of any special array structure.

[1]  Yoram Bresler.  On the resolution capacity of wideband sensor arrays: further results , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[2]  Jean-Pierre Delmas,et al.  Robustness of narrowband DOA algorithms with respect to signal bandwidth , 2003, Signal Process..

[3]  Yimin D. Zhang,et al.  Performance Analysis for Uniform Linear Arrays Exploiting Two Coprime Frequencies , 2018, IEEE Signal Processing Letters.

[4]  Wei Cui,et al.  Low-Complexity Direction-of-Arrival Estimation Based on Wideband Co-Prime Arrays , 2015, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[5]  Wei Cui,et al.  Focused Compressive Sensing for Underdetermined Wideband DOA Estimation Exploiting High-Order Difference Coarrays , 2017, IEEE Signal Processing Letters.

[6]  Siliang Wu,et al.  Simplified and Enhanced Multiple Level Nested Arrays Exploiting High-Order Difference Co-Arrays , 2019, IEEE Transactions on Signal Processing.

[7]  Yimin Zhang,et al.  Generalized Coprime Array Configurations for Direction-of-Arrival Estimation , 2015, IEEE Transactions on Signal Processing.

[8]  Miriam A. Doron,et al.  Wavefield Modeling and Array Processing, Part 111-Resolution Capacity , 1994 .

[9]  Hong Wang,et al.  Coherent signal-subspace processing for the detection and estimation of angles of arrival of multiple wide-band sources , 1985, IEEE Trans. Acoust. Speech Signal Process..

[10]  Wei Cui,et al.  Extension of Co-Prime Arrays Based on the Fourth-Order Difference Co-Array Concept , 2016, IEEE Signal Processing Letters.

[11]  P. Stoica,et al.  The stochastic CRB for array processing: a textbook derivation , 2001, IEEE Signal Processing Letters.

[12]  Siliang Wu,et al.  Underdetermined DOA Estimation Under the Compressive Sensing Framework: A Review , 2016, IEEE Access.

[13]  Arye Nehorai,et al.  Performance Analysis of Coarray-Based MUSIC in the Presence of Sensor Location Errors , 2018, IEEE Transactions on Signal Processing.

[14]  Mostafa Kaveh,et al.  Fisher information matrix of the coherently averaged covariance matrix , 1991, IEEE Trans. Signal Process..

[15]  P. Vaidyanathan,et al.  Coprime sampling and the music algorithm , 2011, 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE).

[16]  Petre Stoica,et al.  Spectral Analysis of Signals , 2009 .

[17]  Y. Bresler,et al.  Sensor-efficient wideband source location , 1989, Proceedings of the 32nd Midwest Symposium on Circuits and Systems,.

[18]  Arye Nehorai,et al.  Coarrays, MUSIC, and the Cramér–Rao Bound , 2016, IEEE Transactions on Signal Processing.

[19]  Mohammed Nabil El Korso,et al.  Conditional and Unconditional Cramér–Rao Bounds for Near-Field Source Localization , 2010, IEEE Transactions on Signal Processing.

[20]  Wei Cui,et al.  Underdetermined wideband DOA estimation of off-grid sources employing the difference co-array concept , 2017, Signal Process..

[21]  Piya Pal,et al.  Cramér–Rao Bounds for Underdetermined Source Localization , 2016, IEEE Signal Processing Letters.

[22]  Siliang Wu,et al.  Low Complexity DOA Estimation for Wideband Off-Grid Sources Based on Re-Focused Compressive Sensing With Dynamic Dictionary , 2019, IEEE Journal of Selected Topics in Signal Processing.

[23]  Miriam A. Doron,et al.  Wavefield modeling and array processing. III. Resolution capacity , 1994, IEEE Trans. Signal Process..

[24]  Mostafa Kaveh,et al.  On the statistical sufficiency of the coherently averaged covariance matrix for the estimation of the parameters of wideband sources , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[25]  P. P. Vaidyanathan,et al.  Sparse Sensing With Co-Prime Samplers and Arrays , 2011, IEEE Transactions on Signal Processing.

[26]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[27]  P. P. Vaidyanathan,et al.  Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom , 2010, IEEE Transactions on Signal Processing.

[28]  B. Friedlander,et al.  ON THE CRAMER RAO BOUND FOR DIRECTION FINDING OF CORRELATED SIGNALS , 1990, 1990 Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 1990..

[29]  Arye Nehorai,et al.  Wideband Gaussian Source Processing Using a Linear Nested Array , 2013, IEEE Signal Processing Letters.

[30]  Yimin D. Zhang,et al.  DOA Estimation Using Compressed Sparse Array , 2018, IEEE Transactions on Signal Processing.

[31]  P. P. Vaidyanathan,et al.  Cramér-Rao bounds for coprime and other sparse arrays, which find more sources than sensors , 2017, Digit. Signal Process..

[32]  Petre Stoica,et al.  Performance study of conditional and unconditional direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..