On the Cramér-Rao bound of wideband direction of arrival estimation

The Cramér-Rao Bound( CRB) for wideband Direction of Arrival (DOA) estimation of multi-source impinging on a randomly distributed array is derived. Non-matrix expressions for the elements of Fisher information matrix are provided for computational convenience. The derived CRB can be divided into two terms, one depends on signals' characteristics and another depends on array geometry, and so an insight into theoretical performance of DOA estimation can be provides. The first term 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 estimates can be obtained for signals with more high frequency energies. The second term 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.