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The Cramr-Rao bound (CRB) for wideband direction of arrival (DOA) estimates of multi-source impinging on a randomly distributed array is derived. The computational expressions for the elements of Fisher information matrix in arbitrary array are provided also. The derived CRB can be divided into two terms, one depends on signals’ characteristics and the other depends on array geometry, and so an insight into theoretical performance of DOA estimation can be provided. The first term of CRB shows that the DOA estimation performance not only depends on SNR but also the signal bandwidth and spectral density, thus it can be found that better DOA estimation can be obtained for signals with more high frequency energies. The second term of CRB shows that DOA estimates vary with different array geometries and source angles. These properties provide us some useful tip to design an efficient signal and array configuration. Simulation results confirmed the results mentioned above.
The Cram r R-bound (CRB) for wideband direction of arrival (DOA) estimates of multi-source impinging on a random distributed array is derived. The computational expressions for the elements of Fisher information matrix in arbitrary array are provided also. derived CRB can be divided into two terms, one depends on signals’ characteristics and the other depends on array geometry, and so an insight into theoretical performance of DOA estimation can be provided. The first term of CRB shows that the DOA estimation performance not only depends on SNR but also the signal bandwidth and spectral density, thus it can be found that better DOA estimation can be obtained for signals with more high frequency energies. The second term of CRB shows that DOA estimates vary with different array geometries and source angles. These properties provide us some useful tip to design an efficient signal and array configuration.